7885-4-X VESIAC State-of-the-Art Report SOUND VELOCITIES IN ROCKS AND MINERALS ORSON L. ANDERSON ROBERT C. LIEBERMANN Lanmont Geological Observatory Columbia University Palisades, New York November 1966 Geophyics Laboratory THE INSTITUTE OF SCIENCE AND TECHNOLOGY THE UNIVERSITY OF MICHIGAN Ann Arbor, Michigan

WILLOW RUN LABORATORIES ACKNOWLEDGMENTS Most of the original experimental data. cited in this report were taken by either Dr. Edward Schreiber or Dr. i'Naohiro Soga of the Mineral Physics Laboratory, Lamont Geological Observatory, Columbia University. Their contributions are gratefully acknowledged. We have also profited from discussions with Dr. John Nafe. Dr. Soga provided translations of several Japanese papers. Drs. Jack Oliver and James Dorman have critically reviewed the manuscript and made valuable comments. The manuscript was supervised by Mrs. Paula McCafferty. We are indebted to the following people for their contributions in the form of private correspondence or prepublication copies of their work: N. I. Christensen, C. F. Cline, R. G. McQueen and S. P. Marsh, J. E. Nafe and C. L. Drake, G. Simmons, R. D. Tooley, G. P. Woolard, and M. H. Manghnani. Funds for the research which supported the experimental work of Schreiber and Soga came from the Advanced Research Projects Agency, monitored by the Air Force Office of Scientific Research under Contract AF 49(638)-1355, and from Air Force Contract AF 33(615)-1700, monitored by Wright-Patterson Air Force Base. Figures in this report were adapted from the following sources: figure 1 from D. Bancroft, Physical Review, Vol. 59, 1941, pp. 588-593, Fig. 1; figure 3 from F. Birch, American Mineralogist, Vol. 35, 1950, pp. 644-650, Fig. 1; figures 4, 6, 17, and 19 from F. Birch, Journal of Geophysical Research, Vol. 65, 1960, pp. 10831102, Figs. 1, 2, 3, and 5; figures 5, 7, and 18 from G. Simmons, Journal of Geophysical Research, Vol. 69, 1964, pp. 1123-1130, Figs. 2, 3, and 5; figure 8 from G. Simmons, Proceedings of the Institute of Electrical and Electronics Engineers, Vol. 53, No. 10, pp. 1337-1346, Fig. 5; figure 16 from D. Tocher, Transactions of the American Geophysical Union, Vol. 38, 1957, pp. 89-94, Fig. 6; figure 20 from T. J. Ahrens and S. Katz, Journal of Geophysical Research, Vol. 68, 1963, pp. 529537, Fig. 6; figure 21 from D. S. Hughes and C. Maurette, Revue de'Institut Francais du Petrole et Annales Combustibles Liquides, Vol. 12, 1957, pp. 730-752, Fig. 9; figure 22 from J. Ide, Journal of Geology, Vol. 45, 1937, pp. 689-716, Fig. 4; figure 23 from F. Birch, Bulletin of the Geological Society of America, Vol. 54, 1943, pp. 263-286, Fig. 4; figures 25 and 26 from H. J. McSkimin, Journal of the Acoustical Society of America, Vol. 31, 1959, pp. 287-295, Figs. 2 and 9.

WILLOW RUN LABORATORIES PREFACE VESIAC, the VELA Seismic Information Analysis Center, is an information collection, analysis, and dissemination facility established at the Willow Run Laboratories of the Institute of Science and Technology of The University of Michigan. The contracts are sponsored by the Advanced Research Projects Agency under the Office of the Secretary of Defense and the Department of the Army. The purpose of VESIAC is to analyze the research information related to the VELA UNIFORM Program of Project VELA and to function as a central facility for this information. The facility will serve all authorized recipients of VELA UNIFORM research information by issuing subject bibliographies with abstracts and special reports as required. In addition, VESIAC will periodically summarize the progress of the research being conducted. VESIAC is under the technical direction of the Geophysics Laboratory of the Willow Run Laboratories. In its operation VESIAC draws upon members of this laboratory and other members of the Institute and the University. iii

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WILLOW RUN LABO'RATORIES ABSTRACT This state-of-the-art report summarizes experiments and data on sound velocities in rocks and minerals and projects useful lines of research. The report discusses in detail the three common measuring techniques now employed: (1) resonance methods, (2) pulse-transmission methods (time-of-flight), and (3) ultrasonicinterferometric methods. Promising techniques, both direct and indirect, are described; the most important of these is the resonance of small spheres. Methods of estimating elastic constants at high pressure and high temperature are indicated. The data extant on the sound velocities in rocks and minerals are considerable and are tabulated in several appendixes. The lack of systematic coverage and quality of these data are discussed. A method of estimating unmeasured properties in a class of rocks, using data already reported for that class, is reviewed. Techniques of estimating isotropic sound velocities from single-crystal elastic-constant data are reviewed. V

WILLOW RUN LABORATORIES CONTENTS Acknowledgments................................. ii Preface...................................... iii A bstract...................................... v List of Figures.................................. viii List of Tables................................... ix List of Symbols.................................. xi 1. Introduction.................................. 1 2. Techniques.................................. 2 3. New Methods of Determining Velocity: Direct and Indirect......... 21 4. Critique.................................... 43 5. Data on V and V for Rocks and Minerals.................. 44 s p 6. Preface to Appendixes............................ 61 Appendix 1: Properties of Rocks at Standard Temperatures and Pressures............................ 64 Appendix 2: Compressional Velocity Versus Pressure (10 bars to 10 kb)... 91 Appendix 3: Shear Velocity Versus Pressure (10 bars to 10 kb).......102 Appendix 4: Compressional Velocity Versus Temperature (25~C to 600~C). 111 Appendix 5: Shear Velocity Versus Temperature (25~C to 600~C)..... 113 Appendix 6: Petrographic Modal Analyses of Certain Rocks in Appendixes 1 Through 5............................ 115 Appendix 7: Chemical Analyses of Certain Rocks in Appendixes 1 Through 5............................ 121 Appendix 8: References for Data in Appendixes 1 Through 5.......... 123 Appendix 9: Properties of Polycrystalline Aggregates of Certain Minerals (Calculated from Elastic Constants of Single Crystals)..... 136 References.................................... 159 Bibliography................................... 167 Distribution List................................. 177 vii

WILLOW RUN LABORATORIES FIGURES 1. V/Vo As a Function of d/X for Various a in the Resonant Extensional Vibrations of Thin Cylinders.................. 5 2. Elastic Moduli of Polycrystalline A1203 As a Function of Porosity...... 8 3. Schematic Diagram for the Circuit of the Composite Oscillator........ 10 4. Arrangement of the Specimen and Transducers for the PulseTransmission Technique........................... 12 5. Schematic Diagram for the Variable-Delay-Line Method of Pulse Transmission................................. 12 6. Oscilloscope Traces for Vp Measurements on Nipissing Diabase at 8 kb..14 7. Oscilloscope Traces for Vs Measurements on Westerly Granite Using AC-Cut Quartz Transducers......................... 14 8. Reflected Compressional Wave and Refracted Shear (Os)and Compressional (0D) Waves Produced by Compressional Waves Incident at Angle 1.... 16 9. Principle of Ultrasonic-Interferometry Technique.............. 17 10. Ultrasonic Interferometer........................... 19 11. Shear Velocity As a Function of (i - 1) for Various Minerals........ 31 2 12. Longitudinal (Compressional) Velocity As a Function of (f - 1) for Various Minerals............................. 31 13. Isotropic Young's Modulus of Tantalum As a Function of Temperature.. 35 14. Comparison of Predicted and Observed Values of the Bulk Modulus and Its Temperature Derivative As a Function of Temperature...... 42 15. Elastic Behavior of Granite and Gabbro Clans As a Function of Compressional Velocity Based on the Equations Relating the Elastic Moduli of a Homogeneous, Isotropic, Perfectly Elastic Material...... 46 16. Variation of Compressional Velocity of Barre Granite As a Function of Axial Compression and Hydrostatic Pressure.............. 51 17. Compressional Velocity of Barre Granite As a Function of Hydrostatic Pressure................................... 52 18. Shear Velocity of Westerly Granite As a Function of Hydrostatic Pressure....................................52 19. Compressional Velocity of Various Rocks As a Function of Hydrostatic Pressure............................ 52 20. Compressional and Shear Velocities of Solenhofen Limestone As a Function of Hydrostatic Pressure......................... 52 21. Compressional (VD) and Shear (VR) Velocities As a Function of Hydrostatic Pressure at Various Temperatures.............. 54 22. Effect of Thermal Cycling at Room Pressure on the Compressional Velocity of Quincy Granite.........................55 23. Relative Frequency of the Resonant Shear-Mode Vibrations in Cylinders of Certain Rocks As a Function of Temperature............... 55 viii

WILLOW RUN LABORATORIES 24. Relative Frequency of the Pseudo-Resonance Modes in Polycrystalline A1203 As a Function of Temperature................ 56 25. Compressional Velocity of Fused Silica As a Function of Temperature at Room Pressure......................... 57 26. Shear Velocity of Fused Silica As a Function of Temperature at Room Pressure............................. 57 TABLES I. Summary Outline of Techniques for Measuring Sound Velocities...... 3 II. Elastic Constants of Polycrystalline MgO and Al 203 Determined by Resonance Method.............. 7 III. Elastic Moduli of Pore-Free Polycrystalline MgO and A1203................................ 8 IV. Elastic Constants of Polycrystalline Al 203 and MgO Determined by Various Methods........... 9 V. Relationship Between Sound Velocities and Elastic Moduli of Isotropic Bodies............................ 9 VI. Calculation of Shear Velocity from the Thermal Debye Temperature and Comparison with Measured Values.................24 VII. Conversion Table Between Z and Poisson's Ratio............. 29 VIII. Comparison of Isotropic Elastic Moduli Computed from the. Debye Temperature 8 and the Bulk Modulus K and the Experimental Values...............................30 IX. Calculated Sound Velocities from Refractive Index Data for Minerals Obeying Birch's Law (M/p - 20)...............32 X. Comparison of Drickamer's Measured Compression on MgO up to 350 kb with Calculated Compression Using 4-kb Data........39 XI. Comparison of Drickamer's Measured Compression on A1203 up to 300 km with Calculated Compression Using 4-kb Data......39 XII. Comparison of Shock-Wave Compression from McQueen and Marsh on MgO up to 1257 kb with Calculated Compression Using 4-kb Data... 40 ix

WILLOW RUN LABORATORIES- SYMBOLS a, b, c Crystallographic axes C.. Elastic constants Co Bulk sound velocity C Specific heat at constant pressure p d Diameter E Young's modulus f Natural frequency h Planck's constant A H Enthalpy k Boltzmann's constant K = B Bulk modulus s Length of specimen m Mass M Molecular weight n Mean index of refraction N Avogadro's number p Number of atoms in the formula P Pressure Q. Quality factor whose inverse is a measure of the damping S.. Elastic compliances t time V Mean sound velocity m V = VD Velocity of compressional waves Vs = VR Velocity of shear waves Z Critical parameter a, y, y Angles between crystallographic axes y Gruneisen's' constant 0 Debye temperature; thermal ( ot) or acoustic (0a) X Wavelength At Shear modulus p Density a Poisson's ratio xi

WILLOW RUN LABORATORIESSOUND VELOCITIES IN ROCKS AND MINERALS 1 INTRODUCTION Geophysics and certain other fields of geology have the task of correlating field measurements of seismic velocity (i.e., in situ measurements of sound velocity) with laboratory measurements of sound velocity taken on isolated rocks and minerals. The goal of this task is a better understanding of the structure and history of the earth's interior and crust and the development of techniques to solve geologic problems. This task is important because sound velocity is one of the few experimental properties measurable at depth in the earth. Section 2 of this report is a survey of the experimental techniques now employed which are used with confidence by experimentalists.. Section 3 discusses several methods which are presently being explored and have promise of becoming standard methods; some ideas of extrapolation to higher pressures and temperatures are indicated. Section 4 discusses the status of the field and includes a review of a new method of correlating existing data on rocks to predict unmeasured properties with an example of its use on basalts. The data are presented in the appendixes, which allow the reader to retrieve data in various ways: velocity vs. temperature, velocity vs. pressure, mineralogical and petrological content, references, and single-crystal data on important minerals. These appendixes are included as a reference for researchers in the field. While this state-of-the-art report was being completed, Dr. Gene Simmons kindly sent us an advance copy of a review paper entitled "Ultrasonics in Geology." Since readers of this report will have access to that review, certain topics covered by Simmons have been de-emphasized here. Therefore, several topics receive less attention in this report than their importance would otherwise warrant. In particular, we do not emphasize greatly the pulse-transmission technique, since much of Simmon's review is concerned with that technique alone. The reader will also find that there is a certain amount of overlap between the two reviews: this was unavoidable in presenting a balanced picture of the present state of the art. In this report, all of section 3, most of section 4, and the appendixes represent topics not covered by Simmons' review. 1

WILLOW RUN LABORATORIES 2 TECHNIQUES 2.1. GENERAL Three basic types of methods are now used to measure sound velocity directly or indirectly through the measurement of elastic constants: (1) resonance methods, in which the specimen is somehow induced to vibrate at its natural resonance frequencies; (2) pulse-transmission (time-of-flight) methods, in which the transit time of a high-frequency pulse through a dimension of the specimen is measured; and (3) ultrasonic-interferometry methods, in which internal reflections of the same wave train are made to interfere so that a null, or pseudo-resonance, can be achieved by suitably controlling the wavelength of the imposed pulse. The choice of method depends upon the circumstances of the experiment, such as the size and quality of the specimen, the electronic resources of the apparatus, and the personal preferences of the experimenter. The best compromise found by F. Birch and his colleagues for most rocks is the pulse-transmission method. With this technique, sound velocities have been measured versus pressure and temperature even on field specimens. On the other hand, resonance and interferometric techniques have proved to be the most reliable for single crystals, synthetically prepared polycrystalline aggregates, and fine-grained, low-porosity rocks. The cogent details of each method are summarized in table I. The common choice of specimens until recently has been between rocks and gem-quality minerals. Multiple reflections at high frequency cannot be obtained from rocks because of the low quality of the specimen; therefore, the method used must be either resonance or pulse transmission. For gem-quality crystals, ultrasonic interferometry is commonly used (resonance is used in a few cases) because a higher accuracy can be achieved than with pulse transmission. High accuracy is required because of the strong dependence of sound velocity on direction, even in isometric single crystals. Difficulties arise in correlating single-crystal constants with the isotropic values of sound velocity, Vp and Vs, which are the desired quantities in geophysics. There is a practical difp s ficulty stemming from the immense amount of basic data required to determine the variation of the elastic constants of a low- symmetry crystal with pressure and temperature. A theoretical difficulty stems from the need for considerable mathematical dexterity in crystal tensor analysis for the proper interpretation of these data. There is now, however, a third choice. Because of recent advances in ceramic technology, it is possible to prepare a polycrystalline specimen of a mineral which approaches gem quality. On such a specimen, the variation of V and V with pressure and temperature can be deter2

WILLOW RUN LABORATORIES mined by using ultrasonic interferometry to a precision that cannot be achieved by pulse transmission. Such a synthetically prepared aggregate avoids the theoretical difficulty of integration of single-crystal determinations and the experimental difficulties attending the measurements of velocity on rocks versus pressure and temperature. Using this method, the values of V and V have been determined up to 4 kb and up to 1500~C on periclase and corundum. These s difficulties are avoided, however, at the price of another: obtaining a suitable synthetic specimen. TABLE I. SUMMARY OUTLINE OF TECHNIQUES FOR MEASURING SOUND VELOCITIES High High Method Frequency Pressure Temperature Accuracy Resonance Resonance of Cylinders and Prisms 1-30 kc/s Vp, No Yes 5% V = 22f/n Vs, Yes Composite Oscillator 90-250 kc/s No Yes 1-2% V = 21f/n Wedge 1-12 Mc/s No No 5% V = 2Hf Pulse Transmission Variable Delay Line 50 kc/s to 10 Mc/s Yes Yes 1-3% V = A/t Pulse Echo 10 Mc/s Yes No 0.5% V = 2t/t Total Internal Reflection 1-5 Mc/s P < 2kb No 0.5-1.0% V = Vliq/(sin ic) Ultrasonic Interferometry Phase Comparison 10-60 Mc/s Yes Yes 0.01% V = 2tfn/(n + y/27r) Pulse Superposition 10-60 Mc/s Yes Yes 0.04% V = 21/a 2.2. RESONANCE METHODS 2.2.1. RESONANCE VIBRATIONS OF CYLINDERS AND PRISMS. For many years the elastic properties of materials were determined by various static experiments: bending, twisting, compressing, or otherwise deforming a specimen. These methods proved satisfactory for metals and glasses, but were unreliable for rocks because of an appreciable inhomogeneity 3

WILLOW RUN LABORATORIES of composition, texture, etc. Ide [1] introduced the dynamic method of resonance vibrations of cylindrical specimens in various modes: extensional, flexural, and torsional. The resonance method is a standing-wave phenomenon based upon the principle of an open organ pipe in which the length contains an integral number of half-wavelengths, f = n(X/2). The phase velocity of the wave is then V = Xf = 2kf/n or V = 2Hf for the fundamental frequency. Birch [2] included a correction factor: V = 2ff/(1 + ) 1/2 The principal modes of vibration are the extensional, the flexural, and the torsional. Cylindrical specimens are commonly used to avoid shape corrections due to nonuniform crosssections. Pochhammer [3] and Love [4] have derived theoretical expressions to describe the motion for the extensional and torsional modes of vibration of thin cylindrical rods. For the torsional mode, the velocity is always that of a shear wave traveling in an unbounded medium (L/p), and these theoretical solutions apply rigorously regardless of the length of the rod, even when it is so short as to become a disk [5]. Although the fit to the theoretical solution is not as precise for the extensional mode, it has been shown experimentally [6] that if the lengthto-diameter ratio (f/d) is greater than 5 or 6 the wave travels with the "bar velocity," (E/p)1/, of the Pochhammer-Love solution within a negligible error. Bancroft [5] and Silaeva and Shamina [7] have discussed the effect of the diameter-towavelength ratio (d/X) upon the motion. There is no dispersion for the torsional mode, but experimental results for the extensional mode agree with the Pochhammer-Love theory only for d/X < 1.4 (see fig. 1). As d/X - co, the velocity approaches the Rayleigh-wave phase velocity. For these reasons and others of a practical nature, the frequency range used is on the order of 1 to 30 kc/s. The energy necessary to induce the vibrations is coupled into the specimen via a transducer (electromagnetic, magnetostrictive, electrostatic, piezoelectric). The receiver may be located at either end of the specimen or may be slid along the rod to locate the position of the nodes and antinodes of the wave. Measurements may be made on jacketed specimens in a pressure medium and at high temperatures. The motion of the extensional modes is damped at high pressures, but the torsional modes are unaffected. The equipment is simple to construct and fairly accurate. It is possible to work with very porous aggregates, although the specimens must be uniform in the direction of the axis of the cylinder [8]. Errors, including uncertainties due to grain size and porosity, limit the accuracy to ~ 5%, but the method has been most useful for obtaining V of rocks at high temperatures and pressures. 4

WILLOW RUN LABORATORIES _.0 0.80 0 2 0 4 0 I.6 0.8 0 — 1. 6 18 2.0 2.2 2.4 FIGURE 1. V/V AS A FUNCTION OF d/X FOR VARIOUS a IN THE RESONANT EXTENSIONAL VIBRATIONS OF THIN CYLINDERS. Vo = bar velocity = (E/p)l/2, d = diameter of rod, L = X = wavelength, o = Poisson's ratio [5]. The corrections which must be made for measurements made on cylindrical specimens are simple. However, resonant measurements in ceramic and metallurgical research have in general been made on rectangular prisms, using the commonly referred to Forster's method which requires rather detailed shape corrections [9]. All equipment and techniques for measuring the mechanical resonance frequencies of prismatic specimens are described in detail by Spinner and Tefft [10], Wachtman and Tefft [11], and others. One disadvantage of this method arises from the limitation on the size of the specimen. When the length is less than 3 in., the torsional fundamental resonance frequency of a material having high elastic moduli, such as Al203, MgO, or SiC, exceeds 40 kc/s, so special equipment 0 0.2 0.4 0.6 08 0 1.2 12.0 22 23 and experimental techniques are required to obtain accurate results. Moreover, all three dimensions (length, width, and thickness) are critically involved in the calculation of the elastic moduli from the resonance frequency. From a practical point of view, it issons quite difficult to fabricate small specimens with a uniform cross-sectional dimension. Another problem to be considered is the shape-correction factor in the equation relating the elastic moduli to the resonance frequency. Although the value computed from Pickett's theoretical equation [9] agrees fairly well with the empirically determined value when the ratio of cross-sectional width to depth is near 1, the former gives a higher value than the latter by about 1.8% when the ratio approaches 10 [12]. A similar difference in the correction factor between the empirical and theoretical relations has been obtained when the depth-to-length 5

- WILLOW RUN LABORATORIES ratio is increased [13]. Therefore, it has been recommended that for rectangular specimens the ratio of length to either cross-sectional dimension should not be less than 3 to 1 [10]. When an accuracy within 0.1% is required, the ratio is preferably not less than 6 to 1. Therefore, it is difficult to determine the elastic moduli of specimens in massive structure. One advantage of the resonance method is its applicability to measurements of the elastic constants at high temperature. There are many reports available on the temperature dependence of the elastic constants of ceramic compounds such as Al203, MgO, ThO, etc. [14-17]. Such data not only provide knowledge of elastic properties at elevated temperature, but also are necessary to determine other physical constants, such as the Grunetsen constant at high temperature, which is an important parameter in the theory of thermodynamics. To determine the Gruneisen constant, very accurate data on the temperature dependence of bulk modulus are required. Since the bulk modulus is determinable only indirectly from the data of Young's modulus and the shear modulus, a little discrepancy in these elastic moduli between two data obtained by different investigators could represent a large difference in the values of bulk modulus. The use of resonance techniques such as F6rster's method to determine elastic constants is well known to metallurgists and ceramic engineers. It has not been used extensively in the geological sciences. Its feasibility has been demonstrated recently by results on synthetically prepared polycrystalline aggregates of MgO and A1203. To prove the point, we now review some work recently completed by Anderson and Soga [18]. Hot-pressed specimens of polycrystalline MgO and Al 203 were supplied by Avco Corporation. Two rectangular bars of different sizes, approximately 9.7 x 1.6 x 0.9 cm and 9.0 x 0.9 x 0.6 cm, were cut from a disk specimen. The bulk densities of the specimens were obtained from the mass and volume calculated from the dimensions. The elastic moduli were determined by the dynamic resonance method using Magnatest Elastomat Type FM- 500. Young's modulus was computed independently from the flexural flatwise and edgewise vibrations, and the shear modulus was computed from the torsional vibration. The correction to elastic moduli for size, shape, and Poisson's ratio was made by using the equations and tables presented by Spinner and Tefft [10]. The results are shown in table II. In figure 2, Young's modulus and shear modulus of polycrystalline Al203 are given as a function of porosity of the specimen. The scatter of the data probably results from the inhomogeneity of the specimen. To ensure the extrapolation of these values to the zero porosity, the elastic moduli of another polycrystalline Al203 having higher density were measured. This is a specimen known as "Lucalox," commercially sold by General Electric; it has cylindrical shape, so the corrections for shape and Poisson's ratio are simplified. The figure includes these data. 6

WILLOW RUN LABORATORIES TABLE II. ELASTIC CONSTANTS OF POLYCRYSTALLINE MgO AND Al203 DETERMINED BY RESONANCE METHOD [18] Young's Modulus Specimen (kb) Shear No. Density Porosity Flatwise Edgewise Modulus (g/cm3) (%) (kb) MgO 1 3.581 0.06 3097 3090 1306 MgO 2 3.572 0.31 3092 3060 1304 MgO 3 3.567 0.45 3087 3076 1301 Al23 0 5 3.941 1.13 3850 3864 1579 203 A1203 6 3.923 1.58 3700 3729 1507 Al203 7 3.913 1.83 3732 3768 1520 A1203 8 3.865 3.04 3545 3556 1445 Al203 9 3.843 3.59 3342 3382 1373 Al203 10 3.801 4.62 3447 3463 1408 Al203 11 3.787 5.00 3249 3299 1335 Al1 0 12 3.972 0.35 3986* 3981* 161 2 3 Lucalox *The values are from the fundamental mode, first overtone, and second overtone of flexural vibration. The extrapolation of Young's modulus to the zero porosity gives the value of 3100 kb for MgO and 4020 kb for Al203; that of the shear modulus gives 1305 kb for MgO and 1640 kb for A1203. Table III compares these values with data reported by various investigators. The agreement is quite good. Table IV compares the elastic constants of polycrystalline AlO23 and MgO obtained by the resonance method with the results obtained on the same specimens by the ultrasonic-interferometry method (sec. 2.4). The agreement of he data seems excellent, especially for the specimen Al203 (I); this was ideal for the comparison because it was fabricated uniformly with less than 0.5% porosity and because it was cylindrical so that no shape correction for shear modulus and little correction for Young's modulus are required in the resonance technique. This proves that the bar resonance method is quite adequate to obtain elastic constants with high precision. Once both Young's modulus and the shear modulus are known, the velocities of sound can be computed from the standard equations given in table V. 7

WILLOW RUN LABORATORIES i ~,, ~.I~,., ~.. 4200 (4020)4 4000 q \I 3800 YOUNG'S MODULUS X3600 1700 3400 1600 -,e 3200 SHEAR MODULUS. 1500- 1, 1400 - 1300 0 1 2 3 4 5 POROSITY (%) FIGURE 2. ELASTIC MODULI OF POLYCRYSTALLINE A1203 AS A FUNCTION OF POROSITY [18, 19] TABLE III. ELASTIC MODULI OF PORE-FREE POLYCRYSTALLINE MgO AND Al203 [18] MgO A1203 Young's Shear Young's Shear Reference Modulus Modulus Modulus Modulus Spriggs et al. [20, 21] 3178 1395 4060 Chung et al. [22, 23] 3050 1290 4050 1650 Knudsen [24] - - 4102 Anderson and Soga [18] 3100 1305 4020 1640 8

WILLOW RUN LABORATORIES TABLE IV. ELASTIC CONSTANTS OF POLYCRYSTALLINE Al203 AND MgO DETERMINED BY VARIOUS TECHNIQUES MgO (II) A1203 (I) A1203 (II) Avco D64B GE Lucalox Avco 1495A Sample 1 Sample 12 Sample 5 Modulus P = 3.572 p = 3.972 p = 3.941 (kb) Ultrasonic Ultrasonic Ultrasonic Interferometry Resonance Interferometry Resonance Interferom etry Resonance Young's 3053 3080 3988 3985 3903 3853 Shear 1286 1304 1613 1616 1583 1575 Bulk 1624 1611 2516 2487 2436 2318 TABLE V. RELATIONSHIP BETWEEN SOUND VELOCITIES AND ELASTIC MODULI OF ISOTROPIC BODIES K& tI K&E K& E & a E& u 2 4 3K+E 1 - a E(1 - o) 4M - E p 3K 9K- E 1 + o (1 + a)(1 - 2a) 3j - E -2 E 1 - 2a E pV. 3K 3K M s 3K9K- E K2+ 2a 2 t 2a 2.2.2. COMPOSITE OSCILLATOR. The composite-oscillator method applies the basic principles of the method of resonant vibrations of cylinders to single-crystal or polycrystalline specimens. Balamuth [25] and Rose [26] have developed the theoretical basis for this method, and Birch [27] has outlined their work: if a crystal specimen (mass = ml, resonant frequency = fl) is cemented to a piezoelectric crystal of the same cross section (mass = m2, resonant frequency = f2), the resultant "composite oscillator" will have a resonant frequency f given [26] by: mlf1 tan 7r(f/fl) + m2f2 tan r(f/f2) = (1) If f, fl, and f2 are nearly equal (+10%), then equation 1 simplifies (~2%) to [27]: m2 fi = f + (f - f)m (2) If f and f2 can be measured, then fl may be obtained from equation 2. Compressional- and shear-cut piezoelectric crystals are used to excite the extensional and shear vibrational modes. 9

WILLOW RUN LABORATORIES For the extensional mode, V 2fll = (E/p)1/2 For the extensional mode, V= 2f (E/p); as in the resonance method, the propagation velocity is distorted if f/d < 5 [5], but Birch [27] estimates the error to be less than 1% for f/d > 2. There are no such conditions for the shear mode in which the velocity corresponding 1/2 to the fundamental frequency is Vs = (/J/p)/. The shape of the cross section is not important for the extensional mode, but the shear mode becomes complicated for shapes other than circular cylinders [28]. X-cut quartz bars of square cross section with two electrodes are thus convenient for the extensional vibrations, while Y-cut quartz rods of circular cross section with four electrodes are most useful for the shear mode. An alternating potential applied to the electrodes in the piezoelectric crystals induces the required vibrations in the composite oscillator. The range of frequencies employed in this method is 90 to 250 kc/s, depending upon the natural frequency of the specimen. Occasionally, the specimen is driven at an overtone for convenience, but too large a ratio of m2 to m1 exaggerates the frequency difference (f - f2) in equation 2 [27]. The resonant frequency of the freely vibrating composite oscillator is determined by monitoring the electrical impedance between the electrodes (see fig. 3). This impedance exhibits a sharp decrease at the resonant frequencies. This method can be used on single-crystal specimens as small as a few millimeters in length with an accuracy of 1% to 2% and is readily adaptable to measurements at high temperatures. However, it requires the use of a set of quartz crystals of various lengths so that the frequency of the composite oscillator falls near fl and f2. This method has not been used for measurements at elevated pressures. QUARTZ F.J r " OSCILLATOR R VOLTMETER SAMPLE FIGURE 3. SCHEMATIC DIAGRAM FOR THE CIRCUIT OF THE COMPOSITE OSCILLATOR [27] 10

WILLOW RUN LABORATORIES 2.2.3. WEDGE. The composite-oscillator method requires a set of quartz crystals of various lengths to provide a range of frequencies. Since the resonant frequency of a piezoelectric crystal is inversely proportional to its length, a crystal wedge provides a source of continuously varying frequency in one crystal. Bhagavantam and Bhimasenachar [29] have adopted the use of X-cut quartz and Y-cut tourmaline wedges (f = 1 to 12 Mc/s) for this purpose. Bhagavantam [30] provides an outline of this method. The piezoelectric crystal and the specimen are juxtaposed between two electrodes, forming a parallel plate condenser. This condenser is then placed in a glass cell with the lower plate just touching the surface of a liquid medium such as carbon tetrachloride. As the electrical oscillator excites the wedge, an ultrasonic beam passes through the specimen and into the liquid. The transmitted beam is observed by means of the Debye-Sears diffraction effects. The points of maximum intensity in the pattern correspond to the resonant frequencies of the crystal specimen. As in the other methods, the velocities of the elastic waves are then calculated from V = 2f I and V = 2f 2, corresponding 1/2 1/2 e s s to the bar (E/p)/ and the shear (//p)/2 velocities, respectively. This method is capable of determining velocities within 5% [30] and is suitable for work on single crystals and fine-grained, low-porosity rocks or polycrystalline aggregates of single crystals. It requires only small specimens but is not suitable to work at high pressures or temperatures. Sundara Rao [31] has raised some doubts about the use of wedges because of spurious peaks in their emitted spectra. Since the resonant points are determined by monitoring the intensity of the transmitted beam, errors will be introduced if all frequencies in the piezoelectric crystal are not excited equally. 2.3. PULSE- TRANSMISSION METHODS 2.3.1. THE VARIABLE DELAY LINE. The ultrasonic-pulse-transmission technique is based upon the creation of a short train of high-frequency vibrations and the measurement of its propagation time through the specimen. Attempts prior to World War II [32] to use travel times of pulses failed because of the lack of adequate electronic equipment [33]. The development of pulse circuitry and fast-writing oscilloscopes during the war-time research and the studies at the Bell Telephone Laboratories of the piezoelectric properties of crystals made this method feasible [34]. The pulses (50 kc/s to 10 Mc/s) are generated by crystal transducers attached to the specimen (see fig. 4). The pulse transmission time (or "time of flight") is measured by direct observation of the time between the "shot" and the arrival of the pulse or by matching the onset of the pulse transmitted through the specimen with that of a pulse transmitted through a 11

WILLOW RUN LABORATORIES variable-length mercury delay line (see fig. 5). Simmons [36] has an excellent discussion of the advantages and disadvantages of the various transducers (ceramic and single crystal) used to generate the compressional- and shear-wave pulses. Input Electrode Transducer Sample SPECIMEN Rubber tubing PULSE ( GENERATOR TransducerVARIABLE Electrode DELAY -— Output pu DUAL TRACE J~~~~~~~~~~I ~~OSCILLOSCOPE FIGURE 4. ARRANGE- FIGURE 5. SCHEMATIC DIAGRAM FOR THE VARIABLE-DELAYMENT OF THE SPECIMEN LINE METHOD OF PULSE TRANSMISSION [35] AND TRANSDUCERS FOR THE PULSE-TRANSMISSION TECHNIQUE [33] There are certain theoretical and practical considerations when designing an experiment using the pulse-transmission technique [7, 33]. Love [4] showed that the first motion resulting from an arbitrary disturbance in an isotropic medium is propagated with the velocity of com/K + 4C/3\1/2 pressional plane waves in an unbounded medium, (K+ 4/3 A number of investigators have experimentally verified this by comparing the observed V with that calculated from independently measured elastic constants [7, 33, 37-39]. The most convenient shape for the specimen is a right circular cylinder. For clear observation of the compressional arrival the length-to-diameter ratio f/d should be less than about 5 [40]; as k/d increases, more of the initial compressional energy is delayed by boundary reflections and eventually Vp recedes into the noise level, and the observed first arrival travels 12

WILLOW RUN LABORATORIES - with the bar velocity (E/p) [33]. It has been determined experimentally [41] that the diameter-to-wavelength ratio (d/X) must be greater than about 5 to minimize dispersion for the compressional pulse. When the wavelength becomes less than about three times the diameter of the grains in the specimen, the energy is scattered and the pulse becomes distorted [37]. Within the range of these dimensional restrictions, the compressional-wave velocity is found to be independent of the frequency of the transmitted pulse [42-44]. There is no dispersion predicted or observed for pulses generated by the shear-wave transducers. Much of the work using the pulse-transmission technique has dealt only with the first arrival (either compressional or shear, depending upon the transducer). Iida and Kumazawa [45, 46] used the direct second arrival to determine Vs without much success. Hughes et al., [39] determined V by using a secondary arrival, the so-called PSP phase, which accompanies a P wave traveling longitudinally in a cylinder. Part of the P-wave energy is converted to S-wave energy at the cylinder wall, traverses the cylinder obliquely as an SV wave, and is reconverted to P at the opposite wall. The delay time (PSP - P) of this phase depends only upon Vp, Vs, and d, so its determination leads directly to a value for Vs. This method has proved somewhat satisfactory for metals, limestones, marbles, and quartzites, but for coarse-grained rocks there are serious errors in the transformed pulse caused by interference and reflection at grain boundaries [47]. The precision of these measurements is low (good to two significant figures at best) because of a low signal-to-noise ratio and the remaining P motion [36]. The amount of pulse distortion is increased at high pressures [48]. Finally, unless the medium is isotropic and uniform, there is no unique delay time for the secondary arrival [33], but it does give a rough idea of V while measuring Vp [36]. This P-S conversion used for the PSP ars p rival is found to be negligibly small for d/X > 20 [37]. For the measurement of V itself, see s reference 35. The pulse-transmission technique has been used extensively in the last 15 years because it does not require homogeneous or isotropic specimens, can be used for porous specimens, and is readily adaptable for measurements at high pressures and temperatures. Chick of Brown University is presently working on modifications of this method to improve the accuracy attainable. The crux of the method is to compare two waveforms, one of which is often badly distorted; the measurement therefore depends upon the operator's judgment of the position of a crest or the onset of a wave (see figs. 6 and 7). At present, the accuracy of this method is 1% to 3%, which is quite adequate when dealing with imperfect rock specimens but is not as good as is desired for very fine grained specimens or single crystals [36]. An improvement sufficient to determine with confidence the pressure derivative of the sound velocity would be most welcome. 13

WILLOW RUN LABORATORIES / r s 0.2 t FIGURE 6. OSCILLOSCOPE TRACES FOR Vp MEA- FIGURE 7. OSCILLOSCOPE TRACES FOR Vs MEASUREMENTS ON NIPISSING DIABASE AT 8 kb. The SUREMENTS ON WESTERLY GRANITE USING AC-CUT lowest photograph shows microsecond timing marks QUARTZ TRANSDUCERS. The lower trace on the exon the trace; on the other, reading from the left, can panded time scale shows the Hg signal set for the be seen the electrical pickup from the pulse, the beginning of S [5]. first arrival, PSP, and a reflection of P from the outer end of the backing piece. The middle photograph shows the same pulse as the lower one with a faster sweep, the pulse now displaced from the screen. The top photograph shows the same pulse again, with still faster sweep; only the first arrival with the Hg signal slightly displaced from coincidence is shown [33]. 14

WILLOW RUN LABORATORIES 2.3.2. PULSE ECHO. For very fine grained materials (<0.5 mm) which can transmit high-frequency pulses without distortion, Birch [33] prefers "pulse-echo" technique of Lazarus [49]. This is essentially a pulse-transmission technique in which the time delay for a pulse to propagate through the specimen, be reflected at the free end, and return to the transducer is determined by displaying the applied pulse and the successive echoes on the linear time scale of an oscilloscope. Lazarus corrects for the time delay in the seal between the transducer and the specimen and for the change of length with pressure. The circuitry required is considerably simpler than that of McSkimin's interferometric techniques, and it is possible to attain an accuracy of i 0. 5% [50]. 2.3.3. TOTAL INTERNAL REFLECTION. The total-internal-reflection method utilizes the basic principles of pulse transmission with some modification of the apparatus. A plane compressional wave incident upon a liquid-solid interface produces both a refracted compressional wave and a refracted shear (SV) wave (see fig. 8). The sound velocity in solids is generally higher than in liquids, so, as in optics, when a beam of ultrasonic energy passes from a liquid to a solid, the phenomenon of "total internal reflection" will occur beyond a critical angle of incidence. For elastic waves, there are two such critical angles, one for compressional and one for shear waves if the velocity of the liquid is less than the shear velocity in the solid. The velocity in the solid is then V = V iq/sin icrit. Bez-Bardili [51] was the first to use this principle to determine sound velocities. In this method, a plate of the sample is rotated in the path of an ultrasonic beam in a liquid. As the specimen is rotated, the transmitted signal first exhibits a sharp dip in intensity at the compressional critical angle and then vanishes entirely at the shear critical angle. Bez-Bardili detected the emergent beam using the Debye-Sears diffraction method of optics. Schneider and Burton [52] used a second piezoelectric crystal to detect the transmitted beam. Krishnamurthi and Balakrishna [53] have adapted the pulse technique of Pelham and Galt [54] to sound-velocity measurements. The use of the pulsed input allows the elimination of internal reflections in the system which may be a serious handicap with a continuous wave input [55]. Krishnamurthi and Balakrishna [53] and Gregory [55] estimate that the critical angle can be determined within 0.10, which corresponds to a velocity uncertainty of about 0.5% to 1.0% for compressional waves. The shear critical angle can usually be determined slightly more accurately than the compressional angle. Krishnamurthi and Balakrishna also noted that because of refraction the emergent beam is shifted laterally with respect to the incident beam (see fig. 8), so the receiving transducer must either cover a large area or be capable of being moved laterally to pick up the transmitted beam. 15

WILLOW RUN LABORATORIESeD es FIGURE 8. REFLECTED COMPRESSIONAL WAVE AND REFRACTED SHEAR (Os) AND COMPRESSIONAL (OD) WAVES PRODUCED BY COMPRESSIONAL WAVE INCIDENT AT ANGLE 01. At critical angles the refracted waves disappear. Note lateral shift of incident beam as it traverses the crystal [36]i, Velocities are observed to decrease and attenuation of the transmitted signal is observed to increase with increasing grain size of the specimen [56], and the results become doubtful when the grain dimensions approach the wavelength of the applied signal. For the frequencies generally used (1 to 5 Mc/s), this limits the method to materials in which the average grain diameter is less than 1 mm. The total-internal-reflection method may be applied to inhomogeneous materials if these materials are elastically isotropic within the dimensions of the specimens. Gregory [55] obtained reliable values of Vs at elevated pressures using jacketed specimens. This method has not yet been used at pressures above 1 kb, and the transducer system would probably have to be modified for use at higher pressures [36]. Bhagavantam [30] found this method unsuitable for high-temperature work, but Simmons [36] states that the apparatus of King and Fatt [57] could be easily adapted for measurements at high temperatures. 16

WILLOW RUN LABORATORIES 2.4. ULTRASONIC-INTERFEROMETRY METHOD 2.4.1. GENERAL COMMENTS. The review by Simmons [36] of this method is adequate for most purposes. Simmons' remarks should be expanded for those readers especially interested in measurements on minerals or well-sintered aggregates. During the past 15 years, ultrasonic-interferometric techniques have been developed to the 4 point where the sound-velocity measurement to within 1 part in 10 can be made. The principle of this method is shown schematically in figure 9. On one end of the specimen a quartz transducer is cemented with a very viscous grade of polystyrene fluid, such as Dow Chemical Company V-9, which transduces a high-frequency electromagnetic signal into a sound wave. Arrows in figure 9 represent the directions of the incident wave and the first reflected waves. The same transducer records a series of echoes of decreasing amplitude, separated by equal time intervals (t) as shown in the figure. The sound velocity of the specimen is determined by measuring the transit time of one wave or by counting the number of waves in a specimen of known thickness. X-cut quartz is used to obtain the longitudinal sound velocity (Vp), and Y-cut or AC-cut is used for the shear sound velocity (Vs). In an isotropic substance, such as a wellsintered ceramic, the two velocities V and V are sufficient to describe all elastic properties p s of the specimen when the density is known. TRANSDUCER INCIDENT WAVE REFLECTED WAVE (I) REFLECTED WAVE (2) It-.TIME FIGURE 9. PRINCIPLE OF ULTRASONIC-INTERFEROMETRY TECHNIQUE [18] 17

WILLOW RUN LABORATORIES — As described by McSkimin [58], the main advantage of the ultrasonic method is its applicability to small specimens without loss of accuracy. Measurement to within 1 part in 10 can be obtained. If the error within 1 part in 10 is allowed, it is possible to measure the elastic constants of a specimen as small as 2 mm thick and 10 mm in diameter. Another advantage is its applicability under high pressure. However, measurement at temperatures higher than 3000C cannot be made because of the temperature limitations of the seal and the transducer. The chief disadvantage of the interferometric method is that high frequencies must be used. The absorption of sound varies at some high power of frequency, so velocity measurements cannot be made on solids which have many defects, pores, or grains. Transmission of high frequencies cannot be observed when the porosity is greater than about 5% because of the scattering of the sound at the pores. Although the construction of such a system (see fig. 10) is not complicated except for a few electronic parts such as a harmonic generator and a mixer, the specimen must be prepared with great care. To obtain accurate results, which cannot be done on a small specimen by any other method, flatness to 1/4 wavelength of light and parallelism to within 10 sec of arc may be necessary. Since such a specimen can be prepared only by specially equipped shops, the cost becomes extremely high when many specimens are needed. Various methods have been introduced to solve the problem of accurately measuring the time interval or number of waves in the specimen. The phase-comparison method and the pulse-superposition method have been successful for measuring sound velocities of small specimens. 2.4.2. PHASE COMPARISON. The phase-comparison method consists of superimposing the echoes of two pulses which have made different numbers of round trips [59]. If the echoes are made exactly in phase by a critical adjustment of the carrier frequency, the expression for phase angles may be written as 21cw y _ n=-2rn (3) ly _., n 2,ffn (3) where V is the velocity of propagation, co = 2Ir times the pseudoresonant frequency (fn) I is n thickness, n is the number of waves, and y is the phase shift caused by the seal between the transducer and the specimen. Consequently, the velocity is expressed by 2.f nV = n (4) 18

- WILLOW RUN LABORATORIESMcSkimin [59] has proven experimentally that size and shape effects are reduced to effectively zero whenever there are at least 100 wavelengths of sound in the specimen thickness. High frequencies (10-20 Mc/s) are generally used to minimize these effects. FREQUENCY PULSE COUNTER GENERATOR CONSTA, LN T CONSTANT GATED HARMONIC WAVE GENERATOR OSCILLATORG R _ 15 MC t tt -, 60 MC TRANSDUCER SPECIMEN ~ --- 1_, -60 MC LOCAL i OSCILLATOR |, - 20 MC ATTENUATOR] a.dF. SCOPE AMPLIFIER SCOPE FIGURE 10. ULTRASONIC INTERFEROMETER [18] The main advantage of this phase-comparison method is that the absolute velocity can be determined very accurately without the error introduced from coupling, since the transducer coupling effect can be evaluated. This method also makes it possible to measure the velocity on a specimen with linear dimensions as small as 2 mm. The experimental details of the phase-comparison technique are discussed by Anderson and Schreiber [60]. 2.4.3. PULSE SUPERPOSITION. The pulse-superposition method uses an RF pulse applied to the transducer at intervals approximately equal to the round-trip delay time of waves traveling in the specimen [61]. So that the superposed echoes can be observed just after the 19

WILLOW RUN LABORATORIES last applied pulse, a few applied pulses are omitted periodically. When the echoes are brought into phase by adjusting the time spacing T between applied signals, a maximum in the resulting pulse amplitude occurs. This satisfies the equation 6 = T_ l _ r (5) p f\p 2T where 6 is the round-trip delay time, f is the radio frequency in the pulse, n is an integer which may be either positive or negative, and y is a phase angle associated with waves reflected at the transducer end. Since T is approximately some multiple p of 6, the applied pulse occurs once for every round-trip delay when p = 1. Usually, a number of measurements of T at various frequencies between fy, the resonance frequency of the transducer, and 0.9fy are made to obtain the difference in T between fy and another frequency f. An important experimental procedure is to find the resonance corresponding to n = 0 [61]. If n = 0, the delay time is given by 6 = T + (y/27rf) (6) The velocity in the sample is V = 2f/6, where I is the sample length. The advantage of the pulse-superposition method is that the coupling to the transducer is taken into account, so that this method is well suited to measurements aimed at pressure and temperature variations. The effect of coupling between transducer and specimen can be made negligibly small. The accuracy of this method is within a few parts in 10, while that of the phase-comparison method is within 1 part in 10 [62]. With pulse superposition, however, it is possible to send a strong signal into the specimen so that the velocity can be measured even if the attenuation is high. The pulse-superposition method has been successfully used to measure the sound velocities on specimens with more than 1% porosity, while the phase-comparison method failed at that porosity. The limitations of both techniques are expected to depend upon various factors besides porosity, such as grain size and grain-boundary condition. Anderson and Schreiber have made precision measurements on synthetic polycrystalline specimens of periclase (MgO) [60] using the phase-comparison method and upon corundum (A1203) [63] using the pulse-superposition method. Their measurements of Vp and V at room temperature and pressures up to 4 kb provide an accurate determination of the pressure derivatives of the sound velocities: MgO: V = 9.7662 + 7.711 x 10 P km/s P V = 5.9635 + 4.351 x 10 P km/s s 20

WILLOW RUN LABORATORIES Al203 V = 10.845 + 5.175 x 103 P km/s p V = 6.3730 + 2.207 x 10-3 P km/s s These results are given here because of the significance of these oxides in the composition of the earth and because the data in the appendixes (MS01-03, AA02-03) cannot adequately represent the precision of this work. The experimental details of the pulse-superposition technique are given by Schreiber and Anderson [63]. 3 NEW METHODS OF DETERMINING VELOCITY: DIRECT AND INDIRECT 3.1. RESONANCE OF SMALL SPHERES; DIRECT MEASUREMENT OF V s The shear velocity and internal friction of a small sphere can be determined by measuring the fundamental free-oscillation frequencies of the sphere and the decay of its vibration. A brief description of the method developed by Fraser and LeCraw [64] follows. The sphere is placed on a shear-mode piezoelectric transducer which vibrates with an imposed electric field so that the frequency can be controlled. When the frequency of the vibrating transducer is equal to the appropriate free oscillations of the sphere, energy will be absorbed from the electromechanical system, resulting in an abrupt change of the waveform pattern on the oscilloscope. The appropriate mode number can be determined by analyzing the series of resonance frequencies, since the series of frequencies of free oscillation is given by the equation f =a (7) n nd where V is the shear-wave velocity, d is the diameter, and a is a number dependent upon the order number n and the type of oscillation and can be obtained by solving the appropriate spherical wave equations as outlined by Love [4]. This technique is well known in seismology as a means of estimating phase velocities within the earth and determining its elastic constants by measuring the period of free oscillations of the earth after a large earthquake. Until quite recently, however, it has not been applied to small specimens because of the complicated electronic setup. Fraser and LeCraw [64] recently proved, using single crystals of yttrium gallium garnet and yttrium aluminum garnet as 21

WILLOW RUN LABORATORIES examples, that this method can be used to measure the elastic and anelastic properties of solids as functions of both frequency and temperature. The internal friction is determined as follows. The transducer, which vibrates at one of the sphere's resonant frequencies, is switched to a receiver so that the free decay of the sphere's vibration is recorded on an oscilloscope. The internal friction can be calculated from this decay curve. The disadvantage is that only the shear velocity can be determined directly. To describe the elastic properties of an isotropic polycrystalline solid, two independent elastic constants are necessary. Another technique must be used to obtain one more elastic constant. By measuring the spheroidal mode in addition to the torsional mode, it may be possible to define both sound velocities. A preliminary experiment was performed by D. Fraser of Bell Telephone Laboratories, Inc., on the polycrystalline MgO obtained from the University of California. The diameter of the MgO specimen used was about 0.45 cm. The shear sound velocity was measured as 6.0 km/s, which agrees well with the value obtained on the same sample by means of the ultrasonic technique (5.966 km/s). The technique of resonance of small spheres will be an important one in determining a small specimen's elastic constants. In general, it is difficult to determine the shear modulus rather than the Young's of a solid because the torsional fundamental resonant frequency in the standard-resonance technique is much higher than the flexural fundamental resonant frequency and therefore exceeds the upper limit of the standard-resonance technique when the rod is short. This new technique will solve this problem. There are three major advantages to this thiechnique. First, shear velocity can be determined on a sphere as small as 2 mm in diameter. Such a small sphere can be fabricated fairly easily by successively grinding away the corners of a polyhedron and then applying a tumbling process of a two-pipe technique. Second, no bond is required between the transducer and specimen in this technique; thus the errors introduced by absorption of energy in the bond are eliminated. This is ideal for determining the internal-friction measurement. Third, spheres are easy to fabricate. Even with specimens as small as 2 mm, sphericity can be maintained to within 0.1%,*.limiting the error in V to ~0.5%. s For geology this technique is especially promising. Since the diameters of the specimens may be as small as a few millimeters, it may be possible to measure the shear velocity of individual grains of a rock and compare the results with velocity in the rock itself. Resonance *D. Prentiss, private communication. 22

WILLOW RUN LABORATORIES of dense rocks, where the Q is not too low, is possible by making spheres up to 10 cm in diameter. A problem which must be solved before this technique can fulfill its promise in mineralogy is the mode splitting due to anisotropy of a crystalline lattice. This field of theoretical mechanics would be suitable for PhD theses. 3.2. SPECIFIC HEAT OF A POWDER: INDIRECT MEASUREMENT OF V s The isotropic shear velocity V of inorganic materials such as minerals and rocks can be s estimated from low-temperature specific-heat measurements [65]. This property promises to be very useful because it enables one to determine the seismic shear velocity of a material independently of the state of aggregation of the samples. This correspondence between acoustics and calorimetry is based upon a principle of lattice dynamics which states that at sufficiently low temperatures the optical vibrations of a solid are quiescent and the vibrational energy arises solely from acoustic vibrations. This correspondence is conveniently stated in terms of Debye temperatures. The low-temperature specific heat is represented by a scalar parameter called the thermal Debye temperature, 0t, and the acoustic contribution of specific heat is represented by the acoustic Debye temperature, 0. Thus, at temperatures near absolute zero, a 0t =a (8) t a In terms of the sound velocities for an isotropic body [66, 67], h(_9pN\3/2 11/3 0 =k k4*M/p (V + (9) where h, k, and N are physical constants, M/p is the mean atomic weight (molecular weight divided by the number of atoms determining the molecular weight), pis the density, and Vs and V are the shear and compressional velocities, respectively. It is more convenient to write the above expression in terms of the mean sound velocity, V: 3 2 1 (10) + t- (10) V 3 v v3 V V V m s p Combining equations 8, 9, and 10, we have 1/3 6t = 231.3 (M/p) V (11) 23

WILLOW RUN LABORATORIES Vm is in kilometers per second, and the numerical factor arises from the physical and numerical constants in the preceding equations. Both V and V are needed to define 0t. A closer examination, however, reveals that to a good approximation V alone defines 0t. This can be demonstrated by solving for the ratio of V /Vm and substituting for V /Vs the equivalent function of Poisson's ratio a. Anderson [68] showed that if the Poisson's ratio has a value between 0.15 and 0.35, which includes most materials, V ((M/ km/s (12) Equation 12 is the desired equation which has practical uses in geophysics. Knowledge of the mean atomic weight, density, and the low-temperature specific heat (from which 0t can be s defined) is sufficient to compute Vs. A few examples showing the use of equation 12 are given in table VI; the agreement is shown to be quite good for MgO, A1203, and W. TABLE VI. CALCULATION OF SHEAR VELOCITY FROM THE THERMAL DEBYE TEMPERATURE AND COMPARISON WITH MEASURED VALUES Debye Temp. Calc. Shear Meas. Shear Ref. for (Thermal Mean Atomic Velocity Velocity Measured (Sp. Heat) Weight Density from Eq. 12 (Polycryst.) Shear Solid 6t M/p p V V Velocity (OK) (gm/cm3) (km/s) (km/s) MgO 946 [69] 20.3 3.583 6.02 5.993 75 6.02 65 A1203 1045 [70] 20.4 3.986 6.45 6.44 22 BeO 1200 [71] 12.5 3.01 6.87 7.11 76 Al 428 [72] 26.98 2.698 3.29 3.13 47 Fe 445 [73] 55.84 7.872 3.06 3.20 47 W 380 [74] 183.90 19.20 2.89 2.86 77 Discrepancies between measured and calculated values of V can arise in three ways. First, equation 8 may not be completely valid. This question has been discussed by Alers [78], who found that equation 8 holds for crystalline nonmetals. Equation 8 may not be valid for metals because of the electronic contribution of specific heat. This is demonstrated in table VI by errors resulting from using equation 12 on Al and Fe. Second, the approximation that 24

WILLOW RUN LABORATORIES V = 0.9V is not valid for materials with a very low Poisson's ratio. The value of C for BeO s m is 0.11, and there is a corresponding lack of agreement for Vs, as shown in table VI. Third, the value of St derived from specific-heat data may be incorrectly determined. The method of finding 0 from specific. heat recommended by Barron et al. [79] should be followed. Specific-heat measurements are often reported at liquid-nitrogen or higher temperatures. Values of C in this temperature range will probably lead to poor estimates of V by equation 12, p s since C is then influenced by optical vibrations in addition to the acoustic vibrations. From the results of Alers [78], it would appear that equation 8 is valid for all crystalline materials of interest to petrology. It may, however, not apply to inorganic glasses. It has been proven that equation 8 does not hold for vitreous silica [80], but that it does hold for quartz. Therefore, equation 12 may not be useful for obtaining the shear velocity of glasses of geological interest, such as obsidian and tektites. It should be possible to measure V by suitable low-temperature specific-heat techniques s on all types of geological specimens: rocks, crystals, sediments, dust, pumice, or aggregates. The resulting value of V will be independent of microstructure effects arising from grain boundaries and pores, and will correspond to the dense isotropic solid at zero porosity. If the material retrieved from the lunar surface is dust or small pebbles, equation 12 may prove to be a practical method of measuring the shear velocity of the rocks from which the material was derived. The calculation of V by equation 12 is as accurate as other standard techniques for meas surements on rocks and crystals. Pores and grains make the determination of V on fields specimen aggregates using resonance or acoustics somewhat uncertain. The determination of V on single crystals is uncertain because of the tensor properties of the crystal; V must be s s determined by an imposed averaging scheme. For example, if one averages the single-crystal elastic constants of alumina [81], one can say only that the true value of V lies somewhere between the Voigt limit, Vs = 7.453 km/s, and the Reuss limit, V = 6.349 km/s [68]. 55s 3.3. COMPRESSION OF A SOLID: DIRECT MEASUREMENT OF BULK MODULUS K IN A PRESS OR IN A SHOCK WAVE This method is an old one reported in the literature, but it is included here because, although it is used for minerals, it is not a standard method of determining the velocity of sound of rocks. The compression measurement consists of measuring the variation of volume (or length) of a substance with pressure and finding the limiting slope of the data at zero pressure to determine the compressibility, or its reciprocal, the bulk modulus. There are three methods: an isothermal measurement of volume (or length) change, typified by the experiments of 25

WILLOW RUN LABORATORIES Bridgman [82] and Weir [83]; measurement of the lattice constants with pressure by X-rays, typified by the experiments of Drickamer and Perez-Albuerne [84], McWhan [85], and Takahashi and Bassett [86]; and compression deduced from shock waves, typified by McQueen and Marsh [87]. While shock-wave measurements yield VK7-, the other measurements yield K. Isothermal-compression measurements, such as those made by Weir and McWhan, can be made upon powders; this can be important to geological problems. The chief disadvantage of this method is that when compression is applied to rocks, spurious effects of grains, pores, and cracks cause erroneous results. Brace [88] comments that "For most purposes, further measurement of rock compressibility is pointless. Efforts might be profitably expended on refinement of mineral compressibilities or their extension to higher pressure and temperature." 3.4. INFRARED REFLECTION OF A DIATOMIC SOLID: INDIRECT MEASUREMENT OF K This method is of special usefulness since it applies only to diatomic solids. It has been used successfully to find the bulk modulus of MgO, SiC, and ZnO [75]. It would presumably be useful for CoO, NiO, MnO, BN, and ZnS, but not for Fe203, SiO2, quartz, etc. The method and its application to MgO have been described by Anderson and Glynn [75]. The advantages of the infrared-reflectivity method stem from the fact that the measurement is obtained from an optical signal reflected from a surface. The method is nondestructive. It requires little thickness of specimen and requires no holder, clamp, or transducer. The signal can be transmitted through appropriate windows. Consequently, it can be used on thin films or on specimens which are heated to very high temperatures. The most critical requirement is to obtain a highly polished flat surface. A coarse surface causes scattering of infrared and results in the reduction of reflectivity. However, the same absorption band can be achieved even though such a reduction of reflectivity occurs for porous materials. Therefore, the bulk modulus of a material with zero porosity can be obtained from the data of the same material having fairly high porosity. The chief disadvantage is that only one elastic constant is found, so that the shear constant or Poisson's ratio cannot be determined. Another disadvantage is that the value of compressibility is determinable only within a few percent. However, it may be the only method available for examining the elasticity of a thin film. It is unfortunate that structures more complicated than diatomic solids show structured reflection bands which cannot be analyzed by this method. A description of the results found by Anderson and Glynn for MgO is given below. 26

WILLOW RUN LABORATORIES The reflection band was measured on the polycrystalline MgO specimen of gem quality obtained from the University of California. The reflectivities were determined by a point-bypoint measurement. The intensity of the reflection from the sample onto a thermocouple was compared with that of the reflection from the front surface of a high-quality rhodium mirror. The mirror was assumed to have a reflectivity of 97% for wavelengths greater than 1 pI. By analysis of the reflection band between 4 and 30 /z, the absorption wavelength X was 0 found to be 25.0 ~ 0.1 /I. The index of refraction was 1.783, and the dielectric constant was 9.8. These measurements used in the appropriate equation [75] gave the value of the bulk modulus as K = 1640 kb. The ultrasonic measurement on the same specimen was K = 1711 kb. The main source of error is the determination of X and the dielectric constant. 0 3.5. A COMPOSITE METHOD USING THE DEBYE TEMPERATURE AND THE BULK MODULUS: INDIRECT MEASUREMENT OF V AND V p s Surveys of the literature often reveal that even when data on the sound velocities are missing, there nevertheless are data on the specific heat and the isothermal compressibility. The latter data are prevalent because these measurements can be taken on granular or crystalline materials. Scalar quantities can be obtained even for monocrystals. By combining the methods described in sections 3.2 and 3.3, Soga and Anderson [18] showed that exact equations would be deduced for given values of Poisson's ratio a. If K and C are known, the other isotropic moduli and velocities are easily found. The two critical equations are defined in terms of a critical parameter Z, -1/3 1/2 h- 4 Mi- (13) which is a function of a, according to 1/3 Z = - (14) 1~+ a +2 2(1 +a)] 3(1- c)J 3(1- 2c)J where h is Planck's constant, k is Boltzmann's constant, N is Avogadro's number, p is the density, M is the molecular weight of the solid, p is the number of atoms in the molecule, and 0 is the Debye temperature. Thus, M/p is known from the composition, and given p, K, and 0, Z can be calculated. Then the value of C is found which gives the same value of Z. In this way a and Z are both 27

WILLOW RUN LABORATORIES found. The two sound velocities are then given by PV2=3K(1 - c) pV 3K(i + a) and pV2= 3K(1 2or) s 2 (1 + a) To aid in the conversion, a listing of Z versus a is given in table VII. An example showing the precision of this method for four oxide compounds is given in table VIII. It is evident that the computed values of the elastic moduli are quite accurately determined by this method. 3.6. ESTIMATING SOUND VELOCITIES FROM THE REFRACTIVE INDEX: INDIRECT MEASUREMENT OF V AND V s p Only a few physical properties can be measured on microscopically sized solids such as grains of powders; perhaps the easiest measurement is of the refractive index. The measurement of sound velocity, on the other hand, is not an easy task under the best circumstances and becomes quite difficult for small samples. The difficulty is compounded if the sample is a crystalline solid of low symmetry. The relative difficulty of the two measurements is demonstrated by the fact that there is a great amount of refractive-index data in the literature on oxides, while the data on sound velocity are scanty by comparison. Any method of using refractive-index data to estimate the sound-velocity data is valuable to researchers concerned with the mechanical properties of minerals and inorganic compounds. Anderson [91] showed that for oxide compounds the compressional and shear sound velocities can be estimated from two properties determinable on very small samples: (1) the mean refractive index n, and (2) a compositional parameter called the mean atomic weight, M/p (the molecular weight divided by the number of atoms in the formula). This new method is apparently restricted to oxide compounds (simple oxides like MgO, silicates like Mg2SiO4, and complicated minerals like tourmaline). A large number of oxides have the same value of M/p, so that within broad limits the index of refraction alone determines the sound velocity irrespective of phase, composition, or crystalline symmetry. This is analogous to the determination of density from the refractive index (the Gladstone-Dale law) commonly used by mineralogists. In this discussion, sound velocity is the isotropic sound velocity that a dense polycrystalline solid would have at zero porosity, and refractive index is the arithmetic mean of the crystalline refractive indexes. 28

- WILLOW RUN LABORATORIES TABLE VII. CONVERSION TABLE BETWEEN Z AND POISSON'S RATIO Poisson's Ratio 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.000 1.3279 1.3260 1.3241 1.3222 1.3203 1.3184 1.3166 1.3147 1.3128 1.3109 0.010 1.3090 1.3071 1.3052 1.3034 1.3015 1.2996 1.2977 1.2958 1.2940 1.2921 0.020 1.2902 1.2883 1.2865 1.2846 1.2827 1.2808 1.2790 1.2771 1.2752 1.2734 0.030 1.2715 1.2696 1.2677 1.2659 1.2640 1.2621 1.2603 1.2584 1.2565 1.2547 0.040 1.2528 1.2510 1.2491 1.2472 1.2454 1.2435 1.2417 1.2398 1.2379 1.2361 0.050 1.2342 1.2324 1.2305 1.2286 1.2268 1.2249 1.2231 1.2212 1.2194 1.2175 0.060 1.2157 1.2138 1.2120 1.2101 1.2082 1.2064 1.2045 1.2027 1.2008 1.1990 0.070 1.1971 1.1953 1.1934 1.1916 1.1897 1.1879 1.1860 1.1842 1.1824 1.1805 0.080 1.1787 1.1768 1.1750 1.1731 1.1713 1.1694 1.1676 1.1657 1.1639 1.1620 0.090 1.1602 1.1584 1.1565 1.1547 1.1528 1.1510 1.1491 1.1473 1.1454 1.1436 0.100 1.1418 1.1399 1.1381 1.1362 1.1344 1.1325 1.1307 1.1288 1.1270 1.1252 0.110 1.1233 1.1215 1.1196 1.1178 1.1159 1.1141 1.1123 1.1104 1.1086 1.1067 0.120 1.1049 1.1030 1.1012 1.0993 1.0975 1.0957 1.0938 1.0920 1.0901 1.0883 0.130 1.0864 1.0846 1.0827 1.0809 1.0790 1.0772 1.0753 1.0735 1.0716 1.0698 0.140 1.0680 1.0661 1.0643 1.0624 1.0606 1.0587 1.0569 1.0550 1.0531 1.0513 0.150 1.0494 1.0476 1.0457 1.0439 1.0420 1.0402 1.0383 1.0365 1.0346 1.0328 0.160 1.0309 1.0290 1.0272 1.0253 1.0235 1.0216 1.0197 1.0179 1.0160 1.0142 0.170 1.0123 1.0104 1.0086 1.0067 1.0048 1.0030 1.0011 0.9992 0.9974 0.9955 0.180 0.9936 0.9917 0.9899 0.9880 0.9861 0.9843 0.9824 0.9805 0.9786 0.9767 0.190 0.9749 0.9730 0.9711 0.9692 0.9673 0.9655 0.9636 0.9617 0.9598 0.9579 0.200 0.9560 0.9541 0.9522 0.9504 0.9485 0.9466 0.9447 0.9428 0.9409 0.9390 0.210 0.9371 0.9352 0.9333 0.9314 0.9295 0.9276 0.9257 0.9237 0.9218 0.9199 0.220 0.9180 0.9161 0.9142 0.9123 0.9103 0.9084 0.9065 0.9046 0.9027 0.9007 0.230 0.8988 0.8969 0.8949 0.8930 0.8911 0.8891 0.8872 0.8853 0.8833 0.8814 0.240 0.8794 0.8775 0.8755 0.8736 0.8716 0.8697 0.8677 0.8658 0.8638 0.8619 0.250 0.8599 0.8579 0.8560 0.8540 0.8520 0.8501 0.8481 0.8461 0.8441 0.8421 0.260 0.8402 0.8382 0.8362 0.8342 0.8322 0.8302 0.8282 0.8262 0.8242 0.8222 0.270 0.8202 0.8182 0.8162 0.8142 0.8122 0.8101 0.8081 0.8061 0.8041 0.8021 0.280 0.8000 0.7980 0.7959 0.7939 0.7919 0.7898 0.7878 0.7857 0.7837 0.7816 0.290 0.7796 0.7775 0.7754 0.7734 0.7713 0.7692 0.7671 0.7651 0.7630 0.7609 0.300 0.7588 0.7567 0.7546 0.7525 0.7504 0.7483 0.7462 0.7441 0.7419 0.7398 0.310 0.7377 0.7356 0.7334 0.7313 0.7291 0.7270 0.7248 0.7227 0.7205 0.7184 0.320 0.7162 0.7140 0.7119 0.7097 0.7075 0.7053 0.7031 0.7009 0.6987 0.6965 0.330 0.6943 0.6921 0.6899 0.6877 0.6854 0.6832 0.6810 0.6787 0.6765 0.6742 0.340 0.6720 0.6697 0.6674 0.6651 0.6629 0.6606 0.6583 0.6560 0.6537 0.6514 0.350 0.6491 0.6468 0.6444 0.6421 0.6398 0.6374 0.6351 0.6327 0.6303 0.6280 0.360 0.6256 0.6232 0.6208 0.6184 0.6160 0.6136 0.6112 0.6088 0.6063 0.6039 0.370 0.6015 0.5990 0.5965 0.5941 0.5916 0.5891 0.5866 0.5841 0.5816 0.5791 0.380 0.5765 0.5740 0.5715 0.5689 0.5663 0.5638 0,5612 0.5586 0.5560 0.5534 0.390 0.5508 0.5481 0.5455 0.5428 0.5402 0.5375 0.5348 0.5321 0.5294 0.5267 0.400 0.5240 0.5212 0.5185 0.5157 0.5129 0.5101 0.5073 0.5045 0.5017 0.4989 0.410 0.4960 0.4931 0.4902 0.4873 0.4844 0.4815 0.4785 0.4756 0.4726 0.4696 0.420 0.4666 0.4636 0.4605 0.4575 0.4544 0.4513 0.4482 0.4450 0.4419 0.4387 0.430 0.4355 0.4323 0.4291 0.4258 0.4225 0.4192 0.4159 0.4125 0.4092 0.4058 0.440 0.4023 0.3989 0.3954 0.3919 0.3883 0.3848 0.3812 0.3775 0.3739 0.3702 0.450 0.3665 0.3627 0.3589 0.3551 0.3512 0.3473 0.3433 0.3393 0.3353 0.3312 0.460 0.3270 0.3228 0.3186 0.3143 0.3100 0.3056 0.3011 0.2966 0.2920 0.2873 0.470 0.2826 0.2777 0.2728 0.2679 0.2628 0.2576 0.2524 0.2470 0.2415 0.2359 0.480 0.2301 0.2243 0.2182 0.2120 0.2056 Oo1991 0.1923 0.1852 0.1779 0,1703 0.490 0.1623 0.1539 0.1451 0.1357 0.1256 0.1146 0.1025 0.0887 0.0724 0.0512 29

WILLOW RUN LABORATORIESTABLE VIII. COMPARISON OF THE VALUES COMPUTED FROM 8 AND K AND THE EXPERIMENTAL VALUES OF ISOTROPIC ELASTIC MODULI [18] Material Young's Modulus Shear Modulus (kb) (kb) Computed Experimental Computed Experimental MgO 3180 3100 ~ 50 [19] 1340 1310 ~ 20 [19] A1203 4150 4040 ~ 60 [19] 1660 1640 ~ 30 [19] BeO 3810 3880 [89] 1430 1470 [89] TiO2 2790 2835** 1085 1117** *Since the compressibility used in the computation is based on static measurements, the computed values should be compared with the isothermal elastic constants. For the shear modulus the isothermal value is equal to the adiabatic, while for Young's modulus the isothermal is about 1% lower than the adiabatic at room temperature. **Based on the single-crystal data by Wachtman et al. [90]. The relation between sound velocity and refractive index is based upon the fact that for oxides the elastic constants are unique functions of the specific volume [92] and the refractive index is a unique function of the density [93]. As a result, by properly accounting for the molecular weight, the sound velocity is shown to be a unique function of the refractive index. A major parameter classifying the oxides is the mean atomic weight M/p. Most existing data on sound velocity are for oxides with a mean atomic weight near 20. For such oxides, the sound velocities are given by the empirical equations: (2 V = 3(n - 1)km/s (15) s V = 5(n2- 1)km/s (16) These equations are plotted as solid lines in figures 11 and 12. The data for the oxides are listed in table IX and plotted as open circles in figures 11 and 12. It is seen that the correlation is valid for oxides representing various molecular weights, crystal symmetries, and compositions. The sound-velocity data are taken from references listed by Anderson and Nafe [92] and the refractive-index data from references in Anderson and Schreiber [93]. For oxides with the same refractive index, the mean atomic weight increases as the sound velocity decreases. This effect is shown for three garnets plotted in figures 11 and 12 as filled circles. The velocity data on two natural garnets were reported by Verma [94]. Garnet 1 con30

WILLOW RUN LABORATORIES sists of a solid solution of spessarite and almandite, and garnet 2 is predominately almandite. The refractive-index values for these garnets are given by Verma as 1.814 and 1.817. The mean atomic weights calculated from Verma's data are 24.0 and 24.5. The third garnet is synthetic, a yttrium aluminum garnet grown at Bell Telephone Laboratories. The elastic constants were reported privately by E. G. Spencer. The isotropic elastic constants are computed by the Voigt-Reuss-Hill averaging scheme [95], yielding V = 8.60 km/s and Vs = 4.95 km/s. The rep s fractive index is 1.833, and M/p is 23.10. The elastic constant data for ZnO, where the mean atomic weight is 40.6, is given by Bateman [96]. The resulting velocities are V = 5.96 km/s and V = 2.84 km/s. These low velocities for a material with such a high value of refractive index, 2.03, suggest that a high value of M/p materially lowers the sound velocity. These data are plotted as crossed circles in figures 11 and 12. t" AL203 7 At 203'10- SPINEL 6 -?MgO TOPAZ OMgO hi: /OSPINEL - - ~- TOURMALINE OTOPAZ E GARNET / E 5- FORSTERITE FORSTERITEGARNET 3 GA RN GARNET 2 R 3 >e/ GARNET GGARRNET2 ~ ^ >- TOURMALINEE GARNET/ - OC -QUARTZ/ 0 _20 VITREOUS 0 / 0 0 - SILICA - - 7 A -QUARTZO Ww~// > >3L Zn / -- / /`_1M- = 2 5 -- - VITREOUS 1 Z 2- P SILICA / /.M40 - /M~ — y/f."~ p,-"~ zj r; /- - - -// B> 5:/ / /[^_____] - / / / 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ~ (-2) MEAN INDEX OF REFRACTION 3 I 0 0.5 1.0 11.5 2.0 2.5 3.0 3.5 (.T2 -_) 5 -, MEAN INDEX OF REFRACTION FIGURE 11. SHEAR VELOCITY AS A FUNCTION OF FIGURE 12. LONGITUDINAL (COMPRESSIONAL) (n2 - 1) FOR VARIOUS MINERALS. Solid line: V = VELOCITY AS A FUNCTION OF (ff2 - 1) FOR 3(jn2 - 1) [91]. VARIOUS MINERALS. Solid line: Vp = 5(f - - )[91]. 31

WILLOW RUN LABORATORIESTABLE IX. CALCULATED SOUND VELOCITIES FROM REFRACTIVE-INDEX DATA FOR MINERALS OBEYING BIRCH'S LAW (M/p Z 20)* Mean Measured Calc. Calc. Ideal Molecular Atomic Refractive Measured Shear Long. Mineral Chemical Weight Weight Index Density Velocity Velocity Name Formula M M/p n p n - 1 3(n -1) 5(ii- 1) (km/s) (km/s) Fused Silica SiO2 60.06 20.03 1.459 2.20 1.129 3.4 5.6 Tridymite SiO2 60.06 20.03 1.471 2.27 1.164 3.5 5.8 Cristobalite SiO2 60.06 20.03 1.486 2.34 1.208 3.6 6.0 Leucite KAISi206 218.26 21.82 1.501 2.47 1.253 3.8 6.3 Keatite SiO2 60.06 20.03 1.519 2.50 1.307 3.9 6.5 Carnegieite NaAlSiO4 142.07 20.29 1.521 2.51 1.313 3.9 6.6 Orthoclase KAISi308 278.35 21.41 1.522 2.55 1.316 3.9 6.6 Anorthoclase KNaAl2Si6016 540.6 20.79 1.524 2.58 1.323 4.0 6.6 Microcline KASi 308 278.35 21.41 1.526 2.56 1.328 4.0 6.6 Albite NaAlSi 08 262.25 20.17 1.530 2.61 1.340 4.0 6.7 Chalcedony SiO2 60.06 20.03 1.535 2.63 1.356 4.1 6.8 Carnegieite NaAlSiO4 142.07 20.29 1.536 2.62 1.359 4.1 6.8 Quartz SiO2 60.06 20.03 1.547 2.65 1.393 4.2 7.0 Anorthite CaA2 Si208 278.22 21.40 1.583 2.77 1.506 4.5 7.5 Enstatite MgSiO3 100.41 20.08 1.590 2.87 1.528 4.6 7.6 Coesite SiO2 60.06 20.03 1.595 2.92 1.544 4.6 7.7 Sarcolite Ca Al Si312 498.47 21.67 1.608 2.93 1.586 4.8 7.9 Akermanite (Mg, Ca)3Si207 272.66 -22.00 1.635 3.12 1.673 5.0 8.4 Andalusite Al2SiO5 162.05 20.25 1.639 3.15 1.686 5.1 8.4 Mullite Al Si2013 425.94 20.28 1.644 3.23 1.702 5.1 8.5 A12 13 Mullite Al Si2013 425.94 20.28 1.647 3.03 1.713 5.1 8.6 6 2 13 Forsterite Mg2SiO4 140.73 20.10 1.652 3.22 1.729 5.2 8.6 Enstatite MgSiO3 100.41 20.08 1.654 3.18 1.736 5.2 8.7 Clinoenstatite MgSiO3 100.41 20.08 1.655 3.28 1.739 5.2 8.7 Jadeite NaAlSi206 202.16 20.21 1.659 3.43 1.752 5.3 8.8 Sillimanite Al2SiO5 162.05 20.25 1.667 3.23 1.779 5.3 8.9 Olivine (Mg, Fe) SiO? (20.10?) 1.671 3.34 1.792 5.4 9.0 2 4 Diopside CaMgSi206 216.58 21.65 1.676 3.28 1.809 5.4 9.0 Hypersthene MgSiO3 100.41 20.08 1.688 3.37 1.849 5.5 9.2 Schefferite MgCaSi204 184.58 23.07 1.688 3.39 1.849 5.5 9.2 Jeffersonite MgCaSi206 216.58 21.65 1.694 3.39 1.870 5.6 9.4 Pigeonite MgSiO3 100.41 20.08 1.697 3.42 1.880 5.6 9.4 Pyrope Mg2 l 3Si3012 405.85 20.29 1.705 3.51 1.907 5.7 9.5 Kyanite A12SiO5 162.05 20.25 1.720 3.60 1.960 5.9 9.8 Spinel MgA1204 142.28 20.32 1.723 3.60 1.990 6.0 10.0 Periclase MgO 40.32 20.16 1.736 3.58 2.010 6.0 10.0 Corundum A1203 101.96 20.39 1.762 4.00 2.100 6.3 10.5 Stishovite SiO2 60.06 20.03 1.806 4.28 2.262 6.8 11.3 *Ranked in order of increasing refractive index. 32

WILLOW RUN LABORATORIES More velocity data must be analyzed before the effect of large M/p on velocity can be conclusively determined. Our best estimates are given by the dashed lines in figures 11 and 12, which represent guides for future work. These dashed lines must be regarded as tentative. The solid lines in figures 11 and 12 representing equations 15 and 16 are not likely to be changed significantly by new data taken on solids with values of M/p near 20. Equations 15 and 16 are used to compute the sound velocities of oxide compounds and minerals with M/p = 20.5 ~ 1.5. These minerals are listed in table IX, along with the reported data on M/p, refractive index, density, and the computed velocities. The refractive index and density data are taken from reference 97. This method, which is valuable for oxide compounds, does not apply to other compounds [911 because their moduli are not unique functions of specific volume. 3.7. ESTIMATING SOUND VELOCITIES FROM SINGLE-CRYSTAL ELASTIC CONSTANTS: INDIRECT MEASUREMENT OF V AND V p s To find the effect of calcite on sound velocity in rocks, it is desirable to know the value of Vp and Vs for pure calcite. Such values for a mineral are seldom available; instead, the elastic constants of the mineral are often found. These will, in general, not be isotropic, so the formula for determining Vp and Vs, which represent the velocity through perfectly dense polycrystalline aggregates, in terms of the elastic constants is required. Unfortunately, the exact formulas have not yet been found, but simple formulas do exist which give the upper possible limits and the lower possible limits. For further details on an easy method, see reference 68. This method, called the Voigt-Reuss-Hill method, consists of finding the upper and lower limits of the bulk modulus and the shear modulus and then taking the arithmetic average. The following holds for any crystal class. The bulk modulus (maximum) by the Voigt approximation is: Kv = (C11 + C12 + C33) + (C + C23 + C13) (17) The shear modulus (maximum) by the Voigt approximation is: V = 5(C11 + C22 + C33) - (C12 + C23 + C31) + 5(C44 55 66C (18) The bulk modulus (minimum) by the Reuss approximation is: 1 K = (S1 + S22 + S33) + 2(S12 + S23 + 13) (19) 33

WILLOW RUN LABORATORIES The shear modulus (minimum) by the Reuss approximation is: 15 4(S11 22 + - 4(S12 + 23 + 13) (44 + S55 + S66) (20) Given the elastic constants, Cij, it is possible to find the four values KV, KR, X, VLR from equations 17-20. The Voigt-Reuss-Hill approximation is now found from the arithmetic mean of equations 17-20: AH = V WLR) (21) and the expected velocities are KH +4/3H p N V = H (22) s p For a discussion of how well these approximations taken from the crystal data predict the measured polycrystalline values, see reference 79. The extrapolated values of the moduli at zero porosity are the values of the measurement which must be used (see fig. 2, for example). Appendix 9 shows the calculations in detail for a number of crystals of interest to geology. To follow through the analogy on calcite, we would find that Vp is probably 6.3 km/s, but between 5.9 and 6.7; and V is probably 3.3 km/s but between 2.9 and 3.6, according to the Voigts Ruess-Hill approximation (see p. 18 of app. 9). These values of the elastic constants representing limits, K and KR, pV and gR, are probably too extreme (or low); but the values of the Hill mean are quite close to the expected values. This conclusion is substantiated by the recent theoretical work of Peselnick and Meister [98] who have applied the variational principles of anisotropic elasticity [99, 100] to polycrystalline aggregates of crystals possessing hexagonal and trigonal symmetries. They conclude that: The important feature here is that the variational method does effect a considerable improvement in both the shear and bulk moduli bounds, even though it may be meaningless from the experimental view to ask for such precision. Except for zinc, cadmium and calcite, the Hill values and the average value of the effective bounds are very nearly the same (<0.5% of each other). This agreement strengthens the use of the Hill average for practical approximations. 34

WILLOW RUN LABORATORIES Even for zinc, cadmium, and calcite, the worst cases indicated by Peselnick and Meister, the agreement of the Hill mean with the variational mean is satisfactorily close. The following listing is taken from table V of reference 98. Material Bulk Modulus Shear Modulus Hill Variational Hill Variational Mean Mean Mean Mean Cd 534.8 554.5 332.2 327.3 Zn 683.2 685.5 394.5 410.2 CaCO3 747 751 307 301 We conclude that the use of the Hill mean is well established empirically by good agreement with another approximate method of calculation. One example of the experimental confirmation of the Voigt-Ruess-Hill approximation is given by the work of Soga [101] on tantalum. Soga measured the elastic constants of singlecrystal tantalum and computed the Young's modulus over a 5000 temperature range by the VoigtRuess-Hill schemes. His values of EV, ER, and EH are plotted in figure 13, and the value of E is compared with Koster's measurements of E for polycrystalline tungsten [102]. The agreement is excellent. 2000 o POLYCRYSTALLINE DATA BY KOSTER:n 1900 X -"' "e -_ ^" ^ Ev FROM SINGLE D 1800 - _ ec ~6 CRYSTAL DATA' ^ _ ~ ""e ~-., BY SOGA -~. ~ ~ EN-"~,,, ER -a 1700 R z 0 o 1600 1500. 0 100 200 300 400 500 TEMPERATURE (C) CHANGE IN ISOTROPIC YOUNG'S MODULUS OF To WITH TEMPERATURE FIGURE 13. ISOTROPIC YOUNG'S MODULUS OF TANTALUM AS A FUNCTION OF TEMPERATURE [101] 35

WILLOW RUN LABORATORIES 3.8. ESTIMATING SOUND VELOCITIES FROM THE SPECIFIC VOLUME: CRUDE AND INDIRECT MEASUREMENT OF V AND V p s Birch [103] showed that a majority of known oxide compounds with low iron content have a mean atomic weight virtually independent of composition, phase, or symmetry; this value of M/p is near 21. An extended list of these compounds is found in table I of Anderson and Schreiber [93]. Birch [104] showed that V is roughly proportional to density for oxide compounds at constant M/p. Lines were drawn by Birch and represented by V = a + bp (23) where the value of a was displaced lower for higher M/p. Simmons [35] showed roughly the same relation for shear velocity, and a similar relationship for V in sediments was shown by Nafe and Drake [105]. These relationships are empirical. Anderson and Nafe [92] found relationships between bulk modulus and specific volume and between shear modulus and specific volume. These relationships were not theoretically derived from first principles, but were shown to be related to interatomic potentials and can be regarded as quasitheoretical. The relationships are in K= -3.5 in V + constant (24) where V is the volume per ion pair given by 2M/pp. A similar relationship holds for Ap. The correlation included the minerals hematite, calcite, quartz, olivine, periclase, corundum, beryl, stishovite, spinel, topaz, garnet, and spodumene. A large value of M/p is found for hematite, while a small value is found for beryl and spodumene. Presumably, then, M/p does not affect the value of the constants in equation 24. Empirically, we have K 2.9 x 106 V35 kb (25) and J 1.9x 106 V kb (26) These guides are rough but useful. For example, the specific volumes per ion pair [92] for corundum, olivine, and orthoclase are 10.24, 12.59, and 16.73 cc/mole. Using equation 25, we compute K = 2600, 1240,'and 465 kb, which compare with the measured values 2512, 1313, and 473 kb. Using the above numerical values, we can estimate the sound velocities. The result of this approach is that the relationships between sound velocity and density, at constant M/p, are =P VP(o) (27) 36

WILLOW RUN LABORATORIES and vs = v ( % (28) o / where x and y have values near 5/4 [92]. Equations 27 and 28 must be confirmed by further work, but they indicate how one might expect the velocities to change from dense rock to dense rock (or mineral to mineral) as the ambient density of the rocks changes. 3.9. DETERMINING THE ELASTIC CONSTANTS AND VELOCITY AT VERY HIGH PRESSURES: DIRECT AND INDIRECT MEASUREMENTS OF Vp, Vs, AND p The most obvious way to find the velocity of sound at high pressures is to measure it at the desired pressure. Sufficient measurements have been made at pressures up to about 10 kb that experiments in this pressure range can be considered routine. Great experimental obstacles have prevented many measurements above about 10 kb. There are two ways to extend the measurements to higher pressure. One is to attempt measurements at the desired pressure and accept the resulting problems in pressure calibration and attenuation; the other is to attempt to extrapolate measurements of high accuracy made at lower pressure, the range of measurements being limited by the demands in precision. An example of progress in the first method is the experiment of Ahrens and Katz [106, 107], who designed an ultrasonic-interferometric system to operate through opposing anvils (called Bridgman anvils) of a uniaxially loaded press. Using this technique, they were able to measure V and V through the phase transition calcite to aragonite. The main feature is p s that the transducers are outside the pressure system. There are attending problems in measurement of the path length, and in estimates of "effective pressure" in a nonuniform stress environment. Vigorous efforts to improve this experimental technique are underway, and we may expect further progress. An alternative to the Bridgman anvils is the "belt" apparatus, which is being improved by Montgomery at Minnesota Mining and Metallurgy Research Laboratories as a method of measuring V and V in the 60- to 100-kb range. p s An example of the other method is the work of Anderson [108, 109] and Anderson and Schreiber [60, 63, 93]. Using the most precise techniques available, they have taken measurements of sound velocity versus pressure up to 4 kb on synthetic polycrystalline aggregates of very high quality. Their results for polycrystalline MgO and Al203 were given in section 2.4.3. One wonders whether or not these equations can be extrapolated to higher pressures. Anderson [108] proposed that the bulk modulus could be extrapolated, namely K=K~ P-0 (29) 37

WILLOW RUN LABORATORIES Thus, the velocities are not linearly extrapolated, since the dimensions of velocity and elastic moduli are different. From the previous data, we have K = 1692 + 3.95P kb, MgO (30) K = 2504 + 4.00P kb, Al203 (31) By comparing the values of compression predicted from equation 29 with measured compression, we can determine to what pressures equations 30 and 31 hold. The predicted equation [108] is: n( = n1 + K')] (32) or in =-0.253 n[ + 3.95 169 MgO (33) in(v =-0.25 2n + 4.00(24Al 0 (34) /(r) o 2 L4.0^^ ))^X (34)0 2 Equations 33 and 34 successfully duplicated the isothermal compression experimental data of Perez-Albuerne and Drickamer [84] on MgO up to 350 kb, and the data of Hart and Drickamer [110] on Al203 up to 304 kb, the limits of these measurements. Further, equation 33 duplicated the shock-wave compression experiments of McQueen and Marsh [111] up to 1257 kb. The accuracies were within a few percent as indicated by tables X, XI, and XII. From this we conclude that equation 30 holds up to 1257 kb and equation 31 holds up to at least 300 kb, even though the data upon which these equations were based were measured only up to 4 kb. The agreement is remarkably accurate. This indicates that the hypothesis that K' is a constant 0 is proven up to very high pressures. The velocity functions up to pressures where K' is still constant cannot be found until there is some information on the range of pressure where dA/dP is a constant, or, alternatively, where do/dP is a constant. On the other hand, one can be precise about the equation for the seismic parameter 0, V2 4V2 K (km/s)2 (35) p s p since 0 is a function only of K and p. Anderson [109] showed that up to the pressure where equation 29 holds K' -1/K <?>N,(P)=c k[^ 1+KIJ -Yj t(36) 38

WILLOW RUN LABORATORIES TABLE X. COMPARISON OF DRICKAMER'S [84] MEASURED COMPRESSION ON MgO UP TO 350 kb WITH CALCULATED COMPRESSION USING 4-kb DATA Drickamer's Predicted from 4-kb Measured Compression Measurements in =-0.253n[1 + 3.95(162)] Measured Calculated P V/Vo V/V Error (kb) (%) 25 0.987 0.986 -0.10 50 0.974 0.972 -0.21 75 0.963 0.960 -0.31 100 0.951 0.948 -0.32 150 0.930 0.927 -0.32 200 0.910 0.908 -0.22 250 0.893 0.890 -0.34 300 0.877 0.874 -0.35 350 0.862 0.860 -0.23 TABLE XI. COMPARISON OF DRICKAMER'S [111] MEASURED COMPRESSION ON A1203 UP TO 300 kb WITH CALCULATED COMPRESSION USING 4-kb DATA Drickamer's Predicted from 4-kb Measured Compression Measurements in()= - 0.25n[1 + 4.00(24)] Measured Calculated P V/V V/Vo Error (kb) (%) 63 0.98 0.976 -0.4 128 0.96 0.954 -0.6 192 0.94 0.935 -0.5 256 0.92 0.918 -0.2 288 0.91 0.910 0.0 304 0.905 0.906 -0.1 39

WILLOW RUN LABORATORIES TABLE XII. COMPARISON OF SHOCK-WAVE COMPRESSION FROM MCQUEEN AND MARSH [112] ON MgO UP TO 1257 kb WITH CALCULATED COMPRESSION USING 4-kb DATA McQueen and Marsh Measured Shock Predicted from 4-kb Compression Measurements InV = -0.23 In[ + 3.95(1)] Measured Calculated P V/Vo V/Vo Error (kb) (%) 304.2 0.872 0.874 +0.23 483.6 0.831 0.827 -0.48 528.2 0.818 0.817 -0.12 615.7 0.799 0.799 0.00 683.1 0.787 0.787 0.00 855.8 0.758 0.759 +0.13 904.3 0.755 0.750 -0.67 949.8 0.746 0.745 -0.13 979.9 0.744 0.741 -0.41 1102.4 0.726 0.725 -0.14 1137 0.721 0.721 0.00 1257 0.708 0.708 0.00 Thus, the explicit functions of 4 can be written, the one for MgO holding to 1257 kb and the one for A1203 holding to at least 300 kb: MgO: = 48.1[1 + 3.91(P/1717)]0.742 (km/s) (37) A1203: = 63.4[1 + 3.98(P/2520)]0 748 (km/s)2 (38) In equations 37 and 38, the adiabatic values of K and K' were used, which are slightly different 0 0 from the isothermal values used in equations 33 and 34. This technique, of course, is limited to the pressures below phase transitions. Up to phase transition, it has excellent promise as a method of measuring velocity. To a fair approximation, equations 35 and 36 are linear with pressure to 100 kb. 40

WILLOW RUN LABORATORIES 3.10. DETERMINING THE ELASTIC CONSTANTS AT VERY HIGH TEMPERATURE: DIRECT AND INDIRECT MEASUREMENTS OF Vp, Vs, AND f Appendix 4 gives a survey of measurements of velocity in rocks taken on several types up to 2000C and on a few up to 500~C or 6000C. Such measurements can be considered a standard method. This topic is included in this section because of the promise that measurements on suitably prepared polycrystalline aggregates can be extended to the 1500~C level. For rocks, there is an important experimental condition to be considered, which was emphasized in Simmons' review: irreversible effects can be created by heating a rock. To remind the reader that an apparent temperature discontinuity of velocity in rocks may be spurious, we quote Birch [112]: It has been known since the time of Ide (1937) that the consequence of heating rocks at ordinary pressure is a progressive loosening of structure which leads to irreversible decreases of velocity.... In our experience... in high-temperature studies of Vs (Birch, 1943 and unpublished), the practice has been to raise the pressure to 4000 kg/cm2 or more before heating. Even then, it is often necessary to carry out several cycles of heating and cooling in order to obtain a linear, reversible effect. In a number of cases, linear, reversible curves to as much as 500~C have been obtained; beyond this point, most rocks begin to exhibit an accelerated rate of decrease of velocity with temperature, which may sometimes be'real', sometimes an effect of damage which presumably would not occur under the relatively steady conditions of the crust. To reach temperatures above 600~C, the rock aggregate structure must be avoided. Dense polycrystalline ceramic specimens of MgO and Al 203 have been prepared by Soga and Anderson [19], and they have achieved accurate measurements of the elastic constants to over 11000C. Anderson [113] derived an equation for the variation of the adiabatic bulk modulus with temperature. It is given by KK Y6PT[H(O, T K=K -oo7 0 T0 / T (39) In equation 39 every constant except K, the bulk modulus at 0~K and 1 atmosphere, is determined or calculated from experiment. p is the density, M/p is the mean atomic weight, y is the Gruneisen constant, and 6 is a temperature- independent dimensional parameter given by d In (K/dT) (40) -d in (V/dT) The quantity in brackets in equation 39 is the thermal heat given by a table of Debye functions, using the Debye temperature 0 and the actual temperature T. Thus the parameters in equation 39 can be determined by measurements in a small temperature range, and the bulk modulus 41

WILLOW RUN LABORATORIES can be predicted at higher temperatures. Figure 14 shows the comparison between predicted bulk modulus and the actual data of Soga. Another form of equation 39 is [19] K=K H(T) oo M/p H(T) where H(T) is the measured enthalpy. At high temperature the enthalpy is linear with temperature, so that K(T)= K(To) - /p[H(T) - H(To)] (41) Thus, the bulk modulus can be estimated as high as the enthalpy can be measured. Data on H often exist up to 20000C. Some data on the velocities at very high temperature may be found by use of equation 41, but the exact relationships have yet to be determined. LU 0.3B POLYCRYSTALLINE (SOGA) 0.2 — 0 2 I I I I I I I I ac o| 0.1 SINGLE CRYSTAL 1700 1650 o X _ 0 - \\ SINGLE *' 1600 CRYSTAL 1600 - D: V, I 0 *\ _1 \ D 1550- \ m~i -c - POLYCRYSTALLINE DATA (SOGA) N\ 1500 FIGURE 14. COMPARISON OF PREDICTED AND OBSERVED VALUES OF THE BULK MODULUS (Bs = K) AND ITS TEMPERATURE DERIVATIVE AS A FUNCTION OF TEMPERATURE [114] 42

WILLOW RUN LABORATORIES 4 CRITIQUE 4.1. PURPOSE This report was planned to be of assistance to two kinds of readers: (1) the experimentalist who is designing apparatus to measure sound velocity, and (2) the geophysicist or geologist who has limited data on a material and wants also the value of the sound velocity in that material. 4.2. EXPERIMENTS TO PERFORM In general, we feel that the pulse-transmission technique used by Birch will continue to be the most important method of obtaining data on real rocks. This technique represents a good compromise between accuracy of the experiment and quality of the specimen. There will be a perceptible shift from measurements on real rocks to measurements on synthetically prepared polycrystalline specimens. On synthetic specimens of high quality, interferometric methods can be used to measure accurate velocities with pressure and temperature. This method allows the precision required to find good pressure and temperature derivatives. Also on such specimens the temperature range can be substantially extended. The resonance of small spheres will emerge as the most important new measurement technique. The ability to make good measurements on very small specimens will extend substantially our knowledge of mineralogy. Such a potential should hasten the solution of experimental and theoretical problems presently restricting its application. These problems will be less difficult than finding minerals of sufficient size to be measured by other techniques. For geophysicists interested in understanding the inaccessible regions of the globe, methods of extrapolation will require the precision of ultrasonic interferometry. We expect that kind of experiment to grow among experimental geophysicists. The geophysicist who is also interested in internal friction measurements (not covered by this report) will tend to promote resonance or interferometric methods. 4.3. ESTIMATING SOUND VELOCITY FROM LIMITED DATA The average researcher needing to know V or V will not be in a position to measure the s p property itself. Section 2 and the appendixes were written and presented especially for this reader. We have indicated how some limited data can be found. There are a number of indirect methods for determining the velocity of sound in minerals. If the Debye temperature is known, Vs can be estimated. If the index of refraction and the 43

WILLOW RUN LABORATORIES composition are known, Vs and V can be estimated. If the density is known and M/p can be s p determined, a rough estimate can be made. A method of estimating velocities at very high pressure depends upon the condition that the bulk modulus is linear with pressure. The fact that the bulk modulus is linear with temperature will help estimates of the sound velocities at very high temperatures. The reader will often encounter the case where some data on rocks are available at a particular pressure and temperature, but he qurequires data at another pressure or temperature. In this case, he can use the fact that the Poisson's ratio does not change substantially with pressure or temperature, and obtain Poisson's ratio at any condition of pressure and temperature. In this way a considerable amount of information on a rock can be estimated from limited data by using standard equations. This is the method proposed by Nafe and Drake [115] for basalts and will be discussed further in section 5, which deals with the data on rocks and how they are classified in this report. 5 DATA ON Vs AND Vp FOR ROCKS AND MINERALS 5.1. GENERAL COMMENTS The data extant on rock and mineral velocities, as has been pointed out by Simmons [36], are not yet so numerous as to be unmanageable. Velocities have been measured versus pressure and temperature for several hundred rocks. An overabundance of data exists for certain common rocks such as granite, marble, and sandstone while very little is known about other rocks. The data also are not of uniform quality and precision because of differences in techniques and competence of investigators. Much of the best data were obtained by Birch and his former students and colleagues who learned their techniques in the Dunbar laboratory and who are now leaders in their own right. The contributions of Birch's school, both quantitative and qualitative, have placed us in a position to assess the future in this field. In the appendixes we have attempted to present all of the data available as of June 1965 on the velocities of rocks and minerals. These data have been classified in a number of ways to expedite the retrieval of any desired information. In appendix 1, the properties (density, porosity, mean atomic weight, and compressional and shear sound velocities) of a multitude of rocks and minerals at room temperature and atmospheric pressure are given. The variation of V and V with pressure and temperature is presented in appendixes 2 through 5. The p 4 44

WILLOW RUN LABORATORIES petrographic modal analyses and the chemical analyses available for the rocks of appendixes 1 through 5 are given in appendixes 6 and 7. Appendix 8 is a reference table for all of the velocity data in appendixes 1 through 5 and is included so that the appendixes may be used as a reference source independently of the text of the report. In appendix 9, the properties of polycrystalline aggregates of certain minerals are calculated from the elastic constants of single crystals. The details involved in the preparation and presentation of the data in the appendixes are discussed more fully below. The data in appendixes 1 through 3 have been organized and presented from a petrographic and mineralogical point of view. For a geophysicist, it would perhaps have been preferable to use a physical parameter such as density [33] to classify the data. Such a geophysical classification has great merit when the data are of uniform quality and precision. The data in the appendixes, as mentioned above, is not homogeneous. Since it was impossible to assign a quality factor to each bit of data, we group the data according to rock and mineral type and allow the reader to compare them. Many schemes have been devised throughout the years to predict the elastic behavior of rocks on the basis of the known data. One of the schemes is discussed in detail in section 5.9. Recently, Nafe and Drake [115] presented a scheme based on the equations relating the elastic moduli of a homogeneous isotropic elastic material. The authors have applied their scheme to rocks of the granite and gabbro clans, the latter including gabbro, norite, diabase (dolerite), and basalt. These two clans are especially well suited to such a treatment since Poisson's ratio and the density are roughly constant for all the rocks in a class. Nafe and Drake assume: granite: p = 2.65, r = 0.26 gabbro: p = 3.00, r = 0.28 Then, if one other elastic parameter is known, the elastic behavior is determined. Nafe and Drake plotted all the elastic parameters against the compressional sound velocity (see fig. 15). This selection of V as the indicator variable is desirable inasmuch as V is the most acp p curately determinable parameter experimentally. Although it is necessary to use a different set of curves for every rock type, this scheme is useful in providing a graphical means of determining the degree to which a rock specimen behaves as a homogeneous isotropic elastic material. The following subsections deal with explanations of the appendixes themselves. 45

WILLOW RUN LABORATORIES 14 E 105 bars / 105 bars /3 megabars Vs km/sec 12 P kilobors / Granite -- 0 2.65 ( 0.26 10- Gabbro -- y=3.00 C=0.28 8 /'I ~o 1 2 3 4 5 6 7 E FIGURE 15. ELASTIC BEHAVIOR OF NV J VP km/sec 0 I 2 3 4 5 6 7 8 FIGURE 15. ELASTIC BEHAVIOR OF GRANITE AND GABBRO CLANS AS A FUNCTION OF COMPRESSIONAL VELOCITY BASED ON THE EQUATIONS RELATING THE ELASTIC MODULI OF A HOMOGENEOUS, ISOTROPIC, PERFECTLY ELASTIC MATERIAL [115] 5.2. PETROGRAPHY The rocks in appendixes 1-3 are classified petrographically using the system of Williams, Turner, and Gilbert [116] (see Preface to Appendixes, p. 61). The igneous rocks are arranged by degree of crystallinity and the volume percentages of mafic minerals and free silica. Those with mafic percentages less than 70% are divided into three groups according to the percentage of free silica: (1) oversaturated rocks which contain free silica of primary origin; (2) saturated rocks which contain neither free silica nor any un46

WILLOW RUN LABORATORIES ~ saturated minerals; and (3) undersaturated rocks which consist either wholly or in part of unsaturated minerals of mafic or feldspathic nature. Within these three groups the rocks may be separated into eucrystalline, generally extrusive or deep intrusive in origin, and dyscrystalline, generally extrusive or shallow intrusive in origin, according to the degree of crystallinity. The order of presentation within 1, 2, and 3 is approximately from acid to basic with the eucrystalline form followed by its dyscrystalline counterpart. The igneous rocks in which mafic minerals constitute greater than 70% of the volume are classified under the ultramafic clan. Chemically, these rocks are generally ultrabasic with their SiO2 content less than 45%; notable exceptions are the bronzitites (app. 7, p. 121). Various fragmental igneous rocks and glasses conclude the subsection on igneous rocks. A few identifying remarks on certain of the igneous rocks in this study are necessary. Albitite is a predominantly albite dike rock. Keratophyre (AD04) is an albite andesite. Norite is a gabbro with hypersthene predominating over the clinopyroxene. Strictly speaking, the olivine basalts from Hawaii and elsewhere presented in appendix 1 (BA07, BA08, BA09, BA11, BA18, BA21, BA23) should be in the nonfeldspathic group of the undersaturated rocks, but are presented with the remainder of the basalts for comparison. The trap rocks of the Deccan plateau of India are assumed to be close to basaltic composition [116, 117]. The term diabase has been adopted for rocks of gabbroic composition and texture intermediate between gabbro and basalt, in preference to the English term dolerite used in the Indian literature (see DB06, DB22). Harzburgite is a peridotite with orthopyroxenes accompanying the olivine. Chrysotile is the fibrous variety of serpentinite formed generally under static conditions, while antigorite is the flaky variety generally formed under stress conditions. The diabase glass (DB15) was produced by the General Electric Company from the Mt. Holyoke trap rock which is sometimes called the Westfield diabase. The chemical analysis in appendix 7 is that of the glass, but the modal analysis in appendix 6 is that of the parent rock. The metamorphic rocks are not rigorously classified, but are ranked in approximate order of increasing metamorphic grade. The charnockites are included with the metamorphic rocks because many of them have the megascopic appearance of an acid plutonic gneiss [116]. An alternative classification would have been to include them with the igneous rocks as enstatite-hypersthene granites. The sedimentary rocks are classified by the origin of their constituent material. The detrital rocks, containing primarily allogenic material, are the sandstones, shales, greywackes, and kaolin. The chemical and organic rocks, composed primarily of authigenic constituents, are the limestones, dolomites, and chalk. 47

WILLOW RUN LABORATORIES 5.3. MINERALOGY The majority of the mineral specimens are single crystals, while some are polycrystallinrie aggregates of either natural or synthetic origin. Still others are really ore rocks composed primarily of one mineral (e.g., MG05, PR07, PR08). The minerals in appendixes 1 through 3 are classified by the system of Deer, Howie, and Zussman [118] (see Preface to Appendixes, p. 62). The silicate minerals are classified according to the structural arrangement of the individual silica tetrahedra (SiO4): (a) Ortho- and ring silicates: independent tetrahedra (-SiO4) and double tetrahedra (-Si2O7) (b) Single-chain silicates: infinite, one-dimensional, single-strand chains of tetrahedra (-SiO3) (c) Double-chain silicates: infinite, one-dimensional, double-strand chains of tetrahedra (-Si4 (d) Sheet or layered silicates: infinite, two-dimensional sheets of tetrahedra (-Si205) (e) Framework silicates: (-S.02) The nonsilicates are classified according to chemical composition: (a) Oxides (b) Sulfides (c) Sulfates (d) Carbonates (e) Halides (f) Carbon 5.4. APPENDIX 1, EXPLANATION Appendix 1 includes data on the properties of rocks and minerals at or near room temperature and atmospheric pressure. All the measurements were taken at temperatures from 0~C to 300C and pressures from 0 to 50 bars (1 bar = 0.98692 atmospheres = 1 x 106 dynes/ 2 2 cm = 1.01971 kg/cm ). Readings with an apostrophe added were taken at 25 to 50 bars. The density (RHO) and, when available, the porosity (POR) are included. Verification of the anticipated inverse dependence of velocity upon porosity is possible for certain rocks (SS33-SS38), but for other specimens (PX01-PX05 and SS21-SS32) the dependence is less clear. 48

- WILLOW RUN LABORATORIES The mean atomic weight (M/p) has been calculated by Birch [104] from the chemical analyses of some of the rocks in his study. These values of M/p are applicable also to certain specimens in Simmons [35] and Verma [94] (see OV01, GT03, GT04). Further values of M/p could be calculated from the chemical analyses of appendix 7 and added to appendix 1. Still others could be calculated from the petrographic analyses of appendix 6 and the representative M/p values for minerals given by Birch [104] and Anderson and Schreiber [93]. Both compressional (VP1) and shear (VS1) sound velocities are given for the rocks. A second shear velocity (VS2) for minerals is included when available. In certain cases (notably in the work of Alexandrov and Ryzhova [119-121], Ryzhova [122], and Ryzhova and Alexandrov [123]) the directions of polarization of the shear modes are presented in the original paper but are not included here. In appendixes 1 through 5, geographical origin (or catalog number for the Russian collection) is given for each specimen. In certain cases, descriptive or mineralogical adjectives are appended. The indexing system is used to aid in cross referencing rock data, petrographic and/or chemical analyses, and sources of data. Each rock and mineral type is assigned a twoletter index (see Preface to Appendixes, p 63) and a number is attached to this letter index. Each index refers to an individual specimen and/or a separate source of data. The only duplication is that Birch [124] quoted mean compressional velocities for serpentinites (SE15, SE16, SE17, SE18) from the data of Birch [33] for the same serpentinites (SE10, SE11, SE13, SE12, respectively). Directional notation included in appendixes 1 through 5 indicates the direction of propagation of the sound wave through the specimen. X, Y, and Z refer to mutually perpendicular directions which have no specific relation to rock or crystal orientation. PAR and PERP refer to propagation directions either parallel or perpendicular to some structural feature of the rock such as foliation, bedding, schistosity, banding, or crystal alignment. The symbols [001] [010], etc., refer to directions of zone axes along which the velocities have been measured in single crystals. Alexandrov and Ryzhova [119-121] and Ryzhova [122] have used an orthogonal system of coordinates for their velocity determinations, as pointedoutby Christensen [125]. This transition for the crystals of the monoclinic system results in measurements of velocities in directions parallel to the c and b crystallographic axes and inclined (3~ - 90~) to the a axis (see H001, H002, AE01, MI01, AZ01, AB05, OL02, OL03, OL04, LA01, LA02, LA03). The feldspars, which are triclinic (except orthoclase), are treated as having monoclinic symmetry by the Russian authors since a and y are close to 90~ (~ 50). Measurements of velocities in the layered silicates (see MU01, BI01, CH01, CH02, PH01, TC01) indicate that all the velocities 49

WILLOW RUN LABORATORIES in the X-Y plane are equivalent where the Z axis is perpendicular to the (001) cleavage. This is in agreement with the observation that i is commonly close to 90~ for minerals of the mica group [117],and these minerals are treated by the Russian authors as possessing hexagonal symmetry. Thus the [010] velocities are representative of the values in any direction in the X-Y plane which is parallel to the (001) cleavage. Nephelite (NE01, NE02) is a member of the hexagonal system and the notation used by the Russians ([100], [011]) is not the proper one for this class. These directions should be treated as any two mutually perpendicular directions in the plane of the a crystallographic axis. Even after these corrections, some ambiguity remains in the work on single crystals, since the energy propagation is not always found to be perpendicular to the faces of the specimen because of the tensorial character of the crystal properties [126]. A few remarks on data selection are appropriate. In general, the data from all of the rocks in a paper were presented, but in the work of Hirasawa [127] only the velocities of representative specimens were chosen; for the schists, specimens were chosen which best illustrate the extreme anisotropy mentioned by the author in his abstract. Christensen's [125] metagabbro was omitted, as were the data on the terrigeneous muds and globegerina ooze of Laughton [128], certain poorly consolidated shales of Hughes and his colleagues, and the volcanics of Iida and Kumazawa [45, 46] (see further comment below). For the data found in foreign publications in which the velocity anisotropy was significant, all the values were presented since much of the work is not well known nor easily accessible in the United States. For the rocks of Woeber et al. [129], the mean velocities are given unless the anisotropy exceeded 10%. For the suite of rocks studied by Birch [33] and Simmons [35, 130], the anisotropy frequently disappeared at elevated pressures and rarely exceeded 2% to 3% for the oversaturated and saturated rocks at 10 kb [104]. All three values were reported for the dunites, serpentinites, bronzitites, pyroxenites, and harzburgites of these papers. For the gneisses and schists, we took the velocities either parallel and perpendicular to the foliation or the two extreme values if no indication was given as to orientation. For Christensen's [125] metamorphic rocks, all three mutually perpendicular velocities were presented regardless of degree of anisotropy. From Tooley [131], only selected means of the velocities in marble were presented since the author has stated in a personal communication that "thermallyinduced structural damage makes this marble elastically isotropic." 5.5. APPENDIXES 2 AND 3, EXPLANATION AND COMMENTS Appendixes 2 and 3 include data on the variation of the compressional and shear sound velocities with pressure. All measurements were taken at temperatures between 0~ and 30~C. 50

WILLOW RUN LABORATORIES The pressure range is from atmospheric pressure (1 bar) to 10 kb (9869 atmospheres). The pressures of the column headings are accurate within 3%. The special symbols which follow certain readings refer to pressures other than those of the column headings; these are fully explained on the first pages of appendixes 2 and 3. This notation may seem somewhat cumbersome, but it was considered necessary to enable presentation of all of the available data. The pressures are hydrostatic unless otherwise indicated. "Axial pressure" (see LS28, LS44, SS57, SS63, SS66) refers to the pressure of uniaxial compression along the direction of propagation. Tocher [34] has observed that uniaxial compression parallel to the direction of propagation has approximately the same effect on the compressional velocity as hydrostatic pressure; compression perpendicular to the direction of propagation does not seem to affect the compressional velocity appreciably (see fig. 16). "Differential pressure" (P - Pi) of Gardner et al. [132] (see SS52) refers to the pressure difference between externally applied hydrostatic pressure and the internal pore pressure for sedimentary rocks. "Net overburden pressure" (P - nPi) of Banthia et al. [133] (see SS48, SS51) refers to the differential pressure e when a factor n (less than unity) reduces the effect of the pore pressure. For the rocks from Birch and Bancroft [134] and Ide [135] the values of the dynamic shear modulus were used to calculate the shear velocity, assuming the density to be constant with temperature and pressure. 6.25 -Velocity Under Hydrostoaic Presiure (After Birch) > o- Velocity II Axial Comprlesion " — Vlocity.J AiAol CompCeetion - _6.00-.... <5.75- BARRE GRANITE 5.57 0525 I u 0 500 1000 1500 2000 PRESSURE - KSC FIGURE 16. VARIATION OF COMPRESSIONAL VELOCITY OF BARRE GRANITE AS A FUNCTION OF AXIAL COMPRESSION AND HYDROSTATIC PRESSURE [34] Both the compressional and the shear sound velocities of rocks and minerals generally increase with increasing pressure (see fig. 17 and 18). The rapid increase at low pressures is due to a decrease in porosity as shown by Birch and Hughes, closing of cracks and defects [88, 136], and an increase in the mechanical contact between the grains [137] (see fig. 19). At higher pressures, the velocity increase results from changes in the intrinsic properties of the rock 51

WILLOW RUN LABORATORIES such as finite compression of the crystals. For certain specimens (see LS01, LS21, LS22, LS23, SS45, OB02, QU02), the sound velocity is observed to decrease when the pressure exceeds a certain value (see fig. 20). 6.5' 3.7 6. iA ond B I VP -- KM/SEC 3.5 1% 6.0 / - 3.3vs / 3.1 - GRANITE 1 5.5 BARRE,VERMONT 2.9 WESTERLY GRANITE f WESTERLY GRANITE 2.7 5. 0 2.5 I I I I I I I I I 2.5 500 5 10 15 0 1 2 3 4 5 6 7 8 9 10 PRESSURE, KILOBARS PRESSURE (kb) FIGURE 17. COMPRES- FIGURE 18. SHEAR VELOCITY OF WESTERLY SIONAL VELOCITY OF GRANITE AS A FUNCTION OF HYDROSTATIC BARRE GRANITE AS A PRESSURE. The lower curve was obtained with FUNCTION OF HYDROSTAT- increasing pressure, the upper curve with decreasIC PRESSURE. Dots indi- ing pressure. Crosses represent data from refercate measurements with in- ence 133. [34] creasing pressure, circles with decreasing pressure. [33] _ ________6.5-.I. II I, I, I' I Vp 7VP~~~~.. MELLEN GABBRO 2 6- HOLYOKE DIABASE 3 / RUN'2 PORT HENRY / *- MAGNETITE ORE I / /CHELMSFORD GRANITE 3.2 5- 4. j CALCITE CALCITEoARACONITE * I' 10,000,/ t0 l so ________________________________________ W-VfI 2. 4!feic~o ------ i~ooio~oo ^ 10 20 30 PRESSURE [Rb] PRESSURE, BARS PRESSUREKb FIGURE 19. COMPRESSIONAL VELOCITY OF VARI- FIGURE 20. COMPRESSIONAL AND SHEAR VELOCOUS ROCKS AS A FUNCTION OF HYDROSTATIC PRES- ITIES OF SOLENHOFEN LIMESTONE AS A FUNCSURE. Vp is plotted against log P here to emphasize TION OF HYDROSTATIC PRESSURE. The anomalous the behavior below 1 kb. [33] decrease of V above 5-6 kb is shown. [107] 52

WILLOW RUN LABORATORIES For the limestones, Ahrens and Katz [107] have attributed this velocity inversion to a phase transition from calcite to aragonite with a concomitant density increase. Using the Solenhofen limestone specimen of Ahrens and Katz, Gordon and Vaisnys [138] have measured the compressional velocity at pressures up to 10 kb and observed no velocity decrease; the authors suggest that the velocity decreases observed by Ahrens and Katz are associated with the onset of the diffusionless calcite I to calcite II transformation. Simmons [36 has substantiated the occurrence of the velocity inversion for limestone without prescribing the mechanism.* A different approach to the problem is provided by the data in appendix 9. The arithmetic mean longitudinal (compressional) velocity of aragonite (5.840) is indeed lower than that of calcite (6.259- 6.333), but the Voigt-Reuss limiting bounds are seen to overlap in every case. The arithmetic mean shear velocity, on the other hand, is higher for aragonite (3.657) than for calcite (3.264-3.423) with the bounds again overlapping. This overlapping, the small differences in predicted velocities, and the disagreement of the predicted and observed [107] shear-velocity behavior all lead us to doubt that a clear answer to the problem is presently available. The changes of velocity associated with phase changes has been discussed by Birch [104]. These changes will undoubtedly become even more significant when considering pressures in the shock-wave domain. 5.6. APPENDIXES 4 AND 5, EXPLANATION AND COMMENTS Appendixes 4 and 5 include data on the variation of compressional and shear sound velocities with temperature. The temperature range is from room temperature (0~ to 25~C) to 6000~C. Due to the limited amount of data, the rocks and minerals are presented in alphabetical order by index instead of by petrographical and mineralogical groups as in appendixes 1 through 3. The pressure of each measurement is also indicated. It should be noted that Hughes and his colleagues measured velocity vs. pressure at constant values of temperature (see fig. 21), but never actually measured velocity vs. temperature at constant pressure. Simmons [36] refers to the work of Ide [6] as the first indication that measurements of elastic properties of rocks vs. temperature at atmospheric pressure destroys the rock and provides only irreproducible data (see fig. 22). Birch [112] pointed out that due to looseness of grains, cracks, porosity, and other rock defects, the only valid measurements of velocity vs. temperature are *Professor Birch (private communication, January 1966) informs us that the work of Wang at Harvard clearly indicates that the transition in calcium carbonate rocks is not calcite to aragonite, but one of the diffusionless transformations of Bridgman [147]. 53

WILLOW RUN LABORATORIES those conducted at elevated pressures (see fig. 23). Even when this approach is used, it is important to demonstrate the lack of hysteresis [36]. In view of these considerations, only those measurements conducted at pressures greater than 1 kb were included in appendixes 4 and 5; specifically, the work of certain Japanese and Indian investigators has been omitted. VD EN KM/S 6,30 25 ~C -- - -. 6,20 - 6,10- 3 i 0"C 6,00 VR, 5,903,70 - --- - 25 5,80- 3,60 - | 0 — oo'c -',,. 2000C V 3,50 VR 0 500 1500 0 500 1000 1500 2000 3000 4000 5000 PRESSION EN BARS FIGURE 21. COMPRESSIONAL (VD) AND SHEAR (VR) VELOCITIES AS A FUNCTION OF HYDROSTATIC PRESSURE AT VARIOUS TEMPERATURES [139] This criterion of elevated pressures is not necessary for work on single crystals of gem quality or on polycrystalline aggregates in which departures from homogeneity are negligible. Schreiber and Anderson [63] have measured the sound velocity vs. temperature for a synthetic specimen of MgO and also for polycrystalline A1203 (AA02) over the same range, -80~C to +25~C. The precision of the interferometric methods enables them to detect even small changes in velocity within this narrow temperature range (see fig. 24). Using Forster's dynamic resonance method, Soga has been able to obtain data on the elastic moduli of synthetic polycrystalline aggregates (grain size <40 gl, porosity < 1%) of MgO and A1203 (same as MS0103, AA02-03) at temperatures in excess of 1000~C [19]. This extension of the temperature range more clearly delineates the temperature gradients of the elastic moduli. Measurements of the velocity vs. temperature for fused silica (QU05, QU06) at atmospheric pressure were included to show the marked contrast in behavior between silica and 54

WILLOW RUN LABORATORIES'.0 1006 0 N^ s. ^x-Quartz diorite, 30CO \.8 M-',p e k psrGranite, Barre, 35)0.98 4.0.97 Eclogite, 5000 3. 2 GRAN ITE.9e 3.0 - ~.95 2.5 -.94 2.0 -.93.oi \ ce b IidGabbro, 5000;.15..92 1.0.91 of their volcanic rocks tothe mount Granite, Rockport, 4000 0.5! ______"__.90 - -_100 I00 200 300 400 500 600 700 0 100 200 300 400 500 C O C. FIGURE 22. EFFECT OF THERMAL CY- FIGURE 23. RELATIVE FREQUENCY OF THE RESCLING AT ROOM PRESSURE ON THE COM- ONANT SHEAR-MODE VIBRATIONS IN CYLINDERS PRESSIONAL VELOCITY OF QUINCY GRAN- OF CERTAIN ROCKS AS A FUNCTION OF TEMPERAITE. Reproduced by permission of the Uni- TURE. Measurements were taken at the elevated versity of Chicago Press from J. M. Ide, Jour- pressures (in kilograms per square centimeter) innal of Geology, Vol. 45, 1937 [6]. dicated. [8] rocks (see fig. 25 and 26). This anomalous increase of velocity with temperature was first noticed by Iida [140]. Iida and Kumazawa [46] have attempted to relate the anomalous behavior of their volcanic rocks to the amount and polymorph (cristobalite or quartz) of free silica in the rocks; this explanation is dubious since the experiments were conducted at atmospheric pressure and the velocities are so extremely low as to be questionable. 5.7. APPENDIXES 6 AND 7, EXPLANATION Appendixes 6 and 7 include the petrographic modal analyses and the chemical analyses available for the rocks in appendixes 1 through 5. 55

WILLOW RUN LABORATORIES 1.005000o AT 25'C: Vp 10.845 KM/SEC. V8 = 6.3730 KM/SEC. 1.004000 - SHEAR 1.003000 - 0 ILL9 1.002000 LONGITUDINAL 1.001000 - 1.oo 000000oo I I I I I I I I -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 TEMPERATURE (~C) FIGURE 24. RELATIVE FREQUENCY OF THE PSEUDORESONANCE MODES IN POLYCRYSTALLINE A1203 AS A FUNCTION OF TEMPERATURE [63] The rocks and minerals are presented in alphabetical order by index. Inset entries indicate that the analysis also applies to these specimens, although the specimens are not necessarily identical. (They often are different cores of the same rock or different rocks from the same locality.) The references for the analyses are included at the end of appendixes 6 and 7. These are not necessarily references to the original source, but to the papers from which we obtained the analyses. In certain cases, notably with respect to the Daly collection at Harvard, the analyses are old but are quoted from recent papers of Birch [17, 104] and apply as well to rocks studied earlier. All of this should be evident in the cross-indexing system. 5.8. APPENDIX 8, EXPLANATION Appendix 8 lists the references for the velocities of appendixes 1 through 5. More complete references with titles included are given in the bibliography. This appendix has been included to enable easy reference to the source of the data. 56

WILLOW RUN LABORATORIES 1.045 1.016 1.040- 1.014 __ Vo= ^ ^- V/ 1.035 5.97x 105 CM/SEC - V (250 C) 1.012 3.76 x105 CM/SEC 1.030~- - - C --- -— (250 C) 0 / 1.010 1.025 BO v O.o2o -- 1.0 0 -8 4,Q S__1.0 15 * BUFFER ROD TECHNIQUE < 1.006 o MOLTEN TIN COUPLING / 1.,e 13o MOLTEN Pb-Sn-Bi 1.010- ~ COUPLING 1.004- - 1.005 | - - -— I- PRISM MODE CONVERTER 1.000 11.1!... 1.002 B-~~ ---- PARALLELOGRAM MODE 1.000 -/- --- -- -- -- --- -- -- -- -- 1. CONVERTER 0 50 100 150 200' 250 300 350 400 450 500 TEMPERATURE IN DEGREES CENTIGRADE 001 160 200 240 20 320 0 40 80 120 160 200 240 280 320 TEMPERATURE IN DEGREES CENTIGRADE FIGURE 25. COMPRESSIONAL VELOCITY OF FUSED FIGURE 26. SHEAR VELOCITY OF FUSED SILICA AS SILICA AS A FUNCTION OF TEMPERATURE AT ROOM A FUNCTION OF TEMPERATURE AT ROOM PRESSURE PRESSURE [58] [58] 5.9. APPENDIX 9, EXPLANATION AND COMMENTS Appendix 9 includes data on the properties of isotropic polycrystalline aggregates of certain minerals as calculated from the measured elastic constants and/or compliances of single crystals. These calculated properties correspond to a homogeneous isotropic elastic solid with random orientation of crystal grains and zero porosity. Simmons [141] has recently published an excellent and comprehensive compilation of the available single-crystal data and computed the isotropic elastic moduli. This work is an invaluable reference for investigators in the field and we do not wish to duplicate this work. We have included in appendix 9 only the data on the naturally occurring minerals, certain of which are of particular interest to the geophysicist or the geologist in the study of the composition of the interior of the earth. The methods employed in these calculations are described in detail by Anderson [68] and are only summarized here. Hill [142] derived a method for calculating the elastic moduli for polycrystalline aggregates, pointing out from energy considerations that the two classical approximations of Voigt [143] and Reuss [144] were limits and suggesting an explanation of the fact that measured values were intermediate. Voigt averaged over all crystal orientations using the assumption that the strain is uniform throughout a grain. Reuss did the averaging by assuming the stress to be uniform 57

WILLOW RUN LABORATORIES throughout a grain. Hill showed that the Voigt approximation tends to make the elastic moduli larger than they should be so that the Reuss approximation tends to make them smaller, so that the true isotropic values of K and /p are given by the equations in section 3.7. Another important elastic constant relating single crystals and polycrystalline aggregates is the elastic constant, ca, used in calculating the Debye temperature 0. The Debye temperature is an important parameter of a solid. It is found in equations describing properties that arise from atomic vibrations and in theories involving phonons. One of the standard methods of calculating the Debye temperature is from elastic-constant data, since 0 is proportional to the sound velocity (averaged) by the equation h(3p Np/3 where h/k have the usual meanings of quantum mechanics, N is Avogadro's number, p is the density, M is the molecular weight of the solid, and p is the number of atoms in the molecule (p = 2 for NaCl, 3 for CaF2). The value V ca/p is often called the mean sound velocity, V. For isotropic materials, the relationship of V to the compressional sound velocity and the shear sound velocity is given by S /2 i-1/3 V 3 3 + 173 In this case, the results are valid for truly isotropic materials such as glass and for polycrystalline materials for which the shear and compressional sound velocities V and V are s p invariant with direction. Application to crystal classes with lower symmetry than isotropy is hindered by the problem of finding Vm. Since 0 is a scalar, it follows the Vm must also be a scalar, and herein lies the difficulty of this method. The stress is a tensor quantity, and for each direction in a crystal there are three velocities, each of which is a complicated function of the stress components. The expression for Vm is [95]: 3 \-1/3 m vV- This integral is solved by numerical methods as follows: The three sound velocities, V1, V2, V3, are found for an arbitrary direction and then stored; the process is repeated for a 58

WILLOW RUN LABORATORIES large sample of directions throughout all directions in space; and a numerical summation using Simpson's rule is made in place of the volume integral. This method is the rigorous way to find the mean sound velocity, but it is impractical to use except with high-speed computers. The solution of the equation requires knowledge of the elastic constants of the crystal. Alternatively, the mean sound velocity may be predicted from the isotropic moduli. The Voigt and Reuss moduli are used to calculate compressional and shear velocities which are in turn averaged to obtain the Hill velocities: Vp=-i(V +VpR) Vs = (VsV + VsR) These isotropic velocities can then be used to predict the mean sound velocity: Vma = J -1(. + l p1-1/3 ^ - P 3I 3 V s whose value is close to the value obtained from the numerical integration (V ). In appendix 9, the collected single-crystal data are used in an IBM 7090 program designed to compute the isotropic moduli using the Voigt and Reuss approximations and to compute the mean sound velocity, Vm, using numerical integration. The following are read into the computer program as input data: the elastic constants, C.i, or the elastic compliances, S..; the density; the molecular weight of the crystal; the limits of integration (for a cubic crystal the limits correspond to one-fourth of the sphere); and the increment of angles in the numerical integration (usually 5~). The elastic compliances are computed from the elastic constants, or vice versa, by a subroutine which inverts any n x n matrix of reasonable size. After the mean sound velocity V is computed and the Debye temperature 0 is calculated from it, the Voigt and Reuss values of the bulk modulus K and the shear modulus /i are determined. From K and j., the other moduli and the various sound velocities are obtained for each approximation from the equations: Young's modulus: E = 39K 3KI.+ ji Longitudinal modulus: pV2 = K + 4j/3 59

WILLOW RUN LABORATORIES 3K- 2[, Poisson's ratio: = 2(3K + 2) Longitudinal (compres- V = (K+ 4 -/3) sional) velocity: P Shear velocity: V = (li/p) / Bulk velocity: C = (K/p)1/2 0 Mean (average) velocity: V = 3 + A m I V-1/ The arithmetic means of all of these quantities are also given in appendix 9. A comparison of the mean sound velocity determined from the numerical integration, Vm, with that predicted from the isotropic moduli, Vm, offers a check on the validity of the Hill scheme. In each case, a percentage error is calculated: V - V m m V m Values of A less than a few percent increase our confidence in the validity of the Hill scheme for determining the isotropic moduli of polycrystalline aggregates from the elastic constants of single crystals. In appendix 9, the source of the single-crystal data and the temperatures at which the measurements were taken are indicated for each entry. The elastic constants for the magnetite specimens CU193701 and CU193702 (p. 149) are identical. Clark and Strakna [145] obtained their values from Doraiswami [146J; this duplication was overlooked until the appendixes were in final form. 60

WILLOW RUN LABORATORIES 6 PREFACE TO APPENDIXES PETROGRAPHIC CLASSIFICATION OF ROCKS IN APPENDIXES 1-3 IGNEOUS ROCKS EUCRYSTALLINE DYSCRYSTALLINE OVERSATURATED ROCKS GRANITE RHYOLITE QUARTZ MONZONITE QUARTZ LATITE GRANODIORITE DACITE QUARTZ DIORITE —TONALITE QUARTZ GABBRO SATURATED ROCKS SYENITE TRACHYTE LATITE DIORITE ANDESITE ALBITITE-OLIGOCLASITE KERATOPHYRE GABBRO —NORITE DIABASE BASALT ANORTHOSITE TRAP UNDERSATURATED ROCKS FELDSPATHOIDAL SYENITES ULTRAMAFIC ROCKS FRAGMENTAL ROCKS DUNITE VOLCANIC BRECCIA PERIDOTITE TUFF HARZBURGITE BASALTIC SCORIA PYROXENITE GLASSES BRONZITITE OBSIDIAN SERPENTINITE DIABASE GLASS CHRYSOTILE ANTIGORITE PORPHYRY METAMORPHIC ROCKS SEDIMENTARY ROCKS SCHIST DETRITAL ROCKS SLATE SANDSTONE GNEISS GREYWACKE CHARNOCK I TE SHALE MARBLE KAOLIN QUARTZITE CHEMICAL AND ORGANIC ROCKS AMPH I BOL I T E LI ESTONE ECLOGITE CHALK DOLOMITE 61

WILLOW RUN LABORATORIES STRUCTURAL CLASSIFICATION OF MINERALS IN APPENDIXES 1-3 ORTHO- AND RING SILICATES FRAMEWORK SILICATES OLIVINE GROUP SI02 GROUP OLIVINE QUARTZ MONTICELLITE FUSED SILICA GARNET GROUP OPAL GARNET ALKALI FELDSPARS GROSSULARITE ORTHOCLASE ALMANDITE-PYROPE MICROCLINE AL2SI05 GROUP AMAZONITE SILLIMANITE PLAGIOCLASE FELDSPARS OTHERS ALBITE ZIRCON OLIGOCLASE IDOCRASE LABRADORITE STAUROLITE BYTOWNITE FELDSPATHOIDAL GROUP NEPHELITE SINGLE CHAIN SILICATES NON-SILICATES PYROXENE GROUP DIOPSIDE AUGITE OXIDES AEGIRITE MAGNESIA JADEITE ALUMINA PYROXENOID GROUP HEMATITE WOLLASTONITE LIMONITE SPINEL MAGNETITE DOUBLE CHAIN SILICATES SULFIDES PYRITE PYRRHOTITE AMPHIBOLE GROUP GALENA ANTHOPHYLLITE SULFATES TREMOLITE ANHYDRITE HORNBLENDE CARBONATES CALCITE ARAGONITE SHEET OR LAYERED SILICATES MAGNESITE HALIDES HALITE MUSCOVITE CARBON PHLOGOPITE GRAPHITE BIOTITE TALC CLINOCHLORE LEICHTENBERGITE 62

WILLOW RUN LABORATORIES CODE INDEX FOR ROCKS AND MINERALS IN APPENDIXES 1-8 AA ALUMINA (CORUNDUM) MA MARBLE AB ALBITITE MG MAGNETITE AD ANDESITE MI MICROCLINE AE AEGIRITE MN MAGNESITE AH ANHYDRITE MO MONTICELLITE AM AMPHIBOLITE MS MAGNESIA (PERICLASE) AN ANORTHOSITE MU MUSCOVITE AP ANTHOPHYLLITE NE NEPHELITE AR ARAGONITE NG NORITE AND GABBRO AU AUGITE OB OBSIDIAN AZ AMAZONITE OL OLIGOCLASITE AND OLIGOCLASE BA BASALT OR ORTHOCLASE BI BIOTITE OV OLIVINE BR BRONZITITE PE PERIDOTITE BY BYTOWNITE PH PHLOGOPITE CA CALCITE PO PORPHYRY CH CLINOCHLORE PR PYRITE CK CHARNOCKITE PT PYRRHOTITE CL CHALK PX PYROXENITE DB DIABASE QD QUARTZ DIORITE DC DACITE QG QUARTZ GABBRO DO DOLOMITE QL QUARTZ LATITE DP DIOPSIDE QM QUARTZ MONZONITE DT DIORITE QU QUARTZ (AND SILICA AND OPAL) DU DUNITE QZ QUARTZITE EC ECLOGITE RH RHYOLITE GA GALENA SC SCHIST GD GRANODIORITE SE SERPENTINITE (INCL. ANTIGORITE AND CHRYSOTILE) GN GNEISS SH SHALE GP GRAPHITE SI SILLIMANITE GR GRANITE SL SLATE GT GARNET SN SPINEL GY GREYWACKE SS SANDSTONE HA HALITE ST STAUROLITE HB HARZBURGITE SY SYENITE HE HEMATITE TA TRACHYTE HO HORNBLENDE TC TALC ID IDOCRASE TP TRAP JD JADEITE TR TREMOLITE KA KAOLIN TU TUFF LA LABRADORITE VB VOLCANIC BRECCIA LM LIMONITE WO WOLLASTONITE LS LIMESTONE ZR ZIRCON LT LATITE 63

WILLOW RUN LABORATORIES Appendix 1 PROPERTIES OF ROCKS AT STANDARD TEMPERATURES AND PRESSURES (SOURCES OF DATA LISTED IN APPENDIX 8) (DATA AT ROOM TEMPERATURE AND PRESSURE UNLESS OTHERWISE SPECIFIED ~ PRESSURE=25-50 BARS. RHO=DENSITY. POR=POROSITY IN PERCENT. M/P=MEAN ATOMIC WEIGHT. VP1=COMPRESSIONAL VELOCITY IN KM./SEC. VS1=SHEAR VELOCITY. VS2=SECOND SHEAR VELOCITY —FOR MINERALS) ROCKS IGNEOUS ROCKS ROCK RHO POR M/P VP1 VS1 VS2 INDEX OVERSATURATED GRANITE 2.619 * 20.9 4.1 *. GR25 WESTERLYRoI. GRANITE 2.66 *. 5.76 *. GR03 WESTERLY,R.I. GRANITE 2.636 * 20.9 2.77. GR37 WESTERLYR. I. GRANITE 2.64 2.28 GR80 WESTERLY,R. I GRANITE 2.64 2.68 GR85 WESTERLYR.I. GRANITE 2.621. 20.9 5.1 *. GR26 QUINCYMASS. GRANITE SURFACE 2.61 2.78 GR81 100 FT. 2.59 3.26 GR83 235 FT. 2.64 2.75 GR82 OUINCYMASS. GRANITE 2.64 2.53 GR78 QUINCY,MASS. GRANITE 2.624. 20.6 5.0 ~. GR27 ROCKPORTMASS. GRANITE 2.638 * 20.6 3.07 GR38 ROCKPORT,MASS. GRANITE 2.62 2.55 GR79 ROCKPORT,MASS. GRANITE 2.63 2.66 GR84 ROCKPORT,MASS. GRANITE 2.626. 20.8 4.2 *. GR29 CHELMSFORD,MASS. GRANITE 2.655.. 5.1 *. GR31 BARREVT. GRANITE 2.665 * 20.8 2.79 * GR40 BARRE,VT. GRANITE X 2.66 4.77 2.70 GR87 Y 2.66 4.22 2.83 GR87 Z 2.66 5.09 2.89 GR87 WOODBURY,VT. 64

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX GRANITE 2.625. 20.7 37 3. GR28 STONE MT.,GA. GRANITE 2.639. 20.7 2.43 * GR39 STONE MT.,GA. GRANITE 2.662 *. 5.9.. GR32 SACRED HEARTMINN. GRANITE 2.610 5.5213.04' GR42 BEAR MT..TEX. GRANITE RED *.. 4.39 *. GR22 COLORADO GRANITE GREY *.. 4.95 *. GR23 COLORADO GRANITE ALTERED..~ 4.03 ~* GR24 COLORADO GRANITE 5.64 2.87 GR41 BARRIEFIELD,ONT. GRANITE 2.672.. 5.7.. GR33 BARRIEFIELD,ONT. GRANITE 2.683.. 5.7 ~. GR36 LATCHFORDONT. GRANITE 2.679 *. 6.1 ~. GR35 ENGLEHARTONT. GRANITE... 4.64 3.07. GR06 USSR 137 GRANITE 2.62 0.41 * 4.56 *. GR07 USSR 137 GRANITE *.. 4.95 2.90 * GR04 USSR 247 GRANITE *.. 5.30 3.50 * GR05 USSR 248 GRANITE 5.50 3.63 GR77 USSR 249 GRANITE 2.58.. 4.60 ~. GR08 USSR 732 GRANITE 2.62.. 5.00 2.93. GR09 USSR 1776 GRANITE PAR 2.620.. 6.57.. GR18 PERP 2.623.. 5.98.~ GR18 KONDAVIDUINDIA GRANITE PAR *.. 6.21 2.89 * GR19 PERP... 6.41 3.02 * GR19 INDIA 1 GRANITE PAR *.. 6.02 2.82 * GR20 PERP.. * 6.13 2.95. GR20 INDIA 2 GRANITE PAR *.. 5.77 2.63. GR21 PERP... 6.08'2.93. GR21 INDIA 3 GRANITE 2.80 7.16 2.37 GR86 HYDERABAD,INDIA GRANITE A 2.676.. 5.7.. GR34 HYDERABADINDIA GRANITE B 2.654.. 5.4. GR30 HYDERABADINDIA 65

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX GRANITE PINK 2.732.. 7.14.. GR10 PINK 2.74.. 6.40.. GR11 PINK 2.68.. 5.85.. GR12 PINK 2.606.. 6.58.. GR13 GREY 2.82.. 6.41.. GR14 GREY 2.66.. 6.20.. GR15 GREEN 2.76.. 7.08.. GR16 2.7.. 6.4 3.3. GR17 HYDERABAD,INDIA GRANITE 2.8.. 5.69.. GR01 HIDAKAJAPAN GRANITE 2.6.. 5.92.. GR02 HIDAKAJAPAN GRANITE-1 2.54 4.86 GR88 FUKUI, JAPAN GRANITE-7 2.45 5.38 GR89 KYOTO, JAPAN GRANITE 1 2.86.. 5.75 3.27. GR60 2 2.77.. 5.77 3.50. GR61 3 2.79.. 5.38 3.16. GR62 4 2.76.. 5.89 3.37 * GR63 5 2.77.. 5.63 3.16 * GR64 6 2.65.. 4.91 2.89 * GR65 7 2.78.. 4.45 2.70 * GR66 8 2.77.. 4.86 3.00 * GR67 9 2.71.. 4.56 2.78. GR68 10 2.70.. 5.40 3.05. GR69 11 2.68 *. 4.83 2.96 * GR70 12 2.62.. 5.02 3.10. GR71 13 2.94.. 5.30 3.03 * GR72 14 2.87.. 5.18 2.88. GR73 15 2.77.. 4.09 2.51. GR73 16 2.70.. 5.71 3.55 o GK74 17 2.70.. 4.77 2.81. GR75 18 2.77.. 4.62 2.85. GH76 JAPAN SUITE RHYOLITE 2.39 4.10 2.46 RH02 CHAFFEE CO.,COLO. RHYOLITE X 2.05 3.47 1.95 RH03 Y 2.05 3.19 2.06 RH03 Z 2.05 3.16 1.94 RH03 CASTLE ROCK,COLO. RHYOLITE 2.75 6.99 3.19 RHO1 SUJARGARH (BIKANEER),INDIA QTZ. MONZONITE 2.628 5.26'2.89' QM03 WESTERLY,R.I. QUARTZ MONZONITE 2.65 5.82 3.46 QM04 WESTERLY, R.I. QTZ. MONZONITE 2.644.. 5.1. QM02 PORTERVILLECAL. QTZ. MONZONITE 2.652... 3.16. QM01 PORTERVILLECAL. 66

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX QUARTZ LATITE X 2.46 3.89 2.23 QLO1 Y 2.46 3.50 2.14 QLO1 Z 2.46 3.76 2.32 QLOl CHAFFEE CO.~COLO. GRANODIORITE 2.705 *. 4.4 *. GD01 BUTTE,MONTANA GRANODIORITE 2.63 *~. 3.14 * GD02 WESTONMASS. QUARTZ DIORITE 2.906 *. 5.5 ~* QD03 DEDHAM.MASS. QUARTZ DIORITE 2.928 ~.. 3.39. QD05 DEDHAM,MASS. QUARTZ DIORITE 2.798 *. 5.1 * * D02 SAN LUIS REY QUAD.,CAL. TONALITE 2.763.. 5.1.. QD01 VAL VERDECAL. TONALITE 2.76... 3.12. QD04 VAL VERDE.CAL. DACITE 2.67 o.O0 j.j V~01 BOULDER,COLO. QUARTZ GABBRO 2.99 6.46 3.50 QG01 SALEM, MASS. SATURATED SYENITE 2.780 ~ 22.1 5.7 ~. SY02 SUDBURYONTARIU SYENITE 2.79 2.43 SY03 PENINSULA STATIONONTARIO SYENITE 2.72.. 5.00 2.99 * SY01 USSR 31 TRACHYTE 2.60 5.18 2.83 TA02 HAWAII TRACHYTE 2.61 4.94 2.49 TA03 HAWAII TRACHYTE 2.62 6.00 3.32 TA04 BANNOCKBURN TWP.,ONTARIO TRACHYTE-TUFF X 2.42 3.96 2.59 TA05 Y 2.42 4.74 2.12 IA05 Z 2.42 4.65 2.66 TA05 CRIPPLE CREEKCOLO. LATITE X 2.45 4.10 2.38 LTO1 Y 2.45 3.7u 2.10 LrO1 Z 2.45 3.51 2.15 LT01 CHAFFEE CO.,COLO. DIORITE 3.025-.. 3.06' DT01 SALEMMASS. DIORITE 2.91 5.34 3.24 DT02 JACKSON, WYO. ALBITITE 2.615 *. 6.07 ~. ABOl SYLMAR PA. ALBITITE 2.615 *.. 3.43 * AB02 SYLMARPA. ALBITITE 2.62... 3.32 * AB03 SYLMAR PA. 67

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX OLIGOCLASITE 2.687.* 6.40 * * OL01 SYLMARPA. ANDESITE 2.618 5.23'2.73' AD04 SALIDACOLO. ANDESITE 2.70 5.66 3.22 AD08 SAN JUAN CO., COLO. ANDESITE 2.68 5.41 3.33 AD07 BOULDER CO.,COLO. ANDESITE... 5.36 *. ADO1 COLORADO ANDESITE-HORN. X 2.32 2.71 1.75 AD05 Y 2.32 2.77 1.80 AD05 Z 2.32 2.50 1.64 AD05 MT. SHASTACAL. ANDESITE *.. 5.23.. AD03 ANDESITE-VESICULAR 2.57 5.46 3.04 AD06 CHAFFEE CO.,COLO. ANDESITE BRECCIA 2.73 4.76 3.17 AD09 OURAY, COLO. KERATOPHYRE 2.612 * * 6.16 o. AD02 WALES GABBRO 3.054 * 21.8 5.8 * NG07 FRENCH CREEKPA. GABBRO 3.033 3.27 NG18 FRENCH CREEK,PA. GABBRO 3.05 3.30 NG21 FRENCH CREEKPA. GABBRO 2.931. 21.8 6.8 * NG05 MELLENWISC. GABBRO 2.90 3.37 NG19 MELLEN,WISC. GABBRO 2.874... 3.59 * NG08 SAN MARCOSCAL. GABBRO 2.96 6.07 NG16 USSR 38 GABBRO 2.96 6.46 NG15 USSR 82 GABBRO 2.8.. 6.88. NG02 HIDAKA,JAPAN NORITE 3.057 6.18'3.24' NG10 ESSEX CO.,N.Y. NORITE 2.86 3.16 NG17 SUDBURY,ONTARIO NORITE 2.85 3.62 NG20 SUDBURY,ONTARIO NORITE 2.978. * 6.6. NG06 PRETORIATRANSVAAL NORITE 2.984.. 3.56 * NG09 PRETORIATRANSVAAL NORITE 2.93 *. 6.50 * NG01 USSR 466 NORITE 2.95 * 6.4 *. NG04 USSR 466 NORITE 3.08.. 6.60 * NG03 KONDAPALLIINDIA 68

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX ANORTHOSITE 2.678.. 6.73.. ANO1 TAHAWUSN.Y. ANORTHOSITE 2.712.. 6.28.. AN05 WHITEFACE MT.~N.Y. ANORTHOSITE 2.770. ~ 6.5.. AN02 STILLWATERMONT. ANORTHOSITE 2.750... 3.56 * AN06 STILLWATER MONT. ANORTHOSITE 2.74... 3.59 * AN07 STILLWATER MONT. ANORTHOSITE-GABBRO 2.75 6.73 3.69 AN09 DULUTH. MINN. ANORTHOSITE 2.708 * 21.1 6.54.. AN04 NEW GLASCOWQUE. ANORTHOSITE 2.807 * 21.3 5.7.. AN03 BUSHVELD.TRANSVAAL DIABASE 2.97 5.96 3.38 DB23 MT. TOM, MASS. DIABASE 2.977. 22.0 6.25.. DB09 HOLYOKEMASS. DIABASE 2.96 3.76 DB21 VINAL HAVENME. DIABASE 2.962 3.76 DB18 VINAL HAVENME. DIABASE 3.012 * 22.0 6.76 ~. DB11 FREDERICKMD. DIABASE 3.017 * 22.0. 3.71 * DB13 FREDERICK MD. DIABASE 3.013 3.67 DB19 FREDERICKMD. DIABASE 2.976 * 22.0 6.14 *. DB08 CENTREVILLEVA. DIABASE 2.984. 22.0 * 3.49 * DB12 CENTREVILLE VA. DIABASE 3.003. 22.2 6.4 *~ DB10 KEWEENAWANSUDBURY.ONT. DIABASE 2.989 3.52 DB20 KEWEENAWANONTARIO DIABASE 2.964. 21.8 6.55.. DB07 NIPISSINGoCOBALTONT. DIABASE... 6.33 3.75 * DBO1 USSR 3 DIABASE 3.04 0.4 * 6.37.. DB02 USSR 3 DIABASE 3.08.. 6.3.. DB03 USSR 3 DIABASE 2.85.. 5.61 3.16 * DB04 USSR 288 DIABASE 3 2.903 *~ 6.51. DB16 PRIBRAMCZECH. DIABASE 7 2.879.. 6.47.. DB17 PRIBRAMCZECH. DIABASE 3.12 6.62 3.31 DB22 HYDERABAD INDIA 69

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX DIABASE PAR 3.086.. 7.84 *. DB06 PERP 2.995.. 6.91 *. DB06 HYDERABAD,INDIA DIABASE 3.12. * 5.15.. DB05 HYDERABAD,INDIA BASALT 2.97 6.48 3.58 BA22 SOMERSET CO., N.J. BASALT 2.67 5.37 3.07 BA19 CHAFFEE CO., COLO. BASALT 2.73 5.56 2.95 BA20 JEFFERSON CO., COLO. BASALT 2.82 2.06.. 2*53 * BA05 GUADALUPE MOHOLE SITE BASALT *.. 5.53 3.34. bA03 USSR 4 BASALT 2.88 0.47 * 5.57 *. BA04 USSR 4 BASALT 2.63 *. 5.57 3.40. BA02 USSR BASALT 2.91 * * 5.68 * * BA01 INDIA BASALT-OLIVINE 2.0 4.80 2.56 bA07 HAWAII BASALT-OLIVINE 2.30 4.65 2.50 BA08 HAWAII BASALT-OLIVINE 2.36 5.50 3.10 BA09 HAWAII BASALT-OLIVINE 2.60 5.52 2.76 BAll HAWAII BASALT-OLIVINE 2.44 2.99 1.75 bA18 WASHINGTON BASALT-OLIVINE 2.83 5.74 3.39 BA21 BOULDER CO., COLO. BASALT-OLIVINE 3.00 5.92 3.55 BA23 LINTZ, GERMANY BASALT-THOLEIITIC 2.40 4.82 2.35 BA12 HAWAII BASALT-THOLEIITIC 2.40 4.64 2.26 BA13 HAWAII BASALT-ANKARAMITE 2.40 5.08 3.02 BA10 HAWAII BASALT-ANKARAMITE 2.51 5.10 2.38 BA16 HAWAII BASALT-MUGEARITE 2.31 3.50 1.68 BA15 HAWAII BASALT-ALKALIC 2.33 4.24 2.07 BA17 HAWAII BASALT-VESICULAR 2.00 3.05 BA14 HAWAII TRAP 3.02 *. 6.4. TP01 DECCAN,GULBERGA,INDIA TRAP PAR 2.767. * 8.61.. TP02 PERP 2.777. 6.97 *. TP02 DECCAN GULBERGAINDIA 70

WILLOW RUN LABORATORIES ROCK RHO- POR M/P VP1 VS1 VS2 INDEX TRAP PAR 2.863 *. 8.58 *~ TP03 PERP 2.886.. 6.93.~ TP03 DECCANRUTLAMINDIA TRAP 3.10 6.87 3.19 TP04 DECCANIGADPURI (BOMBAY),INDIA UNDERSATURATED SYENITE-SODALITE 2.52 6.45 2.79 SY04 KISHENGARH (RAJASTHAN),INDIA SYENITE-NEPHELINE 2.70 6.16 2.75 SY05 SIVAMALAI (MADRAS),INDIA ULTRAMAFIC DUNITE X 3.258. 20.9 6.4 *. DU07 Y 3.274 * 20.9 8.0 *~ DU07 Z 3.269 20.9 6.5 DUO7 BALSAM GAPN.C. DUNITE 3.275 4.12 DU19 BALSAM GAP,N.C. DUNITE X 3.25 6.52 3.59 DU20 Y 3.25 6.66 3.84 DU20 Z 3.25 5.88 3.65 DU20 JACKSON CO., N.C. DUNITE X 3.306 ~* 7.90 * DU08 Y 3.302 *. 7.34. DU08 Z 3.304 7.85 DU08 ADDIEN.C. DUNITE ALTERED 3.00 *. 6.31 * DU04 ALTERED 2.962.. 5.46. DU04 3.244 * 21.0 7.0. DUO5 WEBSTERN.C. DUNITE 3.264. 21.0. 4.01 DUll WEBSTER N.C. DUNITE X 3.312 * 20.9 8.3 *. DUO9 Y 3.310. 20.9 7.2 *. DU09 Z 3.314 20.9 7.6 DUO9 TWIN SISTERS MT.,WASH. DUNITE 3.326 * 20.9 * 4.60 * DU13 TWIN SISTERS MT.,WASH. DUNITE PAR 3.262 *. 8.27 *. DUOl PERP 3.211.. 7.55.. DUO1 MT. DUN,NEW ZEALAND DUNITE X 3.255 * 21.1 7.9 *. DUO6 Y 3.257 * 21.1 7.2 *. DUO6 Z 3.262 21.1 7.3 DUO6 MT. DUNNEW ZEALAND DUNITE 3.270. 21.1. 4.17 * DU12 MT.DUNNEW ZEALAND DUNITE X 3.777 * 24.3 7.0.. DU10 Y 3.717. 24.3 6.6 *. DU10 Z 3.737 24.3 6.6 DU10 MOOIHOEK MINEiTRANSVAAL DUNITE 3.760 * 24.3 * 3.68. DU14 MOOIHOEK MINETRANSVAAL 71

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX DUNITE X 3.1.. 7.40.. DU03 Y 3.1.. 7.32 2. DU03 Z 3.1.. 7.53.. DU03 NEW GUINEA DUNITE X 3.3.. 7.80 4.0. DU02 Y 3.3 7.97 DU02 Z 3.3.. 8.26.. DU02 JAPAN 8A DUNITE 7.9 DU21 JAPAN PERIDOTITE X 2.67 4.07 2.50 PE13 Y 2.67 4.06 2.31 PE13 Z 2.67 4.00 2.25 PE13 MURFREESBORO, ARK. PERIDOTITE 3.35.. 8.50. PE08 PERIDOTITE 25 SERP 3.16.. 7.78.. PE09 PERIDOTITE 50 SERP 2.97.. 7.06. PE10 PERIDOTITE 75 SERP 2.85. 6.38 * PE11 PERIDOTITE 100SERP 2.60. 5.68. PE12 PERIDOTITE 3.28 * * 7.40 4.02 PE04 USSR 455 PERIDOTITE 3.28.. 6.8.. PE01 USSR 455 PERIDOTITE 3.21 6.97 3.66 PE03 USSR 462 PERIDOTITE 3.34.. 7.7..PE02 USSR 609 PERIDOTITE X 3.3.. 7.92 4.2 PE05 Y 3.3.. 8.24.. PE05 Z 3.3 7.83 PE05 JAPAN 8 PERIDOTITE X 3.2 *. 8.08 4.0 * PE06 Y 3.2.. 7.74.. PE06 Z 3.2.. 8.37.. PE06 JAPAN 9 PERIDOTITE X 3.3.. 7.50.. PE07 Y 3.3.. 7.73.. PE07 Z 3.3.. 7.25.. PE07 JAPAN 12 HARZBURGITE X 3.380.. 6.7.. HBO1 Y 3.371.. 7.3. HB01 Z 3.356 6.6 HB01 BUSHVELD TRANSVAAL PYROXENITE X 3.239 6.7 PX06 Y 3.244. 6.4.. PX06 Z 3.259.. 7.2.. PX06 SONOMA CO.,CAL. PYROXENITE 2.93 6.45 3.27 PX07 HAWAII 72

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX PYROXENITE 3.24 0.37. 7.14 3.90. PXO1 USSR 457 PYROXENITE 3.15 0.21. 6.75 3.50 * PX05 USSR 468 PYROXENITE 3.29 0.32 * 7.62 4.14 * PX02 USSR 469 PYROXENITE 3.22 0.41. 5.90 3.26. PX03 USSR 470 PYROXENITE 3.24 0.42. 6.75 3.60 * PX04 USSR 472 BRONZITITE X 3.283 * 21.2 7.20 *. BRO1 Y 3.284. 21.2 7.58.. BRO1 Z 3.271 21.2 7.48 BR01 STILLWATER,MONTANA BRONZITITE 3.287. 21.2 * 4.45 * BR03 STILLWATER,MONT. BRONZITITE 3.27 *.. 4.50 * BR04 STILLWATER MONT. BRONZITITE 3,272 4.50 BR06 STILLWATER,MONT. BRONZITITE X 3.304. 21.0 6.2 * BR02 Y 3.264. 21.0 5.0 * BR02 Z 3.297 21.0 5.9 BR02 BUSHVELDTRANSVAAL BRONZITITE 3.289 4.37 BR07 BUSHVELDTRANSVAAL SERPENTINITE X 2.768 6.18' SE14 Y 2.887 7.05' SE14 Z 2.792 6.70' SE14 MIDDLEFIELDMASS. SERPENTINITE 2.798 *. 6.4.. SE13 LUDLOW,VT. SERPENTINITE 2.798 6.4 SE17 LUDLOW,VT. SERPENTINITE 2.806 *.. 3.61 * SE09 LUDLOWVT. SERPENTINITE 2.710.. 5.8 * SE12 CAL. SERPENTINITE 2.710 5.8 SE18 CALIF. SERPENTINITE 2.718... 3.12 SE08 CAL. SERPENTINITE 2.70 0.4 ~ 6.13 * SE06 USSR 240 SERPENTINITE.. 6.60 * SE05 USSR SERPENTINE 10 2.6. 5.80 ~. SE01 IWAUCHIDAKEJAPAN SERPENTINE 11 X 2.5. 5.08 ~ SE03 Y 2.5.. 4.60. SE03 Z 2.5.. 4.95. SE03 NITTO MINEJAPAN SERPENTINE 14 2.6.. 5.54.. SE02 TARIJAPAN 73

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX SERPENTINE 15 X 2.7.. 4.81.. SE04 Y 2.7.. 3.34.. SE04 Z 2.7.. 4.08.. SE04 HAMATONBETSUJAPAN CHRYSOTILE X 2.598.. 5.5.. SE10 Y 2.603.. 5.8.. SE10 Z 2.601 5.5 SE10 THETFORD,QUE. CHRYSOTILE 2.601 5.6 SE15 THETFORDQUE. CHRYSOTILE 2.602... 2.71. SE07 THETFORDQUE. ANTIGORITE X 2.620.. 4.0 *. SEll Y 2.603.. 5.7 ~. SEll Z 2.618 4.5 SE11 LUDLOW,VT. ANTIGORITE 2.614 4.7 SE16 LUDLOWVT. PORPHYRY 2.92.. 6.52 3.81 * P01 USSR 290 FRAGMENTAL ROCKS VOLCANIC BRECCIA 2.19 4.22 2.49 VB01 PARK CO.,COLO. TUFF X 1.38 1.41 0.83 TU01 Y 1.38 1.36 0.82 TU01 Z 1.38 1.51 0.97 TU01 SAN LUIS OBISPOCAL. BASALTIC SCORIA X 2.23 3.73 2.21 BA24 Y 2.23 4.53 2.69 tA24 Z 2.23 4.72 2.63 bA24 KLAMATH FALLS9ORE. GLASSES OBSIDIAN 2.376.. 5.80. OB01 MODOCCAL. OBSIDIAN 2.440 3.53 OB02 MODOC,CALIF. OBSIDIAN 2.35 5.82 3.57 OB03 LAKE CO.,ORE. DIABASE GLASS 2.750. 6.30. DB15 GENERAL ELECTRIC CO. METAMORPHIC ROCKS ROCK RHO POR M/P VP1 VS1 VS2 INDEX SCHIST-TALC 2.914. 4.9.* SC01 CHESTER,VT. SCHIST-ACTIN X 3.217.. 5.62.. SC02 Y 3.199. 7.32.. SC02 CHESTER,VT. 74

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX SCHIST-PAR 2.800 *. 6.5.. SC03 PERP 2.796. * 4.6.* SC03 WOODSVILLEVT. SCHIST-CHLORITE X 2.877. * 5.9.. SC04 Y 2.897 *. 3.3 ~. SC04 CHESTER VT. SCHIST 2.95 *.. 3.34. SC12 FRAMINGHAMMASS. SCHIST 1 2.70.. 3.02 * SC13 FRAMINGHAMMASS. SCHIST 2 2.73... 2.76 * SC14 FRAMINGHAMMASS. SCHIST 2.82.. 6.16 2.05. SCll SCHIST PAR *.. 6.20 * * SC10 PERP... 6.20 ~. SC10 USSR SCHIST PAR *. * 7.45 2.67 * SC07 PERP *.. 8.16 2.83 * SC07 INDIA 1 SCHIST PAR * *. 7.74 2.61. SC08 PERP *.. 8.03 2.74 * SC08 INDIA 2 SCHIST PAR *.. 5.82 2.53 * SC09 PERP... 6.42 2.65 * SC09 INDIA 3 SCHIST *.. 5.96 2.85. SC06 HYDERABADINDIA SCHIST 2.97 5.96 2.85 SC22 HYDERABAD,INDIA SCHIST 2.97 * * 4.89 2.20 * SC05 YELLANDLAPADINDIA SCHIST-QTZ PAR 2.78 4.56 SC23 PERP 2.78 2.65 SC23 JAPAN 5 SCHIST-QTZ PAR 2.74 6.30 SC24 PERP 2.74 2.52 SC24 JAPAN 52 SCHIST-EP-QTZ PAR 2.44 5.99 SC25 PERP 2.44 4.36 SC25 JAPAN 114 SCHIST-MG-QTZ PAR 3.79 6.39 SC26 PERP 3.79 5.56 SC26 JAPAN 115 SCHIST-GREEN PAR 2.93 5.52 SC27 PERP 2.93 3.90 SC27 JAPAN 30 SCHIST-GREEN PAR 3.16 6.24 SC28 PERP 3.16 4.88 SC28 JAPAN 34 SCHIST-GREEN PAR 2.88 6.14 SC29 PERP 2.88 4.62 SC29 JAPAN 118 SLATE X.. 4.95 *. SL04 Y... 6.28 *. SL04 EVERETT MASS. 75

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX SLATE 2.67... 2.89. SL05 EVERETTMASS. SLATE X 2,741.. 4.97.. SL06 Y 2.734.. 5.81.. SLO6 MEDFORD,MASS. SLATE 3.07.. 5.62 2.27. SLO1 HYDERABAD,INDIA SLATE 2.64.. 4.21 2.08 * SL02 BIHAR,INDIA SLATE 2.60.. 5.22 2.99. SL03 KURNOOLINDIA GNEISS PAR 2.642. 20.8 3.7.. GN15 PERP 2.646. 20.8 2.9 ~. GN15 PELHAM,MASS. GNEISS PAR 2.64 1.85 GN29 PERP 2.64 1.73 GN29 PELHAM,MASS. GNEISS PERP 2.64 2.35 GN30 PELHAM,MASS. GNEISS 2.91... 3.42 * GN17 SOLOMON'S PONDMASS. GNEISS PAR 2.768. 4.9.. GN14 PERP 2.762.. 3.6.. GN14 BETHLEHEM,N.H. GNEISS PAR 2.684.. 5.6.. GN13 PERP 2.664.. 4.5.. GN13 HELL GATEN.Y. GNEISS PAR 2.65... 2.49. GN16 PERP 2.65... 2.62. GN16 HELL GATEsN.Y. GNEISS PAR 2.684.. 6.29.. GN08 PERP 2.788.. 5.48.. GN08 UXBRIDGEENGLAND GNEISS 2.87.. 3.87 2.20. GN09 USSR 286 GNEISS 2.70.. 3.44 2.15. GN10 USSR 287 GNEISS 2.84.. 6.1. GN12 USSR 460 GNEISS 2.68.. 5.2.. GN11 USSR 740 GNEISS 2.83.. 6.77.. GNO1 INDIA GNEISS 2.74.. 6.74 3.13 * GN02 HYDERABAD,INDIA GNEISS 2.80.. 7.55 3.08. GN03 BIHAR,INDIA GNETSS 2.76.. 7.12 2.95. GN04 TRIHINOPOLYINDIA GNEISS PAR 6.24 2.63 GN05 PERP... 7.87 2.65. GN05 INDIA 1 GNEISS PAR... 6.13 2.37 * GN06 PERP... 6.93 2.47. GN06 INDIA 2 76

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX GNEISS PAR... 6.08 2.32. GN07 PERP... 6.62 2.39 * GN07 INDIA 3 CHARNOCKITE 2.60.. 7.13 3.12. CKO1 KONDAPALLIINDIA CHARNOCKITE 2.64. * 7.58 3.26 * CK02 PALLAVARAM,INDIA CHARNOCKITE AK1 2.61 *. 6.1 3.1 * CK03 AK2 2.68 *. 6.0 3.0. CK04 IK1 2.66.. 6.3 3.1. CK05 IK2 2.83.. 6.3 3.2. CK06 BK1 2.68.. 6.5 3.3. CK07 BK2 2.67.. 6.4 3.4. CK08 UK1 3.12.. 6.7 3.7. CK09 UK2 3.36 *. 6.6 3.7. CK10 UK3 3.07 *. 6.6 3.5. CK11 KONDAPALLIINDIA CHARNOCKITE 2.740 *. 6.15.. CK12 PALLAVARAMINDIA CHARNOCKITE AP1 2.63.. 6.0 3.1 * CK13 AP2 2.42 *. 6.1 3.0. CK14 BP1 3.06 *. 6.3 3.2. CK15 BP2 3,06 *. 6.2 3.2. CK16 BP3 3.05 *. 6.4 3.2. CK17 BP4 3.01 *. 6.4 3.3. CK18 BP5 2.99 *. 6.5 3.3 * CK19 PALLAVARAM,INDIA CHARNOCKITE 2.64 7.58 3.27 CK20 MADRAS,INDIA MARBLE X 2.705 *. 4.7 MA09 Y 2.703.. 5.9 *. MA09 Z 2.704 4.8 MA09 DANBYVT. MARBLE PERP 2.71 2.05 MA58 PAR 2.71 2.85 MA58 PROCTORVT. MARBLE 2.71 2.71 MA57 PROCTOR,VT. MARBLE 2.71 5.34 2.83 MA60 TATE. GA. MARBLE PERP C 5.96 3.96 MA11 PAR C 6.08 3.87 MAll YULE,COLO. MARBLE 37 2.66 *. 6.33 3.51. MA48 38 2.58.. 5.90 3.28 * MA49 39 2.75 *. 5.70 3.20. MA50 40 2.59 *. 5.53 2.99 * MA51 41 2.62 *. 5.25 2.92. MA52 42 2.88.. 4.68 2.43. MA53 43 2.82.. 5.31 2.75. MA54 44 2.64 *. 6.62 3.31. MA55 45 2.75 *. 5.20 2.53. MA56 ITALY MARBLE 2.93.. 5.61 3.47. MA03 RAJAPUTANA,INDIA 77

-WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX MARBLE FINE 2.72 *. 7.11 2.66 * MA01 MEDIUM 2.74 *. 7.05 2.64. MA01 COARSE 2.74.. 6.78 2.59. MA01 MAKRANA INDIA MARBLE 2.86 *. 7.07 3.40 * MA05 RAMAGUNDAMgINDIA MARBLE PAR 2.85 *. 6.46.. MA06 PERP 2.84 *. 5.57 *. MA06 JUBBALPORE INDIA MARBLE PAR 2.71.. 6.41.. MA07 PERP 2.70.. 4.33 *. MA07 RAJAPUTANAINDIA MARBLE 2.88 7.33 2.74 MA59 MANDITOG (HYDERABAD),INDIA MARBLE 2.88 *. 6.83 3.81. MA02 HYDERABAD,INDIA MARBLE 2.80 *. 7.33 2.74 * MA04 MANDITOG,INDIA MARBLE 35 2.39 *. 5.38 3.00 * MA46 RYUKYU ISLANDS MARBLE 36 2.70 *. 6.00 3.30. MA47 KOREA MARBLE 1 2.66 *. 5.62 3.26 * MA12 2 2.73.. 5.97 3.32. MA13 3 2.80 *. 5.34 2.96. MA14 4 2.93.. 6.08 3.73. MA15 5 2.76 *. 5.48 2.92. MA16 6 2.76.. 6.14 3.22. MA17 7 2.73.. 5.09 2.80. MA18 8 2.73 *. 5.89 2.96. MA19 9 2.79.. 5.85 3.46. MA20 10 2.74 *. 5.89 2.83 * MA21 11 2.72.. 6.02 3.54. MA22 12 2.68 3.75 2.02 MA23 13 2.66 *. 5.11 3.12. MA24 14 2.83.. 5.25 3.13. MA25 15 2.66.. 6.15 3,84. MA26 16 2.72.. 6.05 3.48. iA 27 17 2.70.. 6.37 3.31. MA28 18 2.80 *. 5.92 3.64. MA29 19 2.76.. 6.48 3.92 * MA30 20 2.76 *. 6.34 3.43 * MA31 21 2.76.. 5.98 3.04. MA32 22 2.72.. 5.80 3.07. A 33 23 2.79.. 6.10 3.70 * MA34 24 2.72.. 5.41 3.15. MA35 25 2.82 *. 5.67 3.10. MA36 26 2.74.. 6.94 3.86. MA37 27 2.70.. 6.16 3.76. MA38 28 2.69.. 6.10 3.70. MA39 29 2.62.. 6.01 3.50. MA40 30 2.70.. 6.19 3.75. MA41 31 2.72.. 6.23 3.38. MA42 32 2.72.. 5.72 3.18. MA43 33 2.73 *. 6.02 3.10 * MA44 34 2.80.. 5.14 2.72 * MA45 JAPAN SUITE 78

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX QUARTZITE 2.647.. 5.6. QZ03 MONTANA QUARTZITE PAR... 4.80.. QZ01 PERP..~ 3.30.. QZ01 USSR 1 QUARTZITE PAR... 5.90.. QZ02 PERP... 5.90.. QZ02 USSR 2 QUARTZITE 5.55 3.40 QZ15 USSR 22 QUARTZITE 2.716.. 5.70 * * QZ04 INDIA 7 OUARTZITE 2.64 *. 6.60 2.75. QZ05 GUNTURINDIA 2 QUARTZITE 2.56 *. 5.61 3.03 * QZ06 WARANGAL,INDIA QUARTZITE 2.54 *. 5.06 2.70 * QZO7 KARIMMAGARINDIA QUARTZITE... 5.62 3.03 * QZ08 MANDITOGINDIA QUARTZITE 2.56 5.61 3.03 QZ16 MANDITOG (HYDERABAD),INDIA QUARTZITE 2.61.. 6.11 3.08. QZ09 YELLANLAPADINDIA 8 QUARTZITE 2.56.. 6.15 3.08. QZ10 KHAMMAM,INDIA 5 AMPHIBOLITE X 3.108 *. 6.09 *. AM04 Y 3.124.. 7.31 *. AM04 MADISON CO.,MONT. AMPHIBOLITE 3.070... 3.90 * AM05 MADISON CO.,MONT. AMPHIBOLITE 2.95 6.80 3.53 AM11 HAWAII AMPHIBOLITE... 7.40. AM02 USSR 1 AMPHIBOLITE 3.05.. 6.20 3.45. AM01 USSR 289 AMPHIBOLITE X 3.0 *. 7.22.. AM03 Y 3.0 *. 4.98 *. AM03 Z 3.0 *. 6.16 ~* AM03 HIDAKA,JAPAN ECLOGITE 3.441. 22.2 7.31.. EC10 HEALDSBURGCAL. ECLOGITE 3.44. 22.2. 4.26 * EC03 HEALDSBURGCAL. ECLOGITE 3.360... 3.83. EC06 OCCIDENTALCAL. ECLOGITE 2.81 5.97 2.94 EC15 HAWAII ECLOGITE 2.71 5.69 2.77 EC16 HAWAII ECLOGITE 3.376. 21.7 5.2.. EC09 SUNNMORE,NORWAY ECLOGITE 3.577... 4.07. EC04 NORWAY 1552 79

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX ECLOGITE 3.578... 3.70. EC05 NORWAY 1553 ECLOGITE 3.36 7.84 EC02 SCOTLAND ECLOGITE 1 3.338.. 6.6.. tC14 2 3.376.. 7.17. EC08 KIMBERLEY DIST.,O.F.S. ECLOGITE 3.328.. 6.64.. EC07 TANGANYIKA ECLOGITE X 3.2.. 7.39.. ECO1 Y 3.2.. 6.64.. EC01 Z 3.2.. 7.60 *. EC01 HIDAKA,JAPAN SEDIMENTARY ROCKS ROCK RHO POR M/P VP1 VS1 VS2 INDEX SANDSTONE 2.61... 3.04. SS07 BROOKLINEMASS. SANDSTONE 2.64 3.36 SS47 ALLENTOWNPA. SANDSTONE 2.66 3.39 SS46 ALLFNTOWN,PA. SANDSTONE 2.659 *. 3.9.. SS13 CATSKILLN.Y. SANDSTONE 2.543 5.1. 3.67. SS11 CAPLEN DOME,GALVESTON CO.,TEX. SANDSTONE 2.514 9.. 3.73 *. SS12 TRAVIS PEAKMARION CO.,TEX. SANDSTONE... 4.65 2.76. SS02 SANDSTONE RED *.. 4.31. SS03 GOLDEN,COLO. SANDSTONE WHITE.. 3.18 *. SS04 GOLDEN,COLO. SANDSTONE 1.78' bS51 AUSTIN SANDSTONE 20 2.16' SS14 BANDERA SANDSTONE 2.10' SS49 BANDERA SANDSTONE 2.66.. 5.15 1.97. SS01 BARAKER SANDSTONE 20 1.74' SS15 BEREA SANDSTONE 1.83' SS48 BEREA SANDSTONE 1.92' SS52 BEREA SANDSTONE 2.51 8.5 4.15, SS44 MCKEE SANDSTONE 17 2.05' SS16 SEMINOLE 80

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX SANDSTONE 2.08 21.9 2.42' SS43 STEVEN SAND SANDSTONE 2.31 13.7 3.73' SS42 TENSLEEP SANDSTONE 13 1.75' SS17 TENSLEEP SANDSTONE 2.04' SS50 TORPEDO SANDSTONE 17 1.99' SS18 TORPEDO SANDSTONE 8 2*30' SS19 WEBER SANDSTONE 3.30 2.15 SS41 USSR 94 SANDSTONE 2.18 7.7. 2.94 1.89 * SS08 USSR 204 SANDSTONE 2.95 1.90 SS39 USSR 205 SANDSTONE 2.14 15. * 3.22 1.92 * SS09 USSR 208 SANDSTONE 2.15 7.9. 3.13 1.94 * SS10 USSR 209 SANDSTONE 2.70 *. 4.85 3.03 * SS05 USSR 213 SANDSTONE 4.90 3.07 SS40 USSR 213 SANDSTONE 20. * 2.64.. SS33 17.6. 3.10.. SS34 11.2. 3.63.. SS35 10.5 * 3.66 * SS36 6.0. 3.84.. SS37 0.3 * 4.00 * SS38 FRANCE SANDSTONE 2.44. 4.09. SS06 INDIA SANDSTONE 2.61 1.12 * 6.85 2.19 * SS21 2.47 9.75 * 4.51 2.13 * SS22 2.63 5.17. 6.19 2.62. SS23 2.62 4.00 * 6.03 2.38 * SS24 2.64 1.35 * 6.54 2.40. SS25 2.60 9.38 * 6.03 2.13 * SS26 2.62 3.87 * 5.83 2.54 * SS27 2.50 7.88 * 4.99 2.49 * SS28 2.62 2.58. 6.05 2.36 * SS29 2.62 0.58. 6.10 2.05 * SS30 2.59 5.57. 5.61 2.40 * SS31 2.62 2.31 * 6.47 2.26 SS32 INDIA GREYWACKE 2.679.. 5.4.. GY1l NEW ZEALAND GREYWACKE 2.705 *. 5.4 *. GY02 QUEBEC GREYWACKE 6 2.749.. 6.19 3.90 * GY03 PRIBRAMCZECH. GREYWACKE U2-U7 2.688 *. 6.06 3.61 * GY04 PRIBRAMCZECH. 81

WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX SHALE 3.07 5.62 2.27 SH03 HYDERABAD,INDIA SHALE 2.78.. 5.79 1.97. SH01 INDIA SHALE 3.07.. 4.93 ~* SH02 KAOLIN 1.62.. 3.12 1.64 * KAO1 KAOLIN 1.58 1.44 0.93 KA02 DRYBRANCHGA. LIMESTONE 2.69 *. 3.15 *. LS03 NAZARETH,PA. LIMESTONE *.. 3.85 *. LS04 INDIANA LIMESTONE *.. 5.12 2.87. LS19 USSR LIMESTONE 2.62 1.8. 4.78.. LS20 USSR 246 LIMESTONE... 5.54.. LS18 DACHSTEIN, AUSTRIA LIMESTONE 2.656 *. 5.97 2.88 * LSO1 SOLENHOFEN,BAVARIA LIMESTONE 2.543 *. 5.5 *~ LS02 SOLENHOFENBAVARIA LIMESTONE 2.581 5.56 LS45 SOLENHOFEN,BAVARIA LIMESTONE 2.605 2.75 LS41 SOLENHOFENBAVARIA LIMESTONE 4.0 2.62' LS27 SOLENHOFENBAVARIA LIMFSTONE 2.67 *.. 3.14. LS29 2.59... 2.9. LS30 6.14.. LS31.. 5.88.. LS32 R 2.485.. 5.38 2.98 * LS33 8068 2.517.. 5.55 3.05. LS34 S4 2.558 4.5. 5.65 3.07. LS35 0 2.582.. 5.84 3.17. LS36 A5 2.591 3.6. 5.90 3.13. LS37 S10 2.599 3.3. 5.96 3.15. LS38 F 2.661 *. 6.12 3.22. LS39 SOLENHOFENBAVARIA LIMESTONE 2.80 *. 7.07 3.40. LS05 RAMAGUNDAMINDIA LIMESTONE 2.84 *. 6.36 3.08. LS06 PIDUGURALLA,INDIA LIMESTONE 2.81 6.26 3.07 LS07 VINDHYA PRADESH,INDIA LIMESTONE 2.86.. 6.24 3.02. LS08 MADHYA PRADESHINDIA LIMESTONE 3.00 *. 6.21 3.10. LS09 BHIMA,INDIA LIMESTONE PAR 2.700.. 6.18 *. LS10 PERP 2.721 *. 5.10 *. LS10 BHIMAINDIA 82

-WILLOW RUN LABORATORIES ROCK RHO POR M/P VP1 VS1 VS2 INDEX LIMESTONE PAR 2.697.. 6.72 *. LS11 PERP 2.647 *. 4.17 *. LS11 KURNOOL,INDIA LIMESTONE PAR *.. 6.59 3.09 * LS12 PERP *.. 7.37 3.26 LS12 INDIA 1 LIMESTONE PAR *.. 6.78 3.26 * LS13 PERP *.. 7.01 3.42 * LS13 INDIA 2 LIMESTONE PAR *.. 6.53 3.16 * LS14 PERP *.. 6.85 3.29 * LS14 INDIA 3 LIMESTONE 2.68 *. 5.98 3.46 * LS15 SHAHABAD,INDIA 4 LIMESTONE 1 2.82 *. 6.40 3.20 * LS40 2 2.66.. 5.89 2.94 * LS16 CUDDAPAHINDIA LIMESTONE 2.780 *. 6.25.. LS17 INDIA 8-11 LIMESTONE 3.00 6.24 3.02 LS42 HYDERABAD,INDIA CHALK 1.67 * * 3.04 1.58. CLO1 DOLOMITE 2.844 *. 5.6 ~ D002 RUTLAND,VT. DOLOMITE 2.845' 6.06' D005 DUNHAM,WILLIAMSTOWNMASS. DOLOMITE 2.83... 3.52 * D003 BETHLEHEMPA. DOLOMITE 2.82 3.58 D006 BETHLEHEM,PA. DOLOMITE 2.58.. 4.69 2.72 * D001 USSR 1745 DOLOMITE 4.56 D007 MINERALS ORTHO- AND RING SILICATES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX OLIVINE GROUP OLIVINE 100 3.324. 20.9 9.87 4.88 4.87 OVol 010.. 20.9 7.73 4.88 4.42 OVOl 001.. 20.9 8.65 5.00 4.54 OVOl BURMA MONTICELLITE 3.014 7.10' M002 CRESTMORE,CAL. MONTICELLITE 2.975... 3.85. MOO1 CRESTMORE,CAL. 83

WILLOW RUN LABORATORIES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX GARNET GROUP GARNET 100 4.247. 24.9 8.51 4.74. GT03 110.. 24.9 8.47 *. GT03 BRAZIL 1 GARNET 100 4.183. 24.3 8.54 4.75. GT04 110.. 24.3 8.51.. GT04 BRAZIL 2 GROSSULARITE 3.561. 22.8 6.3 ~. GTO1 CONNECTICUT ALMAND.-PYROPE 3.950. 24.1 5.9.. GT02 AL2SIO5 GROUP SILLIMANITE X 3.189 9.04' SI02 Y 3.179 9.55' SI02 Z 3.194 9.60' SI02 WILLIAMSTOWN,AUSTRALIA SILLIMANITE 3.187... 4.93. SI01 WILLIAMSTOWNAUSTRALIA OTHERS ZIRCON 100 4.564.. 4.03 1.88 1.76 ZRO1 001 4.604.. 3.15 1.73 1.73 ZRO1 110 4.596 *. 3.54 1.71 2.65 ZRO1 111 4.650.. 3.14.. ZRO1 IDOCRASE 3.144 5.52' ID02 CRESTMORECAL. IDOCRASE 3.140... 3.13 * ID01 CRESTMORE,CAL. STAUROLITE 100 3.385.. 10.07 4.54 5.26 ST01 010 3.367.. 7.42 3.72 5.18 STO1 001 3.325.. 6.66 3.66 4.56 ST01 110 3.358 *. 5.19.. ST01 SINGLE CHAIN SILICATES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX PYROXENE GROUP DIOPSIDE X 3.08 3.36 3.11 DPO1 Y 3.08 5.83 4.07 DPO1 Z 3.08 7.48 3.96 DPO1 QUEBEC AUGITE X 3.26 5.30 3.47 AU01 Y 3.26 2.96 1.97 AU01 Z 3.26 2.95 AU01 NEW YORK 84

WILLOW RUN LABORATORIES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX PYROXENE GROUP (CONT.) AEGIRITE 001 3.50.. 8.21 3.72 4.23 AEO1 110... 7.60 4.07 3.95 AE01 010... 7.20 3.97 3.48 AEO1 101... 6.75 4.43 3.60 AEO1 100... 7.30 3.68 3.78 AE01 011... 8.30 4.65 3.86 AE01 USSR JADEITE 3.33.. 8.60 5.04. JD01 BURMA JADEITE 3.331. 20.4 8.45.. JD03 BURMA JADEITE 3.180 * 20.4 7.6.. JD04 JAPAN JADEITE 3.203 * 20.4 * 4.65 * JD02 JAPAN PYROXENOID GROUP WOLLASTONITF 2.873 5.03' WOO1 DOUBLE CHAIN SILICATES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX AMPHIBOLE GROUP ANTHOPHYLLITE 001... 5.67 2.73 2.75 APO1 010... 8.64 2.70 5.10 APO1 NAZYAMSKY MTS.,S.URALS,USSR TREMOLITE X 2.86 6.25 3.83 TRO1 Y 2.86 3.02 TRO1 Z 2.86 6.08 4.25 TRO1 NEW YORK HORNBLENDE 001 3.124.. 7.85 3.16 4.29 HOO1 110... 6.50 3.56 3.92 HOO1 010... 7.16 4.52 3.53 HOO1 101... 7.11 3.65 3.62 HO01 100... 6.11 3.43 3.18 HO01 011... 7.55 4.20 3.30 H01 USSR 1 HORNBLENDE 001.. 8.13 3.03 4.40 H002 110... 7.01 3.87 3.77 H002 010... 7.54 4.45 3.72 H002 101... 6.18 3.98 4,05 H002 100..* 6.45 3.78 3.46 H002 011.. 7.80 4.48 3.48 H002 USSR 2 HORNBLENDE X 3.32 7.17 3.05 H003 Y 3.32 5.85 3.14 H003 Z 3.32 6.06 3.79 H003 ONTARIO 85

WILLOW RUN LABORATORIES SHEET OR LAYERED SILICATES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX MUSCOVITE 001 2.79.. 4.44 2.03 2.05 MUOl 010.. 8.03 2.06 2.01 MU01 USSR PHLOGOPITE 001 2.81.. 4.28 1.46 1.47 PHO1 010 7.96 1.48 5.19 PHO1 USSR BIOTITE 001 3.05.. 4.21 1.38 1.38 BI01 010... 7.80 1.34 5.06 BI01 USSR TALC 001.. 3.73.. TC01 010 9.00 5.08 TCO1 USSR CLINOCHLORE 001... 5.88 2,.3 2.03 CH01 010... 8.09 4.52 CHO1 SHTSHIMSKY MTS.,S.URALSUSSR LEICHTENBERGITE.. 6.72 2.16 2.16 CH02 8.34 2.05 5.11 CH02 SHISHIMSKY MTS.,S.URALSUSSR FRAMEWORK SILICATES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX SI02 GROUP OUARTZ X... 5.38.. QU0 Y *.. 5.41.. QU01 Z... 6.52.. QU01 FUSED SILICA 2.20. 5.96 3.76. QU04 FUSED SILICA 2.20 5.97 3.76 QU05 FUSED SILICA 2.213.. 5.97.. QU02 FUSFD QUARTZ 6.10 QU06 OPAL.. 5.26.. QU03 ALKALI FELDSPARS ORTHOCLASF X 3.70.. OR01 Y... 5.72.. OR01 Z.. 3.80.. OR01 86

WILLOW RUN LABORATORIES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX ALKALI FELDSPARS (CONT.) MICROCLINE 001 2.56.. 6.95 2.93 2.37 MI01 110... 7.14 3.44 2.88 MI01 010... 8.15 2.14 3.83 MI01 101... 5.20 3.55 3.04 MI01 100... 5.10 3.75 3.04 MI01 011... 6.30 4.96 3.20 MI01 N.KARELIAUSSR MICROCLINE 001 2.571 6.43' MI02 010 2.570 7.67' MI02 100 2.571 4.65' MI02 LABRADOR MICROCLINE X 2.57 4.75 2.97 MI03 Y 2.57 5.57 3.05 MI03 Z 2.57 7.49 3.38 MI03 ONTARIO AMAZONITE 001.. 6.43 2.73 2.37 AZ01 010... 6.81 2.31 3.49 AZ01 100... 4.59 3.47 2.25 AZ01 USSR PLAGIOCLASE FELDSPARS ALBITE 001 2.61.. 7.13 3.19 2.56 AB05 110... 6.38 3.69 2.74 AB05 010... 7.26 2.58 3.56 AB05 101... 5.31 3.40 2.95 AB05 100... 5.42 5.45 3.30 AB05 011... 6.20 4.63 3.10 AB05 USSR ALBITE X.. 4.38 * AB06 Y *. 6.68..AB06 ALBITE X 2.63 6.23 3.10 AB07 Y 2.63 6.73 3.55 AB07 Z 2.63 6.42 2.70 AB07 ONTARIO OLIGOCLASE 001 2.64. 6.88 3.19 2.58 OLu2 110... 6.81 3.72 278 OL02 010.. 7.87 2.71 3.66 OL02 101.. 6.60 3.07 3.13 OL02 100... 5.68 3.7u 2.95 OL02 011... 6.45 4.53 3.36 OL02 CHUPAWHITE SEAUSSN OLIGOCLASE 001 2.64 7.18 3.24 2.59 OL03 110... 8.55 3.72 2.86 OL03 010.. 7.41 2.84 3.58 OL03 101... 5.48 3.48 3.U6 OL03 100... 5.62 3.55 3.35 OL03 011... 6.30 4.62 3.26 OL03 USSR 87

WILLOW RUN LABORATORIES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX PLAGIOCLASE FELDSPARS (CONT.) OLIGOCLASE 001 2.64.. 7.17 3.27 2.65 ULU4 110... 6.67 3.76 2.9U OL04 010... 7.55 2.70 3.61 OL04 101... 5.50 3.52 3.10 OL04 100... 5.7U 3.60 3.37 OL04 011... 6.35 4.70 3.29 OL04 USSR LABRADORITE 001 2.68.. 7.53 3.49 2.83 LA01 110.. 7.38 4.14 2.89 LA01 010... 7.71 2.76 3.53 LA01 101... 7.05 3.65 2.96 LA01 100... 6.10 3.72 3.59 LA01 011... 6.48 4.89 3.63 LA01 GOLOVINOUKRAINE,USSR LABRADORITE 001 2.68.. 7.3U 3.40 2.7u LA02 110... 6.98 3.84 2.95 LA02 010... 7.80 2.78 3.63 LA02 101... 7.25 3.65 3.14 LA02 100... 6.06 3.72 3.44 LA02 011... 6.55 4.76 3.44 LA02 USSR LABRADORITE 001 2.69.. 7.33 3.40 2.72 LA03 110... 7.10 3.90 3.02 LA03 010... 8.00 2.80 3.65 LA03 101... 7.38 3.67 3.17 LA03 100... 6.10 3.74 3.50 LA03 011... 6.64 4.80 3.48 LA03 USSR BYTOWNITE X 2.71 6.69 3.49 BY01 Y 2.71 7.37 3.38 bY01 Z 2.71 6.73 3.54 BY01 MINNESOTA FELDSPATHOID GROUP NEPHELITE 001... 7.12 3.72. NE01 100... 5.61 2.83 3.72 NE01 011... 6.25 3.92 3.26 NE01 1 VISHNFVYE MTS.,URALSUSSR NEPHELITE 001... 6.90 3.63 * NE02 100.... 5.35 2.53 3.63 NE02 011... 6.00 3.90 3.12 NE02 2 BALYKTACH-KHEM RIVERUSbK 88

WILLOW RUN LABORATORIES NON-SILICATES MINERAL RHO PUN M/P Vkl val vo2 InDEA OXIDES MAGNESIA 3.580.. 9.77 5.96 * MSO1 BERKELEY SYNTHETIC MAGNESIA 3.580.. 9.78 5.97 * MS02 BERKELEY SYNTHETIC MAGNESIA 3.572 *. 9.67 6.00 * MS03 AVCO D64B SYNTHETIC ALUMINA 3.822.. lu.45.. AAO1 AD 99 SYNTHETIC ALUMINA 3.972 0.35 10.85 6.37 AA02 G.E. LUCALOX ALUMINA 3.941 1.13 lu.74 6.34 AA03 AVCO 1495A HEMATITE 5.5.. 7.1.. HEO1 HEMATITE X 4.93 6.85 3.91 HE02 Y 4.93 7.04 3.84 HE02 Z 4.93 6.58 3.78 HE02 MICHIGAN LIMONITE X 3.55 5.28 2.95 LMO1 Y 3.55 5.37 2.96 LMO1 Z 3.55 5.42 3.00 LMO1 ALABAMA SPINFL 100 3.63 *. 9.10 6.61 * SNO1 10.30 SNO1 SYNTHETIC MAGNETITE 4.54 * 30.9 5.9 *. MGO1 TRANSVAAL MAGNETITE 4.532 *. 2.3 *. MG02 TAHAWUSN.Y. MAGNETITE 4.866.. 3.8.. MG03 PORT HENRYN.Y. MAGNETITE X 4.81 4.07 2.09 MG04 Y 4.81 4.12 1.57 MG04 Z 4.81 4.34 2.25 MG04 NEWYORK MAGNETITE ORE 3.85 5.29 MG05 JAPAN 108 SULFIDES PYRITE 100 5.016.. 872 4.67 4.67 PRO2 110... 7.94 5.92 4.67 PR02 LEADVILLECOLU. PYRITE X 4.81 7.63 4.76 PRO6 Y 4.81 7.68 4.72 PR06 Z 4.81 7.76 4.87 PR06 COLORADO 89

-WILLOW RUN LABORATORIES MINERAL RHO POR M/P VP1 VS1 VS2 INDEX SULFIDES (CONT.) PYRITE 110 4.929.. 7.91 5.90 4.67 PRO3 1 GLENDONN.C. NPYRITE 100 4.929.. 8.51 4.59 4.57 PR04 110... 7.76 5.70 4.58 PR04 2 GLENDONN.C. PYRITE 4.85 *.. 3.81. PRO1 NORANDA MINtSQUc. PYRITE 100... 8.49 ~ ~ PR05 110 *. * 7.23.. PR05 NEPAL PYRITE ORE 4.51 7.46 PR07 JAPAN 96 PYRITE ORE 4.20 6.31 PR08 JAPAN 104 PYRRHOTITE X 4.55 4.70 2.78 PTO1 Y 4.55 4.66 2.71 PT01 Z 4.55 4.71 2.78 PTO1 ONTARIO GALENA 100 7.564.. 1.88 ~. GAO1 110 7.560.. 3.51. ~ GA01 111 7.565 *. 3.93. ~ GAO1 210 7.563 *. 3.04.. GA01 CHEROKEE CO.,KANSAS SULFATES ANHYDRITE 2.928 *. 4.8 *. AHO1 ANHYDRITE X 6.20 AH02 Y 6.34 AH02 Z 6.21 AH02 CARBONATES CALCITE X 2.705.. 7.12 4.15 3.58 CAO1 Z 2.704 *. 5.44 3.55 * CAO1 CALCITE X *.. 7.03 *. CA02 Y *.. 6.59 *. CA02 Z *.. 4.80 *~ CA02 ARAGONITE 2.917 *. 5.7. * AR01 MEXICO MAGNESITE 2.802 6.92' MN02 MAGNESITE ".848 *.. 4.05. MNO1 HALIDES HALITE *. 4.68.. HAO1 CARBON GRAPHITE X 2.16 3.30 1.77 GPO1 Y 2.16 2.93 1.97 GPO1 Z 2.16 2.94 1.84 GPO1 CEYLON 90

WILLOW RUN LABORATORIES Appendix 2 COMPRESSIONAL VELOCITY VERSUS PRESSURE (10 bars to 10 kb) (SOURCES FOR DATA ARE LISTED IN APPENDIX 8) (VELOCITY UNITS=KM./SEC. COLUMN HEADINGS ARE PRESSURES IN UNITS OF KILOBARS) (ALL MEASUREMENTS AT TEMPERATURES OF 0-30 DEGREES CENTIGRADE) EXPLANATION OF SPECIAL SYMBOLS IN APPENDIXES 2-3 (ALL PRESSURES ARE + OR - 3 PERCENT) SYMBOL EXPLANATION.01 PRESSURE=0.000-0.025 KILOBARS PRESSURE=0.025-0.050 KILOBARS ) PRESSURE=0.070 KILOBARS / PRESSURE=O.170 KILOBARS PRESSURE=0.200 KILOBARS )) PRESSURE=0 300 KILOBARS ( PRESSURE=0.345 KILOBARS (( PRESSURE=0.400 KILOBARS ** PRESSURE=0O470 KILOBARS * PRESSURE=0.600 KILOBARS // PRESSURE=0.900 KILOBARS $ PRESSURE=9 000 KILOBARS + ADD 0.5 KILOBARS TO COLUMN HEADING SUBTRACT 0.5 KILOBARS FROM COLUMN HEADING ++ ADD 1.0 KILOBARS TO COLUMN HEADING ~ — ~ SUBTRACT 1*0 KILOBARS FROM COLUMN HEADING (SYMBOLS IMMEDIATELY FOLLOW THE READINGS TO WHICH THEY APPLY) ROCKS IGNEOUS ROCKS ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND OVERSATURATED GRANITE 2.619 4.1 5.63 5.84 5.97 6.10 6.16 6.23 GR25 WESTERLYR. I GRANITE 2.615. 5.90=5.98 6.06 6.12 6.14 6.18 6.22... GR44 WESTERLYR. I. GRANITE 2.621 5.1. 6.04 6.11 6.20 * 6.30 * 6.37 6.45 GR26 QUINCY.MASS. GRANITE 2.629. 5.92=6.06 6.21 6.30 6.34 6.38 6.40.. * GR43 QUINCY,MASS. GRANITE 2.624 5.0. 5.96 6.18 6.29. 6.39 * 6.43. 6.51 GR27 ROCKPORTMASS GRANITE 2.626 4.2 * 5.64 5.91 6.09. 6.22 * 6.28. 6.35 GR29 CHELMSFORDMASS. GRANITE 2.625 3.7 * 5.42 5.94 6.16. 6.27 * 6.33. 6.40 GR28 STONE MT.,GA. 91

- -W ILLOW RUN L-ABORATORIES ROCK RHO.01.01 0 05 1 2 3' 4 5.6 8 10 IND GRANITE 2.662 5.9 6.24 6.28 6.34 6.38 6.45 GR32 SACRED HEART.MINN. GRANITE 2.672 5.7. 6.21 6.29 6.35. 6.42. 6.46. 6.51 GR33 BARRIEFIELD, ONT. GRANITE. 5.64 5.88 6.22 6.34 6.38 6.41 6.43 6.45.. ~ GR41 BARRIEFIELD,ONT. GRANITE 2.679 6.1. 6.28 6.33 6.37. 6.43. 6.48. 6.57 GR35 ENGLEHART,ONT. GRANITE 2.683 5.7. 6.13 6.19 6.25. 6.30 * 6.34. 6.41 GR36 LATCHFORDONT. GRANITE 2.655 5.1. 5.86 6.06 6.15. 6.25. 6.32. 6.39 GR31 BARRE,VT. GRANITE 2.634 5.77=6.05 6.16 6.22 6.26 6.29 6.31 GR45 WOODBURYVT. GRANITE 2.610 5.52*5.80/6.11 6.23....... GR42 BEAR MT..TEX. GRANITE PINK 2.636. 6.14=6.29 6.34 6.43 6.47 6.50 6.52 6.54.. GR46 LLANO CO.,TEX. GRANITE GREY 2.609. 5.78=5.96 6.10 6.19 6,23 6.25 6.28 6.30 6.34. GR47 LLANO CO.,TEX. GRANITE A 2.676 5.7 6.42 6.46 6.51 6.55 6.61 GR34 HYDERABADINDIA GRANITE B 2.654 5.4. 6.26 6.31 6.38. 6.44. 6.49. 6.56 GR30 HYDERABAD.INDIA GRANITE 2.62 4.64 4*86=511*5.36...... GR06 USSR 137 GRANITE 2.62 4.56 6.06 GR07 USSR 137 GRANITE * 4.95 * 5.30 5.48 5.55-5.55-5.55-... GR04 USSR 247 GRANITE * 5.30 * 5.70 5.84 5.84-..... GR05 USSR 248 GRANITE * 5.50.. 6.09 6.09 6.09 6.08... GR77 USSR 249 GRANITE 2.58 4.60 6.1 6.3 6.3 GR08 USSR 732 GRANITE 2.62 5.00 5.46// GR09 USSR 1776 QTZ MONZONITE 2.628 5.26'5.62/5.90 6.00... QM03 WESTERLYR.I. QTZ MONZONITE 2.644 5.1 5.95 6.07 6.22 6.28 6.37 QM02 PORTERVILLECAL. GRANODIORITE 2.705 4.4 6.27 6.35 6.43 6.48 6.56 GD01 BUTTE, MONT. QTZ DIORITE 2.906 5.5 6.46 6.53 6.60 6.65 6.71 QD03 DEDHAMMASS. QTZ DIORITE 2.798 5.1 6.43 6.52 6.60 6.64 6.71 QD02 SAN LUIS REY QUAD., CAL. TONALITE 2.763 5.1 6.33 6.43 6.49 6.54 6.60 QD01 VAL VERDECAL. SATURATED SYENITE 2.780 5.7 6.58 6.63 6.70 6.73 6*79 SY02 SUDBURY, ONTARIO TRACHYTE 2.712 5.41=5.48 5.55 5.67 5.73 5.76 5.78 TAO1 92

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND DIORITE 3.025 5.78'5.97/6.24 6.30...... DTO1 SALEM,MASS. ALBITITE 2.615 6.07 6.18 6.24 6.31 6.40 6.45 6.52 AB01 SYLMARPA. OLIGOCLASITE 2.687 6.40 6.62 6.65 6.68 6.72 6.76 OL01 SYLMARgPA. ANDESITE 2.618 5.23'5.24/5.27 5.31..... ~ AD04 SALIDACOLO. GABBRO 3.054 5.8 6.74 6.93 7.02 7.11 7.17 7.23 NG07 FRENCH CREEK,PA. GABBRO 2.931 6.8 7.04 7.07 7.09 7.13 7.16 7.21 NG05 MELLENWISC. GARRRO 2.885 6.45=6.61 6.69 6.76 6.78 6.81 6.83 6.84 NG12 DULUTHMINN. GABBRO 2.993 6.69=6.79 6.88 6.95 6.98 7.01 7.03 7.05 NG11 SAN MARCOS.CAL. GABBRO 2.933. 6.60=6.67 6.74 6.80 6.84 6.86 6.88 6.89. NG13 GABBRO 2.96 6.07.. 6.53 6.53 6.53 6.52.... NG16 USSR 38 GARBBRO 2.98 6.46.. 6.80 6,80 6.80 6.80.... NG15 USSR 82 NORITE 3.057 6.18'6.50/6.76 6.88.... NG10 ESSEX CO.,N.Y. NORITE 2.978 6.6 7.02 7.07 7.11 7.16 7.20 7.28 NG06 PRETORIA.TRANS. NORITE 2.95 6.4.. 6.7 7,0... 7.2++ * 7.2++NG04 USSR 466 NORITE 2.93 6.50.. 6.70.. 6,75. * NG01 USSR 466 ANORTHOSITE 2.768 6.73.. 6.86 6.90. 6.94. 6.97. 7.02 ANO1 TAHAWUSN.Y. ANORTHOSITE 2.712 6.28. 6.61 6.69 6.75. 6.82. 6.85. 6.91 AN05 WHITEFACE MT.,N.Y. ANORTHOSITE 2.770 6.5 6.97 7,01 7.05 7.07 7.10 AN02 STILLWATER,MONT. ANORTHOSITF 2.708 6.54 6.64 6.69 6.73 6.78 6.81 6.85 AN04 NEW GLASCOW,QUE. ANORTHOSITE 2.807 5.7 6.92 6.98 7.05 7.13 7.16 7.21 AN03 BUSHVELDTRANSVAAL DIABASE 2.976 6.14.. 6.70 6,76 * 6.82 * 6.86 * 6.93 DB08 CENTREVILLE,VA. DIABASE 2.977 6.25. 6.40 6.43 6.47. 6.52. 6.56. 6.63 DB09 HOLYOKF,MASS. DIABASE 3.012 6.76.. 6.77 6.80. 6.84. 6.88. 6.92 DB11 FREDERICK,MD. DIABASE 2.964 6.55.. 6.64 6.67. 6,71. 6.75. 6.82 DB07 NIPISSINGCOBALT,ONT. DIABASE 3.003 6.4 * 6.67 6.72 6,76 6.81. 6,84. 6.91 B10 KEWEENAWANiSUDBURY9ONT. DIABASE 3.04 6.33 6.40=6.58*6.67.... DB.. D801 USSR 3 DIABASE 3.04 6.37...... 6.95... DB02 USSR 3 DIABASE 3.08 6.3..... 7.0.. DB03 USSR 3 93

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND DIABASE 3 2.903 6.51 * 6.69 6.81 6.88 6.91 DB16 PRIBRAM,CZECH. DIABASE 7 2.879 6.47 * 6.65 6.72 6.77 6.81 6.84 DB17 PRIBRAM,CZECH. BASALT 2.586 5.41=5.57 5.66 5.75 5.79 5.80 5.81 5.82 BA06 CHAFFEE CO.,COLO. BASALT 2.88 5.53 5.70=5.84*5.92 BA03 USSR 4 BASALT 2.88 5.57 6.19 BA04 USSR 4 BASALT 2.63 4.77 5.57// BA02 USSR ULTRAMAFIC DUNITE ALTERED 3.00 6.31.. 6.54 6.62. 6.72 * 6.80 * 6.93 DUO4 ALTERED 2.962 5.46.. 6.07 6.18. 6.28 * 6.40 * 6.62 DU04 3.244 7.0 7.54 7.59 7.65 7.69 7.78 DU05 WEBSTERN.C. DUNITE X 3.258 6.4 7.52 7.54 7.70 7.85 7.91 8.00 DU07 Y 3.274 8.0 8.38 8.42 8.49 8.57 8.63 8.69 DU07 Z 3.258 6.4 7.52 7.54 7.70 7.85 7.91 8.00 DUO7 BALSAM GAPN.C. DUNITE 3.198 7.40=7.54 7.63 7.77 7.82 7.86 7.91 DU16 BALSAM GAPN.C. DUNITE X 3.306 7.90 8.23 8.30 8.35 8.41 8.44 8.51 DU08 Y 3.302 7.34 7.56 7.61 7.73 7.82 7.91 DU08 Z 3.304 7.85 8.07 8.12 8.19 8.29 8.34 8.41 DU08 ADDIEN.C. DUNITE X 3.312 8.3 8.73 8.78 8.85 8.88 8.90 8.95 DUO9 Y 3.310 7.2 7.74 7.83 7.92 7.97 8.00 8.07 DUO9 Z 3.314 7.6 7.86 7.97 8.04 8.12 8.16 8.23 DU09 TWIN SISTERS MT.,WASH. DUNITE 3.160 8.60) 8.87 8.94 8.96 8.98 DU15 TWIN SISTERS MT.,WASH. DUNITE X 3.255 7.9 8.14 8.20 8.25 8.30 8.35 8.43 DU06 Y 3.257 7.2 7.54 7.61 7.66 7.73 7.81 7.91 DU06 Z 3.262 7.3 7.38 7.45 7.48 7.54 7.60 7.66 DUO6 MT. DUNNEW ZEALAND DUNITE X 3.777 7.0 7.40 7.42 7.46 7.50 7.53 7.57 DU10 Y 3.717 6.6 * 6.87 6.90 6.98. 7.06 * 7.10. 7.19 DU10 Z 3.737 6.6 7.12 7.15 7.20 7.26 7.28 7.33 DU10 MOOIHOEK MINETRANS. PERIDOTITE 3.28 6.8 7.3+ 7.5 7.6 7.8 8.0++PE01 USSR 455 PERIDOTITE 3.28 7.40.. 7.70.. 7.70... PE04 USSR 455 PERIDOTITE 3.21 6.97.. 7.83.. 8.02 ~* * PEo3 USSR 462 PERIDOTITE 3.34 7.7... 8.0... 8.2++. PE02 USSR 609 HARZBURGITE X 3.380 6.7 7.61 7.65 7.70 7.73 7.77 7.82 HBO1 Y 3.371 7.3 7.84 7.89 7.91 7.96 8.01 8.05 HBO1 Z 3.356 6.6 7.76 7.80 7.82 7.87 7.91 7.97 HBO1 BUSHVELDTRANSVAAL 94

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND PYROXENITE X 3.239 6.7 7.72 7.79 7.87 7.94 8.00 PX06 Y 3.244 6.4 7.45 7.52 7.65 7.72 7*82 PX06 Z 3.259 7.2 8.03 8.06 8,11 8.14 8.20 PX06 SONOMA CO., CAL. PYROXENITE 3.24 7.14 7.40 7.46 PXO1 USSR 457 PYROXENITE 3.15 6.75 7.05 7,05 PX05 USSR 468 PYROXENITE 3.29 7.62 7.87 8.00 PX02 USSR 469 PYROXENITE 3.22 5.90 6.72 7.05 PX03 USSR 470 PYROXENITE 3.24 6.75 7.67 7.67 PX04 USSR 472 RRONZTITTF X 3.283 7.20 7.60 7.64 7.70 7.73 7.82 BRO1 Y 3.284 7.58 7.67 7.71 7.77 7.81 7.89 BR1l Z 3.271 7.48 7.59 7.61 7.68 7.71 7.79 BRl1 STILLWATER, MONT. BRONZITITE X 3.304 6.2 7.45 7.50 7.57 7.66 7.71 7.80 BR02 Y 3.264 5.0 7.46 7.56 7.71 7.88 8.00 8.13 BR02 Z 3.297 5.9 7.30 7.40 7.53 7,70 7.85 8.12 BR02 BUSHVELDTRANSVAAL SERPENTINITE 2.710 5.8 6.02 6.08 6.15 6.21 6.31 SE12 CALIF. SERPENTINITE 2.710 5.8 6.02 6.08 6.15 SE18 CALIF. SERPENTINITE 2.798 6.4 6.51 6.57 6.67 6.74 6.84 SE13 LUDLOW,VT. SERPENTINITE 2.798 6.4 6.51 6.57 6.67 SE17 LUDLOW,VT. SERPENTINITE X 2.768 6.18'6.21 6.33*6.37 6.42. 6.50 * 6.58 6.63 6.68 SE14 Y 2.807 7.05'7.06 7.08*7.10 7.14 7.18 7.22 7.25 7.27 SE14 Z 2.792 6.70'6.71 6.74*6.76 6.80 6.85 6.89 6.93 6.97 SE14 MIDDLEFIELD,MASS. SERPENTINITE 2.70 6.13 7.36 SE06 USSR 240 SERPENTINITE B 2.433 5.0 5.16 5.24 5.34 5,46 SE19 PUERTO RICO SERPENTINITE B 2.510 4.5 4.68 4.75 4.88 5.06 SE20 PUERTO RICO SERPENTINITE B 2.536 4.7 4.86 4.91 5.01 5.17 SE21 PUERTO RICO SERPENTINITE A 2.599 5.8 5.82 5.86 5.90 5.99 SE22 PUERTO RICO SERPENTINITE A 2.589 5.1 5.24 5,28 5,36 5.48 SE23 PUERTO RICO SERPENTINITE A 2,744 6.17 6.19 6.20 6.23 6.30 SE24 PUERTO RICO SERPENTINITE A 2.732 6.1 6.18 6.21 6.26 6.33 SE25 PUERTO RICO SERPENTINITE A 2.725 6.1 6.07 6.09 6.12 6.19 SE26 PUERTO RICO 95

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND CHRYSOTILE X 2.598 5.5 5.60 5.66 5.73 5.79 5.91 SE10 Y 2.603 5.8 5.83 5.88 5,96 6.03 6.15 SE10 Z 2.601 5.5 5.59 5.65 5.71 5.78 5.93 SE10 THETFORDQUE. CHRYSOTILE 2.601 5.6 5.67 5.73 5.80 SE15 THETFORD,QUE. ANTIGORITE X 2.620 4.0 6.00 6.16 6.28 6.41 6.46 6.57 SEll Y 2.603 5.7 6.94 6.99 7.15 7.26 7.29 7.33 SE11 Z 2.618 4.5 6.06 6.22 6.33 6.44 6.49 6.56 SEll LUDLOW.VT. ANTIGORITE 2.614 4.7 6.46 6.59 6.70 SE16 LUDLOWVT. GLASSES OBSIDIAN 2.376 5.80... 5.78. 5.73. 5.70 * 5.62 OB01 MODOCCAL. DIABASE GLASS 2.750 6.30......... 6.30 DB15 GENERAL ELECTRIC CO. METAMORPHIC ROCKS ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SCHIST PAR 2.800 6.5.. 6.77 6.80 * 6.84 * 6.87. 6.91 SC03 PERP 2.796 4.6.. 6.05 6.10 * 6.17. 6.22. 6.31 SC03 WOODSVILLEVT. SCHIST-CHLOR 2.877 5.9.. 7.17 7.23 * 7.30 * 7.32 * 7.36 SC04 2.897 3.3.. 6.52 6.61. 6.70 * 6.75 * 6.82 SC04 CHESTER QUARRYVT. SCHIST-TALC 2.914 4.9.. 6.30 6.50. 6.71. 6.82. 6.97 SCO1 CHESTER QUARRY.VT. SCHIST-ACTIN 3.217 5.62.. 6.62 6.75. 6.84. 6.92. 7.01 SC02 3.199 7.32.. 7.68 7.79. 7.89 * 7.94. 8.00 SC02 CHESTER QUARRY.VT. SCHIST X 2.75 * 5.4 6.3 *6.44 6.58. 6.70. 6.74 6.77 6.82 SC18 Y 2.76 * 5.3 6.2 *6.44 6.54 * 6.64 * 6.71 6.76 6.77 SC18 Z 2.76 * 5.0 5.61*5.71 5.84. 5.95 * 6.05 6.11 6.17 SC18 THOMASTONCONN. SCHIST 1X 2.99. 5.0 6.2 *6.53 6.72. 7.07. 7.27 7.41 7.50 SC19 1Y 2.95. 5.6 6.55*6.78 7.01. 7.17. 7.29 7.35 7.48 SC19 1Z 3.07 * 4.6 5.8 *6.12 6.61 * 6.92. 7.03 7.19 7.26 SC19 TORRINGTONCONN. SCHIST 2X 2.73 * 5.8 6.53*6.73 6.92. 7.04. 7.17 7.23 7.27 SC20 2Y 2.84 * 5.0 6.05*6.26 6.54 * 6.75 * 6.87 6.92 7.00 SC20 2Z 2.73 * 4.6 5.57*5.74 5.87 * 6.02 * 6.02 6.12 6.20 SC20 TORRINGTONCONN. SCHIST X 2.75. 5.9 6.74*6.87 6.97. 7.16 * 7.20 7.23 7.25 SC21 Y 2.76. 5.6 6.41*6.54 6.66. 6.77. 6.85 6.89 6.93 SC21 Z 2.75.. 5.25*5.41 5.54. 5.63. 5.70 5.78 5.85 SC21 LITCHFIELDCONN. 96

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SLATE X 2.734 5.81.. 6.05 6.13. 6.23 * 6.29. 6.39 SL06 Y 2.741 4.97 5.40 5.56 5.71 5.80 5.96 SL06 MEDFORD,MASS. SLATE X 2.77. 6.28 6.35*6.37 6.41. 6.48 * 6.54 6.59 6.66 SL08 Y 2.75. 6.29 6.33*6.36 6.40 * 6.46 * 6.51 6.57 6.63 SL08 Z 2.77. 4.94 5.04*5.09 5.15. 5.29. 5.41 5.50 5.59 SL08 POULTNEY,VT. GNEISS PAR 2.642 3.7. 5.82 6.04 6.18. 6.30 * 6.35. 6.43 GN15 PERP 2.646 2.9. 5.54 5.83 5.96. 6.09. 6.15. 6.25 GN15 PELHAM,MASS. GNEISS PAR 2.684 5.6. 6.25 6.31 6.39. 6.47 * 6.53. 6.61 GN13 PERP 2.664 4.5. 5.76 5.83 5.94. 6.05 * 6.10 * 6.26 GN13 HELL GATEN.Y. GNEISS PAR 2.768 4.9 *. 6.14 6.22 * 6.30 * 6.36 * 6.43 GN14 PERP 2.762 3.6.. 5.74 5.87. 6.01 * 6.08. 6.13 GN14 BETHLEHEMN.H. GNEISS 1X 2.643. 4.7 5.7 *5.92 6.12. 6.23 * 6.29 6.34 6.37 GN23 1Y 2,621. 5.0 5.9 *6.07 6.18. 6.29 * 6.32 6.37 6.41 GN23 1Z 2.665. 4.6 5.7 *5.91 6.05. 6.15. 6.21 6.24 6.29 GN23 TORRINGTON,CONN. GNEISS 2X 2.661. 4.5 5.5 *5.79 6.04. 6.22. 6.29 6.35 6.39 GN24 2Y 2.651. 4.5 5.7 *5.91 6.09. 6.22. 6.27 6.31 6.35 GN24 2Z 2.650 * 4.6 5.7 *5.85 6.04. 6.09 * 6.15 6.21 6.25 GN24 TORRINGTONCONN. GNEISS 3X 2.742. 5.1 5.9 *6.19 6.32. 6.44 * 6.48 6.54 6.58 GN25 3Y 2.745. 4.7 5.8 *6.06 6.33. 6.42 * 6.48 6.53 6.57 GN25 3Z 2.777. 5.4 6.1 *6.19 6.32. 6.43. 6.50 6.53 6.56 GN25 TORRINGTON,CONN. GNEISS 4X 2.819 * 4.6 5.7 *6.02 6.32 * 6.52 6.60 6.68 6.72 GN26 4Y 2.877 * 4.7 5.8 *6.08 6.28 6.45 6.52 6.57 6.63 GN26 4Z 2.776 5.1 5.8 *5.98 6.14 6.23 6.29 6.34 6.38 GN26 TORRINGTONCONN. GNEISS 5X 2.845. 5.5 6.1 *6.29 6.35. 6.47 * 6.54 6.58 6.63 GN27 5Y 2.850 * 5.7 5.81*5.88 5.99. 6.16 * 6.36 6.49 6.58 GN27 5Z 2.848. 5.2 5.9 *5.98 6.09. 6.18 * 6.24 6.29 6.33 GN27 TORRINGTON.CONN. GNEISS 6X 2.76 * 5.4 6.0 *6.17 6.34. 6.49 * 6.55 6.60 6.65 GN28 6Y 2.75. 5.2 5.9 *6.05 6.24. 6.44 * 6.52 6.57 6.63 GN28 6Z 2.76. 4.1 4.9 *5.16 5.43. 5.66. 5.81 5.90 5.99 GN28 GOSHEN,CONN. GNEISS 2.84 6.1 6.4 +6.5 6.6 6.6 6.7 6.8 GN12 USSR 460 GNEISS 2.68 5.2.. 6,1 +. 6.3.. 6.4. 6.5 GN11 USSR 740 CHARNOCKITE 2.740 6.15 6.24 6.30 6.36 6.40 6.46 CK12 PALLAVARAM,INDIA MARBLE.* 5.87)6.25(6.55 6.65+6.67 6.67 6.66.. MA08 DANBYVT. MARBLE X 2.705 4.7.. 6.48 6.53 * 6.58. 6.59. 6.60 MA09 Y 2.703 5.9.. 6.69 6.76. 6.81. 6.84. 6.87 MA09 Z 2.704 4.8 6.65 6.69 6.77 6.80 6.81 MA09 DANBYVT. MARBLE PERP C * 5.96 6.48=6.63*6.68...... MAll PAR C * 6.08 6.55=6.66*6.67....... MAll YULE COLO. 97

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0,5 1 2 3 4 5 6 8 10 IND QUARTZITE 2*647 5*6. * 6,11 6*15 * 6.22 * 6*26 * 6.35 QZ03 MONTANA QUARTZITE X 2*63 * 5.2 5.83*5,98 6,07 * 6,16 * 6*21 6,24 6.28 QZ12 Y 2,62 5 5,6 5.97*6,05 6*12 * 6,17 * 6,21 6.26 6.28 OZ12 Z 2.63 * 5.6 6.01*6.11 6.18, 6,25 * 6.29 6,31 6.33 QZ12 CLARENDON SPRINGSVT, QUARTZITE X 2.68 * 5.4 6*17*6,27 6.35 * 6.43 6 6*49 6o51 6*55 QZ13 Y 2.66 * 5.2 6.06*6.16 6.23 * 6.29 * 6.35 6.39 6*43 QZ13 Z 2.68 * 5,1 5.78*5.86 5.93 * 6.01 * 6.07 6.12 6.17 QZ13 THOMASTONCONN. QUARTZITE * 5.55.* 5*85 6.00 6.00-. * * *~ QZ15 USSR 22 AMPHIBOLITE 3.108 6.09 6.61 6.65 6.72 6.77 6.83 AM04 3.124 7.31 7.50 7.54 7.59 7.63 7.66 AM04 MADISON CO.,MONT. AMPHIBOLITE 1X 3.05 7.0 7.2 *7.21 7.26 7.37 7.42 7.46 7.49 AM07 1Y 3.04 6.9 7.09*7.13 7.20 7.28 7.33 7.38 7.42 AM07 1Z 3.04 5.6 6.14*6.29 6.45 6.60 6.68 6.73 6.76 AM07 BANTAMCONN. AMPHIBOLITE 2X 3*03 * 5.8 6,7 *6.97 7.25. 7.47 7 7,52 7.58 7.61 AM08 2Y 3.02 * 6.2 6.8 *6,92 7.08 * 7,22 * 7.26 7,29 7.33 AM08 2Z 3.03 * 4.5 5.7 *6.01 6.27 * 6.44 e 6.51 6.55 6.59 AM08 BANTAMCONN. AMPHIBOLITE 1X 3.11 * 6.8 7,2 *7,29 7.45 * 7,61 * 7,73 7*77 7.82 AM09 1Y 3.15 * 6.0 6.9 *7.10 7.32 * 7.52 * 7,60 7.65 7.69 AM09 LITCHFIELDDCONN. AMPHIBOLITE 2X 3.25 * 6,4 6,9 *7.15 7.40. 7,66. 7,75 7,81 7,83 AM10 2Y 3.30 * 6,4 7.1 *7.25 7.49 * 7.65 * 7.72 7.77 7.80 AM10 2Z 3,24 * 5.8 6,7 *6,87 7,07. 7.24 * 7,32 7,36 7.39 AM10 LITCHFIELD.CONN. ECLOGITE 3.441 7.31.. 7.69 7.81 * 7.89 o 7.94. 8.01 EC10 HEALDSBURGCAL. ECLOGITE 3.376 5.2.. 7.13 7.30. 7.46 * 7.54. 7.69 EC09 SUNNMORENORWAY ECLOGITE 1 3.338 6.6 7.49 7.56 7.65 7.79 7.85 7.92 EC14 2 3.376 7.17 * 7.65 7.68 7.73. 7.79 * 7.82. 7.87 EC08 KIMBERLEY DIST.,O.F.S ECLOGITE 3.328 6.64 * 7.30 7.38 7.46 * 7.57 * 7.62 * 7.71 EC07 TANGANYIKA SEDIMENTARY ROCKS ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SANDSTONE 2.659 3.9 * 5.0 5.27 5.44. 5.63 * 5.75 * (5.85)SS13 CATSKILLN.Y. SANDSTONE 2.543 3.67 4.04 4.58 4.87 5.11 5.13 5.28 5.36 SS11 CAPLEN DOME,GALVESTON CO..TEXAS SANDSTONE 2.514 3.73 4.11 5.09 5.37 5.46 5.50 5.53 5.55 SS12 TRAVIS PEAKMARION CO.,TEXAS SANDSTONE (POR=3.3) 5.61** SS58 ORISKANYPENNSYLVANIA 98

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SANDSTONE l(POR=19.0)2.56'3.41=3.67(( SS65 2 3.41)) (AXIAL PRESSURE) SS66 BEREAOHIO SANDSTONE 2.14 4.58 4.69 4.74 4.72 4.70 4.69 SS45 ST.PETERKLONDIKEMO. SANDSTONE 2.31 3.73' 4.05 4.89 5.03 SS42 TENSLEEP,LONGS CREEK,WYO. SANDSTONE (POR=15.3) 3.93(( SS55 TENSLEEP.WYOMING SANDSTONE 1 (POR=7.4) 4.45(( SS56 2 4.29 (AXIAL PRESSURE) SS57 FOX HILLSWYOMING SANDSTONE (POR=23.5) 3.53)) SS59 JELMWYOMING SANDSTONE (POR=29.7) 3.05)) SS60 TEAPOTgWYOMING SANDSTONE (POR=2.3) 4.91** SS61 SUNDANCEWYOMING SANDSTONE (POR=12.5) 3.51(( SS62 CHUGWATER,WYOMING SANDSTONE 1(POR=17.4)3.78/3.93=4.11(( (AXIAL PRESSURE) SS63 2 3.43=3.81(( SS64 TORPEDOOKLAHOMA SANDSTONE 2.08 2.42'2.71 3.62 3.81.. SS43 STEVEN SANDKERN CO.,CAL. SANDSTONE 2.51 4*15'4.45 5.42 5.56....~ SS44 MCKEE SANDSTONE. 3.30.. 3.70 3.75 3.75-3.75.... SS41 USSR 94 SANDSTONE 2.18 2.94.. 3.30.. 3.52.... SS08 USSR 204 SANDSTONE. 2.95.. 3.25 3.43 3.50 3.53.... SS39 USSR 205 SANDSTONE 2.14 3.22.. 3.46...... SS09 USSR 208 SANDSTONE 2.15 3.13.. 3.42.... ~. SS10 USSR 209 SANDSTONE. 4.90 * 4.95 5.05 5.20 5.30 5.30.~ ~ ~ SS40 USSR 213 GREYWACKE 2.679 5.4. 5.63 5.76 5.87. 5.98 * 6.04. 6.13 GYO1 NEW ZEALAND GREYWACKE 2.705 5.4.. 5.92 6.04 * 6.14. 6.20. 6.28 GY02 QUEBEC GREYWACKE 6 2.749 6.19. 6,21 6.23 6.27 6.30 6.33. GY03 PRIBRAM,CZECH. GREYWACKE U2-7 2.688 6.06 o 6.14 6.19 6.23 6.26 6.28.. GY04 PRIBRAM,CZECH. LIMESTONE 2.688.... 5.40 * 5.45 5.40 5.10 4.95 LS23 MANLIUSRAVENAN.Y. LIMESTONE PAR. 2.739. 5.74 5.90 5.98 6.06 6.11 6.14 6.17. * LS21 PERP 2.731. 6.05 6.13 6.17 6.28 6.32 6.39 6.37.. LS21 UPTON CO.,TEXAS LIMFSTONE 1(POR=0.47) 6.61** LS43 2 5.93** (AXIAL PRESSURE) LS44 CALICO 99

WILLOW RUN LABORATORlES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND LIMESTONF 2.656 5.97 6.00 6.03 6.05 6.08 6.11 6.12 6.13. LS01 SOLENHOFENBAVARIA LIMESTONE 2.543 5.5.. 5.59 5.54. 5.56... ~ LS02 SOLENHOFENBAVARIA LIMESTONE 2.602. *. 5.20 * 5.30 5.30 4.85 4.75 LS22 SOLENHOFENBAVARIA LIMESTONE 1 5.06/5.64((5.67* LS24 2 5.57( (AXIAL PRESSURE) LS28 SOLENHOFENBAVARIA LIMESTONE 2.581 5.56 5.76 LS45 SOLENHOFENBAVARIA LIMESTONE 2.62 4.78.... ~. 6.45.. LS20 USSR 246 LIMESTONE * 5.12 5.44=5.67*5.82..... LS19 USSR DOLOMITE 2.844 5.6.. 6.98 7.03 * 7.09 * 7.14. 7.22 0002 RUTLAND,VT. DOLOMITF 2.845 6.06'6.30 6.77 6.93 7.06. 7.17. 7.23 7.30 7.36 D005 DUNHAM,WILLIAMSTOWNMASS. DOLOMITE 2.58 4.69 * 4.92*.. ~ ~ ~ ~ ~ D001 USSR 1745 MINERALS ORTHO- AND RING SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND OLIVINE GROUP MONTICELLITE 3.014 7.10'7.13 7.23*7.27 7.31. 7.36 * 7.40 7.45 7.50 M002 CRESTMORECAL. GARNET GROUP GROSSULARITE 3.561 6.3.. 8.41 8.55. 8.72 * 8.83. 8.99 GTO1 CONNECTICUT ALMAND.-PYROPE 3.950 5.9.. 7.81 7.91. 7.99 * 8.01 * 8.07 GT02 AL2SI05 GROUP SILLIMANITE X 3.189 9.04'9.09 9.22*9.25 9.30. 9.35. 9.39 9.42 9.45 SI02 Y 3.179 9,55'9.57 9.67*9.71 9.75 9.80 9.85 9.88 9.91 SI02 Z 2.194 9.60'9.62 9.66*9.70 9.75 9.79 9.81 9.82 9.84 SI02 WILLIAMSTOWNAUSTRALIA OTHERS IDOCRASE 3.144 5.52'5.62 6.21*6.54 6,95. 7.27 * 7.40 7.47 7.54 ID02 CRESTMORECAL. 100

WILLOW RUN LABORATORIES SINGLE CHAIN SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND PYROXENE GROUP JADEITE 3.33 8.60..... 8.86+... 9.01$JDO1 BURMA JADEITE 3.331 8.45.. 8.67 8.69 * 8.72 * 8.75. 8.78 JD03 BURMA JADEITE 3.180 7.6.. 8.21 8.22. 8.23. 8.24. 8.28 JD04 JAPAN PYROXENOID GROUP WOLLASTONITF 2.873 5.03'5.67 6.98 7.21 7.42. 7.56. 7.64 7.68 7.71 WOO1 FRAMEWORK SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SI02 GROUP FUSED SILICA 2.213 5.97....... 5.53 QU02 ALKALI FELDSPARS MICROCLINE 001 2.571 6.43'6.73 7.28*7.43 7.53. 7.58 7.60 7.60 7.62 MI02 010 2.570 7.67'7.82 8.21*8.25 8.29. 8.33 * 8.37 8.40 8.45 MI02 100 2.571 4.65'4.83 5.12*5.18 5.22. 5.28. 5.31 5.35 5.38 MI02 LABRADOR NON-SILICATES OXIDES MAGNESIA 3.580 9.77 9.78 9.79 MSO1 BERKELEY SYNTHETIC ALUMINA 3.822 10.45 10.55 AAO1 AD-99-SYNTHETIC ALUMINA 3.972 10.85 10.85 10.85 10.86 10.86 AA02 G.E. LUCALOX HEMATITE 5.0 7.1.. 7.72 7.73. 7.74. 7.76. 7.80 HEOl MAGNETITE 4.54 5.9.. 6.32 6.41. 6.52 * 6.58. 6.67 MGO1 TRANSVAAL MAGNETITE 4.532 2.3.. 6.65 6.75. 6.85. 6.92. 6.98 MG02 TAHAWUSN.Y. MAGNETITE 4.866 3.8.. 6.77 6.90. 6.99. 7.04. 7.11 MG03 PORT HENRYN.Y. SULFATES ANHYDRITE 2.928 4.8.. 6.00 6.06. 6.15. 6.19. 6.27 AHl1 CARBONATES ARAGONITE 2.917 5.7.. 5.82 5.85. 5.90 * 5.93, 5.97 ARO1 MEXICO MAGNESITE 2.802 6.92'6.97 7.08*7.11 7.19. 7.27 * 7.33 7.39 7.45 MN02 101

WILLOW RUN LABORATOR RIES Appendix 3 SHEAR VELOCITY VERSUS PRESSURE (10 bars to 10 kb) (SOURCFS FOR DATA ARF LISTED IN APPENDIX 8) (VFLOCITY oJNITS=KrM./SEC. COLUMN HEADINGS ARE PRESSURES IN UNITS OF KILOFBARS) (ALL MEASUREMENTS AT TEMPERATURES OF 0-30 DEGREES CENTIGRADE) EXPLANATION OF SPECIAL SYMBOLS IN APPENDIXES 2-3 (ALL PRESSURES ARE + OR - 3 PERCENT) SYMBOL EXPLANATION.01 PRESSURE=O.000-0.025 KILOBARS ~~' ~ PRESSUR E=O.025-0.050 KILOBARS ) PRESSURE=0.070 KILOBARS / PRESSURE=0.170 KILOBARS -~= ~ PRESSURE=O.200 KILOBARS )) PRS.PRESSURE=0.300 KILOBARS ( PRFSSURE=. 345 KILORARS ({( PRFSSURE=0.400 KILOBARS ** PRESSURE=0.470 KILOBARS * PRESSURE=0.600 KILOBARS // PRESSURE=0.900 KILOBARS $ PRESSURE=9.000 KILOBARS + ADD 0.5 KILOBARS TO COLUMN HEADING ~~- ~ SUBTRACT 0.5 KILOBARS FROM COLUMN HEADING ++ ADD.1.0 KILOBARS TO COLUMN HEADING ~ — ~ SUBTRACT 1.l KILOBARS FROM COLUMN HEADING (SYMBOLS IMMEDIATELY FOLLOW THE READINGS TO WHICH THEY APPLY) ROCKS IGNEOUS ROCKb ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND OVFRSATURATED GRANITE 2.636 2.77 3.27 3.36 3.44 3.51 3.54 3.58 GR37 WESTERLY,R.I. GRANITE 2.615, 3.50=3.52 3.55 3.57 3.58 3.59 3.59... GR44 WESTERLY R.I. GRANITE 2.64 2.28. 3.28 3.37..... GR80 WESTERLY.R. I GRANITF 3.47 GR56 WESTERLY,R.I. GRANITE 2.629. 3.34=3.43 3.44 3.46 3.47 3.48 3.50.. GR43 QUINCY,MASS. GRANITE 2.64 2,53. 3.45 3.53.. 3.61... GR78 QU INCY MASS. GRANITE 3.61 GR53 QUINCYMASS. 102

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND GRANITE 2.638 3.07 3.47 3.54 3.61 3.68 3.71 3.77 GR38 ROCKPORTMASS. GRANITE 2.62 2.55 * 3.42 3.50.. 3.58.... GR79 ROCKPORTMASS. GRANITE 2.62... 3.48... ~ GR50 ROCKPORTMASS. GRANITE 3.59 GR52 ROCKPORTMASS. GRANITE 2.62...... 3.60.. * GR49 CHELMSFORD~MASS. GRANITE 3.59 GR55 CHELMSFORDMASS. GRANITE 3.47 GR54 LYNNFIELD,MASS. GRANITE 2.665 2.79 3.35 3.48 3.52 3.64 3.67 3.70 GR40 BARREVT. GRANITE 2.65.... 3.59+..... GR48 BARREVT. GRANITE 3.59 GR57 BARREVT. GRANITE 2.634. 3.31=3.46 3.56 3.63 3.66 3.67 3.68. GR45 WOODBURYVT. GRANITE 2.639 2.43 3.36 3.53 3.66 3.74 3.76 3.80 GR39 STONE MT.,GA. GRANITE PINK 2.636. 3.27=3.35 3.35 3.39 3.38 3.36 3.37 3.39. GR46 LLANO CO.,TEX. GRANITE GREY 2.609. 3.42=3.55 3.58 3.59 3.60 3.61 3.61 3.61 3.62 GR47 LLANO CO.,TEX. GRANITE 2.610 3.04'3.23/3.40 3.47... GR42 BEAR MT.,TEX. GRANITE 2.87 2.96 3.11 3.16 3.21 3.22 3.23 3.23 GR41 BARRIEFIELDONT. GRANITE 3.55 GR58 BARRIEFIELD.ONT. GRANITE 3.61 GR59 LATCHFORDONT. GRANITE 3.59 GR51 ENGLEHARTONT. GRANITE 2.62 3.07 3.13=3.17*3.23.... GR06 USSR 137 GRANITE ~ 2*90 * 3.16 3.30 3.4U 3.40-3.40-.. GRO4 USSR 247 GRANITE. 3.50 * 3.57 3,63 3.63-..... GR05 USSR 248 GRANITE. 3.63.. 3.85 3.85 3.85 3.85+... GR77 USSR 249 GRANITE 2.62 2.93 3.05// GR09 USSR 1776 QTZ MONZONITE 2.628 2.89'3.09/3.20 3.23... QM03 WESTERLYR.I. QTZ MONZONITE 2.652 3.16 3.55 3.63 3.71 3.78 3.81 3.86 QMO1 PORTERVILLE,CAL. 103

W ILLOW'RU-N LABORATO R I E S ROCK RHO *01 0.1 0.5 1 2 3 4 5 6 8 10 IND GRANODIORITE - 263 3.14 3.45 3.51 3.56 3.58 3.58 3.58 3.59 3.59 3.60SGD02 WESTON MASS. GRANODIORITE 3.58 GD03 MASS. GRANODIORITE 3.56 GD04 QUEBEC QUARTZ DIORITE 2.81.... 3.59..... QD06 SAN LUIS REY QUAD.,CAL. QTZ DIORITE 2.928 3.39 3.65 3.69 3.74 3.78 3.81 3.84 QD05 DEDHAMMASS. TONALITE 2.76 3.12 3.45 3.55 3.60 3.63 3.64 3.65 3.65 3.66 QD04 VAL VERDECAL. TONALITE 3.64 QD07 VAL VERDECAL. SATURATED SYENITE 2.79 2.43. 3.26 3.31 3.34 3.35 3.36.... SY03 PENINSULA ST.,ONT. TRACHYTE 2.712 3.05=3.08 3.09 3.1U 3.11 3.11 3.11 TA01 DIORITE 3.025:3.06'3.17/3. 30 3.33... DTO1 SALEM MASS. ALBITITE- 2.615 3.43 3.54 3.57 3.61 3.65 3.68 3.73 AB02 SYLMARPA. ALBITITE 2.62 3.32 3.37 3.39 3.42 3.43 3.44 AB03 SYLMAR PA. ALBITITE 2.62.... 3.50. ~ AB04 SYLMARPA. ANDESITE 2.618 2.73'2.78/2.83 2.84..... AD4 SALIDAtCOLO. GABBRO 3.033 3.27 * 3.83 3.91.. 3.98.:.. NG18 FRENCH CREEK.PA. GABBRO 2.90 3.37 * 3.67 3.68 * 3.71.. ~. NG19 MELLENWISC. GABBRO 2.90. ~ ~... ~ 3.76 NG14 MELLENWISC. GABBRO 2.885 3.42=3.45 3.47 3.52 3.52 3.53 3.53 3.54 NG12 DULUTH.MINN. GABBRO 2.933 * 3.56=3.59 3.65 3.69 3.71 3.71 3.71 3.72. NG13 GABBRO 2.993 * 3.47=3.48 3.50 3.51 3.51 3.52 3.53 3.54. NG11 SAN MARCOSCAL. GABBRO 2.874 3.59 3.70 3.73 3.76 3.79 3.82 3.84 NG08 SAN MARCOSCAL. NORITE 3.057 3.24'3.38/3.58 3.63...... NG10 ESSEX CO.,N.Y. NORITE 2.86 3.16. 3.61 3.64.. 3.71.... NG17 SUDBURY,ONT NORITE 2.984 3,56 3.81 3.84 3.86 3.89 3.90 3.94 NG09 PRETORIATRANS. ANORTHOSITE 2.750 3.56 3.65 3.69 3.72 3.76 3.77 3.81 AN06 STILLWATER MONT. ANORTHOSITE 2.74 3.59 3.67 3.68 3.68 3.68 3.69 3.69 3.70 3.70$AN07 STILLWATER.MONT. ANORTHOSITE 2.74....... 371- * AN08 STILLWATERMONT. 104

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND DIABASE 2.962 3.76 * 3.83 3.84.. 3.88... * DB18 VINAL HAVEN,ME. DIABASE 2.984 3.49. 3.64 3.68 3.72. 3.75. 3.77. 3.80 DB12 CENTREVILLE,VA. DIABASE 3.017 3.71. 3.75 3.77 3.79. 3.81 * 3.82. 3.85 DB13 FREDERICKMD. DIABASE 3.013 3.67. 3.77 3.79.. 3.83... DB19 FREDERICKMD. DIABASE 2.96..... 385.... ~* B14 FREDERICKMD. DIABASE 2.989 3.52. 3.65 3.71..... DB20 KEWEENAWANONTARIO DIABASE 3 2.903 3.61. 3.64 3.66 3.68 3.69 3.70.. DB16 PRIBRAM,CZECH. DIABASE 7 2.879 3.49. 3.55 3.58 3.60 3.61 3.61. DB 17 PRIBRAMCZECH. DIABASE 3.04 3.75 3.79=3.82*3.87..... B01 USSR 3 BASALT 2.586 3.21=3.23 3.25 3.26 3.26 3.27 3.27 3.27 BA06 CHAFFEE CO.,COLO. BASALT 2.82 2.53 2.57 2.60/ BA05 GUADALUPE MOHOLE SITE BASALT 2.88 3.34 3.36=3.39*3.42...... A03 USSR 4 BASALT 2.63 3.10 3.40// BA02 USSR ULTRAMAFIC DUNITE 3.198. 3.79=3.88 3.99 4.10 4.13 4.15 4.17.0 DU16 BALSAM GAP,N.C. DUNITE 3.275 4.12. 4.44 4.48 4.53 4.55... * DU19 BALSAM GAPN.C. DUNITE 3.265 4.40 DU18 BALSAM GAPqN.C. DUNITE 3.264 4.01 4.25 4.28 4.30 4.33 4.36 4.40 DUll WEBSTER,N.C. DUNITE 3.160. 4.19). 4.46. 4.55 4.53 4.53 DU15 TWIN SISTERS MT.,WASH. DUNITE 3.326 4.60 4.67 4.69 4.72 4.77 4.79 4.83 DU13 TWIN SISTERS MT., WASH. DUNITE 3.270 4.17 4.34 4.37 4.41 4.45 4.48 4.54 DUl2 MT. DUNNEW ZEALAND DUNITE 3.250 4.41+ DU17 MT.DUNNEW ZEALAND DUNITE 3.760 3.68 3.76 3.77 3.80 3.83 3.86 3.90 DU14 MOOIHOEK MINE,TRANS. PERIDOTITE 3.28 4.02.. 4.18.. 4.22... PE04 USSR 455 PERIDOTITE 3.21 3.66. ~ 3.95 * * 4.00 ~* * PE03 USSR 462 105

WILLOW RUN LAB'ORATOrRIESROCK RHO.01 0.1 U.5 1 2 3 4 5 6 8 lu IND PYROXENITE 3.24 3.90 4.U5 4.u6 PX01 USSR 457 PYROXENITE 3.15 3.50 3.58 3.66 PX05 USSR 468 PYROXENITE 3.29 4.14 4.22 4.22 PAU2 USSR 469 PYROXENITE 3.22 3.26 3.66 3.bu PAU3 USSR 470 PYROXENITE 3.24 3.60 3.75 3.75 PX04 USSR 472 BRONZITITE 3.287 4.48 4.54 4.56 4.58 4.62 4.63 4.66 BR03 STILLWATER, MONT. BRONZITITE 3.27 4.50 4.57 4.58 4.59 4.59 4.6U 4.60 4.61 4.62$bR04 STILLWATER, MONT. BRONZITITE 3.272 4.50 * 4.54 4.55 4.58 *... bR06 STILLWATER.MONT. BRONZITITE 3.27 4.58 BR05 STILLWATER, MONT. BRONZITITE 3.289 4.37 * 4.50 4.50. 4.55.... bR07 BUSHVELDTRANSVAAL SERPENTINITE 2.806 3.61 3.69 3.70 3.73 3.77 3.80 3.83 SE09 LUDLOWVT. SERPENTINITE 2.718 3.12 3.17 3.18 3.20 3.23 3.24 3.28 SE08 CAL. CHRYSOTILE 2.602 2.71 2.79 2.81 2,82 2,85 2.87 2.90 SE07 THETFORD,QUE. GLASSES OBSIDIAN 2.440 3.53... 3.49.... OB02 MODOC,CAL. MEIAMORPHIC ROCKb ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SCHIST-CHLOR 2.95 3.34. 3.49 3.55 3.63 3.69 3.73 3.76... SC12 FRAMINGHAMMASS. SCHIST-CHLOR. -...... 3.73... SC16 FRAMINGHAMMASS. SCHIST 1 2.70 3.02. 3.47 3.61 3.71 3.76 3.78... SC13 FRAMINGHAMMASS. SCHIST-1 0.........15 FRAMINGHAM,MASS. SCHIST 2 2.73 2.76. 3.42 3.57 3.63 3.66 3.68 3.69... SC14 FRAMINGHAMMASS. SCHIST-CHLOR..... 3.65.. SC17 QUEBEC SLATE 2.67 2.89.. 2.98 3.07 3.14 3.19... * bL05 EVERETT,MASS. SLATE..... 3.19 * oL7 EVERETTMASS. 106

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND GNEISS PAR 2.64 1.85 * 3.24 3.46... ~ ~. GN29 PERP 2.64 1.73. 3.15 3.32 * 3.56.... GN29 PELHAMMASS. GNEISS...... 3.43... GN22 PELHAM,MASS. GNEISS 2.91 3.42 3.51 3.54 3.57...... GN17 SOLOMON'S PONU,MASS. GNEISS...... 3.59.... GN19 SOLOMON'S POND,MASS. GNEISS PAR 2.65 2.49 * 3.29 3.47 3.55..... GN16 PERP 2.65 2.62. 3.41 3.48 3.52 3.55 3.57 3.58... G,16 HELL GATE,N.Y. GNEISS.... 3.61.... GN18 HELL GATEN.Y. GNEISS-GARNET...... 3.57... GN2u QUEBEC GNEISS...... 3.63.... G 21 QUEBEC MARBLE 2.71 2.71. 3.42 3.48.. 3.51.... MA57 PROCTOR,VT. MARBLE 2.71..... 3.48..... MA1U PROCTOR,VT. MARBLE *. 2.82)3.10(3.17 3.12+3.21 21 1 3.25.. MA08 DANBYRUTLANDVT. MARBLE PERP C. 3.96 4.25=4.40*4.51....... MAll PAR C. 3.87 4.23=4.46*4.49....... MAll YULECOLO. QUARTZITE 2.647..... 4.03 4.05.. QZ11 GEORGIA OUARTZITE...... 4.07. * * * QZ14 PENNSYLVANIA QUARTZITE * 3.40.. 3.70 3.73-3.72-. *~ ~ ~ QZ15 USSR 22 AMPHIBOLITE 3.070 3.90 * 4.13 4.18 4.21. 4.25 * 4.27. 4.30 AM05 MADISON CO.,MUNT. AMPHIBOLITE 3.14...... 4.22.... AM06 MADISON CO.,MONT. ECLOGITE 3.444 4.26. 4.39 4.43 4,48. 4.53. 4.55. 4.58 EC0 3 HEALDSBURGCAL. ECLOGITE 3.28... 4.59... EC12 HEALDSBUKG,CAL. ECLOGITE 3.360 3.83. 4.15 4.22 4.27. 4.33 * 4.35 * 4.38 EC06 OCCIDENTAL,CAL. ECLOGITE 3.44....... 4.32 4.35 ECll OCCIDENTAL,CAL. ECLOGITE 3.28..... 4.59... EC13 CAL. ECLOGITE 3.577 4.07. 4.36 4.41 4.47. 4.52 * 4.55 * 4.60 EC04 NORWAY-1552 ECLOGITE 3.578 3.70 * 4.38 4.46 4.52. 4,58 * 4.61 * 4.66 LC05 NORWAY-1553 107

WILLOW RUN LABORATORIES -. SEDIMENTARY ROCKS ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SANDSTONE 2.61 3.04 * 3.24 3.34 3.4U.... ~ SS07 BROOKLINE,MASS. SANDSTONE,.... 3.40 * * * SS20 BROOKLINEMASS. SANDSTONE 2.66 3.39 * 3.85 3.99. * 4.08 *.. ~ SS46 ALLENTOWN,'PA. SANDSTONE 2.543 * 2.51 2.70 2.85 2.95 2.96 2.98 2.97. SS11 CAPLEN DOME,GALVESTON CO.TEX. SANDSTONE 1(POR=19.0)1.58'2.03=2.17(( SS65 2 2.15)) (AXIAL PRESSURE) SS66 BEREAOHIO SANDSTONE 1.92'2.26 2.35/ (DIFFERENTIAL PRESSURE) SS52 BEREA SANDSTONE 1.83'2.15 2.32/ (NET OVERBURDEN PRESSURE) SS48 BEREA SANDSTONE * 1.74'1.95 2.08/ * *. * *.. * SS15 BEREA SANDSTONE (POR=3.3) 3.47** SS58 ORISKANYPENNSYLVANIA SANDSTONE 1(POR=17.4)2.10/2.13=2.22(( (AXIAL PRESSURE) SS63 2 2.26/2.32=2.40(( 564 TORPEDO,OKLAHOMA SANDSTONE. 1.99'2.12 2.25/.... SS18 TORPEDO SANDSTONE 2.04'2.22 2.31/ (NET OVERBURDEN PRESSURE) SS50 TORPEDO SANDSTONE (POR=15.3) 2.41(( SS55 TENSLEEPWYOMING SANDSTONE * 1.75'1.94 2.06/..... SS17 TENSLEEP SANDSTONE 1 (POR=7.4) 2.51(( SS56 2 2.64 (AXIAL PRESSURE) SS57 FOX HILLS,WYOMING SANDSTONE (POR=23.5) 2.16)) SS59 JELMgWYOMING SANDSTONE (POR=29.7) 1.87)) SS60 TEAPOTWYOMING SANDSTONE (POR=2.3) 2.71** SS61 SUNDANCEgWYOMING SANDSTONE (POR=12.5) 2.34(( SS62 CHUGWATER,WYOMING SANDSTONE * 2.16'2.37 2.44/.... SS14 BANDERA SANDSTONE 2.1012.24 2.32/ (NET OVERBURDEN PRESSURE) SS49 BANDERA SANDSTONE 1.78'1.83 1.87/ (NET OVERBURDEN PRESSURE) SS51 AUSTIN SANDSTONE. 2.05'2.19 2.22/.... SS16 SEMINOLE SANDSTONE * 2.30'2.57 2.66/..... SS19 WEBER 108

WILLOW RUN LABORATORIES ROCK RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND SANDSTONE. 2.15 * 2.20 2.23 2.30 2.31 2.30 ~.. ~ SS41 USSR 94 SANDSTONE 2.18 1.89.. 2.04.. 2.21.... SS08 USSR 204 SANDSTONE. 1.90. 2.00 2.05 2.20 2.21 2.20.... SS39 USSR 205 SANDSTONE 2.14 1.92.. 2.09...... SS09 USSR 208 SANDSTONE 2.15 1.94.. 2.09....... SS10 USSR 209 SANDSTONE. 3.07.. 3.18 3.35 3.43 3.43... ~ SS40 USSR 213 GREYWACKE 6 2.749 3.90. 3.94 3.97 4.02 4.06 4.08.. GY03 PRIBRAM,CZECH. GREYWACKE U2-7 2.688 3.61. 3.63 3.65 3.68 3.69 3.71.. GY04 PRIBRAM,CZECH. LIMESTONE 2.69 3.15 3.27 3.29 3.32 3.33 3.34 LS03 NAZARETHPA. LIMESTONE 3.34 L526 NAZARETHPA. LIMESTONE 2.688..... 2.95. 3.01 3.02 2.93 2.77 LS23 MANLIUSRAVENA,N.Y. LIMESTONE PAR 2.739 3.06 3.13 3.13 3.19 3.22 3.22 3.24 LS21 PERP 2.731 3.13 3.21 3.24 3.28 3.29 3.30 3.29 LS21 UPTON CO,TEX. LIMESTONE 1 3.05** LS43 2 2.86** (AXIAL PRESSURE) LS44 CALICO LIMESTONE 2.656 2.88 2.95 2.99 3.01 3.02 3.03 3.05 3.04 LS01 SOLENHOFENBAVARIA LIMESTONE 2.602. ~.. 2.95. 3.00 3.05 2.95 2.90 LS22 SOLENHOFENBAVARIA LIMESTONE. 2.62'2.69 2.70/........ LS27 SOLENHOFENBAVARIA LIMESTONE 2.605 2.75 * 2.91 2.98.. 3.08 ~... LS41 SOLENHOFEN, BAVARIA LIMESTONE 1 2.77/2.90((2.95* LS24 2 3.03( (AXIAL PRESSURE) LS28 SOLENHOFEN,BAVARIA LIMESTONE 3.08 LS25 SOLENHOFENBAVARIA LIMESTONE * 2.87 2.92=2.98*3.02.... LS19 USSR DOLOMITE 2.83 3.52. 3.87.90 3.94..... D03 BETHLEHEM,PA. DOLOMITE....... 4.0... D004 BETHLEHEM,PA. DOLOMITE 2.58 2.72. 2.80*........ Dool USSR 1745 109

WILLOW RUN LABORATORIES MINERALS ORTHO- AND RING SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND OLIVINE GROUP MONTICELLITE 2.975 3.85. 3.90 3.94 3.97. 4.00 * 4.02. 4.06 MO01 CRESTMORE,CAL. AL2SIO5 GROUP SILLIMANITE 3.187 4.93 * 5.04 5.06 5.08. 5.11. 5.13 * 5.15 SIO1 WILLIAMSTOWNAUSTRALIA OTHERS IDOCRASE 3.140 3.13. 3.63 3.80 3.96. 4.12. 4.19. 4.28 ID01 CRESTMORE,CAL. SINGLE CHAIN SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND PYROXENE GROUP JADEITE 3.33 5.04..... 5.21+ 5.35$JD01 BURMA JADEITE 3.203 4.65. 4.71 4.72 4.75. 4,78. 4,79. 4.82 JD02 JAPAN NON-SILICATES MINERAL RHO.01 0.1 0.5 1 2 3 4 5 6 8 10 IND OXIDES MAGNESIA 3.580 5.96 5.98 5.98 MSO1 BERKELEY SYNTHETIC ALUMINA 3.972 6.37 6.37 6.38 6.38 6.38 6.38 AA02 G.E. LUCALOX SULFIDES PYRITE 4.85 3.81 * 3.87 3.92 3.96 3.98 4.00.... PRO1 NORANDA MINES.QUE. CARBONATES MAGNESITE 2.848 4.05 * 4.08 4.11 4.14, 4.19 * 4.23 * 4.29 MNO1 110

WILLOW RUN LABORATORIES Appendix 4 COMPRESSIONAL VELOCITY VERSUS TEMPERATURE (25~C to 600~C) (SOURCES OF DATA LISTED IN APPENDIX 8) (VELOCITY UNITS=KM./SEC. COLUMN HEADINGS ARE TEMPERATURE IN UNITS OF DEGREES CENTIGRADE. PRES=PRESSURE OF MEASUREMENTS IN UNITS OF KILOBARS.POR=POROSITY) EXPLANATION OF SPECIAL SYMBOLS IN APPENDIXES 4-5 SYMBOL EXPLANATION 25 TEMPERATURE=0-30 DEGREES CENTIGRADE + ADD 50 DEGREES TO COLUMN HEADING SUBTRACT 50 DEGREES FROM COLUMN HEADING ROCK RHO 25 100 200 300 400 500 600 PRES POR INDEX ANDESITE 2.618 5.310 5.273 5.251-.... 1.0 AD04 SALIDA,COLO. BASALT 2.586 5.80 5.79 5.80 5.79... 4.0 * BA06 CHAFFEE CO.,COLO. DIORITE 3.025 6.301 6.232 6.196-... 1.0 * DT01 SALEM MASS. DUNITE 3.160 8.956 8.892 8.886 8.784.. 4.0 * DU15 TWIN SISTERS MT.,WASH. DUNTTE 3.198 7.86 7.83 * 7.40.. 4.0 * DU16 BALSAM GAPN.C. GRANITE 6.429 6.428 6.387 5.796 4.0 GR41 BARRIEFIELDONT. GRANITE 2.610 6.232 6.183... 1.0 GR42 BEAR MT..TEX. GRANITE 2.629 6.38 6.34... 4.0 * GR43 QUINCY,MASS. GRANITE 2.615 6.18 6.18... 4.0. GR44 WESTERLYR. I. GRANITE 2.634 6.29 6,26 6.20 6.04... 4.0 * GR45 WOODBURYVT. GRANITE PINK 2.636 6.50 6.47 6.38 6.25... 4.0 GR46 LLANO CO.,TEX. GRANITE GREY 2.609 6.25 6,18 6.14 6,00 * * 4.0 * GR47 LLANO CO.,TEX. JADEITE 3.33 9.01 8.97 8.90 8.78 8.74 8.67. 9.0. JD01 BURMA LIMESTONE 2.656 6.123 6.023 5.910 5.866... 4.0 * LSO1 SOLENHOFENBAVARIA LIMESTONE PERP 2.739 6.135 6.032 5.980.... 4.0. LS21 PAR 2.731 6.344 6.257 6.160.. 40 LS21 UPTON CO.,TEX. MARBLE * 6.673 6.602 6.468. * * 4.0 * MA08 DANBYVT, MARBLE PERP C. 6.68 6.61 6.17... 1.. MA11 PAR C. 6.67 6.53 6.13.. 1. MAll YULE COLO. 111

WILLOW RUN LABORATORIES ROCK RHO 25 100 200 300 400 500 600 PRES POR INDEX NORITE 3.057 6.877 6.851 6.831-... 1.0 * NG10 ESSEX CO.,N.Y. GABBRO 2.993 7.01 6.98 6.99 6.95 6.62.. 4.0 * NG11 SAN MARCOSCAL. GABBRO 2.885 6.81 6.73 6.64 6.52 *.. 4.0 NG12 DULUTHMINN. GABBRO 2.933 6.86 6.85 6.82 6.76... 4.0 NG13 QTZ MONZONITE 2.628 5.998 5.981 5.892-. *.. 1.0 * QM03 WESTERLYR.I. FUSED SILICA 2.20 5.97 6.02 6.08 6.13 6.18 6.22 0.0 QU05 FUSED SILICA 6.10 6.11 6.12 6.13 6.14 6.16 6.17 0.0 QU06 SANDSTONE 2.543 5.279 5.295 5.225.. 4.0 5.1 SS11 CAPLEN DOMEGALVESTON CO.,TEX. SANDSTONE 2.514 5.533 5.518... 4.0 9.0 SS12 TRAVIS PEAKMARION CO.,TEX. TRACHYTE 2.712 5.76 5.69 5,68 5.62.. 4.0 * TAO1 112

WILLOW RUN LABORATORIES Appendix 5 SHEAR VELOCITY VERSUS TEMPERATURE (25~C to 600~C) (SOURCES OF DATA LISTED IN APPENDIX 8) (VELOCITY UNITS=KM./SEC. COLUMN HEADINGS ARE TEMPERATURE IN UNITS OF DEGREES CENTIGRADE. PRES=PRESSURE OF MEASUREMENTS IN UNITS OF KILOBARS.POR=POROSITY) EXPLANATION OF SPECIAL SYMBOLS IN APPENDIXES 4-5 SYMBOL EXPLANATION 25 TEMPERATURE=0-30 DEGREES CENTIGRADE + ADD 50 DEGREES TO COLUMN HEADING SUBTRACT 50 DEGREES FROM COLUMN HEADING ROCK RHO 25 100 200 300 400 500 600 PRES POR INDEX ALBITITE 2.62 3,496 3,469 3.443 3.414 3.377 3.370 * 3.0 * AB04 SYLMARPA. ANDESITE 2.618 2.844 2.825 2.818- ~ ~ ~ ~ 1.0 * AU04 SALIDAgCOLO. AMPHIBOLITE 3.14 4.224 4.200 4.175 4.151... 5.0 * AM06 MONTANA ANORTHOSITE 2.74 3.712 3.695 3.677 3.660 3.641 3.621 7.5 * AN08 STILLWATER MONT. BASALT 2.586 3.27 3.24 3.24 3.23... 4.0 BA06 CHAFFEE CO.,COLO. BRONZITITE 3.27 4.58 4.54 4.51 4.47 4.43 4.39. 80 * BR05 STILLWATER MONT. DIABASE 2.96 3.85 3.81..... 3.0. DB14 FREDERICK,MD. DIORITE 3.025 3.322 3.312 3.277-.... 1.0. DTO1 SALEM,MASS. DUNITE 3.160 4.533 4.526 4.492 4.433... 4.0 DU15 TWIN SISTERS MT..WASH. DUNITE 3.198 4.15 4,11 3.79.... 4.0 * DU16 BALSAM GAPN.C. DUNITE 3.249 4.406 4.332 4.263 4.194 4.123.. 8.5. DU17 MT.DUN,NEW ZEALAND DUNITE 3.263 4.396 4.340 4,284 4.231 4.180 4.113. 6.0 * DU18 BALSAM GAP,N.C. ECLOGITE 3.44 4.348 4,326 4.267 4.184 4.106 4.017, 6*0 * EC1l OCCIDENTAL CAL. ECLOGITE 3.28 4.585 4,558 4,532 4.505 4.479 4.452 4,425 5.0 * EC12 HEALDSBURGCAL. GRANITE 3.231 3.243 3.196 4.0 GR41 BARR I EFIELD,ONT. GRANITE 2.610 3.474 3.327... 1.0 * GR42 BEAR MT..TEX. GRANITE 2.634 3.67 3,66 3.63.... 4.0 GR45 WOODBURY,VT. GRANITE PINK 2.636 3.36 3.36 3.35... 4.0 GR46 LLANO CO.,TEX. GRANITE GREY 2.609 3.61 3.60 3.59.... 4.0 GR47 LLANO CO.,TEX. 113

WILLOW RUN LABORATORIESROCK RHO 25 100 200 300 400 500 600 PRES POR INDEX GRANITE 2.65 3.59 3.57 3.56 3.54 3.53 3.51 3.46 3.5 * GR48 BARREVT. GRANITE 2.62 3.596 3.577 3.549 3.508.. 5.0 * GR49 CHELMSFORDMASS. GRANITE 2.62 3.48 3.46 3.43 3.40 3.34 3.26 3.15 4.0 * GR50 ROCKPORTqMASS. JADEITE 3.33. 5.37 5.32. 5.13 9.0 * JD01 BURMA LIMESTONE 2.656 3.046 3.004 2.961.... 4.0 LSO1 SOLENHOFENBAVARIA LIMESTONE PERP 2.739 3.222 3.181 3.176... 4.0 * LS21 PAR 2.731 3.296 3.274 3.244.... 4.0 LS21 UPTON CO.,TEX. MARBLE. 3.209 3.146 3.106.... 4.0 MA08 DANBYVT. MARBLE 2.71 3.483 3.438 3.387 3.334.. * * MA10 PROCTORVT. MARBLE PERP C. 4.51 4.29 4.11.... 1.. MAll PAR C * 4.49 4.27 4.14.... 1. * MAll YULECOLO. NORITE 3.057 3.632 3.558 3.529-.... 4.0 NG10 ESSEX CO.,N.Y. GABBRO 2.993 3.52 3.53 3.53 3.52 3.42.. 4.0 NG11 SAN MARCOSCAL. GABBRO 2.885 3.53 3.48 3.46 3.44... 4.0 NG12 DULUTHMINN. GABBRO 2.933 3.71 3.71 3.71 3.68.. 4.0 * NG13 GABBRO 2.90 3.758 3.717 3.672 3.616 3.552 3.477. 5.0 * NG14 MELLENWISC. OTZ DIORITE 2.81 3.59 3.57 3.54... 3.0 QD06 SAN LUIS REY QUAD.*CAL. QTZ MONZONITE 2.628 3.229 3.226 3.181-.... 10 * QM03 WESTERLYR. I. FUSED SILICA 2.20 3.76 3.79+ 3.81 0.0 QU05 QUARTZITE 2.647 4.095 4.037 4.027 4.015 3.998 3.974 3.937 4.0 * QZ11 GEORGIA SANDSTONE 2.543 2.975 2.969 2.944.... 4.0 5.1 SS11 CAPLEN DOME,GALVESTON CO.,TEX. TRACHYTE 2.712 3.11 3.11 3.10 3.05 *.* 4.0 * TA01 114

WILLOW RUN LABORATORIES Appendix 6 PETROGRAPHIC MODAL ANALYSES OF CERTAIN ROCKS IN APPENDIXES (QTZ=QUARTZ. PLAG=PLAGIOCLASE, K-SPAR=POTASSIUM FELDSPAR. AMPH=AMPHIBOLE. PYROX=PYROXENE. OLIV=OLIVINE. ) KEY FOR MINERALS IN THE ANALYSES OF APPENDIX 6 AB ALBITE EN ENSTATITE MU MUSCOVITE AC ACTINOLITE EP EPIDOTE OL OLIGOCLASE AE AEGIRITE FA FAYALITE OM OMPHACITE AL ALMANDITE GR GROSSULARITE OR ORTHOCLASE AN ANORTHITE HO HORNBLENDE ORTHO ORTHORHOMbIC AU AUGITE HY HYPERSTHENE PG PIGEONITE BI BIOTITE ID IDOCRASE PR PYRITE BR BRONZITE IL ILMENITE PY PYROPE CA CALCITE KY KYANITE QU QUARTZ CH CHLORITE MG MAGNETITE UR URALITE CO CORDIERITE MI MICROCLINE SE SERPENTINE CT CHERT MO MONTICELLITE SP SPESSARTITE DI DIALLAGE MONO MONOCLINIC ST STAUROLITE DO DOLOMITE MP MICROPERTHITE TR TREMOLITE DP DIOPSIDE CARB CARBONATES FRAG FRAGMENTS OF CLAY MATERIALS ROCK QTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF AB01 99 AN12 1 AC 2 AB02 AB03 AB04 AD01 35 35 OR 5 HO 20 AU 5 MG 7 AD02 X AN05 X CH 23 AD04 X AN60 X AU X MG 8 AM01 15 35 AN33 45 HO 6 AM04 75 MONO 6 SE 1 AM05 11 ORTHO 8 ORE AM06 AM07 3 19 AN49 73 HO 1 BI 6 17 AM08 4 26 AN42 70 HO 1 BI 2 17 AM09 5 11 AN32 50 HO 34 EP 17 AM10 3 3 AN33 47 HO 47 EP 17 AN02 93 AN80 7 BR 1 AN06 AN03 86 AN80 14 BR 1 AN04 1 94 AN60 5 2 AN08 99 AN85 1 2 BA03 50 AN40 35 AU 10 MG 11 BA04 BA06 60 AN60 5 10 MG 9 10 SE,10 CA BR01 4 HO 94 BR 2 1 BR03 BR05 BR06 115

WILLOW RUN LABORATORIES... ROCK QTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF 8R02 4 AN80 2 HO 92 BR 2 1 BR07 CK03 26 4 52 MP 4 8 4 BI 1 15 CK04 29 15 47 MP 2 1 6 BI 15 CK05 30 15 36 MP 8 2 6 BI 1 15 CK06 27 41 12 MP 19 1 BI 15 CK07 5 40 3 MP 19 HO 31 1 2 BI 15 CK08 3 38 2 MP 13 HO 37 7 BI 15 CK09 2 29 69 EN 15 CK10 14 5 HO 61 6 EN 15 CK11 28 52 HO 19 1 BI 15 CK12 46 38 AN18 8 OR 6 HY 1 BI 1 CK13 49 15 35 MP 1 BI 15 CK14 53 14 34 MP 15 CK15 6 40 9 MP 5 HO 35 5 BI 15 CK16 3 37 16 MP 37 6 BI 15 CK17 4 42 4 MP 31 HO 17 3 BI 15 CK18 3 44 1 MP 32 HO 20 1 BI 15 CK19 2 50 37 HO 11 1 BI 15 DB01 50 10 HO 25 MONO 15 MG 13 DB02 DB03 DB04 25 38 BI 20 ST 6 10 MG DB08 45 AN95 3 45 AU 2 BI 5 1 DB12 DB09 66 AN54 32 AU 2 1 DB10 70 AN50 18 AU 1 2 BI 9 1 DB11 48 AN67 24 AU 1 1 BI 1 DB13 25 HY DB14 DB19 DB15 66 AN34 32 AU 2 MG 2 DB16 34 AN60 17 AU 46 UR 16 DB17 30 AN60 17 AU 50 UR 16 DB21 72 AN60 10 AU 10 3 BI 3 24 DB18 2 HY D004 1 99 DO 4 D006 1 1 98 CARB 25 DT01 X AN30 X X AU 8 DU05 78 FA10 19 SE 1 DUll DU06 97 FA09 3 SE 1 DU12 DU17 DU07 1 HO 97 FA08 2 SE 1 DU'16 DU18 DU19 DU08 80 FA12 19 SE 1 DU09 7 EN 92 FA12 1 SE 1 DU13 DU15 116

WILLOW RUN LABORATORIES ROCK QTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF DU10 90 FA55 10 1 DU14 EC02 X X HO X X RU 23 EC06 63 HO 20 4 MU 13 3 ECll EC07 20 HO 20 HY 12 10 BI 35 EP 1 (AL48PY45GR6AD1) EC08 70 OM 25 5 1 (AL30PY7) EC09 55 OM 26 1 (AL52PY26GR18AD4) EC10 72 OM 24 4 1 EC03 (AL57PY12GR19ADO1SP2) EC12 GDO1 27 40 AN30 23 OR 7 BI 2 CH 1 GD02 34 28 AN15 30 MP 3 MU 4 MG 12 GN09 20 15 AN34 5 15 BI 17 KY 6 25 CO GN10 40 36 AN24 10 BI 6 GN11 21 65 12 BI 2 20 GN12 9 75 16 BI 20 GN14 20 40 AN33 20 OR 16 BI 4 1 GN17 23 53 AN30 21 BI 5 12 GN19 GN23 32 23 AN20 39 MI 5 BI 1 MU 17 GN24 22 26 AN23 41 MI 10 BI 1 MU 17 GN25 21 56 AN31 3 MI 12 HO 7 BI 1 17 GN26 20 46 AN33 17 HO 17 BI 1 17 GN27 9 50 AN35 22 HO 18 BI 1 17 GN28 39 32 AN32 21 BI 4 MU 17 GN29 73(+AB+OR) 13 MI 12 BI 2 24 GN30 GR06 30 25 40 5 BI 19 GR07 GR08 28 68 8 BI 6 20 GR22 25 15 50 MI 11 7 GR23 33 57 OR 5 4 PR 7 GR24 32 5 58 MI 6 7 GR25 28 31 AN20 35 MI 3 BI 1 MU 1 GR37 GR44 GR56 GR26 26 13 AN05 50 MP 10 1 1 GR43 GR53 GR78 GR82 GR27 28 64 MP 6 2 1 GR38 GR50 GR52 GR79 GR84 GR28 26 38 AN05 32 OR 4 MU 1 GR39 117

- WILLOW RUN LABORATORIES' ROCK OTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF GR29 31 31 AN20 31 MI 4 MU 2 CH 1 GR49 GR55 GR30 28 14 AN20 54 OR 1 CH 1 GR31 26 37 AN05 25 OR 9 BI 3 MU 1 GR40 GR48 GR57 GR32 26 27 AN20 41 3 BI 3 1 GR33 20 70 OR 2 BI 5 CH 1 GR41 GR58 GR34 30 19 47 OR 4 1 GR36 27 51 AN05 17 OR 5 1 GR59 GR42 X. X X MI X 8 GR45 40 17 AN20 28 MI 10 BI 5 MU 18 GR46 25 30 AN30 45 MI 18 GR47 20 20 AN20 55 MI 5 BI 18 GR80 19 40 AN05 33 6 BI 1 MG 24 GR81 12 16 AN05 65 MP 4 3 24 GR87 X X X BIX MU 28 GR88 28.9 29 GR89 15.6 29 GY03 2 42 23 EP 16 30 FRAGMENT HBO1 1 2 42 AU 38 FA35 2 BI 9 SE 1 ID01 4 DI 60 ID 4 I002 36 CA LAO1 100 AN57-60 26 LA02 100 AN53 27 LA03 100 AN56 27 LS22 96 CA 22 4 MN LS23 1 99 CA 22 LS45 96 CA 30 MA08 99 CA 5 MA09 MA57 1 99 CA 24 MA58 MI01 21 AN10 79 OR 26 MOO1 83 MO 4 M002 17 CA NGO1 10 37 AN50 5 28 HY 16 BI 4 10 NG04 NG03 X X HY X 23 NG05 72 AN60 14 DI 11 1 BI 2 1 NG14 NG19 NG06 53 AN60 1 46 PG-AU-HY 1 NG09 NG07 51 AN65 32 AU 1 BI 1 1 NG18 15 HY 1 NG21 NG08 55 AN60 35 HO 10 MG 9 NG11 118

WILLOW RUN LABORATORIES ROCK QTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF NG10 X AN60 X HO X HY X X 8 NG12 70 AN80 5 AU 20 5 MG 9 NG13 40 AN55 35 HO 15 8 BI 2 MG 9 NG16 60 30 10 MG 13 OL01 98 AN12 2 AC 1 OL02 100 AN15-16 26 OL03 100 AN24 27 OL04 100 AN29 27 PEO1 14 25 56 5 10 PE04 PE02 15 20 60 2 20 PE03 10 AN60 21 61 6 10 PXO1 9 AN60 85 5 1 10 PX02 1 80 17 2 10 PX03 16 76 5 3 10 PX04 8 61 25 3 10 PX05 20 AN60 75 5 10 PX06 1 93 DP 5 FA15 2 SE 1 QDO1 28 50 AN45 7 HO 15 BI 1 1 QD04 QD02 19 50 AN50 13 HO 17 BI 1 QD06 QD03 13 48 AN20 6 21 HO 12 1 QD05 QM01 34 33 AN30 27 OR 4 BI 2 1 QM02 QM03 X X AN90 XX XX 8 QM04 X XBI X MU 28 QZ11 99+ 3 QZ12 96 1 1 MI 2 CA 17 QZ13 69 20 AN27 10 BI 1 17 SC12 27 36 CH 12 SC16 SC13 57 10 AN29 5 MP 19 MU 6 EP 12 SC15 SC14 59 9 AN11 4 MP 20 MU 4 EP 12 SC18 29 35 AN22 5 30 81 1 MG 17 SC19 8 23 AN25 2 14 BI 27 KY 17 23 MU 3 MG SC20 35 15 AN26 1 13 BI 19 KY 17 15 MU 2 MG SC21 44 13 AN25 2 23 BI 3 ST 17 13 MU 1 MG SE06 10 50 SE 13 30 CA SE14 15 70 SE 4 15 DO SE26. 25 75 14 5503 96 7 SS04 92 7 SS15 84 1 2 7 CT 21 SS65 2 CA SS66 SS18 90 1 CT 21 SS63 4 SS64 119

WILLOW RUN LABORATORIES - ROCK QTZ PLAG K-SPAR AMPH PYROX OLIV GARNET MICA OTHER REF SS42 94 2 2 2i SS17 SS55 SS46 80 5 MP 7 MG 24 SS47 1 MI SS56 45 12 1 7 23 CA 21 SS57 10 CT SS58 97 21 5559 82 6 3 4 CT 21 SS60 77 1 3 2 4 CT 21 SS61 43 2 2 MI 50 CA 21 3 CT SS62 75 2 2 15 CA 21 SY02 84 OR 13 AU 2 1 BI 1 SY03 TA01 18 AN60 60 OR 14 3 MG 9 5 ANALCIME REFERENCES FOR PETROGRAPHIC MODAL ANALYSES IN APPENDIX 6 REF. NO. REFERENCE 1 BIRCHF. J.GEOPHYS.RES. V.6591083-110291960 2 BIRCHF. AND H.CLARKAM.J.SCI.*V.2389529-558,613-63591940 3 BIRCHF.,BULL.GEOL.SOC.AM.,V.54,263-2681943 4 SIMMONSG.,J.GEOPHYS.RES.,V69 1117-1121 1964 5 ROBERTSONE.C. BULL.GEOL.SOC.AM. V.6691275-1314,1955 6 VOLAROVICHM.P. ET AL*,BULL.ACAD.SCI.USSRNO.8,712-716,1964 7 AUBERGERM.AND J.S.RINEHARTgJ.GEOPHYS.RES.*V.669191-199,1961 8 HUGHESD.S. AND H.J.JONES,BULL.GEOL.SOC.AM.,V.61,843-856,1950 9 HUGHES,D.S. AND C. MAURETTEGEOPHYSICS,V.22,23-31,1957 10 AFANASYEVG.D.,ET AL.AKAD.NAUK SSSR DOKLADY.V.155,NO.5,1058-1061,1964 11 VOLAROVICHM.P.,Z.I.STAKHOVSKAYA,BULL.ACAD.SCI.USSRNO.5,329-335,1958 12 BIRCHF. AND D.BANCROFT,J.GEOL..,V. 48,752-766,1940 13 TOMASHEVSKAYA,I.S.,BULL.ACAD.SCI.USSRNO.3,281-284,1961 14 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1-188,132-133,1964 15 BALAKRISHNA,S. AND SUBRAHMANYAM,Y.,CURRENT SCI*,V.31,NO.2,62-63,1962 16 PROS,Z.,ET AL,STUDIA GEOPHYS. ET GEOD.,CZECH.,V.6,NO,4,347-368,1962 17 CHRISTENSEN,N.,J.GEOPHYS.RES., TO BE PUBLISHED 18 HUGHESgD.S. AND C. MAURETTE,GEOPHYSICSV.219277-284,1956 19 FANG,WEI-CHING,BULL.ACAD.SCI.USSRNO.10,1004-1008,1961 20 VOLAROVICH,M.P.,ET AL,AKAD.NAUK SSSR DOKLADYV.157,NO.6,1349-1351,1964 21 GREGORY,A.R.,PROC.ROCK MECH.SYMP.,5TH,439-471,PERGAMON PRESS,1963,N.Y. 22 AHRENS,T.J. AND S.KATZ,J.GEOPHYS.RES.,V.68,529-538,1963 23 PRASADA RAO,G.H.S.V.,PROC.IND.ACAD.SCI.,V.25A,238-246,1947 24 ZISMAN,W.A.,PROC.NATL.ACAD.SCI.U.S.,V.19,653-665,1933 25 ZISMANW.A.,PROC.NATL.ACAD.SCI.U.S.,V.19,666-679,1933 26 ALEXANDROV,5.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.2,129-13191962 27 RYZHOVA,T.V.,BULL.ACAD.SCI.USSR,NO.7,633-635,1964 28 WOEBER,A.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 29 SHIMOZURU,D.,JAP.J.GEOPHYS.,V.2,NO.3,85 PP.,1960 30 GREGSONV.G.,ET ALAFCRL63-662,STANFORD RES.INST.,FINAL REPT.,1963 120

WILLOW RUN LABORATORIES Appendix 7 CHEMICAL ANALYSES OF CERTAIN ROCKS IN APPENDIXES 1 THROUGH 5 ROCK SI02 AL203 FE203 FE 0 MG 0 CA 0 NA20 K20 H20 TI02 MN 0 REF AN03 47.5 32.3 0.7 0.4 0.4 16.0 1.9 0.4 0.2 0.2 1 AN04 53.7 27.2 0.3 1.4 0.5 11.3 3.8 0.7 0.8 0.1 1 BR01 54.7 1.8 0.5 9*2 30.2 2.2. * 0.5 0.2 1 BR03 BR05 BR02 55.4 1.6 * 9.4 32.5 0.5 * * ~ 0.1 0.2 1 BR07 55.30 2.20 0.45 10.05 29.80 1.80 0.30 0.10 0.10 0.15 8 DB07 52.5 15.1 0.8 10.7 5.2 6.9 5.5 1.4 1.8 1.0 * 1 DB08 52.3 15.2 1.9 8.6 6.5 11.0 2.1 0.7 0.6 1.1 0.2 1 DB12 DB09 52.7 14.1 2.0 9.8 6.4 9.4 2*6 0.9. * 0.4 1 DB10 49.9 16.3 13.5 6.2 6.6 1.8 2.3 0.8 1.5 * 1 DB11 51.3 15.1 1.1 9.3 8.0 11.4 2.0 0.3 0.4 0.8 0.2 1 DB13 DB14 DB19 D815 52.94 15.52 3.20 8.76 5,80 9.42 2.68 0.81 0.04 0.60 0.16 2 0818 48.24 18.12 1.25 6.70 9.41 11.84 2.56 0.26 0.66 0.82 0.08 8 DB21 DU05 40.9 0.1 8.3 50.1.. * 0.2 * 0.2 1 DU1 1 DU06 39.5 0.9 0.7 7.6 48.8.~ ~ 0.9 * 0.1 1 DU12 DU07 38*4 0.6 1.6 6.6 51.5 0.1 *.. 0.1 1 DU16 DU18 DU19 DU09 40.6 0.1 * 8.0 50.6 0.1 0.1 * 0.1 0.1 0.1 1 DU13 DU10 36.7 1.6. 38.0 22.2 0.5 0.3 *.. 1.1 1 DU14 DU17 37.40 1.54 1.89 6.36 49.92... 1*42 0.13 6 EC09 48.7 11.7 1.4 6.8 16.7 13.9 0.4 0.2 0.1. 1 EC10 48.6 14.0 3.5 9.4 6.6 11.9 3.9 0.2 0.6 1.1 0.3 1 EC03 EC12 GN15 72.5 13.3 1.9 0.6 0.4 1.8 3.6 3.9 1.5 0.3 1 GR25 72.2 14.4 0.9 1.0 0.4 1.4 3.3 5.5 0.4 0.3 1 GR37 GR44 GR26 74.9 11.6 2.3 1.3 0.1 0.4 4.3 4.6 0.3 0.2 * 1 GR43 GR78 GR27' 77.6 11.9 0.6 0.9 * 0.3 3.8 5.0 0.2 0.3 1 GR38 GR50 GR79 GR28 73.4 14.4 0.1 0.7 0.3 1.1 4.0 5.1 0.4 0.3 * 1 GR39 GR31 69.6 15.4 2.7 *, 1.8 5.4 4.3 1.0.. 1 GR40 GR48 121

WILLOW RU N LABORATORIES ROCK SI02 AL203 FE203 FE 0 MG 0 CA 0 NA20 K20 H20 TI02 MN 0 REF GTO1 39.1 19.6 3.7 1.7 0.2 34.9. ~ 0.1 0.2 0.4 1 GT02 36.3 20.2 0.1 32.0 4.8 2.0. ~* 2.5 1.7 1 GT03 35.4 21.0 * 19.1 0.1 0.4... 23.8 1 GTO4 36.3 21.0 * 37.1 3.6 1.5.... 0.4 1 HBO1 41.2 1.2 4.0 8.2 34.4 1.4 0.2 0.3 5.2 0.3 * 1 IDC1 37.41 17.89 3.16 6.47 4.80 33.78 0.35 * 0.62 * 1.52 3 ID02 JD02 58.5 23.5 0.5. 0.8 1.3 13.6 0.3 0.2.. 1 JD04 JD03 59.3 24.8 0.3 0.2 0.3 0.8 14*1 0.2... 1 MG01 1.2 1.6 65.7 12.0 0.5 U.2 U.1. U.7 16.3 0.5 1 NF01 43.42 31.29 0.29 1.72 0.05 0.72 14.93 6.50. 0.05 0.02 7 NF02 43.14 31.03 0.10 1.56 0.15 1.17 15.22 6.50. 0.06 0.02 7 NG07 52.80 13.04 0.31 8.74 9.98 11.94 1.61 0.48 0.31 0.84 0.19 1 NG18 NG14 47.62 22.48. 8.74 7.38 9.66 2.84 0.32 0.56 0.42 0.15 1 NG05 NG19 OB01 73.6 13.6 0.6 1.3 0.3 1.4 4.2 4.3. 0.3 * 4 OB02 OV01 41.2 8.0 49.7 0.1 0.1 1 SE26 37.75 1.79 4.15 3.64 36.61 1.99 0.43 12.43 0.04 0.09 5 SY02 55.8 14.7 2.6 9.0 1.0 4.6 4.6 4.8 0.8 0.7 * 1 SY03 REFERENCES FOR CHEMICAL ANALYSES IN APPENDIX 7 REF. NO. REFERENCE 1 BIRCHF. J.GEOPHYS.RES.,V.66,2199-2224,1961 2 BIRCHF. AND R.LAWgBULL.GEOL.SOC.AM.,V.46,1219-125091935 3 SIMMONSG.,J.GEOPHYS.RES.,V.69,1117-1121,1964 4 BIRCH,F. AND D.BANCROFTAM.J.SCI.,V.240,457-49091942 5 RIRCHF.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 6 BIRCHF.,BULL.GEOL.SOC.AM.,V.54,263-268,1943 7 RYZHOVA,T.V.AND K.S.ALEXANDROV,BULL.ACAD.SCI.USSRNO.2,1125-1127,1962 8 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 122

WILLOW RUN LABORATORIES Appendix 8 REFERENCES FOR DATA IN APPENDIXES 1 THROUGH 5 (FOR JOURNALS —AUTHORSPUBLICATION) (FOR BOOKS —AUTHORS,TITLE,PUBLISHERYEAR) (COMPLETE REFERENCES GIVEN IN MAIN BIBLIOGRAPHY OF PAPER) CROSS INDEX REFERENCE AAO1 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 AA02 SCHREIBERF.AND O.L.ANDERSONJ.AM.CERAMIC SOC.,TO BE PUBLISHED AA03 SOGA.N.SUMMARY TECH.REPT.,AFOSR 33(615)-17009LAMONT GEOL.OBS.,1965 ABO1 BIRCHF.,J.GEOPHYS.RES. V.6692199-2224,1961 AB02 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-113091964 AB03 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 AB04 BIRCHF. BULL.GEOL.SOC.AM. V.54,263-28691943 ABO5 RYZHOVAT.V.,BULL.ACAD.SCI.USSRgNO.7,633-63591964 AB06 WYLLIE,M.R.J.,ET AL,GEOPHYSICS,V.21,41-70,1956 ABO7 WOEBERA.F.,ET ALGEOPHYSICS,V.28,658-663,1963 ADO1 AU3ERGERgM. AND J.S.RINEHART,J.GEOPHYS.RES.*V.669191-199,1961 AD02 PRASADA RAO,G.H.S.V.,PROC*IND.ACAD.SCI.,V.25A,238-246,1947 AD03 SZEMEREDYP.,TUDOMANY EGYETEM ANNALESgSEC.GEOL.BUDAPESTV.1,89-95,1957 AD04 HUGHESD.S. AND H.J.JONES,BULL.GEOL.SOC.AM.,V.61,843-856,1950 AD05 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 ADC6 WOEBERA.F.,FT ALGEOPHYSICSV.28,658-663,1963 AD07 WOEBERA.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 ADO8 WOEBERA.F.,ET ALGEOPHYSICS,V.28,658-663,1963 AD09 WOEBER,A.F. ET ALGEOPHYSICSV.28,658-663,1963 AEO1 ALEXANDROVK.S.AND T.V.RYZHOVAgBULL.ACAD.SCI.USSRNO.9,871-875,1961 AHO1 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 AH02 WYLLIEM.R.J.,ET AL,GEOPHYSICSV.21,41-70,1956 AMO1 VOLAROVICHM.P.,ET ALBULL.ACAD.SCI.USSR,NO.8,712-716,1964 AM02 KRAVETSV.V.,AKAD.NAUK UKRAYINRSR DOPOVIDI,NO.3,295-298,1961 AM03 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO.JAPANKYOTO UNIVERSITY GEOPHYS. INST.*25-3291963 AM04 BIRCHF.,J.GFOPHYS.RES.,V.65,1083-1102,1960 AM05 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 AM06 BIRCH,F.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 AM07 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED AM08 CHRISTENSENN.I.,J.GEOPHYS.RES*,TO BE PUBLISHED AM09 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED AM10 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED AM11 WOOLARD,G.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNIONV.45,637,1964 AN01 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 AN02 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 AN03 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 AN04 BIRCH,F.,J.GEOPHYS.RES.,V.66,2199-2224,1961 AN05 BIRCH,F. J.GEOPHYS.RES.,V.66,2199-2224,1961 AN06 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 AN07 BIRCHF. AND D.BANCROFTJ.GEOL.,V.48,752-766,1940 AN08 BIRCHF.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 AN09 WOEBERA.F,ET AL,GEOPHYSICSV.28,658-663,1963 APO1 ALEXANDROV K.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.12,1165-1168,1961 ARO1 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-11021,960 AUO1 WOEBER,A.F.,ET ALGEOPHYSICS,V.28,658-663,1963 AZO1 ALEXANDROVK.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.2,129-131,1962 BAO1 BALAKRISHNAS.,TRANS.AM.GEOPHYS.UNIONV.39,711-712,1958 123

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE BA02 SILAEVAO.I.,BULL.ACAD.SCI.USSRNO.2,221-228,1959 BA03 FANG,WEI-CHINGBULL.ACAD.SCI.USSRNO.10,1004-1008,1961 BA04 VOLAROVICHM.P.,ET ALgBULL.ACAD.SCI.USSR,N0.8,1198-1205,1963 BA05 SOMERTONW.H.,ET AL,J.GEOPHYS.RES.,V.68,849-856,1963 BA06 HUGHES,D.S.AND C.MAURETTE,GEOPHYSICS,V.22,23-31,1957 BA07 WOOLARDG.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA08 WOOLARDG.P.AND M.H.MtANGHNANI TRANS.AM.GEOPHYS.UNIONV.45,637,1964 BA09 WOOLARD,G.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA10 WOOLARD,G.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA11 WOOLARD,G.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA12 WOOLARD,G.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNIONV.45,637,1964 8A13 WOOLARDG.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNIONV.45,637,1964 BA14 WOOLARDG.P.AND M.H.MANGHNANI TRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA15 WOOLARD,G.P.AND M.H.MANGHNANI TRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA16 WOOLARD,G.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA17 WOOLARDG.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNION,V.45,637,1964 BA18 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 BA19 WOFBERA.F. ET AL,GEOPHYSICS,V.28,658-663,1963 BA20 WOEBERA.F.,FT AL,GEOPHYSICS,V.28,658-663,1963 BA21 WOFBERA.F.,ET ALGEOPHYSICS,V.28,658-663,1963 BA22 WOEBERA.F.,ET ALGEOPHYSICSV.28,658-663,1963 BA23 WOEBER,A.F.,FT AL,GEOPHYSICS,V.28,658-663,1963 BA24 WOEBER,A.F.,ET ALGEOPHYSICS,V.28,658-663,1963 BI01 ALEXANDROV,K.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.12,1165-1168,1961 BR01 BIRCH,F. J.GEOPHYS.RES.,V.65,1083-110291960 BR02 BIRCH,F. J.GEOPHYS.RES,V.65,1083-1102,1960 BR03 SIMMONS,G. J.GEOPHYS.RES.,V.69,1123-1130,1964 BR04 BIRCH,F. AND D.BANCROFTJ.GEOL.,V.48,752-766,1940 BR05 BIRCHF. BULL.GEOL.SOC.AM.,V.54,263-286,1943 BRC6 BIRCH,F.AND D.BANCROFT,J.GEOL.,V.46959-87,1938 BR07 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87 1938 BYO1 WOEBER,A.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 CA01 BHIMASENACHARJ.,PROC.IND.ACAD.SCI.,V.22A9199-207,1945 CA02 WYLLIEM.R.J.,ET AL,GEOPHYSICS,V.21,41-7091956 CHC1 ALEXANDROV,K.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.12,1165-1168,1961 CHO2 ALFXANDROVgK.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.12,1165-1168,1961 CK01 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 CK02 BALAKRISHNA,S.,GEOL.SOC. INDIA JOUR. V.1,136-143,1959 CK03 BALAKRISHNA,S. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO*.262-63,1962 CK04 BALAKRISHNA,S. AND Y.SUBRAHMANYAM,CURRENT SCI*,V.31,NO.2,62-63,1962 CK05 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK06 BALAKRISHNAS. AND Y.SUBRAHMANYAMCURRENT SCI.,V.31,NO.2,62-63,1962 CK07 BALAKRISHNA,S. AND Y.SUBRAHMANYAMCURRENT SCI.,V.31,NO.2,62-63,1962 CK08 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CKOQ BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK10 BALAKRISHNA,S. AND Y.SUBRAHMANYAMiCURRENT SCI.,V.31,NO.2,62-63,1962 CK11 BALAKRISHNA,S. AND Y.SUBRAHMANYAMCURRENT SCI*,V.31,NO.2,62-63,1962 CK12 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 CK13 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI*,V.31,NO.2,62-63,1962 CK14 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK15 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK16 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK17 BALAKRISHNAS. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK18 BALAKRISHNA.S. AND Y.SUBRAHMANYAM,CURRENT SCI.,V.31,NO.2,62-63,1962 CK19 BALAKRISHNAS. AND Y.SUBRAHMANYAMCURRENI SCI*.V.31,NO.2,62-63,1962 CK20 KRISHNAMURTHIM.AND S.BALAKRISHNAPROC.IND.ACAD.SCI.V.38A,498-501,1953 124

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE CLO1 SUBBARAO,K. AND B. RAMACHANDRA RAO,NATURE,V.180,NO.4573,978,1957 DBO1 FANG,WEI-CHING,BULL.ACAD.SCI.USSR,NO.10,1004-1008,1961 DB02 VOLAROVICH,M.P.,ET AL,BULL.ACAD.SCI.USSR,NO.8,1198-1205,1963 DB03 VOLAROVICHgM.P.,ET ALAKAD.NAUK SSSR DOKLADY,V.157,NO.691349-1351,1964 DB04 VOLAROVICH,M.P.,ET AL,BULL.ACAD.SCI.USSR,NO.8,712-716,1964 DB05 BALAKRISHNAS.,PROC.IND.ACAD.SCI,V.36A,375-380,1952 DB06 PRASADA RAO,G.H.S.V.,PROC.INACADACAD.SCI,V25A,238-246,1947 DB07 BIRCHF. J.GEOPHYS.RES. V.65,1083-1102,1960 DB08 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 DBn9 BIRCH,F. J.GEOPHYS.RES. V.65,1083-1102 1960 DB10 BIRCHF.,J.GEOPHYS.RES* V65,1083-1102,1960 DB11 BIRCH,F.,J.GEOPHYS.RES.,V65,1083-1102,1960 DB12 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 DB13 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 DB14 BIRCH,F.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 DB15 BIRCHF.,J.GEOPHYS.RES. V.65,1083-1102,1960 DB16 PROS,Z.,ET AL,STUDIA GEOPHYS. ET GEOD.,CZECH.,V.69NO.4,347-36891962 DB17 PROSZ.,ET ALSTUDIA GEOPHYS. ET GEOD.,CZECH.,V.69NO.4,347-368,1962 DB18 BIRCHF.AND D.BANCROFT,J.GEOL.,V.46,59-87,1938 DB19 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46959-87,1938 DB20 BIRCH,F.AND D.BANCROFT,J.GEOL.,V.46,59-87,1938 DB21 IDEJ.M. PROC.NATL.ACAD.SCI.,V.229482-496,1936 DB22 KRISHNAMURTHIM.AND S.BALAKRISHNAPROC.IND.ACAD.SCI.V.38A,498-501,1953 DB23 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 DCO1 WOEBER,A.F.,ET ALGEOPHYSICS,V.28,658-663,1963 DO01 SILAEVA,O.I. BULL.ACAD.SCI.USSRNO.2,221-22891959 D002 BIRCH,F. J.GEOPHYS.RES.,V65,1083-1102,1960 D003 BIRCHF. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 0004 BIRCH,F. GEOL.SOC.AM.SPECPEC.PAPERNO62101-117,1955 D005 SIMMONS,G.,JGEOPHYS.RES.,V.69,1117-1121,1964 D006 IDEJ.M PROC.NATL.ACAD.SC I,V.22,482-496,1936 D007 WYLLIE,M.R.J.,ET AL,GEOPHYSICS,V.21,41-70,1956 DP01 WOFBER,A.F.,ET ALgGEOPHYSICS,V.289658-66391963 DT01 HUGHES,D.S. AND H.J.JONES,BULL.GEOL.SOC.AM.,V.61,843-856,1950 DT02 WOEBER,A.F.,ET AL,GEOPHYSICSV.28,658-663,1963 DUO1 PRASADA RAOG.H.S.V.,PROC.IND.ACAD.SCI.,V.25A,238-246,1947 DU02 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPANKYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 DU03 HAYAKAWAM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 DU04 BIRCH,F.,J.GEOPHYS.RES.,V65,1083-1102,1960 DUO5 BIRCHF.,J.GEOPHYS.RES.,V*65,1083-1102,1960 DU06 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 DU07 BIRCHF.,J.GEOPHYS.RES. V.65,1083-1102,1960 DU08 BIRCHF.,J.GEOPHYS.RES.,V.651083-1102,1960 DU09 BIRCH,F. J.GEOPHYS.RES. V.65,1083-1102,1960 DU10 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 DU11 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-11301964 DU12 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 DU13 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 DU14 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-11301964 DU1S HUGHESD.S. AND J.H.CROSS,GEOPHYSICS,V.16,577-593,1951 DU16 HUGHES,D.S.AND C.MAURETTE,GEOPHYSICS,V.22,23-31,1957 DU17 BIRCHF.,BULL.GEOL.SOC.AM.,V54,263-286,1943 DU18 BIRCH,F. BULL.GFOL.SOC.AM.,V.54,263-2861943 DU19 BIRCH,F.AND D.BANCROFT,J.GEOL.,V.46,59-87,1938 125

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE DU20 WOEBERA.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 DU21 SHIMOZURUD. JAP.J.GEOPHYS.,V.2,NO.3985PP.,1960 ECO1 HAYAKAWAM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 EC02 PRASADA RAOG.H.S.V.,PROC.IND.ACAD.SCI.,V.25A9238-246,1947 EC03 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 EC04 SIMMONSG.,J.GEOPHYS.RES.,V69,1123-1130,1964 EC05 SIMMONS,G. J.GEOPHYS.RES.,V.69,1123-1130,1964 EC06 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 EC07 BIRCH,F.,J.GEOPHYS.RES. V.65,1083-1102,1960 EC08 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 FC09 BIRCH,F.,J.GEOPHYS.RES,V.65,1083-1102,1960 EC10 BIRCH,F.,J.GEOPHYS.RES,V.65,1083-1102,1960 ECU1 BIRCH,F.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 EC12 BIRCH,F.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 EC13 BIRCHF.,GEOL.SOC.AM.SPEC.PAPERNO.62,101-117,1955 EC14 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 EC15 WOOLARDG.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNION,V.45,637,1964 EC16 WOOLARDG.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNIONV.45,637,1964 GAO1 BHAGAVANTAMS.AND J.BHIMASENACHAR,PROC.IND.ACAD.SCI.V.20A,298-303,1944 GDO1 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 GD02 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 GD03 BIRCHtF..GEOL.SOC.AM.SPEC.PAPERNO.62,101-117,1955 GD04 BIRCH,F.,GEOL.SOC.AM.SPEC.PAPERNO.62,101-11791955 GNO1 BALAKRISHNAS.,PROC IND.ACAD.SCI I.V.36A,375-380,1952 GN02 BALAKRISHNA,S.,GEOL.SOC. INDIA JOUR.,V.1i136-143,1959 GN03 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1l136-143,1959 GN04 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 GN05 BALAKRISHNA,S.,PROC IND.ACAD.SCI. V.49ANO.6,318-32191959 GN06 BALAKRISHNA,S.,PROC.IND.ACAD.SCI.,V.49A,NO.6,318-321,1959 GN07 BALAKRISHNAS.,PROC IND.ACAD.SCI.,V.49ANO.6,318-321,1959 GN08 PRASADA RAOG.H.S.V*,PROC.IND.ACAD.SCI.,V.25A,238-246,1947 GN09 VOLAROVICH,M.P.,ET ALBULL.ACAD.SCIUSSR,NO.8,712-716,1964 GN10 VOLAROVICH,M.P.,ET AL,BULL.ACAD.SCI.USSR,NO.8,712-716,1964 GNll VOLAROVICH,M.P.,ET ALAKAD.NAUK SSSR DOKLADY,V.157,NO.6,1349-1351,1964 GN12 VOLAROVICHM.P.,ET ALAKAD.NAUK SSSR DOKLADYV.157,NO.6,1349-1351,1964 GN13 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 GN14 BIRCHF.,J.GEOPHYS.RES*,V.65,1083-1102,1960 GN15 BIRCH,F.,J.GEOPHYS.RES. V.6591083-1102,1960 GN16 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 GN17 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 GN18 BIRCH,F.,GEOL.SOC.AM.SPAPC.PAPER,NO.62101-1171955 GN19 BIRCH,F.,GEOL.SOC.AM.SECAPC.PAPERNO.62101-1171955 GN20 BIRCHiF.,GEOL.SOC.AM.SPEC.PAPER,NO.62,101-117 1955 GN21 BIRCH,F.,GEOL.SOC.AM.SPAPC.PAPER,NO.62101-1171955 GN22 BIRCH,F.,GEOL.SOC.AM.SPAPC.PAPER,NO62101-1171955 GN23 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN24 CHRISTENSENN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN25 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN26 CHRISTENSENN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN27 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN28 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED GN29 BIRCH,F.AND D.BANCROFT,J.GEOL.,V.46,59-87,1938 GN30 IDEJ.M.,PROC.NATL.ACAD.SCI.,V.22,482-496,1936 GP01 WOEBERA.F.,ET ALoGEOPHYSICSV.28,658-663,1963 126

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE GROl HAYAKAWAM.IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 GR02 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 GR03 KNOPOFF,L.,TRANS.AM.GEOPHYS.UNION,V.35,969-973,1954 GR04 VOLAROVICHgM.P.,ET AL,DOKLADY ACAD.SCI.USSR,V.13591237-1239,1961 GR05 VOLAROVICHM.P.,ET ALDOKLADY ACAD.SCI.USSR,V.135,1237-123991961 GR06 FANG WEI-CHINGgBULL.ACAD.SC I.USSRNO.10,1004-100891961 GR07 VOLAROVICHgM.P.,ET ALBULL.ACAD.SCI.USSRNO.891198-120591963 GR08 VOLAROVICHM.P.,ET ALAKAD.NAUK SSSR DOKLADY,V.157,NO.6*1349-135191964 GR09 SILAEVAO.I.,BULL.ACAD.SCI.USSRNO.2,221-22891959 GR10 BALAKRISHNA.S. CURRENT SCI * V.21,NO.9241-242 1952 GR1l BALAKRISHNAS. PROC.IND.ACAD.SCI.,V.36A.375-38U,1952 GR12 BALAKRISHNAS.,TRANS.AM.GEOPHYS.UNIONV.39,711-71291958 GR13 PRASADA RAOG.H.S.V.,PROC.IND.ACAD.SCI.V. 25A238-246,1947 GR14 BALAKRISHNAS.,PROC.IND.ACAD.SCI *. V.36A375-38091952 GR15 BALAKRISHNAS.,TRANS.AM.GEOPHYS.UNION.V.39,711-71291958 GR16 BALAKRISHNA.S.,PROC.INDeACAD.SCI.* V.36A375-38091952 GR17 BALAKRISHNAS.,INDIAN MINERALOGISTgV.1,NO.1,57-59,1960 GR18 PRASADA RAOG.H.S.V. PROC.IND.ACAD.SCI.*.V.25A238-24691947 GR19 BALAKRISHNAS.,PROC.IND.ACAD.SCI. V.49AN0.69318-321 1959 GR20 BALAKRISHNA9S.,PROC.IND.ACAD.SCI.V.49ANO.6,318-321,1959 GR21 BALAKRISHNA S.,PROC.IND.ACAD.SCI. V.49A,NO.69318-321 1959 GR22 AUBERGERM. AND J.S.RINEHARTJ.GEOPHYS.RES.,V.66,191-199 1961 GR23 AUBERGERM. AND J.S.RINEHARTJ.GEOPHYS.RES. V.66,191-199,1961 GR24 AUBERGER.M. AND J.S.RINEHART,J.GEOPHYS.RES.oV.66,191-199,1961 GR25 BIRCH.F..J.GEOPHYS.RES. V.65,1083-1102 1960 GR26 BIRCHF. J.GEOPHYS.RES..V.6591083-110291960 GR27 BIRCHgF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 GR28 BIRCHF. oJ.GEOPHYS.RES..V.65 1083-1102 1960 GR29 BIRCHF. J.GEOPHYS.RES.,V.6591083-1102,1960 GR30 RIRCH,F. J.GEOPHYS.RES,V.65,1083-1102,1960 GR31 BIRCH,F.,J.GEOPHYS.RES, V.65,1083-1102,1960 GR32 BIRCH,F*.J.GEOPHYS.RES. V.65,1083-1102,1960 GR33 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 GR34 PIRCH,F. J.GEOPHYS.RES. V.65,1083-1102~1960 GR35 BIRCH, F.,J.GEOPHY.RES.,V.6591083-1102 1960 GR36 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-110291960 GR37 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 GR38 SIMMONS G.,J.GEOPHYS.RES. V.69,1123-1130,1964 GR39 SIMMONSG. J.GEOPHYS.RES.,V.69,1123-1130,1964 GR40 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-113o,1964 GR41 HUGHESD.S. AND J.H.CROSSGEOPHYSICSV.16,577-593,1951 GR42 HUGHESD.S. AND H.J.JONESBULL.GEOL.SOC.AM.,V.61,843-856,1950 GR43 HUGHESD.S.AND C.MAURETTEGEOPHYSICSV.21,277-284,1956 GR44 HUGHESgD.S.AND C.MAURETTE,GEOPHYSICS.V.21,277-284,1956 GR45 HUGHESD.S.AND C.MAURETTE GEOPHYS1CSV.21 277-284,1956 GR46 HUGHES,D.S.AND C.MAURETTEGEOPHYSICSV.21,277-284,1956 GR47 HUGHES,DoS.AND C.MAURETTE,GEOPHYSICSgV.21,277-284,1956 GR48 BIRCHF.BULL.GEOL.SOC.AM. V.54 263-286,1943 GR49 BIRCHF.,BULL.GEOL.SOC.AM.,V.54263-286,1943 GR50 BIRCH,F. BULL.GEOL.SOC.AM. V.54,263-286,1943 GR51 BIRCH,F.,GEOL.SOC.AM.SPCAPC.PAPERNO62,10-117,1955 GR52 BIRCH,F. GEOL.SOC.AM.SPPEC.PAPERNO62,101-117,1955 GR53 BIRCHF.,GEOL.SUC.AM.S'PEC.PAPERNO.6Z,101-117,1955 GR54 BIRCHF.,GEOL.SOC.AM.SPEC.PAPER,NO.629101-117,1955 127

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE GR55 BIRCH,F. GEOL.SOC.AM.SPEPEC.PAPER,NO621u-117,1955 GR56 BIRCH F. GEOL.SOC.AM.SPPEPAPERNO.62101-117,1955 GR57 BIRCHF.,GEOL.SOC.AM.SECAPC.PAPERN.62101-117,1955 GR58 BIRCHF. GEOL.SOC.AM.SPEC.PAPER,NO.629101-117,1955 GR59 BIRCH,F.,GEOL.SOC.AM.SPEC.PAPERNO.62,101-117,1955 GR60 KUBOTERA,A.,J.PHYS.EARTHV.2,33-38.1954 GR61 KUBOTERA,A.,JPHYS.EARTH,V.2,33-38,1954 GR62 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-38,1954 GR63 KUBOTERA,A. J.PHYS.EARIH,V.2,33-38,1954 GR64 KUBOTERA,A. J.PHYS.EARTHV.2,33-38,1954 GR65 KUBOTERA,A. J.PHYS.EARTH,V.2,33-38,1954 GR66 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38.1954 GR67 KUBOTERAA. J.PHYT,.EAKtHv*2,33-38,1954 GR68 KUBOTERA.A. J.PHYS.EARfHV.2,33-38,1954 GR69 KUBOTERAA. J.PHYS.EARTHV.2,33-38,1954 GR70 KUBOTERA,A. J.PHYS.EARTH,V.2,33-38,1954 GR71 KUBOTERA,A. J.PHY5.EARIHv.2,33-38,1954 GR72 KUBOTERA.A. J.PHYS.EARTH,V.2,33-38,1954 GR73 KUBOTERA,A. J.PHYS.EARTH,V. 2,33-381954 GR74 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 GR75 KUBOTERAA.,J.PHYS EARTH,V.2,33-38,1954 GR76 KUBOTERA,A.,J.PHYS EARTH,V.2,33-38,1954 GR77 VOLAROVICHMP.,ET AL,DOKLADY ACAD.SCI.USSR,V.135,1237-1239,1961 GR78 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 GR79 BIRCH,F.AND D.BANCROFI,J.GEOL.,V.46,59-87,1938 GR80 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 GR81 IDJ.M.,PROC.NATL.ACAD.SCI,V.22,482-49691936 GR82 IDEJ.M.,PROC.NATL.ACAD.SCI.,V.22,482-496,1936 GR83 IDEJ.M.,PROC.NATL.ACAD.SC I.V.22,482-49691936 GR84 IDE J.M. PROC.NATL.ACAD.SCI,V.22,482-496,1936 GR85 IDEJ.,PROC.NATL.ACAD.SC I.U.S.,V.22,482-4961936 GR86 KRISHNAMURTHI,M.AND S.BALAKRISHNAPROC.IND.ACAD.SCI.V.38A,498-501,1953 GR87 WOEBER,A.F. ET ALGEOPHYSICS,V.28,658-663,1963 GR88 SHIMOZURU,D.,JAP.J.GEOPHYS.,V.2,N0.3,85PP.,1960 GR8 SHIMOZURU,D.,JAP*JGEOPHYS.,V.2,N0.3,85PP.,196U GT01 BIRCH,F. J.GFOPHYS.RES.,V65,1083-1102,1960 GT02 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 GT03 VERMAR.K., J.GEOPHYS.RES. V.65,757-766,1960 GTO4 VERMAR.K. J.GEOPHYSRES.,V.6b,9757-766,1960 GYO1 BIRCHF.,J.GEOPHYS.RES.,V65,1083-1102,1960 GY02 BIRCHF., J.GEOPHYS.RKEs.v.65,1u83-11lu2196u GY03 PROS,Z.,ET AL,STUDIA GEOPHYS. ET GEOD.,CLECH.,V.6,NO.4,347-368,1962 GY04 PROS,Z.,ET ALSTUDIA GEOPHYS. ET GEOD.,CZECH.,V.6,NO.4,347-368,1962 HAC1 WYLLIE,M.R.J.,ET AL,GEOPHYSICS,V.21,41-70,1956 HB01 BIRCH,F. J.GEOPHYS.RES.,V.65,1083-1102,1 960 HEO1 BIRCH,F. J.GEOPHYS.RES.,V.65,1083-1102,1960 HE02 WOEBER,A.F. ET AL,GEOPHYbICs,V.28,658-663,1963 H001 ALEXANDROV,K.S.AND T.V.RYZHOVA,BULL.ACAD.SCI.USSR,NO.9,871-875,1961 H002 -ALEXANDROVK.5.AND I.v.RTHOvABuLL.ACAD.oCIuCJoRNO.9,871-875,1961 H003 WOEBER,A.F.,ET ALGEOPHYSICS,V.28,658-663,1963 ID01 SIMMONS,G,J.GEOPHYS.RES.,V.69,1123-1130,1964 ID02 SIMMONS,G..J.GEOPHYS.RES.,V.69 1117-1121,1964 JDO1 HUGHESD.S. AND t. NIbHIIAKE,IN GEUPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA,KYOTO,JAPAN,KYOTO UNIVERSITY GEOPIYS [NST.,379-385,1963 JD02 SIMMONSG., J.GEOPHYS.RES,V.69,1123-1130,1964 128

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE JD03 BIRCH F.,J.GEOPHYS.RES,V.65,1083-110291960 JD04 BIRCHF. J.GEOPHYS.RES,V.65,1083-1102 1960 KA01 SUBBARAO,K. AND B. RAMACHANDRA RAO,NAuREv.18uNO.4573,97891957 KA02 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 LAO1 ALEXANDROVqK.S.AND T.V.RYZHOVA,BULL.ACAD.SCI.USSR*NO.29129-131,1962 LA02 RYZHOVA,T.V. *BULL.ACAD.SCI.USSRNO.7633-635tI964 LA03 RYZHOVAT.V.BULL.ACADoCI u.,o,9. 7633 635,1964 LMO1 WOEBERgA.F. ET ALGEOPHYSICS,V.28,658-663,1963 LSO1 HUGHESD.S. AND J.H.CROSSGEOPHYSICSV.16,577-593,1951 LS02 BIRCHF.,J.GEOPHYS.RES*.V.65,1083-1102,1960 LS03 BIRCH,F. AND U.BANtKUr i J.LUL.V'.'9 /^' 1o09.L+U LS04 AUBERGERM. AND J.S.RINEHARTJ.GEOPHYS.RES.,V.66,191-199,1961 LS05 BALAKRISHNAS.,PROC.INDAADACASCI IV.41A912-1591955 LS06 BALAKRISHNA9S.,PROC.IND.ACAD.SC I,V.36A,375-380,1952 LSO7 BALAKRISHNAS. PROC.IND.ACAD.SCI.*V.41A912-15 1955 LS08 BALAKRISHNA~S.,PROC.IND.ACAD.SCI.V.50A,NO.6,363-36591959 LS09 BALAKRISHNAS.,PROC. IND.ACAD.SC I V.36A,375-38091952 LS10 PRASADA RAOG.H.S.V.,PROC.INDAADACAD.SCIV.25A238-246,1947 LS11 PRASADA RAOG.H.S.V. PROC.IND.ACAD.bCI. V.25A9238-24691947 LS12 BALAKRISHNA,S.,PROC.IND.ACAD.SCI.,V.49A,NO.6,318-321,1959 LS13 BALAKRISHNAs. PRUC. INACADACAD.CI,V.49AlU.4 6 318-321,1959 LS14 BALAKRISHNAS.,PROC.IND.ACAD.bCI,v.49ANO.6318-32191959 LS15 BALAKRISHNAS.,PROC.IND.ACAD*SCI.,V.50ANO.6,363-365,1959 LS16 BALAKRISHNAS.,PROC.INACADACASCI.,V.50ANO.6363-365,1959 LS17 RAMANAY.V.,J.SCI.INDu;.*REs.-INDIA. gv.9B,NU.11 446-4479196u LS18 SZEMEREDY,P.,TUDOMANY EGYETEM ANNALESSEC.GEOL.BUDAPESTV.1,89-95,1957 LS19 FANGWEI-CHI iN, (bULL ALAUJ. ~ uoo<.v ~.V lv I vu'- lvb, I 1bI LS20 VOLAROVICH,M.P.,ET AL,BULL.ACAD.SC I.USSRNO.81198-1205,1963 LS21 HUGHESD.S. AND J.H.CROSS,GEOPHYbICbV.16,577-593*1951 LS22 AHRENST.J.AND S. KATZJ.GEOPHYS.RES.,V.68,529-538,1963 LS23 AHRENST.J.AND S. KATZJ.GEOPHYS.RES.*V.68,529-53891963 LS24 WYLLIEM.R.J. ET AL GEOPHYSICSV.27 569-589 1962 LS25 BIRCHF.,GEOL.SOC.AM.SPECPEC.PAPERN0.62101-1171955 LS26 BIRCH,F. GEOL.SOC.AM.SECAPC.PAPERNO.62101-1171955 LS27 VOLAROVICHM.P.,ET ALBULL.ACAD.SCI.USSRNO.5,486-492*1959 LS28 WYLLIEM.R.J. ET ALGEOPHYSICSV.27,569-589*1962 LS29 PESELNICKgL. AND W.F.OUTERBRIDGEJ.GEOPHYS.RES.,V.66,581-588,1961 LS30 PESELNICKL. AND W.F.OUTERBRIDGEiJ.GEOPHYS.RES.,V.669581-58891961 LS31 KINGM.S. AND I.FATT,GEOPHYSICSV.279590-598,1962 LS32 KINGM.S. AND I.FATT~GEOPHYSICSV.27,590-598,1962 LS33 PESELNICK,L. ~ JGEurHT o.t\Eo, v.6 / 41 4441 4 1962 LS34 PESELNICKL.,JGEOPHYS.RES. V.67,4441-4448,1962 LS35 PESELNICKL., JGEOPHYS.RES. V.67,4441-4448 1962 LS36 PESELNICKL.*,JGEOPHYS.RES.,V,67,4441-4448,1962 LS37 PESELNICK,L.,J.GEOPHYS.RES.,V.67,4441-4448,1962 LS38 PESELNICKL.tJ.GEOPHYS.RES.,V.67,4441-4448,1962 LS39 PESELNICKL.,J.GEOPHYS.RES,V.67,4441-4448,1962 LS40 BALAKRISHNA,S. PROC.IND.ACAD.SCI * V.41A,12-15,1955 LS41 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 LS42 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.INDoACAD*SCI*V,38A,498-501,1953 LS43 GREGORY,A.R.,PROC.ROCK MECH.SYMP.,5TH,439-4719PERGAMON PRESS,N.Y.,1963 LS44 GREGORY,A.R.,PROC.ROCK MECH.SYMP.,5TH,439-471,PERGAMON PRESSN.Y.,1963 LS45 GREGSON,V.G.,ET AL,AFCRL63-662,51ANFORD RKEsINSI.,FINAL REPT.,1963 LT01 WOEBER.A.F. ET ALGEOPHYSICbSv.28,658-663,1963 MAO1 BALAKRISHNA,b. CUm^E, oC I.CI* v.28,;..._7,285,1959 MA02 BALAKRISHNA,5.,PROC.INDD.CACAD.C I., V36A,375-38u,1952 129

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE MA03 BALAKRISHNAS.,PROC.IND.ACAD.SCI.,V.36A,375-380,1952 MA04 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.V. 1,136-143,1959 MAO5 BALAKRISHNA,S.,PROC IND.ACAD.SCI.,V.50A,NO.6,363-365,1959 MA06 PRASADA RAO,G.H.S.V.,PROC.IND.ACAD.SCI.,V.25A,238-246,1947 MAC7 PRASADA RAOG.H.S.V.,PROC.INDU.ACAU.sL1*,V 2bA,238-24691947 MA08 HUGHES,D.S. AND J.H.CROSSGEOPHYSICS,V.16,577-593,1951 MA09 BIRCHIF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 MA10 BIRCHF.,BULL.GEOL.SOC.AM. V.54,263-286,1943 MAll TOOLEYR.D. J.GEOPHYS.RES.,V.6793604,1962 MA12 KUBOTERAgA. J.PHYS.EARTH,V*.233-3891954 MA13 KUBOTERAA.,J.PHYS.EARTHV.2933-3891954 MA14 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 MA15 KUBOTERAA. J.PHYS.EARTHV.2,33-38,1954 MA16 KUBOTERAgA. J.PHYS.EARTHV.2,33-38,1954 MA17 KUBOTERAA. J.PHYS.LAKTH.V.2,33 —38, 19!4 MA18 KUBOTERAgA. J.PHYS.EARTHV.2,33-3891954 MA19 KUBOTERAgA.,J.PHYS.EARTHV.2,33-38,1954 MA20 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 MA21 KUBOTERA,A.,J.PHYS.EAKTHV.2,33-38,1954 MA22 KUBOTERA,A.,J.PHYS.EARTHV.2,33-38,1954 MA23 KUBOTERAA.,J.PHYS.EARTH,V.2933-38,1954 MA24 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 MA25 KUBOTERAA.,J.PHYS.EAKIH,9V.2933-38 1954 MA26 KUBOTERA,A.,J.PHYS.EARTHgV.2,33-38,1954 MA27 KUBOTERAgA.,J.PHYS.EARTHV.2933-38 1954 MA28 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA29 KUBOTERAgA.,J.PHYS.EARTHgV.2,33-3891954 MA30 KUBOTERAA.,J.PHYS.EARTHV*2,33-38,1954 MA31 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 MA32 KUBOTERAA..J.PHYS.EARTHV.2,33-3891954 MA33 KUBOTERA,A.,J.PHYS.EARTHV*2,33-38,1954 MA34 KUBOTERA,A.,J.PHYS.EARTH,9V2,33-3891954 MA35 KUBOTERAgA.,J.PHYS.EARTHV.2,33-3891954 MA36 KUBOTERAA., J.PHYS.EARTH,V.2.33-38,1954 MA37 KUBOTERAA. J.PHYS.EARTHV.2,33-3891954 MA38 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA39 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA40 KUBOTERAA.,J.PHYS.EARTH,V.2,33-38,1954 MA41 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA42 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-38,1954 MA43 KUBOTERA,A.,J.PHYS.EARTHV.2,33-38,1954 MA44 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA45 KUBOTERAA.,J.PHYS.EARTH,V*2,33-38,1954 MA46 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-38,1954 MA47 KUBOTERA,A.,J.PHYS.EAKTH,V.2,33-38,1954 MA48 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-3891954 MA49 KUBOTERA,A.,J.PHYS.EARTHV.*233-38,1954 MA50 KUBOTERAA.,J.PHYS.EARTHV.2,33-38,1954 MA51 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-38,1954 MA52 KUBOTERA,A.,J.PHYS.EARTH,V*2,33-38,1954 MA53 KUBOTERAA.,J.PHYS.EAKTH,V.2,33-38,1954 MA54 KUBOTERA,A.,J.PHYS.EARTHV.2,33-38,1954 MA55 KUBOTERA,A.,J.PHYS.EARTH,V.2,33-38,1954 MA56 KUBOTERA,A.,J.PHYS.EARTHV.2,33-38,1954 MA57 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 MA58 IDEJ.M.,PROC.NATL.ACAD.SC I.,V.22,482-496,1936 130

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE MA59 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.*V38A,498-501,1953 MA60 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 MG01 BIRCHF..J.GEOPHYS.RES.,V.6591083-110291960 MG02 BIRCHF. J.GEOPHYS.RES.,V.65,1083-1102,960 MG03 BIRCHF. J.GEOPHYS.RES. V.65,1083-1102,1960 MG04 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 MG05 HIRASAWAgK.,BUTSURI-TANKO,V.15,72-84,(IN JAPANESE),1962 MIOl ALEXANDROVK.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSR*NO.2,129-131.1962 MI02 SIMMONSG.,J.GEOPHYS.RES. V.69,1117-1121.1964 MI03 WOEBER9A.F.,ET ALGEOPHYSICS,V.28,658-66391963 MN01 SIMMONSG.,J.GEOPHYS.RES.,V.69.1123-1130,1964 MN02 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1117-1121,1964 MO01 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 M002 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1117-1121,1964 MSO1 ANDERSONO.L.AND E.SCHREIBERJ.GEOPHYS.RES.~TO BE PUBLISHEDOCT.e1965 MS02 ANDERSON,O.L.AND P.GLYNNJ.PHYS.CHEM.SOLIDSTO BE PUBLISHED MS03 SOGAN.,SUMMARY TECH.REPT.,AFOSR 33(615)-1700,LAMONT GEOL.OBS.,1965 MU01 ALEXANDROVK.S.AND T.V.RYZHOVA,BULL.ACAD.SCI.USSRgNO.1291165-1168,1961 NE01 RYZHOVAT.V.AND K.S.ALEXANDROVBULL.ACAD.SCI.USSRPT.291125-1127,1962 NE02 RYZHOVAT.V.AND K.S.ALEXANDROVBULL.ACAD.SCI.USSRPT.2*1125-1127,1962 NG01 AFANASYEV,G.D.gET ALAKAD.NAUK SSSR DOKLADYV.155,NO.591058-10611964 NG02 HAYAKAWAgM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 NG03 PRASADA RAOG.H.S.V.,PROC.IND.ACAD.SCI.,V.25At238-246,1947 NG04 VOLAROVICHM.P.,ET AL,AKAD.NAUK SSSR DOKLADYgV.157,NO.6,1349-1351,1964 NG05 BIRCHgF.gJGEOPHYS.RES.,V.65,1083-1102,1960 NG06 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-110291960 NG07 BIRCHF. J.GEOPHYS.RES~,V*65,1083-1102,1960 NG08 SIMMONSG.,J.GEOPHYS.RES.,V.691123-1130,1964 NG09 SIMMONSgG. J.GEOPHYS.RES. V.69,1123-113091964 NG10 HUGHESgD.S. AND H.J.JONES,BULL.GEOL.SOC.AM.,V.61,843-856,1950 NG11 HUGHES,D.S*AND C.MAURETTE,GEOPHYSICSV.22,23-311957 NG12 HUGHES.D.S.AND C.MAURETTEGEOPHYSICS.V.22,23-31,1957 NG13 HUGHESD.S.AND C.MAURETTEGEOPHYSICS,V.22,23-31,1957 NG14 BIRCHF.,BULL.GEOL.SOC.AM,V.54,263-286,1943 NG15 VOLAROVICH,M.P.,ET AL,DOKLADY ACAD.SCI.USSR,V.135,1237-1239,1961 NG16 VOLAROVICHM.P.,ET ALDOKLADY ACAD.SCI.USSR,V.135,1237-1239,1961 NG17 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 NG18 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 NG19 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 NG20 IDE,J.M.,PROC.NATL.ACAD.SCI.,V.22,482-496,1936 NG21 IDEJ.M.,PROC.NATL.ACAD.SCI.,V.22,482-496,1936 OB01 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 OB02 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 OB03 WOEBERA.F.,ET AL,GEOPHYSTCSV.28,658-663,1963 OL01 BIRCHgF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 OL02 ALEXANDROV,K.S.AND T.V.RYZHOVABULL.ACAD.SCI.USSRNO.2,129-131,1962 OL03 RYZHOVA,T.V.,BULL.ACAD.SCI.USSRNO.7,633-635,1964 OL04 RYZHOVAT.V.,BULL.ACAD.SCI.USSRNO.7,633-635, 964 OR01 WYLLIEM.R.J.,ET ALGEOPHYSICSV.21,41-70,1956 OV01 VERMAR.K.,J.GEOPHYS.RES.,V.65,757-766,1960 PE01 VOLAROVICHM.P.,ET ALAKAD.NAUK SSSR DOKLADYgV.157,NO.6,3139-1351,1964 PE02 VOLAROVICH,M.P.,ET AL,AKAD.NAUK SSSR DOKLADY,V.157,NO.6,1349-1351,1964 PE03 AFANASYEVG.D.,FT ALAKAD.NAUK SSSR DOKLADYV.155,NO.5,1058-10611964 PE04 AFANASYEV,G.D.,ET ALAKAD.NAUK SSSR DOKLADYV.155,NO.5,1058-10611964 131

WILLOW RUN LABORATORIESCROSS INDEX REFERENCE PE05 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 PE06 HAYAKAWAM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPANKYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 PE07 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 PE08 HESS,H.H.,TRANS.AM.GEOPHYS.UNION,V.40,340-345,1959 PE09 HESSH.H.,TRANS.AM.GEOPHYS.UNION,V.40,340-345,1959 PE10 HESS,HH.H.TRANS.AM.GEOPHYS.UNION,V.40,340-345,1959 PE11 HESS,H.H.,TRANS.AM.GEOPHYS.UNIONV.40,340-345,1959 PE12 HESSH.H. TRANS.AM.GEOPHYS.UNIONV.40,340-345,1959 PE13 WOEBFR,A.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 PH01 ALEXANDROV,K.S.AND T.V.RYZHOVA,BULL.ACAD.SCI.USSRNO.12,1165-1168,1961 PO1 VOLAROVICHM.P.,ET AL,BULL.ACAD.SCI.USSR,NO.8,712-716,1964 PRO1 BIRCH,F. AND D.BANCROFTJ.GEOL*,V.48,752-766,1940 PR02 SIMMONSG. AND F.BIRCH,J.APPL.PHYS.,V.34,2736-2738,1963 PR03 SIMMONSG. AND F.BIRCHJ.APPL.PHYS.,V.34,2736-2738,1963 PR04 SIMMONSG. AND F.BIRCHJ.APPL.PHYS.,V,34,2736-2738,1963 PRO5 BHAGAVANTAMS.AND J.BHIMASENACHAR,PROC.IND.ACAD.SCI.V.20A,298-303,1944 PR06 WOEBERA.F., ET AL GEOPHYS ICSV.28,658-663,1963 PR07 HIRASAWA,K.,BUTSURI-TANKO,V.15,72-84,(IN JAPANESE),1962 PR08 HIRASAWA,K.,BUTSURI-TANKO,V.15,72-84,(IN JAPANESE),1962 PTO1 WOEBER,A.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 PXO1 AFANASYEVG.D.,ET ALAKAD.NAUK SSSR DOKLADYV.155,NO.5,1058-10611964 PX02 AFANASYEV,G.D.,ET ALAKAD.NAUK SSSR DOKLADY,V.155,NO.5,1058-10611964 PX03 AFANASYEV,G.D.,ET AL,AKAD.NAUK SSSR DOKLADY,V.155,NO.5,1058-10611964 PX04 AFANASYEVG.D.,ET AL,AKAD.NAUK SSSR DOKLADYV.155,NO.5,1058-10611964 PX05 AFANASYEV,G.D.,ET AL,AKAD.NAUK SSSR DOKLADY,V.155,NO.5,1058-10611964 PX06 BIRCHF.,J.GEOPHYS.RES,V.65,1083-1102,1960 PX07 WOOLARD,G.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNION,V.45,637,1964 ODO1 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 QD02 BIRCH,F.,JGEOPHYS.RES.,V.65,1083-1102,1960 QD03 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 0D04 BIRCHF. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 QD05 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 OD06 BIRCHF. BULL.GEOL.SOC.AM.,V.54,263-286,1943 OD07 BIRCH,F.,GEOL.SOC.AM.SECAPC.PAPER,NO.62 1-117,1955 QGO1 WOFBERA.F.,ET ALGEOPHYSICS,V.28,658-663,1963 QL01 WOEBERA.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 QMO1 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 QM02 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 QM03 HUGHESD.S. AND H.J.JONESBULL.GEOL.SOC.AM.,V.61,843-856,1950 OM04 WOEBERA.F.,ET AL,GEOPHYSICS,V.28,658-663,1963 QUO 1 WYLLIE,M.R.J.,ET ALGEOPHYSICS,V.21,41-70,1956 QU02 BIRCH,F.,J.GFOPHYS.RES.,V.65,1083-1102,1960 QU03 WYLLIE,M.R.J.,ET AL,GEOPHYSICS,V.21,41-70,1956 QUO4 MCSKIMINH.J. J.ACOUST.SOC.AM.,V.28,484-494,1956 QU05 MCSKIMIN,H.J.,IN PHYSICAL ACOUSTICSED.MASON,ACAD.PRESS,N.Y.,1964 QU06 SHIMOZURUD.,JAP.J.GEOPHYS.,V.2,NO.3,85PP.,1960 OZO1 KRAVFTSV.V.,AKAD.NAUK UKRAYIN,RSR DOPOVIDINO.3,295-298,1961 OZ02 KRAVETSgV.V.,AKAD.NAUK UKRAYIN,RSR DOPOVIDI,NO.3,295-298,1961 OZ03 BIRCHF.,J.GEOPHYS.RES. V.65,1083-1102,1960 QZ04 RAMANAY.V.,J.SCI.INDUS.RES.,INDIA.,V.19B,NO.11,446-447,1960 QZ05 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 QZ06 BALAKRISHNA,S.,PROC.IND.ACAD.SC I,V.41A,12-15,1955 QZ07 BALAKRISHNAS.,PROC.IND.ACAD.SCI. V.41A,12-15,1955 132

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE QZ08 BALAKRISHNA,S,,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 QZ09 BALAKRISHNAS,,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 QZ10 BALAKRISHNA,S.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 QZ11 BIRCH,F.,BULL.GEOL.SOC.AM.,V.54,263-286,1943 QZ12 CHRISTENSENN,NI.,J.GEOPHYS.RES.,TO BE PUBLISHED QZ13 CHRISTENSENN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED OZ14 BIRCHF.,GEOL.SOC.AM.SPEC.PAPERNO.62,101-117,1955 QZ15 VOLAROVICHM.P.,ET AL.DOKLADY ACAD.SCI.USSR,V.13591237-123991961 QZ16 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A,498-501,1953 RH01 KRISHNAMURTHIM.AND S*BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A9498-501o1953 RH02 WOEBERA.F. ET ALgGEOPHYSICS5V.28,658-663,1963 RH03 WOEBERA.F. ET AL,GEOPHYSICSV.28,658-663,1963 SC01 BIRCHF., JGEOPHYS.RES.,V.65,1083-1102,1960 SC02 BIRCHgF.,J.GEOPHYS.RES. V.6591083-1102,1960 SC03 BIRCH,F.,J.GEOPHYS.RES. V.6591083-1102,1960 SC04 BIRCHgF.. J.GEOPHYS.RES. V.65.1083-1102,1960 SC05 BALAKRISHNA,S.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 SC06 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 SC07 BALAKRISHNAS.,PROC.IND.ACAD.SCI.,V.49ANO.6,318-32191959 SC08 BALAKRISHNAS,PROC.INDoACAD.SCI.V.49ANO.6318-321,1959 SC09 BALAKRISHNAS.,PROC.IND.ACAD.SCI.,V.49A,NO.6,318-321,1959 SC1O KRAVETSV.V.AKAD.NAUK UKRAYIN,RSR DOPOVIDI,NO.3t295-298,1961 SC1l SUBBARAOK. AND B. RAMACHANDRA RAO,NATUREV.180,NO.4573,978,1957 SC12 BIRCHF. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 SC13 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 SC14 BIRCHF. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 SC15 BIRCHF.,GEOL.SOC.AM.SPECPECPAPERNO.62101-117,1955 SC16 BIRCH,F.,GEOL.SOC.AM.SPEC.PAPERNO.62,101-117,1955 SC17 BIRCHF.,GEOL.SOC.AM.SPECPEC.PAPERNO.62101-1171955 SC18 CHRISTENSEN.N.I.,J.GEOPHYS.RES.TO BE PUBLISHED SCT1 CHRISTENSENN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED SC20 CHRISTENSENN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED SC21 CHRISTENSENoN.I.,J.GEOPHYS.RES.,TO BE PUBLISHED SC22 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A,498-501,1953 SC23 HIRASAWA,K.,BUTSURI-TANKOV.15,72-849(IN JAPANESE),1962 SC24 HIRASAWAK.,BUTSURI-TANKO,V.15,72-84,(IN JAPANESE),1962 SC25 HIRASAWAK.,BUTSURI-TANKO,V.15,72-84,(IN JAPANESE),1962 SC26 HIRASAWAK.,BUTSURI-TANKOV.15,72-84,(IN JAPANESE)91962 SC27 HIRASAWA,K.,BUTSURI-TANKOV.15,72-84,(IN JAPANESE),1962 SC28 HIRASAWA,K.,BUTSURI-TANKOV.15,72-84,(IN JAPANESE),1962 SC29 HIRASAWAK.,BUTSURI-TANKOV.15,72-84,(IN JAPANESE),1962 SE01 HAYAKAWAM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTOJAPANKYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 SE02 HAYAKAWAM.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPAN,KYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 SE03 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPANKYOTO UNIVERSITY GEOPHYS. INST.,25-32.1963 SF04 HAYAKAWA,M.,IN GEOPHYSICAL PAPERS DEDICATED TO PROFESSOR KENZO SASSA, KYOTO,JAPANKYOTO UNIVERSITY GEOPHYS. INST.,25-32,1963 SF05 KRAVETS,V.V.,AKAD.NAUK UKRAYINRSR DOPOVIDI,NO.3,295-298,1961 SE06 VOLAROVICHM.P.,ET AL,BULL.ACAD.SCI.USSRNO.8,1198-1205,1963 SE07 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 SE08 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-113091964 SE09 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1123-1130,1964 SE10 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 SF11 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1102,1960 133

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE SE12 BIRCH,F,J.GEOPHYS.RES.,V.651083-1102,1960 SE13 BIRCH,F.,J.GEOPHYS.RES.,V.65,1083-1 1021960 SE14 SIMMONS,G.,J.GEOPHYS.RES.,V.69,1117-1121,1964 SE15 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE16 BIRCHF. NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE17 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE18 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE19 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE20 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE21 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE22 BIRCHF.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE23 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE24 BIRCHgF.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE25 BIRCH,F.,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SE26 BIRCHF.o,NATL.RES.COUNCIL PUBL. 1188,132-133,1964 SH01 SUBBARAO.K. AND B. RAMACHANDRA RAO,NATURE,V.180,NO.4573,978,1957 SH02 BALAKRISHNAS.,PROC.IND.ACAD.SCI.,V.36A,375-380,1952 SH03 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A,498-501,1953 SI01 SIMMONSG.,J.GEOPHYS.RES.,V.69,1123-1130,1964 S102 SIMMONS,G. J.GEOPHYS.RES.,V.69,1117-1121,1964 SL01 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-14391959 SL02 BALAKRISHNAS.,GEOL.SOC. INDIA JOUR.,V.1,136-143,1959 SL03 BALAKRISHNA,S.GGEOL.SOC. INDIA JOUR.,V.1,136-143,1959 SL04 WYLLIE,M.R.J.,ET ALGEOPHYSICS,V.21,41-70,1956 SL05 BIRCH,F. AND D.BANCROFTgJ.GEOL.,V.48,752-766,1940 SL06 RIRCH,Fo. J.GEOPHYS.RES. V.6591083-1102,1960 SL07 BIRCH,F. GEOL.SOC.AM.SPEC.PAPER,NO.62,101-117,1955 SL08 CHRISTENSEN,N.I.,J.GEOPHYS.RES.,TO BE PUBLISHED SN01 VERMA~R.K.,J.GEOPHYS.RES.,EV.65757-76691960 SS01 SUBBARAO.K. AND B. RAMACHANDRA RAO,NATUREV.180,NO.4573,978,1957 SS02 ANTSYFEROVM.S.,ET AL,AKAD. NAUK SSSR IZV.,NO*1,85-89,1964 SS03 AUBERGERM. AND J.S.RINEHARTJ.GEOPHYS.RES.,V.66,191-199,1961 SS04 AUBRERGER. AND J.S.RINEHART,J.GEOPHYS.RES.,V.66,191-199,1961 SS05 BAYUKYE.I,BULL.ACAD.SCI.USSR,NO.6,633-,1959 SS06 RALAKRISHNAS.,TRANS.AM.GFOPHYS.UNIONV.399711-712,1958 SS07 BIRCH,F. AND D.BANCROFT,J.GEOL.,V.48,752-766,1940 SS08 BAYUK,YE.I.,BULL.ACAD.SCI USSRPT.2,1173-1177,1960 SS09 BAYUK,YE.I.,BULL.ACAD.SCI USSR,PT.2 1173-1177,1960 SS10 BAYUK,YE.I.,BULL.ACAD.SCI.USSR,PT.2,1173-117791960 SS11 HUGHES,D.S. AND J.H.CROSSGEOPHYSICSV.16,577-593,1951 SS12 HUGHESD.S. AND J.H.CROSSGEOPHYSICS,V.16,577-59391951 SS13 BIRCHF.,J.GEOPHYS.RES.,V 65,1083-1102,1960 SS14 KINGM.S. AND I.FATT,GEOPHYSICS,V.27,590-598,1962 SS15 KING,M.S. AND I.FATTGEOPHYSICS,V.27,590-598,1962 SS16 KING,M.S. AND I.FATTGEOPHYSICS,V.27,590-598,1962 SS17 KINGM.S. AND I.FATTGEOPHYSICS,V.27,590-598,1962 SS18 KINGM.S. AND I.FATT,GEOPHYSICS,V.27,590-598,1962 SS19 KING,M.S. AND I*FAT,GEOPHYSICS,V.27,590-598,1962 SS20 BIRCHF.,GEOL.SOC.AM.SPEC.PAPER,NO.62,101-117,1955 SS21 RAMANAY.V. ET ALIND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-191,1963 SS22 RAMANAY.V.,ET ALIND.J. PURE AND APPL. PHYS.,V.1,NO.5,1901991,1963 SS23 RAMANAY.V.,ET AL,IND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-191,1963 SS24 RAMANAY.V.,ET AL,IND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-191,1963 SS25 RAMANAY.V.,ET AL,IND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-19-1,1963 SS26 RAMANAY.V. ET ALIND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-191,1963 SS27 RAMANAY.V.tET AL,IND.J. PURE AND APPL. PHYS.,V.1,NO,5,190-191,1963 134

WILLOW RUN LABORATORIES CROSS INDEX REFERENCE SS28 RAMANA,Y.V.,ET ALsIND.J. PURE AND APPL. PHYS.,V,1*NO.5,190-19191963 5529 RAMANAY.V.,ET AL,IND.J. PURE AND APPL. PHYS.,V.19NO.5,190-191,1963 SS30 RAMANAY.V.,ET ALIND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-191,1963 SS31 RAMANAY.V.,ET AL,IND.J. PURE AND APPL. PHYS.V.1lNO.5,190-191,1963 532 RAMANAY.V. ET AL,IND.J. PURE AND APPL. PHYS.,V.1,NO.5,190-19191963 SS33 DESBRANDESR.,ET ALINST. FRANCAIS PETROLE REV.,V.14,535-548,1959 SS34 DESBRANDESgR.,ET ALINST. FRANCAIS PETROLE REVV. V14.535-548,1959 SS35 DESBRANDESgR.,ET ALINST. FRANCAIS PETROLE REV.,V.149535-54891959 SS36 DESBRANDESR.,ET ALINST. FRANCAIS PETROLE REV.,V.149535-548,1959 SS37 DESBRANDESgR.,ET AL,INST. FRANCAIS PETROLE REV.,V.14,535-548,1959 SS38 DESBRANDESR.,ET AL,INST. FRANCAiS PETROLE REV.,V*14,535-548,1959 SS39 VOLAROVICHM.P.,ET AL,DOKLADY ACAD.SCI.USSR,V.135,1237-1239,1961 SS40 VOLAROVICHM.P.,ET ALDOKLADY ACAD.SCI.USSRV.135,21237-1239,1961 SS41 VOLAROVICHM.P.,ET AL,DOKLADY ACAD.SCI.USSRV.13591237-1239,1961 SS42 HUGHESD.S. AND J.L. KELLYGEOPHYSICSV.17,739-752,1952 SS43 HUGHESDD.S. AND J.L. KELLY,GEOPHYSICSV.17,739-752,1952 SS44 HUGHESD.S. AND J.L. KELLYGEOPHYSICSV.17,739-75291952 SS45 GREGSONV.G. ET AL,AFCRL63-662,STANFORD RES.INST.FINAL REPT.,1963 SS46 BIRCH,F.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 SS47 IDEJ.M.,PROC.NATL.ACAD.SC I.,V.22,482-4961936 SS48 BANTHIAB.S.,ET ALGEOPHYSICS.V.30,117-121,1965 5549 BANTHIAB.S.ET ALGEOPHYSICSV.30,117-121,1965 550 BANTHIAB.S.,ET AL,GEOPHYSICSV.30,117-121,1965 SS51 BANTHIA,B.S.,ET AL,GEOPHYSICS,V.30,117-121,1965 5552 GARDNER,G.H.F.,ET AL,GEOPHYSICSV.30,111-116,1965 SS55 WYLLIE,M.R.J. ET AL,GEOPHYSICSV.27 569-589,1962 SS556 WYLLIEgM.R.J.,ET AL,GEOPHYSICSV.27 569-589,1962 SS57 WYLLIEM.R.J.,ET ALGEOPHYSICSV.27,569-58991962 SS58 WYLLIEM.R.J.,ET AL,GEOPHYSICS,V.27,569-589,1962 SS59 WYLLIEM.R.J.,ET ALGEOPHYSICSV.27,569-589,1962 SS60 WYLLIEM.R.J.,ET AL,GEOPHYSICSV.27,569-589,1962 SS61 GREGORYA.R. PROC.ROCK MECH.SYMP.,5TH9439-471,PERGAMON PRESSN.Y.,1963 SS62 GREGORY,A.R.,PROC.ROCK MECH.SYMP.,5TH,439-471,PERGAMON PRESS,N.Y.,1963 SS63 GREGORYA.R.RPROC.ROCK MECH.SYMP.,5TH4439-471,PERGAMON PRESSN.Y.,1963 SS64 GREGORY,A.R.,PROC.ROCK MECH.SYMP.,5TH,439-471PERGAMON PRESSN.Y.,1963 5565 WYLLIEM.R.J.,ET ALGEOPHYSICS,V.27 569-589,1962 SS66 WYLLIEM.R.J.,ET ALGEOPHYSICSV.27,569-589,1962 STO1 BHIMASENACHAR,J. AND G.V.RAO,J.ACOUST.SOC.AM.,V.29,343-345,1957 SYO1 BAYUKYE.I.,BULL.ACAD.SCI.USSRNO*.6633-,1959 SY02 BIRCHF.,J.GEOPHYS.RES.,V.65,1083-1102,1960 SY03 BIRCHF.AND D.BANCROFTJ.GEOL.,V.46,59-87,1938 SY04 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A,498-501i1953 SY05 KRISHNAMURTHI,M.AND S.BALAKRISHNA,PROC.IND.ACAD.SCI.V.38A,498-501,1953 TA01 HUGHESD.S.AND C.MAURETTE,GEOPHYSICS,V.22,23-31,1957 TA02 WOOLARDgG.P.AND M.H.MANGHNANITRANS.AM.GEOPHYS.UNIONV.45,637,1964 TA03 WOOLARDG.P.AND M.H.MANGHNANI,TRANS.AM.GEOPHYS.UNIONV.45,637,1964 TA04 WOEBERA.F.,ET ALGEOPHYSICSV.28,658-663,1963 TA05 WOEBERA.F.,FT ALGEOPHYSICS,V.28,658-663,1963 TCO1 ALEXANDROV,K.S.AND T.V.RYZHOVA,BULL.ACAD.SCI.USSRNO.12,1165-1168,1961 TP01 BALAKRTSHNAS.,TRANS.AM.GFOPHYS.UNION,V.39,711-712,1958 TP02 PRASADA RAO,G.H.S.Ve,PROC.IND.ACAD.SCI.,V.25A,238-246,1947 TP03 PRASADA RAOG.H.S.V,,PROC.IND.ACAD.SC!.,V.25A,238-246,1947 TP04 KRISHNAMURTHI,M.AND S.BALAKRISHNAPROC.IND.ACAD.SCI.V.38A,498-501,1953 TRO1 WOEBER,A.F. ET AL,GEOPHYSICSV.28,658-663,1963 TUO1 WOEBERA.F.,ET AL,GEOPHYSICSV.28,658-663,1963 VBO1 WOEBFRA.F.,ET ALGEOPHYSICS,V.289658-663,1963 WOO1 SIMMONSG.,J.GEOPHYS.RES.,V.69,1117-1121,1964 ZRO1 BHIMASENACHARJ.AND G*VENKATARATNAM,J.ACOUST.SOC.AM.,V.27,922-925,1955 135

WILLOW RUN LABORATORIES Appendix 9 PROPERTIES OF POLYCRYSTALLINE AGGREGATES OF CERTAIN MINERALS (CALCULATED FROM ELASTIC CONSTANTS OF SINGLE CRYSTALS) (MODULI UNITS-KILOBARS.) (CRYSTAL CLASS UNDER INDEX.SYMBOLSCU-CUBICHX-HEXAGONALTR-TRIGONAL9 TE-TETRAGONALOR-ORTHORHOMBIC) CODE FOR FIELD IN CROSS INDEX XX****** XX REFERS TO CRYSTAL CLASS.EXAMPLECU-CUBICtTE-TETRAGONAL **XX****. XX REFERS TO THE CATION OR ELEMENT By NUMBER IN LIST BELOW ****XX** XX REFERS TO THE PRINCIPAL ANION BY NUMBER IN LIST BELOW ******XX XX REFERS TO THE NUMBER OF THE LISTING FOR A PARTICULAR SOLID TR453702 TR-TRIGONAL,45-SILICON,37-OXYGEN,02-SECOND LISTING FOR QUARTZ CODE LISTING OF ELEMENTS AND ANIONS BY NUMBER 01 AGSILVER 41 PTPLATINUM 02 ALALUMINUM 42 RB,RUBIDIUM 03 AUGOLD 43 SSULPHUR 04 ASARSENIC 44 SESELENIUM 05 B9BORON 45 SI SILICON 06 BA,BARIUM 46 SNTIN 07 BEBERYLLIUM 47 SB,ANTIMONY 08 BIBISMUTH 48 TATANTALUM 09 BRBROMINE 49 TETELLURIUM 10 CqCARBON 50 TL THALLIUM 11 CACALCIUM 51 TH9THORIUM 12 BLANK 52 TI TITANIUM 13 CL CHLORINE 53 W.TUNGSTEN 14 CDCADMIUM 54 V,VANADIUM 15 CSCESIUM 55 ZNZINC 16 COCOBALT 56 ZR,ZIRCONIUM 17 CRCHROMIUM 57 Y.YTTRIUM 18 CUCCOPPER 58 UURANIUM 19 FEIRON 59 SRSTRONTIUM 20 F FLUORINE 60 N03TNITRATE 21 GA,GALLIUM 61 C03,CARBONATE 22 GE GERMANIUM 62 S04.SULPHATE 23 GDgGADOLINIUM 63 B508,PENTABORATE 24 H.HYDROGEN 64 (NH4)C4H406 4H20, AMMONIUM TARTRATE 25 HGMERCURY 65 NA C4 H406 4H20, SODIUM TARTRATE 26 ITIODINE 66 SI04,ORTHOSILICATE 27 IN9INDIUM 67 (CH02)2, FORMATE HYDRATE 28 KPOTASSIUM 68 P04, PHOSPHATE 29 LILITHIUM 69 NA C6H1206,SODIUM DEXTROSE 30 MGgMAGNESIUM 70 T103,TITINATE 31 MNMANGANESE 71 NH4,AMMONIUM 32 MOMOLYBDENUM 72 AL2SI6018,ALUMINOSILICATE 33 NA,SODIUM 73 NH3,AMMONIA 34 NINICKEL 74 BR03, BROMATE 35 NBgNIOBIUM 36 59NITROGEN 37 OOXYGEN 38 PDPALLADIUM 7,PH S7HORUS 40 PBLEAD CODE FOR SPECIAL MINERALS OF COMPLICATED COMPOSITION 8000 TOURMALINE 8001 TOPAZ 8002 GARNET 3ROAL203.3SI02 (R=MN,FEMG,CA) 8003 SPINEL MGO.XAL203 136

WILLOW RUN LABORATORIES MG2SI04 —FORSTERITE OR306601 R.K.VERMAJ.GEOPHYS.RES. 65(1960),P.762 OR306601 DENSITY= 3.324 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 3240. 590. 790. -0. 0. 0. 34 -0.07 -0.09 -0. 0. 0. 1980. 780. -0. 0O 0. 0.59 -0.16 -0. 0. O. 2490. -0. 0. 0. 48 0O -0. -0. 667. 0. 0. 1.50 -0. -0. 810. -0. 123 O. 793. 1.26 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1337. 824. 2051. 2435. 0.2445 REUSS 1289. 793. 1975. 2347. 0.2446 ARITH.MEAN 1313. 809. 2013. 2391. 0.2446 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.559 4.978 6.341 5.522 REUSS 8.402 4.885 6.227 5.419 ARITH.MEAN 8.480 4.932 6.284 5.471 VMEAN= 5.484 KM/SEC PERCENT ERROR= 0.2479 DEBYE TEMP.= 754.451 ZIRCON TE566601 H.A.HUNTINGTON,,SOLID STATE PHYSICS' VOL7(1958)P.274,ACADEMIC PRESS TE566601 DENSITY= 4.680 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 735. 90. -54. -0. 0. O. 1.39 -0.16 0.14 -0. 0. 0O 735. -54. -0. 0. 0. 1.39 0.14 -0. 0 0. 460. -0. 0. 0. 2.21 -0. 0. O. 138. 0. 0. 7.25 -0. -0. 138. -0. 7.25 0O 160. 6.25 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 210. 217. 485. 500. 0.1252 REUSS 191. 184. 417. 435.. 0.1352 ARITH.MEAN 200. 200. 451. 468. 0.1302 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 3.268 2.153 2.120 2.357 REUSS 3.050 1.981 2.018 2.172 ARITH.MEAN 3.159 2.067 2.069 2.265 VMEAN= 2.254 KM/SEC PERCENT ERROR= 0.5063 DEBYE TEMP.= 304.460 137

WILLOW RUN LABORATORIES GARNET 1 CU800201 R.K.VERMA,J.GEOPHYS.RES.,65,(1960),P.762 CU800201 DENSITY= 4.247 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 3073. 1097. 1097. -0. 0. 0. 0.40 -0.11 -0.11 -0. 0. 0 3073. 1097. -0. 0. 0. 0*40 -0.11 -0. 0. 0. 3073. -0. *0. 0. 0.40 0. -0. -0. 952. 0. 0. 1.05 -0. -0. 952. -0. 1.05 0O 952. 1*05 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1756. 966. 2450. 3044. 0.2675 REUSS 1756. 966. 2449. 3044. 0.2675 ARITH.MEAN 1756. 966. 2449. 3044. 0.2675 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.466 4.770 6.429 5.305 REUSS 8.465 4.769 6.429 5.305 ARITH.MEAN 8.465 4.769 6.429 5.305 VMEAN= 5.399 KM/SEC PERCENT ERROR= 1.7341 DEBYE TEMP.= 740.572 GARNET 2 CU800202 R.K.VERMAJ.GEOPHYSoRESo.659(1960),P.762 CU800202 DENSITY= 4.183 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 3048. 1123. 1123. -0. 0. 0. 0.41 -0.11 -0.11 -0. 0. 0. 3048. 1123. -0. 0- 0. 0.41 -0.11 -0. 0. 0. 3048. -0. 0. 0. 0.41 0. -0. -0. 944. 0O 0. 1.06 -0. -0. 944. -0. 1.06 0. 944. 1.06 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1765. 951. 2419. 3033. 0.2715 REUSS 1765. 951. 2419. 3033. 0.2715 ARITH.MEAN 1765. 951. 2419. 3033. 0.2715 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.515 4.769 6.495 5.307 REUSS 8.515 4.768 6.495 5.307 ARITH.MEAN 8.515 4.769 6.495 5.307 VMEAN= 5.400 KM/SEC PERCENT ERROR= 1.7307 DEBYE TEMP.= 746.533 138

WILLOW RUN LABORATORIES TOPAZ OR800101 W.VOIGTANN.PHYSIK D. CHEMIE,34 (1888) P.981 OR800101 DENSITY= 3.500 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2870. 1280. 850. -00. 0 0. 0.43 -0.13 -0.08 -0. 0 0. 3560. 900. -0. 0. 0. 0 035 -0.07 -0. 0. 0. 3000. -0. 0. 0. 0.38 0. -0. -0. 1100. 0. 0. 0.91 -0. -0. 1350. -0. 0.74 0. 1330. 0*75 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1721. 1183. 2887. 3298. 0.2211 REUSS 1695. 1158. 2829. 3239. 0.2219 ARITH.MEAN 1708. 1170. 2858. 3268. 0.2215 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.706 5.812 7.012 6.430 REUSS 9.619 5.751 6.959 6.363 ARITH.MEAN 9.663 5.782 6.985 6.396 VMEAN= 6.440 KM/SEC PERCENT ERROR= 0.6823 DEBYE TEMP.= 892.284 TOURMALINE TR800001 W.VOIGT,ANN.PHYSIK D. CHEMIE,41(1890) P.712 TR800001 DENSITY= 3.100 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2756. 704. 90. -79. 0. 0 0.39 -0.10 -0*01 0*06 -0. -0. 2756. 90. 79. 0 0. 0.39 -0.02 -0.06 0 0. 1638. -79. 0. 0. 0.62 0.07 -0. -0. 680. 0. 0. 1.49 -0. -0. 680. 0. 1 47 0. 1005. 1.00 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 991. 891. 2056. 2179. 0.1480 REUSS 884. 834. 1903. 1995. 0.1412 ARITH.MEAN 937. 862. 1979. 2087. 0.1446 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.382 5.360 5.653 5.888 REUSS 8.022 5.185 5.339 5.689 ARITH.MEAN 8.202 5.272 5.496 5.789 VMEAN= 5.836 KM/SEC PERCENT ERROR= 0.8165 DEBYE TEMP.= 789.097 139

WILLOW RUN LABORATORIES TOURMALINE TR800002 W.P.MASON,'PIEZOELECTRIC CRYSTALS...'(1950),VAN NOSTRAND TR800002 DENSITY= 3.100 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2720. 400. 350. -68. 0. 0. 0.38 -0.05 -0.07 0*04 -0. -0. 2720. 350. 68. 0. 0. 0.39 -0.07 -0.05 0. 0. 1650. -68. 0. 0. 0.64 0.07 -0. -0. 650. 0. 0. 1.56 -0. -0. 650. 0. 1*54 0O 1160. 0.86 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1032. 891. 2076. 2221. 0.1679 REUSS 975. 821. 1923. 2070. 0.1713 ARITH.MEAN 1004. 856. 2000. 2145. 0.1696 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.463 5.362 5.770 5.897 REUSS 8.170 5.145 5.608 5.662 ARITH.MEAN 8.316 5.254 5.689 5.780 VMEAN= 5.804 KM/SEC PERCENT ERROR= 0.4171 DEBYE TEMP.= 787.844 SI 02 —ALPHA QUARTZ TR453701 R.BECHMANN, PHYS.REV.,110(1958),P.1060 TR453701 DENSITY= 2.650 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 867. 70. 119. 179. 0. 0. 1.26 -0.19 -0.05 -0.43 -0. -0O 867. 119. -179. 0. 0. 1.31 -0.21 0.53 0. 0. 1072. 179. 0. 0. 1.02 -0.37 -0* -0. 579. 0. 0. 2.14 0. 0. 579. 0. 1.73 0O 399. 2.51 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 380. 478. 1010. 1017. 0.0703 REUSS 370. 425. 922. 937. 0.0843 ARITH.MEAN 375. 452. 966. 977. 0.0773 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.196 4.246 3.788 4.624 REUSS 5.946 4.006 3.736 4.373 ARITH.MEAN 6.071 4.126 3,762 4.498 VMEAN= 4.446 KM/SEC PERCENT ERROR= 1.1880 DEBYE TEMP.= 575.933 140

WILLOW RUN LABORATORIES SI 02 —ALPHA QUARTZ TR453702 W.P.MASON,BELL SYST.TECH.J. 22(1943),P.178 TR453702 DENSITY= 2.650 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 861. 51. 105. 183. O 0 0. 1.27 -0.16 -0.03 -0.44 -0 -0. 861. 105. -183. 0. 0. 1.31 -0.20 0.52 0. 0. 1070. 183. 0. 0. 1.02 -0.37 -0. -0. 587. 0. 0. 2.12 0. 0. 587. 0. 1.70 0. 405. 2.47 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 368. 485. 1010. 1014. 0.0561 REUSS 357. 430. 921. 931. 0.0703 ARITH.MEAN 363. 457. 966. 973. 0.0632 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.186 4.276 3.727 4.651 REUSS 5.928 4.030 3.672 4.394 ARITH.MEAN 6.057 4.153 3.700 4.522 VMEAN= 4.468 KM/SEC PERCENT ERROR= 1.2142 DEBYE TEMP.= 578.962 SI 02 —ALPHA QUARTZ TR453703 T.KOGA AND M.ARUGAPHYS.REV.,109,(1958),P.1467 TR453703 DENSITY= 2.649 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 868. 70. 119. -181. 0 0O. 1.26 -0.19 -0.05 0-44 -0. -0. 868. 119. 181. 0. 0. 1.31 -0.22 -0.53 0. 0. 1059. -181. 0. 0. 1.04 0.38 -0. -0. 583. 0. 0. 2.13 -0. -0. 583. 0. 1.72 O. 399. 2e51 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 379. 479. 1011. 1017. 0.0693 REUSS 369. 425. 921. 936. 0.0839 ARITH.MEAN 374. 452. 966. 976. 0.0766 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.197 4.251 3.782 4.629 REUSS 5.942 4.005 3.732 4.371 ARITH.MEAN 6.070 4.128 3.757 4.500 VMEAN= 4.627 KM/SEC PERCENT ERROR= 2.7549 DEBYE TEMP.= 576.057 141

WILLOW RUN LABORATORIES SI02 — BETA QUARTZ HX453701 F.W.KAMMER FT AL.,J.APPL.PHYS.,19(1948)P.265 HX453701 DENSITY= 2.533 GMS/CU CM TEMPERATURE= 873 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1165. 160. 335. -0. 0. 0. 0.94 -0.05 -0.27 -0. 0. 0. 1165. 335. -0. 0. 0. 0.94 -0.27 -0. 0. 0. 1105. -0. 0. 0. 1.07 0. -0. -0. 360. 0. 0. 2.78 -0. -0. 360. -0. 2.78 0. 501. 2.00 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 566. 418. 1006. 1123. 0.2066 REUSS 565. 407. 985. 1108. 0.2094 ARITH.MEAN 565. 412. 995. 1115. 0.2080 VFLOCITY LONG SHEAR BULK AVERAGE VOTGT 6.659 4.061 4.727 4.485 REUSS 6.612 4.009 4.722 4.429 ARITH.MEAN 6.635 4.035 4.724 4.457 VMEAN= 4.491 KM/SEC PERCENT ERROR= 0.7521 DEBYE TEMP.= 562.102 SI02 —BETA QUARTZ HX453703 F.W.KAMMERT.E.PARDUE AND H.F.FRISSELJ.APPL.PHYS.,19(1948)gP.265 HX453703 DENSITY= 2.493 GMS/CU CM TEMPERATURE=1073 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1351. 330. 480. -0. O0 0. 0.87 -0.11 -0.29 -0. 0. 0. 1351. 480. -0. 0 0. 0.87 -0.29 -0. 0. 0. 1245. -0. 0. 0. 1.03 0. -0. -0. 386. 0. 0. 2.59 -0. -0. 386. -0. 2.59 0. 516. 1.94 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 725. 435. 1087. 1305. 0.2523 REUSS 725. 426. 1068. 1293. 0.2545 ARITH.MEAN 725. 430. 1078. 1299. 0*2534 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 7.234 4.176 5.393 4.635 REUSS 7.200 4.132 5.392 4.589 ARTTH.MEAN 7.217 4.154 5.393 4.612 VMEAN= 4.646 KM/SEC PERCENT ERROR= 0.7359 DEBYE TEMP.= 578.576 142

WILLOW RUN LABORATORIES MG O —MAGNESIA —PERICLASE CU303701 S.BHAGAVANTAMPROC.IND.ACAD.SCI.,A41 (1955),P.72 CU303701 DENSITY= 3,593 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2860. 870. 870. O. 0. 0..40 -.09 -.09 0.00 0.00 0.00 2860. 870. 0. 0. 0..40 -.09 0.00 0-00 0.00 2860. 0. 0. 0..40' 0.00 000 0.00 1480. 0. 0. *67 0.00 0.00 1480. 0..67 0.00 1480..67 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1533. 1285. 3015. 3247..1770 REUSS 1533. 1238. 2927. 3184..1818 ARITH.MEAN 1533. 1262. 2971. 3216..1794 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.506 5.982 6.532 6.583 REUSS 9.413 5.870 6.532 6.467 ARITH.MEAN 9.460 5.926 6.532 6.525 VMEAN= 6.610 KM/SEC PERCENT ERROR= 1.2886 DEBYE TEMP.= 922 MG O —MAGNESIA —PERICLASE CU303702 C.SUSSEJ.RECHERCHES,12,(1961)P.21 CU303702 DENSITY= 3.598 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2998. 991. 991. 0. 0. 0..39 -.09 -.09 0.00 0.00 0*00 2998. 991. 0. 0. 0..39 -.09 0.00 0.00 0.00 2998. 0. 0. 0..39 0.00 0.00 0.00 1575. 0. 0..63 0.00 0.00 1575. 0..63 0.00 1575..63 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1659. 1346. 3179. 3455..1867 REUSS 1660. 1282. 3060. 3370..1927 ARITH.MFAN 1660. 1314. 3119. 3412..1897 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.798 6.116 6.791 6.737 REUSS 9.677 5.970 6.791 6.584 ARITH.MEAN 9.738 6.043 6.791 6.661 VMEAN= 6.741 KM/SEC PERCENT ERROR= 1.1884 DEBYE TEMP.= 942 143

WILLOW RUN LABORATORIES MG O —MAGNESIA —PERICLASE CU303706 D.H.CHUNG AND W.G.LAWRENCE.,ARMY RES.OFF.RPT*.7DA-31-124,(1963)ALFRED U CU303706 DENSITY= 3.581 GMS/CU CM TEMPERATURE= 298 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2892. 880. 880. 0. 0. 0..40 -.09 -.09 0.00 0*00 0.00 2892. 880. 0. 0. 0. *40 -.09 0.00 0.00 0.00 2892. 0. 0. 0..40 0.00 0*00 0.00 1546. 0. 0. *64 0*00 0*00 1546. 0. *64 0.00 1546..64 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1550. 1329. 3102. 3323. *1721 REUSS 1550. 1272. 2997. 3247..1777 ARITH.MEAN 1550. 1301. 3050. 3285..1749 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.633 6.093 6.579 6.702 REUSS 9.522 5.961 6.579 6.564 ARITH.MEAN 9.577 6.027 6.579 6.633 VMEAN= 6.715 KM/SEC PERCENT ERROR= 1.2219 DEBYE TEMP.= 936 MG O —MAGNESIA —PERICLASE CU303707 Y.T.CHOU AND R.W.WHITMORE,J.APPL.PHYS.32(1961)P.1920 CU303707 DENSITY= 3.583 GMS/CU CM TEMPERATURE= 300 DEGREES KELVIN FLASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2893. 877. 877. 0. 0. 0..40 -.09 -.09 0.00 0.00 0.00 2893. 877. 0. 0. 0..40 -.09 0.00 0.00 0.00 2893. 0. 0. 0..40 0.00 0.00 0.00 1548. 0. 0..64 0.00 0.00 1548. 0..64 0.00 1548..64 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1548. 1331. 3105. 3324..1714 REUSS 1548. 1274. 3001. 3248..1770 ARITH.MEAN 1548. 1303. 3053. 3286..1742 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.632 6.096 6.574 6.705 REUSS 9.521 5.964 6.574 6.567 ARTTH.MEAN 9.576 6.030 6.574 6.636 VMEAN= 6.718 KM/SEC PERCENT ERROR= 1.2229 DEBYE TEMP.= 937 144

WILLOW RUN LABORATORIES AL2 03 —ALUMINA —CORUNDUM TR023701 J.B.WACHTMANJR. ET ALJ.RES.N.B.S.o 64A (1960) P.213 TR023701 DENSITY= 3.986 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 4q68. 1636. 1109. 235. 0. O. 0.23 -0.07 -0.03 -0.04 -0. -0. 4968. 1109. -235. 0. 0. 24 -0.04 0.06 0. 0. 4981. 235. 0. 0. 22 -0.04 -0. -0. 1474. 0. 0. 0.70 0. 0. 1474. 0. 0.68 O. 1666. 0.60 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2514. 1660. 4082. 4728. 0.2318 REUSS 2504. 1617. 3992. 4660. 0.2343 ARITH.MEAN 2509. 1639. 4037. 4694. 0.2330 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 10.890 6.453 7.941 7.146 REUSS 10.812 6.369 7.925 7*057 ARITH.MEAN 10.851 6.411 7.933 7.102 VMEAN= 7.167 KM/SEC PERCENT ERROR= 0.9117 DEBYE TEMP.=1035.511 AL203 —ALUMINA —CORUNDUM TR023702 B.T.BERNSTFINJ.APPL.PHYS.,TO BE PUBLISHED TR023702 DENSITY= 3.986 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 4902. 1654. 1130. 232. 0. O. 0.24 -0.07 -0.04 -0.04 -0. -0O 4902. 1130. -232. 0. 0. 0.24 -0.04 0.06 0. 0. 4902. 232. 0. 0..22 -0.04 -0. -0. 1454. 0. O. 0.71 O 0 1454. 0. 0.69 0. 1624. 0.62 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2504. 1626. 4010. 4672. 0.2354 REUSS 2494. 1585. 3923. 4607. 0.2378 ARITH.MEAN 2499. 1605. 3967. 4639. 0.2366 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 10.825 6.386 7.925 7.075 REUSS 10.750 6.305 7.909 6.989 ARITH.MEAN 10.787 6.346 7.917 7.032 VMEAN= 7.096 KM/SEC PERCENT ERROR= 0.9098 DEBYE TEMP.=1025.319 145

WILLOW RUN LABORATORIES SAPPHIRE —AL2 03 TR023703 W.A.MAYER AND E.A.HEIDMAN,ACOUST.SOC.AM.AMER.JOUR.32(1960)P.1699 TR023703 DENSITY= 3.986 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 4960. 1350. 1170. -230. 0. 0. 0.23 -0.05 -0.04 0.04 -0. -0. 4960. 1170. 230. 0. 0. 0.23 -0.04 -0.05 0 0. 5020. -230. 0. 0. 0.22 0.04 -0. -0. 1410. 0. 0. 0.73 -0. -0o 1410. 0. 0.71 0. 1805. 0.55 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2480. 1675. 4102. 4713. 0.2275 REUSS 2475. 1625. 4000. 4642. 0.2307 ARITH.MEAN 2478. 1650. 4051. 4678. 0.2291 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 10.873 6.482 7.887 7.174 REUSS 10.790 6.384 7.880 7.071 ARITH.MEAN 10.832 6.433 7.883 7.122 VMEAN= 7.435 KM/SEC PERCENT ERROR= 4.2033 DEBYE TEMP.=1038.516 FE203 —HEMATITE TR193701 W.VOIGTANN.PHYSIK.,22(1907),P.129 TR193701 DENSITY= 5.120 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2470. 560. 160. -130. 0. 0. 0.43 -0.10 -0.02 0.08 -0. -0. 2470. 160. 130. 0 0. 0.43 -0.03 -0.08 0. 0. 2320. -130. 0. 0. 0.44 0.07 -0. -0. 870. 0. 0. 1.18 -0. -0. 870. 0. 1.15 O. 935. 1.07 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1002. 960* 2184. 2283. 0.1386 REUSS 990. 937. 2136. 2238. 0.1403 ARITH.MEAN 996. 948. 2160. 2261. 0.1394 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.676 4.330 4.424 4.750 REUSS 6.611 4.277 4.396 4.692 ARITH.MEAN 6.644 4,304 4.410 4.721 VMEAN= 4.820 KM/SEC PERCENT ERROR= 2.0688 DEBYE TEMP.= 644.292 146

WILLOW RUN LABORATORIES TI02 —RUTILE TE523701 F.BIRCHJ.GEOPHYS. RES.,65,(1960),P.3855 TE523701 DENSITY= 4.264 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2730. 1760. 1490. -0. 0. 0. 0.66 -0.38 -0.09 -0. 0. 0. 2730. 1490. -0. 0. 0. 0*66 -0.09 -0. 0. 0. 4840. -0. 0. 0. 0.26 0. -0. -0. 1250. 0. 0. 0.80 -0. -0. 1250. -0. 0.80 0. 1940. 0.52 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2198. 1259. 3171. 3876. 0.2756 REUSS 2106. 1012. 2617. 3456. 0.2929 ARITH.MEAN 2152. 1135. 2894. 3666. 0.2843 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.533 5.433 7.179 6.037 REUSS 9.002 4.872 7.027 5.436 ARITH.MEAN 9.267 5.152 7.103 5.736 VMEAN= 5.585 KM/SEC PERCENT ERROR= 2.7168 DEBYE TEMP.= -0. TI 02 TE523702 S.K.JOSHI AND S.S.MITRAPROC.PHYS.SOC.LONDON,76,NO.12(1960) P.295 TE523702 DENSITY= 4.260 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2800. 1800. 1400. -0. 0. 0...63 -0.37-0.08 -0. 0. 0. 2800. 1400. -0. 0. 0. 0.63 -0.08 -0. 0. 0. 4600. -0. 0. 0. 0.27 0. -0. -0. 1200. 0. 0. 0.83 -0. -0. 1200. -0. 0.83 0. 1600. 0.62 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2156. 1173. 2979. 3720. 0.2826 REUSS 2102. 992. 2571. 3425. 0.2962 ARITH.MEAN 2129. 1083. 2775. 3572. 0.2894 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 9.344 5.248 7.113 5.839 REUSS 8.965 4.824 7.025 5.385 ARITH.MEAN 9.155 5.036 7.069 5.612 VMEAN= 5.503 KM/SEC PERCENT ERROR= 1.9730 DEBYE TEMP.= 530.717 147

WILLOW RUN LABORATORIES SPINEL —MG AL2 04 CU800301 R.K.VERMA,J.GEOPHYS.RES.,65,(1960),P.762 CU800301 DENSTTY= 3.630 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 3005. 1537. 1537. -0. 0. 0. 0.51 -0.17 -0.17 -0. 0. 0. 3005. 1537. -0. 0. 0. 0.51 -0.17 -0. 0. 0. 3005. -0. 0. 0. 0.51 0. -0. -0. 1586. 0. 0. 0.63 -0. -0. 1586. -0. u.63 u. 1586. 0.63 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2026. 1245. 3101. 3687. 0.2589 REUSS 2026. 1083. 2758. 3470. 0.2732 ARITH.MEAN 2026. 1164. 2929. 3579. U.2660 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 10.077 5.856 7.471 6.497 REUSS 9.777 5.462 7.471 6.079 ARITH.MEAN 9.927 5.659 7.471 6.288 VMEAN= 6.321 KM/SEC PERCENT ERROR= 0.5229 DEBYE TEMP.= 889.255 CR2FE04 —CHROMITE CU171901 M.S.DORAISWAMIPROC.IND.ACAD.bCI.A25,t1947)P.413 Cu1719ul DENSITY= 4.450 GMS/CU CM TEMPERATURF= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASIIC MODULI(1/KBAR*100U) 3225. 1437. 1437. -U. U. O..43 1 -13 -v13 -u. uv v, 3225. 1437. -0. 0. 0. U.43 -U013 -0O 0. 0O 3225. -0. OU. U u.43 u. - -U - 1167. 0. 0. 0.86 -0. -0. 1167. -0. 0.86 O. 1167. 0.86 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 2033. 1058. 27u4. 3443. u,2799 REUSS 2033. 1040. 2665. 3420. 0.2815 ARITH.MEAN 2033. 1U49. Zbd*. >J. uv.Uu/ VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.796 4.875 6.759 5.430 REUSS 8.765 4.834 6.759 5.386 ARITH.MEAN 8.781 4.854 6.759 5.408 VMEAN= 5.492 KM/SEC PERCENT ERROR= 1.5255 DEBYE TEMP.= 704.089 148

WILLOW RUN LABORATORIES FE304 —MAGNET ITE CU193701 M.S.DORAISWAMI,PROC.INDIAN ACAD.,CI.,A25(1947)P.413 CU193701 DENSITY= 5.200 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2730. 1060. 1060. -0. O0.. 0.47 -0.13 -0.13 -0. 0O O0 2730. 1060. -0. 0. 0. 0.47 -0.13 -0. 0. 0O 2730. -0. 0. 0. 0.47 0. -- -G970. 0. 0 1.03 -0. -0 970. -0. 1.03 0O 970. 1.03 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1617. 916. 2311. 2838. 0.2622 REUSS 1617. 911. 23u1. 2831. 0.2628 ARITH.MEAN 1617. 914. 2306* 2835. 0.2625 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 7.387 4.197 5.575 4.665 REUSS 7.378 4.185 5.575 /.653 ARITH.MEAN 7.383 4.191 5.575 4.659 VMEAN= 4.737 KM/SEC PERCENT ERROR= 1.6392 DEBYE TEMP.= 631.711 FE304 —MAGNETITE CU193702 A.E.CLARK AND R.E.STRAKNA,J.APPL.PHYS.32(1961)P.1172 CU193702 DENSITY= 5.200 GMS/CU CM TEMPERATURE= 296 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 2730. 1060. 1060. -0. 0 0. 0.47 -0.13 -0.13 -0. 0. 0. 2730. 1060. -0. 0. 0. 0.47 -0.13 -0. 0. 0. 2730. -0. 0. 0 047 0. -0. -0. 970. 0. 0. 1.03 -0. -0. 970. -0. l.u3 u. 970. 1.03 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1617. 916. 2311. 2838. 0.2622 REUSS 1617. 911. 2301. 2831. 0.2628 ARTTH.MEAN 1617. 914. 2306. 2835. 0.2625 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 7.387 4.197 5.575 4.665 REUSS 7.378 4.185 5.575 4.653 ARITH.MEAN 7.383 4.191 5.575 4.659 VMEAN= 4.737 KM/SEC PERCENT ERROR= 1.6392 DEBYE TEMP.= 631.711 149

-WILLOW RUN LABORATORIES PYRITE CU194301 G.SIMMONS AND F.BIRCHJ.APPL.PHYS.,34(1963)P.2737 CU194301 DENSITY= 4.929 GMS/CU CM TEMPERATURE= 298 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 3818. 310. 310. -0. 0. O. 0.27 -0.02 -0.02 -0. 0. 0. 3818. 310. -0. 0. 0. 0.27 -0.02 -0. 0. 0. 3818. -0. 0. 0. 0.27 0. -0. -0. 1094. 0. 0. 0.91 -0. -0. 1094. -0. 0.91 0O 1094. 0.91 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 1479. 1358. 3119. 3290. 0.1555 REUSS 1479. 1288. 2995. 3196. 0.1626 ARITH.MEAN 1479. 1323. 3057. 3243. 0.1591 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 8.169 5.248 5.478 5.763 REUSS 8.052 5.111 5.478 5.620 ARITH.MEAN 8.111 5.180 5.478 5.691 VMEAN= 5.767 KM/SEC PERCENT ERROR= 1.3211 DEBYE TEMP.= 711.616 ZN S —SPHALERITE CU554302 N.G.EINSPRUCH AND R.J. MANNING,J.OF THE ACOUST.SOC.OF AMER.35(1963)215 CU554302 DENSITY- 4.079 GMS/CU CM TEMPERATURE= 302 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 976. 590. 590. -0. 0 O. 1.88 -0.71 -0.71 -0. 0. 0 976. 590. -0. 0O 0 1.88 -0.71 -0. 0. 0. 976. -0. 0 0. 1.88 O. -0. -0. 451. O0 0. 2.22 -0. -0. 451. -0. 2.22 0. 451. 2*22 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 719. 348. 898. 1182. 0.3057 REUSS 719. 294. 776. 1110. 0.3201 ARITH.MEAN 719. 321. 837. 1146. 0.3129 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 5.384 2.920 4.197 3.258 REUSS 5.217 2.684 4.197 3.005 ARITH.MEAN 5.300 2.802 4.197 3.131 VMEAN= 3.146 KM/SEC PERCENT ERROR= 0.4548 DEBYE TEMP.= 344.203 150

- WILLOW RUN LABORATORIES ZN S —SPHALERITE CU554303 D.BERLINCOURTH.JAFFE AND L.R.SHIOZAWA,PHYS.REV.129(1963.P.1013 CU554303 DENSITY= 4.088 GMS/CU CM TEMPERATURE= 298 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1046. 653. 653. -0. 0. 0. 1.84 -0.71 -0.71 -0. 0. 0. 1046. 653. -0. 0. 0. 1.84 -0.71 -0. 0. 0. 1046. -0. 0. 0. 1.84 0. -0. -0. 461. 0. 0. 2.17 -0. -0. 461. -0. 2.17 Uo 461. 2.17 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POIbbON RAIIO VOIGT 784. 355. 926. 1258. 0.3167 RFUSS 784. 300. 797. 1184. 0.3305 ARITH.MEAN 784. 327. 862. 1221. 0.3236 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 5.546 2.947 4.379 3.293 REUSS 5.380 2.707 4.379 3.035 ARITH.MEAN 5.463 2.827 4.379 3.164 VMEAN= 3.180 KM/SEC PERCENT ERROR= 0.4844 DEBYE TEMP.= 348.081 BA S04 —BARITE 0R066201 H.B.HUNTINGTON,tSOLID STATE PHYS.',VOL7(1958)P.274 ACADEMIC PRESS 0R066201 DENSITY= 4.499 GMS/CU CM TEMPERATURE= 288 DEGREES KtLVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 880. 477. 269. -0. 0. 0. 1.73 -0*99 -0.17 -0. 0. 0. 781. 289. -0. 0. 0. 2.00 -0.30 -0. 0. 0. 1040. -0. 0. 0. 1.09 0. -0. -0. 117. 0. O. 8.55 -0. -0. 279. -0. 3.58 0. 255. 3.92 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 530. 241. 628. 852. 0.3154 REUSS 529. 205. 544. 802. 0.3286 ARITH.MEAN 530. 223. 586. 827. 0.3220 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.351 2.316 3.432 2.587 REUSS 4.222 2.133 3.429 2.392 ARITH.MEAN 4.287 2.224 3.431 2.489 VMEAN= 2.481 KM/SEC PERCENT ERROR= 0.3241 DEBYE TEMP.= 304.718 151

WILLOW RUN LABORATORIES BA S04 —BARITE OR066202 T.SESHAGIRI RAOPROC.INDIAN ACAD.SCI*,A33(1951),P.251 OR066202 DENSITY= 4.432 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MUDULI(1/KBAK*1000) 862. 523. 341. -0. U. U. i*.o -u.7. -uo., -U. U. U. 917. 356. -0. 0. 0. 1.74 -0.27 -0. 0. 0. 1084. -0. 0. 0. 1.10 0. -0. -0. 120. 0. 0. 8.33 -0. -0. 287. -0. 3.48 0. 274. 3.65 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 589. 246. 647. 917. 0.3282 REUSS 588. 211. 566. 870. 0.3397 ARITH.MEAN 589. 228. 607. 893. 0.3340 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.548 2.354 3.646 2.635 REUSS 4.430 2.183 3.643 2.450 ARITH.MEAN 4.489 2.269 3.645 2.543 VMEAN= 2.544 KM/SEC PERCENT ERROR= 0.0318 DEBYE TEMP.= 309.722 SRS04 —CELESTITE OR596201 T.SESHAGIRI RAO,PROC INDIAN ACAD.SCI.,A33(1951),P.251 OR596201 DENSITY= 3.955 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1044. 773. 605. -0. 0. 0. 2.20 -1.39 -0.37 -0. 0. 0. 1061. 619. -0. 0. 0. 2.19 -0.40 -0. 0. 0. 1286. -0. 0. 0. 1.14 0. -0. -0. 135. 0. 7.41 -0. -0. 279. -0. 3.58 0. 27. 37.04 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 821. 181. 506. 1062. 0.4228 REUSS 820. 86. 249. 934. 0.4494 ARITH.MEAN 820. 133. 377. 998. 0.4361 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 5.182 2.140 4.555 2.421 REUSS 4.860 1.473 4.552 1.678 ARITH.MEAN 5.021 1.806 4.553 2.050 VMEAN= 2.019 KM/SEC PERCENT ERROR= 1.4978 DEBYE TEMP.= 260.581 152

WILLOW RUN LABORATORIES CALCITE TR116101 JoBHIMASENACHAR.PROC.INDIAN ACAD.SCI*.A22(1945),P.199 TR116101 DENSITY= 2.705 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1374. 440. 450. 203. 0 0. 1.01 -0.37 -0.18 -0.71 -0. -0. 1374. 450. -203. 0* 0. 1.43 -1.02 1.67 0. 0O 801. 203. 0O 0. 2.41 -1.93 -0. -0. 342 0. 0. 5.48 0. 0. 342. 0. 2.92 O. 467. 2.14 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 692. 377. 958. 1195. 0.2853 REUSS 584. 262. 683. 933. 0.3048 ARITH.MEAN 638. 320. 821. 1064. 0.2950 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.647 3.735 5.058 4.156 REUSS 5.871 3.111 4.644 3.477 ARITH.MEAN 6.259 3.423 4.851 3.816 VMEAN= 3.838 KM/SEC PERCENT ERROR= 0.5765 DEBYE TEMP.= 492.059 CALCITE TR116102 L.PESELNICK AND R.A.ROBIEJ.APPL.PHYS.*33(1962),P.2889 TR116102 DENSITY= 2.712 GMS/CU CM TEMPERATURE= 298 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1371. 482. 568. 200. 0. 0O 1.08 -0.28 -0.43 -0.53 -0. -0. 1371. 568. -200. 0. 0. 1.77 -1.55 2.06 0. 0. 811. 200. 0. 0. 3.24 -2.49 -0. -0O 350. 0. 0 5.76 0. 0O 350. 0O 2*86 0. 445. 2.25 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 754. 358. 927. 1232. 0.3158 REUSS 639. 227. 609. 942. 0.3412 ARITH.MEAN 697. 293. 768. 1087. 0.3285 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.739 3.633 5.273 4.055 REUSS 5.894 2.894 4.855 3.250 ARITH.MEAN 6.316 3.264 5.064 3.652 VMEAN= 3.680 KM/SEC PERCENT ERROR= 0.7430 DEBYE TEMP.= 471.371 153

WILLOW RUN LABORATORIES CALCITE TR116103 L.PESELNICK AND R.A.ROBIEJ.APPL.PHYS.,34(1963)P.2495 TR116103 DENSITY= 2.712 GMS/CU CM TEMPERATURE= 298 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1445. 571. 534. -205. 0. O. 1.07 -0.49 -0.15 0.88 -0. -0. 1445. 534. 205. 0. 0. 1.67 -1.29 -2.16 0- 0. 831. -205. 0. 0. 2.73 2.43 -0. -0. 327. 0. 0. 6.49 -0. -0. 327. 0. 3.06 0. 437. 2.29 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 778. 357. 929. 1254. 0.3165 REUSS 627. 230. 616. 934. 0.3362 ARITH.MEAN 702. 294. 772. 1094. 0.3263 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.798 3.628 5.354 4.052 REUSS 5.867 2.914 4.806 3.270 ARITH.MEAN 6.333 3.271 5.080 3.661 VMEAN= 3.684 KM/SEC PERCENT ERROR= 0.6109 DEBYE TEMP.= 472.458 ARAGONITE OR116101 W.VOIGTANN.PHYSIK,24(1907)P.290 OR116101 DENSITY= 2.930 GMS/CU CM TEMPFRATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1630. 380. 17. -0. 0- 0.68 -0.30 0.04 0. -0. -0. 890. 160. -0. 0. 0. 1.29 -0.23 -0. 0. 0. 860. -0. 0. 0. 1*21 0O -0. -0. 430. 0. 0. 2.33 -0. -0. 260. -0. 3.85 O. 427. 2.34 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 499. 412. 969. 1048. 0.1774 REUSS 455. 373. 878. 952. 0.1781 ARITH.MEAN 477. 392. 924. 1000. 0.1777 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 5.980 3.748 4.128 4.127 REUSS 5.699 3.567 3.940 3.928 ARITH.MEAN 5.840 3.657 4,034 4.027 VMEAN= 4.012 KM/SEC PERCENT ERROR= 0.3945 DEBYE TEMP.= 533.224 154

.-..WILLOW RUN LABORATORIES NA CL —HALITE CU331301 K.SPANGENBERGAND S.HAUSSUHL,ZEIT KRIST.,109,(1957)P.422 CU331301 DENSITY= 2.164 GMS/CU CM TEMPERATURE= 295 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 493, 131. 131. 0. 0. 0. 2.28 -.47 -.47 0.00 0*00 0.00 493. 131. 0. 0. 0. 2.28 -.47 0.00 0.00 0.00 493. 0. 0. 0. 2.28 0.00 0.00 0.00 128. 0. 0. 7.81 0.00 0.00 128. 0. 7.81 0.00 128. 7.81 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 251. 149. 373. 450..2554 REUSS 251. 144. 364. 444..2583 ARITH.MEAN 251. 147. 369. 447..2568 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.562 2.625 3.409 2.915 REUSS 4.534 2.588 3.409 2.875 ARITH.MEAN 4.548 2.606 3.409 2.895 VMEAN= 2.942 KM/SEC PERCENT ERROR= 1.5835 DEBYE TEMP.= 304 NA CL —HALITE CU331303 D.LAZARUS, PHYS.REV.,76,(1949)P.545 CU331303 DENSITY= 2.162 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 491. 123. 123. 0. 0 0. 2.26 -.45 -.45 0.00 0.00 0.00 491. 123. 0. 0. 0. 2.26 -.45 0.00 0.00 0.00 491. 0. 0. 0. 2.26 0. 000 00 000 128. 0O 0. 7.81 0.00 0.00 128. 0. 7.81 0.00 128. 7.81 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 245. 150. 374. 446..2490 REUSS 245. 145. 365. 439..2523 ARITH.MEAN 245. 148. 369. 443..2506 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.542 2.637 3.370 2.926 REUSS 4.510 2.596 3.370 2.882 ARITH.MEAN 4.526 2.616 3.370 2.904 VMEAN= 2.950 KM/SEC PERCENT ERROR= 1.5604 DERYE TEMP.= 306 155

WILLOW RUN LABORATORIES NA CL —HALITE CU331304 E.P.PAPADAKIS,J.APPL.PHYS.34(1963)P.1875 CU331304 DENSITY= 2.162 GMS/CU CM TEMPERATURE= 300 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 490. 128. 128. 0. 0. 0. 2.28 -.47 -.47 0.00 0*00 0.00 490. 128. 0. 0. 0. 2.28 -.47 0.00 0.00 0.00 490. 0. 0. 0. 2.28 0*00 0.00 0.00 130, 0. 0. 7.69 0.00 0.00 130. 0. 7.69 0.00 130. 7.69 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 248. 150. 375. 449..2510 REUSS 248. 146. 367. 444..2537 ARITH.MEAN 248. 148. 371. 446..2524 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.557 2.637 3.391 2.927 REUSS 4.531 2.602 3.391 2.890 ARITH.MEAN 4.544 2.620 3.391 2.908 VMEAN= 2.956 KM/SEC PERCENT ERROR= 1.5982 DEBYE TEMP.= 306 K CL —SYLVITE CU281301 K.SPANGENBERGAND S.HAUSSUHLZEIT KRIST.,109,(1957)P.422 CU281301 DENSITY= 1.988 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 398. 62. 62. -0. O 0 O. 2.62 -0.35 -0.35 -0. 0. 0. 398. 62. -0. O. 0. 2.62 -0.35 -0. 0. 0. 398. -0. 0. 0. 2*62 O. -0. -0. 63. 0. 0. 15.87 -0. -0. 63. -0. 15.87 0. 63. 15.87 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 174. 105. 262. 314. 0.2701 REUSS 174. 84. 217. 286. 0.2921 ARITH.MEAN 174. 94. 240. 300. 0.2811 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 3.974 2.298 2.958 2.551 REUSS 3.793 2.055 2.958 2.293 ARITH.MEAN 3.883 2.177 2.958 2.422 VMEAN= 2.420 KM/SEC PERCENT ERROR= 0.0905 DEBYE TEMP.= 229.067 156

WILLOW RUN LABORATORIES K CL —SYLVITE CU281303 K.SPANGENBERGAND S.HAUSSUHLZEIT KRIST.,109,(1957)P.422 CU281303 DENSITY= 1.980GMS/CU CM TEMPERATURE=295 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 408. 6Q. 69. 0. 0. 0. 2.57 -.37 -.37 0.00 0.00 0.00 408. 6q. O. 0. 0. 2.57 -.37 0.00 0.00 0.00 408. 0. 0. 0. 2.57 0.00 0.00 0.00 64. 0. 0. 15.62 0.00 0.00 64. 0. 15.62 0.00 64. 15.62 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 181. 106. 266. 323..2762 REUSS 182. 85. 221. 295..2974 ARITH.MEAN 181. 95. 243. 309..2868 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 4.042 2.315 3.031 2.572 REUSS 3.863 2.074 3.031 2.316 ARITH.MEAN 3.952 2.195 3.031 2.444 VMEAN= 2.443 KM/SEC PERCENT ERROR=.0369 DEBYE TEMP.= 160.065 CA F2 —FLUORITE CU112001 L.RFRGMANN,9DER ULTRASCHALL...t(1954) S.HIRZELVERLAG CU112001 DENSITY= 3.180 GMS/CU CM TEMPERATURE= 293 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1628. 433. 433. -0 0. 0. 0.69 -0.15 -0.15 -0. 0. 0. 1628. 433. -0. 0. 0. 0.69 -0.15 -0. 0. 0. 1628. -0. 0. 0. 0.69 0. -0. -0. 334. 0. 0. 2.99 -0. -0. 334. -0. 2.99 0. 334. 2.99 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 831. 439. 1121. 1417. 0.2827 REUSS 831. 406. 1046. 1372. 0.2902 ARITH.MEAN 831. 422. 1084. 1395. 0.2865 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.675 3.717 5.113 4.138 REUSS 6.568 3.571 5.113 3.983 ARITH.MEAN 6.622 3.644 5.113 4.061 VMEAN= 4.111 KM/SEC PERCENT ERROR= 1.2313 DEBYE TFMP.= 506*231 157

WILLOW RUN LABORATORIES CA F2 —FLOURITE CU112002 D.R.HUFFMAN AND M.H.NORWOODPHYS.REV.,117u(1960)P.709 CU112002 DENSITY= 3.179 GMS/CU CM TEMPERATURE= 300 DEGREES KELVIN ELASTIC CONSTANTS (KBARS.) ELASTIC MODULI(1/KBAR*1000) 1640. 530. 530. -0. 0. 0 0.72 -0.18 -0.18 -0. 0. 0. 1640. 530. -0. 0. 0. 0.72 -0.18 -0. O. 0O 1640. -0. 0. O. 0.72 0. -0. -0. 337. 0. O. 2.97 -0. -0. 337. -0. 2.97 0O 337. 2.97 BULK MOD SHEAR MOD YOUNG MOD LONG MOD POISSON RATIO VOIGT 900. 424. 1100. 1466. 0.3014 REUSS 900. 400. 1045. 1433. 0.3065 ARITH.MEAN 900. 412. 1072. 1449. 0.3040 VELOCITY LONG SHEAR BULK AVERAGE VOIGT 6.789 3.653 5.320 4.077 REUSS 6.714 3.546 5.320 3.964 ARITH.MEAN 6.751 3.599 5.320 4.021 VMEAN= 4.078 KM/SEC PERCENT ERROR= 1.4128 DEBYE TEMP.= 501.166 158

WILLOW RUN LABORATORIES REFERENCES 1. J. Ide, "Comparison of Statically and Dynamically Determined Young's Modulus of Rocks," Proc. Natl. Acad. Sci. U. S., Vol. 22, 1936, pp. 81-92. 2. F. Birch, "The Effect of Pressure on the Modulus of Rigidity of Several Metals and Glasses," J. Appl. Phys., Vol. 8, 1937, pp. 129-133. 3. L. Pochhammer, "Ueber die Fortpflanzungsgeschwindigkeit Kleiner Schwingungen in einem unbegrentzen isotropen Kreiscylinder," J. Reine u. Angew. Math., Vol. 81, 1876, p. 324. 4. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, 1927 (also Dover, 1944). 5. D. Bancroft, "The Velocity of Longitudinal Waves in Cylindrical Bars," Phys. Rev., Vol. 59, 1941, pp. 588-593. 6. J. M. Ide, "The Velocity of Sound in Rocks and Glasses As a Function of Temperature," J. Geol., Vol. 45, 1937, pp. 689-716. 7. 0. T. Silaeva and 0. G. Shamina, "The Distribution of Elastic Pulses in Cylindrical Specimens," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 1, 1958, pp. 17-24. 8. F. Birch, "Elasticity of Igneous Rocks at High Temperatures and Pressures," Bull. Geol. Soc. Am., Vol. 54, 1943, pp. 263-286. 9. G. Pickett, "Equations for Computing Elastic Constants from Flexural and Torsional Resonant Frequencies of Vibration of Prisms and Cylinders," Am. Soc. Testing Mater. Proc., Vol. 45, 1945, pp. 846-865. 10. S. Spinner and W. E. Tefft, "Method for Determining Resonance Frequencies and for Calculating Elastic Moduli from These Frequencies," Am. Soc. Testing Mater. Proc., Vol. 61, 1961, pp. 1221-1238. 11. J. B. Wachtman, Jr., and W. E. Tefft, "Effect of Suspension Position on Apparent Values of Internal Friction Determined by Forster's Method," Rev. Sci. Instr., Vol. 29, 1958, pp. 517-520. 12. S. Spinner and R. C. Valore, Jr., "Comparison of Theoretical and Empirical Relations Between the Shear Modulus and Torsional Resonance Frequencies for Bars of Rectangular Cross-Section," J. Res. Natl. Bur. Stds., Vol. 60, 1958, pp. 459-464. 13. S. Spinner, T. W. Reichard, and W. E. Tefft, "A Comparison of Experimental and Theoretical Relations Between Young's Modulus and the Flexural and Longitudinal Resonance Frequencies of Uniform Bars," J. Res. Natl. Bur. Stds., Vol. 64A, 1960, pp. 147-155. 14. J. B. Wachtman, Jr., and D. G. Lam, Jr., "Young's Modulus of Various Refractory Materials As a Function of Temperature," J. Am. Ceram. Soc., Vol. 42, 1959, pp. 254-260. 15. C. Susse, "Mesure des Constants Elastique du Flourure de Lithium et du Periclase en Fonction de la Temperature et de la Pression," J. Rech. Centre Natl. Rech. Sci., No. 54, 1961, pp. 23-59. 159

WILLOW RUN LABORATORIES 16. S. Spinner, L. Stone, and F. P. Knutsen, "Temperature Dependence of the Elastic Constants of Thoria Specimens of Varying Porosity," J. Res. Natl. Bur. Stds., Vol. 67C, 1963, pp. 93-100. 17. D. H. Chung and W. G. Lawrence, "Relation of Single-Crystal Elastic Constants to Polycrystalline Isotropic Elastic Moduli of MgO: II. Temperature Dependence," J. Am. Ceram. Soc., Vol. 47, 1964, pp. 448-455. 18. 0. L. Anderson and N. Soga, Elastic Constants of Small Sintered Ceramic Specimens (Summary Technical Report on AFOSR Contract No. AF 33(615)1700), Lamont Geological Observatory, Columbia University, Palisades, N. Y., 31 May 1965. 19. N. Soga and O. L. Anderson, "A Simplified Method for Calculating the Elastic Moduli of Ceramic Powder from Compressibility and Debye Temperature Data," J. Am. Ceram. Soc., Vol. 49, 1966, pp. 318-322. 20. R. M. Spriggs, "Effect of Open and Closed Pores on Elastic Moduli of Polycrystalline Alumina," J. Am. Ceram. Soc., Vol. 45, 1962, p. 454. 21. R. M. Spriggs, L. A. Brissette, and T. Vasilos, "Effect of Porosity on Elastic and Shear Moduli of Polycrystalline Magnesium Oxide," J. Am. Ceram. Soc., Vol. 45, 1962, p. 400. 22. D. H. Chung, J. J. Swica, and W. B. Crandall, "Relation of Single-Crystal Elastic Constants to Polycrystalline Isotropic Elastic Moduli of MgO," J. Am. Ceram. Soc., Vol. 46, No. 9, 1963, pp. 452-457. 23. D. H. Chung, W. B. Crandall, and W. G. Lawrence, "Elastic and Anelastic Properties of Fine-Grained Polycrystalline Alumina at Elevated Temperatures," Bull. Ceram. Res. No. 297, College of Ceramics, Alfred University, Alfred, N. Y., 1961. 24. F. P. Knudsen, "Effect of Porosity on Young's Modulus of Alumina," J. Am. Ceram. Soc., Vol. 45, 1962, pp. 94-95. 25. L. Balamuth, "A New Method for Measuring Elastic Moduli and the Variation with Temperature of the Principal Young's Modulus of Rocksalt Between 78~Kand 273~K," Phys. Rev., Vol. 45, 1934, pp. 715-720. 26. F. C. Rose, "The Variation of the Adiabatic Elastic Moduli of Rocksalt with Temperature Between 80~K and 270~K," Phys. Rev., Vol. 49, 1936, pp. 50-54. 27. F. Birch, "A Simple Technique for the Study of the Elasticity of Crystals," Am. Mineralogist, Vol. 35, 1950, pp. 644-650. 28. W. G. Cady, Piezoelectricity, McGraw-Hill, 1946. (Revised ed., Vol. I, pp. 1-405, and Vol. II, pp. 406-822, Dover, 1964). 29. S. Bhagavantam and J. Bhimasenchar, "Elastic Constants of Crystals," Proc. Indian Acad. Sci., Sect. A, Vol. 20, 1944, pp. 298-303. 30. S. Bhagavantam, "Elastic Properties of Single Crystals and Polycrystalline Aggregates," Proc. Indian Acad. Sci., Sect. A, Vol. 41, 1955, pp. 72-90. 31. R. V. G. Sundara Rao, "A Modified Method for the Determination of Elastic Constants of Crystals," Proc. Indian Acad. Sci., Sect. A, Vol. 28, No. 5, 1948, pp. 475-477. 160

WILLOW RUN LABORATORIES 32. D. Bancroft, "An Electronic Interval-Timer for Laboratory Seismometry," Trans. Am. Geophys. Union, Vol. 21, 1940, pp. 695-696. 33. F. Birch, "The Velocity of Compressional Waves in Rocks to 10 Kilobars," J. Geophys. Res., Vol. 65, 1960, pp. 1083-1102. 34. D. Tocher, "Anistropy in Rocks Under Simple Compression," Trans. Am. Geophys. Union, Vol. 38, 1957, pp. 89-94. 35. G. Simmons, "Velocity of Shear Waves in Rocks to 10 Kilobars, I," J. Geophys. Res., Vol. 69, 1964, pp. 1123-1130. 36. G. Simmons, "Ultrasonics in Geology," Proc. IEEE, Vol. 53, Sec. 10, 1965, pp. 1337-1346. 37. P. W. Mason and H. J. McSkimin, "Attenuation and Scattering of High Frequency Sound Waves in Metals and Glasses," J. Acoust. Soc. Am., Vol. 19, 1947, pp. 464-473. 38. W. Roth, "Scattering of Ultrasonic Radiation in Polycrystalline Metals," J. Appl. Phys., Vol. 19, 1948, pp. 901-910. 39. D. S. Hughes, W. L. Pondrom, and R. L. Mims, "Transmission of Electric Pulses in Metal Rods," Phys. Rev., Vol. 75, 1949, pp. 1552-1556. 40. 0. T. Silaeva, "The Methods of Studying the Elastic Properties of Specimens of Rocks Under Pressure," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 2, 1959, pp. 145-149. 41. L. Y. Tu, J. N. Brennan, and J. A. Sauer, "Dispersion of Ultrasonic Pulse Velocity in Cylindrical Rods," J. Acoust. Soc. Am., Vol. 27, 1955, pp. 550-555. 42. A. Kubotera, "Determination of Elastic Wave Velocities in Rocks by Means of Ultrasonic Impulse Transmission," J. Phys. Earth, Vol. 2, 1954, pp. 33-38. 43. Ye. I. Bayuk, "Methods of Determining the Elastic Parameters of Specimens of Rocks," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 6, 1959, p. 633. 44. L. Peselnick and R. A. Robie, "Elastic Constants of Calcite," J. Appl. Phys., Vol. 33, 1962, pp. 2889-2892. 45. K. Iida and M. Kumazawa, "Measurements of Elastic Wave Velocities in Rocks at High Temperatures," Nagoya Univ. J. Earth Sci., Vol. 7, No. 1, 1959, pp. 49-64. 46. K. Iida and M. Kumazawa, "Elastic Wave Velocity and Thermal Expansion of Volcanic Rocks at High Temperatures: Part II," Nagoya Univ. J. Earth Sci., Vol. 9, No. 1, 1961, pp. 33-53. 47. D. S. Hughes and C. Maurette, "Elastic Wave Velocities in Granite," Geophysics, Vol. 21, 1956, pp. 277-284. 48. V. G. Gregson, T. J. Ahrens, and C. F. Peterson, Dynamic Properties of Rock (Final Report under Contract AF 19(604)-8419), AFCRL-63-662, Stanford Research Institute, Stanford, Calif., 15 August 1963. 49. D. Lazarus, "The Variation of the Adiabatic Elastic Constants of KC1, NaCl, CuZn, Cu, and Al with Pressure to 10,000 Bars," Phys. Rev., Vol. 76, No. 4, 1949, pp. 545-553. 161

WILLOW RUN LABORATORIES 50. R. Viswanathan, "Pulse Method of Determining Acoustic Velocities in Solids," Ind. J. Pure Appl. Phys., Vol. 2, No. 2, 1964, pp. 53-56. 51. W. Bez-Bardili, "Uber ein Ultraschall-Totalreflektometer zur Messung von Schallgeschwindigkeiten sowie der elastischen Konstanten fester K6rper," Zeit. Physik, Vol. 96, 1935, pp. 761-786. 52. W. C. Schneider and C. J. Burton, "Determination of the Elastic Constants of Solids by Ultrasonic Methods," J. Appl. Phys., Vol. 20, 1949, pp. 48-58. 53. M. Krishnamurthi and S. Balakrishna, "Measurement of Ultrasonic Velocities in Some Indian Rocks," Proc. Indian Acad. Sci., Sect. A, Vol. 38, 1953, pp. 498-501. 54. J. R. Pellam and J. K. Galt, "Ultrasonic Propagation in Liquids: Application of Pulse Technique to Velocity and Absorption Measurements at 15 Megacycles," J. Chem. Phys., Vol. 14, 1946, pp. 608-614. 55. A. R. Gregory, "Shear Wave Velocity Measurement of Sedimentary Rock Samples Under Compression," Proceedings of the Fifth Rock Mechanics Symposium, Pergamon Press, 1963, pp. 439-471. 56. S. Balakrishna, "Transmission of Ultrasonics Through Rocks," Proc. Indian Acad. Sci., Sect. A, Vol. 41, 1955, pp. 12-15. 57. M. S. King and I. Fatt, "Ultrasonic Shear Wave Velocities in Rocks Subjected to Simulated Overburden Pressure," Geophysics, Vol. 27, 1962, pp. 590-598. 58. H. J. McSkimin, "Measurement of Ultrasonic Wave Velocities and Elastic Moduli for Small Solid Specimens at High Temperatures," J. Acoust. Soc. Am., Vol. 31, 1959, pp. 287-295. 59. H. J. McSkimin, "Measurement of Elastic Constants at Low Temperatures by Means of Ultrasonic Waves-Data for Silica and Germanium Single Crystals, and for Fused Silica," J. Appl. Phys., Vol. 24, 1953, pp. 988-997. 60. 0. L. Anderson and E. Schreiber, "The Pressure Derivatives of the Sound Velocities of Polycrystalline Magnesia," J. Geophys. Res., Vol. 70, No. 20, 1965, pp. 5241-5248. 61. H. J. McSkimin, "Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids," J. Acoust. Soc. Am., Vol. 33, 1961, pp. 12-16. 62. H. J. McSkimin, "Ultrasonic Methods for Measuring the Mechanical Properties of Liquids and Solids," Physical Acoustics, ed. by W. P. Mason, Academic Press, 1964, pp. 272-334. 63. E. Schreiber and 0. L. Anderson, "The Pressure Derivatives of the Sound Velocities of Polycrystalline Alumina," J. Am. Ceram. Soc., in press. 64. D. B. Fraser and R. C. LeCraw, "Novel Method of Measuring Elastic and Anelastic Properties of Solids," Rev. Sci. Instr., Vol. 35, No. 9, 1964, pp. 1113-1115. 65. 0. L. Anderson, "An Approximate Method of Estimating Shear Velocity, Vs, from Specific Heat," J. Geophys. Res. Letters, Vol. 70, No. 18, 1965, pp. 4726-4728. 66. T. H. K. Barron, "Gruneisen Parameters for the Equation of State of Solids," Ann. Phys. (N. Y.), Vol. 1, No. 1, 1957, pp. 77-90. 162

WILLOW RUN LABORATORIES 67. E. Gruneisen; "The State of Solids," (in German), Handbuch der Physik, Springer, Vol. 10, 1926, pp. 1-52. 68. 0. L. Anderson, "The Determination and Some Uses of Isotropic Elastic Constants of Polycrystalline Aggregates Using Single-Crystal Data," Physical Acoustics, ed. by W. P. Mason, Academic Press, 1965, Vol. III-B, Chap. 2. 69. T. H. K. Barron, W. T. Berg, and J. A. Morrison, "Heat Capacity of Crystalline Magnesium Oxide," Proc. Roy. Soc. London, Ser. A, Vol. 250, 1959, pp. 70-80. 70. J. B. Wachtman, Jr., T. G. Scuderi, and G. W. Cleek, "Thermal Expansion of Aluminum Oxide and Thorium Oxide from 100~ to 1100~K," J. Am. Ceram. Soc., Vol. 45, No. 7, 1962, pp. 319-323. 71. P. G. Khubchandani and S. Sanatani, "Scattering of Cold Neutrons in Beryllium Oxide," J. Phys. Chem. Solids, Vol. 24, No. 6, 1963, pp. 782-784. 72. N. E. Phillips, "Heat Capacity of Al Between 0.1~C and 4.0O~K," Phys. Rev., Vol. 114, No. 3, 1959, pp. 676-685. 73. C. H. Cheng, C. T. Wei, and P. A. Beck, "Low-Temperature Specific Heat of Body-Centered Cubic Alloys of 3d Transition Elements," Phys. Rev., Vol. 120, No. 2, 1960, pp. 426-436. 74. K. Clusius and P. Franzosini, "Ergebnisse der Tieft temperaturforschung," Z. Naturforsch., Vol. 14A, 1955, p. 99. 75. 0. L. Anderson and P. Glynn, "Measurement of Compressibility in Polycrystalline MgO Using the Reflectivity Method," J. Phys. Chem. Solids, Vol. 26, 1965, pp. 1961-1967. 76. C. F. Cline, University of California, private correspondence, 1964. 77. B. T. Bernstein, "Elastic Properties of Polycrystalline Tungsten at Elevated Temperatures," J. Appl. Phys., Vol. 33, No. 6, 1962, p. 2140. 78. G. A. Alers, "Use of Sound Velocity Measurements in Determining the Debye Temperature of Solids," Physical Acoustics, ed. by W. P. Mason, Academic Press, 1965, Vol. III-B, Chap. 1. 79. T. H. K. Barron, W. T. Berg, and J. A. Morrison, "Properties of Alkali Halide Crystals at Low Temperature," Phys. Rev., Vol. 115, No. 6, 1959, pp. 1439-1445. 80. 0. L. Anderson, "The Debye Temperature of Vitreous Silica," J. Phys. Chem. Solids, Vol. 12, 1959, pp. 41-52. 81. J. B. Wachtman, W. E. Tefft, D. G. Lam, Jr., and R. P. Stinchfield, "Elastic Constants of Synthetic Single Crystal Corundum at Room Temperature," J. Res. Natl. Bur. Stds., Vol. 64A, 1960, pp. 213-238. 82. P. W. Bridgman, Collected Experimental Papers, Harvard University Press, Cambridge, Mass., Vol. 1-7, 1964. 83. C. E. Weir, "Isothermal Compressibilities of Alkaline Earth Oxides at 21~C," J. Res. Natl. Bur. Stds., Vol. 56, No. 6, 1956, pp. 187-189. 84. E. A. Perez-Albuerne and H. G. Drickamer, "The Effect of High Pressures in the Compressibilities of Seven Crystals Having the NaCl or CsC1 Structures," J. Chem. Phys., Vol. 43, No. 4, 1965, p. 1381. 163

- WILLOW RUN LABORATORIES 85. D. B. McWhan, "Compressibility of Cadmium and Zinc to 100 Kbars," J. Appl. Phys., Vol. 36, No. 2, 1965, pp. 664-665. 86. T. Takahashi and W. A. Bassett, "High Pressure Polymorph of Iron," Science, Vol. 145, No. 3631, 1964, pp. 483-486. 87. R. G. McQueen and S. P. Marsh, "Equation of State for Nineteen Metallic Elements from Shock-Wave Measurements to Two Megabars," J. Appl. Phys., Vol. 31, No. 1, 1960, pp. 1253-1269. 88. W. F. Brace, "Some New Measurements of Linear Compressibility of Rocks," J. Geophys. Res., Vol. 70, 1965, pp. 391-398. 89. R. E. Frywell and B. A. Chandler, "Creep, Strength, Expansion and Elastic Moduli of Sintered BeO as a Function of Grain Size, Porosity, and Grain Orientation," J. Am. Ceram. Soc., Vol. 47, No. 6, 1964, pp. 283-291. 90. J. B. Wachtman, Jr., W. E. Tefft, and D. G. Lam, Jr., "Elastic Constants of Rutile (TiO2)," J. Res. Natl. Bur. Stds., Vol. 66A, No. 6, 1962, pp. 465-471. 91. 0. L. Anderson, "An Approximate Method of Estimating the Sound Velocities from Refractive Index Data," submitted to Am. Mineralogist. 92. 0. L. Anderson and J. L. Nafe, "The Bulk Modulus-Volume Relationship for Oxide Compounds and Related Geophysical Problems," J. Geophys. Res., Vol. 70, No. 16, 1965, pp. 3951-3963. 93. 0. L. Anderson and E. Schreiber, "The Relation Between Refractive Index and Density for Minerals Related to the Earth's Mantle," J. Geophys. Res., Vol. 70, No. 6, 1965, pp. 1463-1471. 94. R. K. Verma, "Elasticity of Several Highly Dense Crystals," J. Geophys. Res., Vol. 65, 1960, pp. 757-766. 95. 0. L. Anderson, "A Simplified Method for Calculating the Debye Temperature from Elastic Constants," J. Phys. Chem. Solids, Vol. 24, No. 3, 1963, pp. 909-917. 96. T. B. Bateman, "Elastic Moduli of Single Crystal Zinc Oxide," J. Appl. Phys., Vol. 33, No. 1, 1962, pp. 3309-3312. 97. E. S. Larsen and H. Berman, "The Microscopic Determination of the Nonopaque Minerals," Bulletin No. 848, U. S. Department of the Interior, Government Printing Office, 1934. 98. L. Peselnick and R. Meister, "Variational Method of Determining Effective Moduli of Polycrystals: (A) Hexagonal Symmetry, (B) Trigonal Symmetry," J. Appl. Phys., Vol. 36, No. 9, 1965, pp. 2879-2884. 99. Z. Hashin and S. Shtrikman, "On Some Variational Principles in Anisotropic and Non-Homogeneous Elasticity," J. Mech, Phys. Solids, Vol. 10, 1962, p. 335-342. 100. Z. Hashin and S. Shtrikman, "Variational Approach to Theory of Elastic Behavior of Polycrystals," J. Mech. Phys. Solids, Vol. 10, 1962, p. 343-352. 101. N. Soga, "The Gruneisen Constant and a Parameter 6 of Tantalum and Tungsten at Elevated Temperature," submitted to J. Appl. Phys., 1965. 102. W. Koster, "Die Temperaturabhangigkeit des Elastizitats Modulus reiner Metalle," Z..Metallkunde, Vol. 39, No. 1, 1948, pp. 1-9. 164

WILLOW RUN LABORATORIES 103. F. Birch, "Elasticity and Constitution of the Earth's Interior," J. Geophys. Res., Vol. 57, 1952, pp. 227-286. 104. F. Birch, "The Velocity of Compressional Waves in Rocks to 10 Kbars, 2," J. Geophys. Res., Vol. 66, 1961, pp. 2199-2224. 105. J. E. Nafe and C. L. Drake, "Variation with Depth in Shallow and Deep Water Marine Sediments of Porosity, Density and the Velocities of Compressional and Shear Waves," Geophysics, Vol. 22, 1957, pp. 523-552. 106. T. J. Ahrens and S. Katz, "An Ultrasonic Interferometer for High Pressure Research," J. Geophys. Res., Vol. 67, 1962, pp. 2935-2944. 107. T. J. Ahrens and S. Katz, "Ultrasonic Observation of the Calcite-Aragonite Transition," J. Geophys. Res., Vol. 68, 1963, pp. 529-537. 108. 0. L. Anderson, "Two Methods of Estimating Compression and Sound Velocity at Very High Pressures," Proc. Natl. Acad. Sci. U.S., Vol. 54, No. 3, 1965, pp. 667-673. 109. 0. L. Anderson, "Seismic Parameter p: Computation at Very High Pressure from Laboratory Data," Bull. Seism. Soc. Am., Vol. 56, 1966, pp. 725-732. 110. H. V. Hart and H. G. Drickamer, "Effect of High Pressure in Lattice Parameters of A1203," J. Chem. Phys., in press, 1965. 111. R. G. McQueen and S. P. Marsh, private communication, 1964. 112. F. Birch, "Interpretation of the Seismic Structure of the Crust in the Light of Experimental Studies of Wave Velocities in Rocks," Contributions in Geophysics in Honor of Beno Gutenberg, Pergamon Press, 1958, Chap. 12. 113. 0. L. Anderson, "A Derivation of Wachtman's Equation for the Temperature Dependence of Elastic Moduli of Oxide Compounds," Phys. Rev., Vol. 144, 1966, pp. 553-557. 114. N. Soga and 0. L. Anderson, "The High Temperature Elastic Properties of Polycrystalline MgO and A1203," submitted to J. Am. Ceram. Soc. 115. J. F. Nafe and C. L. Drake, "The Physical Properties of Rocks of Basaltic Composition," in symposium volume on basalts, ed. by H. Hess, Interscience, Wiley, 1965, in press. 116. H. Williams, F. J. Turner, and C. M. Gilbert, Petrography, Freeman, 1954, pp. 1-406. 117. C. S. Hurlbut, Jr., Dana's Manual of Mineralogy, Wiley, 1959, p. 519. 118. W. A. Deer, R. A. Howie, and J. Zussman, Rock-Forming Minerals, Wiley, 1963, 5 volumes. 119. K. S. Alexandrov and T. V. Ryzhova, "The Elastic Properties of RockForming Minerals, I: Pyroxenes and Amphiboles," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 9, 1961, pp. 871-875. 120. K. S. Alexandrov and T. V. Ryzhova, "Elastic Properties of Rock-Forming Minerals, II: Layered Silicates," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 12, 1961, pp. 1165-1168. 121. K. S. Alexandrov and T. V. Ryzhova, "Elastic Properties of Rock-Forming Minerals, III: Feldspars," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 2, 1962, pp. 129-131. 165

WILLOW RUN LABORATORIES 122. T. V. Ryzhova, "Elastic Properties of Periclase," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 7, 1964, pp. 633-635. 123. T. V. Ryzhova and K. S. Alexandrov, "Elastic Properties of Rock-Forming Minerals," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 12, 1962, pp. 1125-1127. 124. F. Birch, "Velocity of Compressional Waves in Serpentinite from Mayagiiez, Puerto Rico," A Study of Serpentinite, National Academy of Science-National Research Council, Publication No. 1188, 1964, pp. 132-133. 125. N. I. Christensen, "Compressional Wave Velocities in Metamorphic Rocks at Pressures to 10 Kilobars" (abstract), Trans. Am. Geophys. Union, Vol. 46, 1965, p. 162 (1965 AGU Meeting). 126. H. J. McSkimin and P. Andreatch, "Analysis of the Pulse Superposition Method for Measuring Ultrasonic Wave Velocities As a Function of Temperature and Pressure," J. Acoust. Soc. Am., Vol. 34, 1962, pp. 609-615. 127. K. Hirasawa, "On the Result of Physical Measurements for Pyrite Ore and Crystalline Schist in the Sazare Mine. Especially on the Elastic Wave Velocity," Butsuri-Tanko, Vol. 15, No. 2, 1962, pp. 72-84. 128. A. S. Laughton, "Sound Propagation in Compacted Ocean Sediments," Geophysics, Vol. 22, 1957, pp. 233-260. 129. A. F. Woeber, S. Katz, and T. J. Ahrens, "Elasticity of Selected Rocks and Minerals," Geophysics, Vol. 28, 1963, pp. 658-663. 130. G. Simmons, "Velocity of Compressional Waves in Various Minerals at Pressures up to 10 Kilobars," J. Geophys. Res., Vol. 69, 1964, pp. 1117-1121. 131. R. D. Tooley, "Sonic Velocity in Yule Marble" (abstract), J. Geophys. Res., Vol. 67, 1962, p. 3604. 132. G. H. F. Gardner, M. R. J. Wyllie, and D. M. Droschak, "Hysteresis in the Velocity-Pressure Characteristics of Rocks," Geophysics, Vol. 30, 1965, pp. 111-116. 133. B. S. Banthia, M. S. King, and I. Fatt, "Ultrasonic Shear-Wave Velocities in Rocks Subjected to a Simulated Overburden Pressure and Internal Pore Pressure," Geophysics, Vol. 30, 1965, pp. 117-121. 134. F. Birch and D. Bancroft, "The Effect of Pressure on the Rigidity of Rocks," J. Geol., Vol. 46; 1938, Part I, pp. 59-87; Part II, pp. 113-141. 135. J. M. Ide, "The Elastic Properties of Rocks: a Correlation of Theory and Experiment," Proc. Natl. Acad. Sci., U. S., Vol. 22, 1936, pp. 482-496. 136. J. B. Walsh, "The Effect of Cracks on the Compressibility of Rock," J. Geophys. Res., Vol. 70, No. 2, 1965, pp. 381-390. 137. D. Shimozura, "Elasticity of Rocks and Some Related Geophysical Problems," Japan. J. Geophys., Vol. 2, No. 3, 1960. 138. R. B. Gordon and R. J. Vaisnys, "On the Ultrasonic Observation of the Calcite Aragonite Transition," J. Geophys. Res., Vol. 69, 1964, pp. 4920-4921. 139. D. S. Hughes and C. Maurette, "Determination des vitesses d'ondes elastiques dans diverses roches en fonction de la pression et de la temperature," Rev. Inst. Francais Petrole et Ann. Combustibles Liquides, Vol. 12, 1957, pp. 730-752. 166

WILLOW RUN LABORATORIES 140. K. lida, "Changes in Rigidity and Internal Friction of Amorphous Silica with Temperature," Bull. Earthquake Res. Inst., Tokyo Univ., Vol. 13, 1935, pp. 665-680. 141. G. Simmons, "Single Crystal Elastic Constants and Calculated Aggregate Properties," J. Grad. Res. Ctr., Vol. 34, No. 1 and 2, 1965. 142. R. Hill, "The Elastic Behavior of a Crystalline Aggregate," Proc. Phys. Soc. London, Vol. 65A, 1952, pp. 349-354. 143. W. Voigt, Lehrbuch der Kristallphysik, B. G. Teubner, Leipzig, 1928. 144. A. Reuss, "Berechnung de Fliessgrenze von Mischkristallen auf Grund der Plastizitatsbedingung fur Einkristalle, Z. angew. Math. u. Mech., Vol. 9, 1929, pp. 49-58. 145. A. E. Clark and R. E. Strakna, "Elastic Constants of Single Crystal YIG," J. Appl. Phys., Vol. 32, 1961, p. 1172. 146. M. S. Doraiswami, "Elastic Constants of Magnetite, Pyrite, and Chromite," Proc. Indian Acad. Sci., Sect. A, Vol. 25, 1947, pp. 413-416. 147. C. Wang, "Velocity of Compressional Waves in Limestones, Marbles, and a Single Crystal of Calcite to 20 Kilobars,' J. Geophys. Res., Vol. 71, 1966, pp. 3543-3548. BIBLIOGRAPHY References from appendixes 6, 7, and 8 which have not been cited in the text are included here in complete form. Also included are additional references which may be of interest to the energetic reader and to investigators in this field. Adadurov, G. A., D. B. Balashov, and A. N. Dremin, "A Study of the Volumetric Compressibility of Marble at High Pressures," Bull. Acad, Sci. USSR, Geophys. Ser. (English Transl.), No. 5, 1961, pp. 463-466. Adams, F. D., and E. G. Coker, "An Investigation into the Elastic Constants of Rocks, More Especially with Reference to Cubic Compressibility," Carnegie Inst. Wash. Publ., No. 46, 1906, 69 pp. Adams, L. H., "The Compressibility of Fayalite and the Velocity of Elastic Waves in Peridotite with Different Iron-Magnesium Ratios," Gerlands. Beitr. Geophys., Vol. 31, 1931, pp. 315-321. Adams, L. H., and R. E. Gibson, "The Compressibilities of Dunite and of Basalt Glass and Their Bearings on the Composition of the Earth," Proc. Natl. Acad. Sci. U. S;, Vol. 12, 1926, pp. 275-283. Adams, L. H., and R. E. Gibson, "The Elastic Properties of Certain Basic Rocks and of Their Constituent Minerals," Proc. Natl. Acad. Sci. U. S., Vol. 15, 1929, pp. 713-724. Adams, L. H., and R. E. Gibson, "The Cubic Compressibility of Certain Substances," Wash. (D.C.) Acad. Sci. J., Vol. 21, 1931, pp. 381-390. Adams, L. H., and E. D. Williamson, "The Compressibility of Minerals and Rocks at High Pressures," J. Franklin Inst., Vol. 195, 1923, pp. 475-529. 167

WILLOW RUN LABORATORIES Afanas'yev, G. D., M. P. Volarovich, Ye. I. Bayuk, and N. Ye. Galdin, "Investigation of Elastic Wave Velocities in Ultrabasic Rocks of the Monchegorsk Pluton Under Conditions of High Confining Pressure," Dokl. Akad. Nauk SSSR, Vol. 155, No. 5, 1964, pp. 1058-1061. Ahrens, T. J., and V. G. Gregson, Jr., "Shock Compression of Crustal Rocks: Data for Quartz, Calcite, and Plagioclase Rocks," J. Geophys. Res., Vol. 69, 1964, pp. 4839-4874. Alexandrov, K. S., and T. V. Ryzhova, "Elastic Properties of Crystals (Review)," Soviet Phys. Cryst. (English Transl.), Vol. 6, No. 2, 1961, pp. 226-252. Al'tshuler, L. V., S. B. Kormer, M. I. Brazhnik, L. A. Vladimirov, M. P. Speranskaya, and A. I. Funtikov, "The Isentropic Compressibility of Aluminum, Copper, Lead and Iron at High Pressures," Soviet Phys. JETP (English Transl.), Vol. 11, 1960, pp. 766-775. Anderson, O. L., "Conditions for a Density Minimum in the Upper Mantle," J. Geophys. Res., Vol. 70, 1965, pp. 1457-1461. Anderson, O. L., and E. Schreiber, "Measurement of P and S Sound Velocities Under Pressure on Laboratory Models of the Earth's Mantle," (Semiannual Technical Summary Report on Contract No. AF 49(638)-1355), Lamont Geological Observatory, Columbia University, Palisades, N. Y., June 1964. Antsyferov, M. S., N. G. Antsyferova, and Ya. Ya. Kagan, "Investigation of the Velocities of Propagation and Absorption of Elastic Waves in Frozen Sand," Akad. Nauk. SSSR Izv. Ser. Geofiz., No. 1, 1964, pp. 85-89. Antsyferov, M. S., "Propagation of Ultrasonic Waves in Dry Sand Under Pressure," Bull. (Izv.) Soviet Acad. Sci., No. 12, 1964. Atanasoff, J. V., and P. J. Hart, "Dynamical Determination of the Elastic Constants and Their Temperature Coefficients for Quartz," Phys. Rev., Vol. 59, 1941, pp. 85-96. Auberger, M., and J. S. Rinehart, "Ultrasonic Velocity and Attenuation of Longitudinal Waves in Rocks," J. Geophys. Res., Vol. 66, 1961, pp. 191-199. Balakrishna, S., "Granular Structure in Rock Sections and Transmission of Sound," Current Sci. (India), Vol. 21, No. 9, 1952, pp. 241-242. Balakrishna, S., "Sound Velocities in Some Indian Rock Specimens," Proc. Indian Acad. Sci., Sect. A, Vol. 36, 1952, pp. 375-380. Balakrishna, S., "Transmission of Ultrasonics Through Rocks," Proc. Indian Acad. Sci. Sect. A, Vol. 41, 1955, pp. 12-15. Balakrishna, S., "Velocity of Compressional Waves in Some Indian Rocks," Trans. Am. Geophys. Union, Vol. 39, 1958, pp. 711-712. Balakrishna, S., "Ultrasonic Velocities in Some Metamorphic Rocks," Geol. Soc. India J., Vol. 1, 1959, pp. 136-143. Balakrishna, S., "Effect of Dimensional Orientation on Ultrasonic Velocities in Some Rocks," Proc. Indian Acad. Sci. Sect. A, Vol. 49, No. 6, 1959, pp. 318-321. Balakrishna, S., "Ultrasonic Velocities in Relation to the Degree of Metamorphism in Limestones," Proc. Indian Acad. Sci., Sect. A, Vol. 50, No. 6, 1959, pp. 363365. 168

WILLOW RUN LABORATORIES Balakrishna, S., "Elastic Wave Velocities in Makrana Marbles," Current Sci. (India), Vol. 28, No. 7, 1959, p. 285. Balakrishna, S., "Effect of Granular Texture on Ultrasonic Velocities in Some Rocks," Indian Mineralogist, Vol. 1, No. 1, 1960, pp. 57-59. Balakrishna, S., and Y. Subrahmanyam, "Variation of Ultrasonic Velocities in Charnockites," Current Sci. (India), Vol. 31, No. 2, 1962, pp. 62-63. Bastien, P., and P. Azou, "Ultrasonic Determination of the Elastic and Inelastic Properties of Solids," Appl. Mater. Res., Vol. 2, 1963, pp. 170-180. Bayuk, Ye. I., "The Investigation of the Elastic Properties of Rock Samples Taken from a Deep Borehole at High Pressures," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 12, 1960, pp. 1173-1177. Bechmann, R., "Elastic and Piezoelectric Constants of Alpha-Quartz," Phys. Rev., Vol. 110, 1958, p. 1060. Belikov, B. P., "Elastic Properties of Rocks," English transl. in Ceskeslovenska Akad. Ved. Studia Geophys. et Geod., Vol. 6, No. 1, 1962, pp. 75-85. Bergmann, L., Der Ultroschall und seine Anwendung in Wissenschaft und Technik. G. vUllig u berarbeitete und er weiterte tuf, S. Hirzel, Zurich, 1954. Berlincourt, D., H. Jaffe, and L. R. Shiozawa, "Electroelastic Properties of the Sulfides, Selenides, and Tellurides of Zinc and Cadmium," Phys. Rev., Vol. 129, 1963, pp. 1009-1017. Bernstein, B. T., "Elastic Constants of Synthetic Sapphire at 27~C," J. Appl. Phys., Vol. 34, 1963, pp. 169-172. Bhagavantan, S., and J. Bhimasenachar, "Elastic Constants of Diamond," Nature, Vol. 154, 1944, p. 546. Bhagavantam, S., and T. Seshagiri Rao, "Elastic Constants of Galena," Nature, Vol. 168, 1951, p. 42. Bhimasenachar, J., "Elastic Constants of Calcite and Sodium Nitrate," Proc. Indian Acad. Sci. Sect. A, Vol. 22, 1945, pp. 199-207. Bhimasenachar, J., "Elastic Constants of Corundum," Current Sci. (India), Vol. 18, 1949, pp. 372-373. Bhimasenachar, J., and G. Venkata Rao, "Elastic Constants of Staurolite," J. Acoust. Soc. Am., Vol. 29, No. 3, 1957, pp. 343-345. Bhimasenachar, J. and G. Venkataratnam, "Elastic Constants of Zircon," J. Acoust. Soc. Am., Vol. 27, No. 5, 1955, pp. 922-925. Birch, F., "The Effect of Pressure upon the Elastic Parameters of Isotropic Solids, According to Murnaghan's Theory of Finite Strain," J. Appl. Phys., Vol. 9, 1938, pp. 279-288. Birch, F., "Physics of the Crust," Geol. Soc.Am.,Spec. Papers, No. 62, 1955, pp. 101-117. Birch, F., "Elastic Constants of Rutile," J. Geophys. Res., Vol. 65, 1960, pp. 38553856. 169

WILLOW RUN LABORATORIES Birch, F., "Some Geophysical Applications of High-Pressure Research," Solids Under Pressure, ed. by W. Paul and D. M. Warschauer, McGraw-Hill, 1963, pp. 137-162. Birch, F., and D. Bancroft, "New Measurements of the Rigidity of Rocks at High Pressures," J. Geol., Vol. 48, 1940, pp. 752-766. Birch, F., and D. Bancroft, "The Elasticity of Glass at High Temperatures, and the Vitreous Basaltic Substratum," Am. J. Sci., Vol. 240, 1942, pp. 457-490. Birch, F., and H. Clark, "The Thermal Conductivity of Rocks and Its Dependence upon Temperature and Composition," Am. J. Sci., Vol. 238, 1940, pp. 529-558 and 613-635. Birch, F., and R. R. Law, "Measurement of Compressibility at High Pressures and High Temperatures," Bull. Geol. Soc. Am., Vol. 46, 1935, pp. 1219-1250. Birch, F., and R. P. Dow, "Compressibility of Rocks and Glasses at High Temperatures and Pressures: Seismological Application," Bull. Geol. Soc. Am., Vol. 47, 1936, pp. 1235-1256. Birch, F., J. F. Schairer, and H. C. Spicer, "Handbook of Physical Constants," Geol. Soc. Am., Spec. Papers, No. 36, 1942. Birch, F., E. C. Robertson, and S. P. Clark, Jr., "Apparatus for Pressures of 27,000 Bars and Temperatures of 1400~C," Ind. Eng. Chem., Vol. 49, 1957, pp. 1965-1966. Boyd, F. R., "Geological Aspects of High Pressure Research," Science, Vol. 145, No. 3627, 1964, pp. 13-20. Brace, W. F. "Brittle Fracture of Rocks," Proceedings of the Symposium on State of Stress in Earth's Crust, Santa Monica, 1963, Elsevier, 1964, pp. 111-180. Bridgman, P. W., "The Failure of Cavities in Crystals and Rocks under Pressure," Am. J. Sci., Vol. 45, 1918, pp. 243-268. Bridgman, P. W., "The Compressibility of Thirty Metals As a Function of Pressure and Temperature," Proc. Am. Acad. Arts Sci., Vol. 58, 1923, pp. 165-242. Bridgman, P. W., "The Thermal Conductivity and Compressibility of Several Rocks Under High Pressures," Am. J. Sci., Vol. 7, 1924, pp. 81-102. Bridgman, P. W., "The Compressibility of Several Artificial and Natural Glasses," Am. J. Sci., Vol. 10, 1925, pp. 359-367. Bridgman, P. W., "Linear Compressibility of Fourteen Natural Crystals," Am. J. Sci., Vol. 10, 1925, pp. 483-498. Bridgman, P. W., "The Linear Compressibility of Thirteen Natural Crystals," Am. J. Sci., Vol. 10, 1928, pp. 287-296. Bridgman, P. W., "The Compression of Eighteen Cubic Compounds," Proc. Am. Acad. Arts Sci., Vol. 67, 1932, pp. 345-375. 2 Bridgman, P. W., "The Linear Compression of Iron to 30,000 kg/cm," Proc. Am. Acad. Arts Sci., Vol. 74, 1940, pp. 11-20. Bridgman, P. W., "The Compression of 39 Substances to 100,000 kg/cm," Proc. Am. Acad. Arts Sci., Vol. 76, 1948, pp. 55-70. 170

W — ILLOW RUN LABORATORIES 2 Bridgman, P. W., "Rough Compressions of 177 Substances to 40,000 kg/cm," Proc. Am. Acad. Arts Sci., Vol. 76, 1948, pp. 71-87. 2 Bridgman, P. W., "Linear Compressions to 30,000 kg/cm Including Relatively Incompressible Substances," Proc. Am. Acad. Arts Sci., Vol. 77, 1949, pp. 189234. Bridgman, P. W., The Physics of High Pressure, 2nd ed., T. Bell and Sons, London, 1949, 445 pp. Bruckshaw, J. McG., and P. C. Mahanta, "The Variation of the Elastic Constants of Rocks with Frequency," Petroleum, Vol. 17, 1954, pp. 14-18. Cannaday, F. X., "Modulus of Elasticity of a Rock Determined by Four Different Methods," Report of Investigations No. 6533, Bureau of Mines, 1964. Chou, Y. T., and R. W. Whitmore, "Single and Double Pile-Up of Dislocations in MgO Crystals," J. Appl. Phys., Vol. 32, 1961, pp. 1920-1926. Desbrandes, R., X. Reverdy, and A. Lagarde, "Contribution to the Study of the Velocity of Seismic Waves," Rev. Inst. Francais Petrole et Ann. Combustibles Liquides, Vol. 14, No. 4-5, 1959, pp. 535-548. Dremin, A. W., and G. A. Adadurov, "Shock Adiabatic for Marble," Soviet Phys. Dokl. Akad. Nauk SSSR, Vol. 128, 1959, pp. 970-973. Durand, M. A., "The Temperature Variation of the Elastic Moduli of NaC1, KC1 and MgO," Phys. Rev., Vol. 50, 1936, pp. 449-455. Duvall, G. E., and G. R. Fowles, "Shock Waves," High Pressure Physics and Chemistry, Vol. 2, ed. by R. S. Bradley, Academic Press, 1963. Einspruch, N. G., and R. J. Manning, "Elastic Constants of Compound Semiconductors-ZnS, PbTe, GaSb," J. Acoust. Soc. Am., Vol. 35, 1963, pp. 215-216. Emelin, V. I., and K. S. Chuprov, "The Ultrasonic Method to Determine the Dynamic Elastic Parameters of Rocks under Field Conditions," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 4, 1962, pp. 312-315. Fang, Wei-Ch'ing, "A Dynamic Pulse Method for Determining the Elastic Parameters of Rock Samples at High Isotropic Pressures," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 10, 1961, pp. 1004-1008. Galt, J. K., "Mechanical Properties of NaCl, KBr, KC1," Phys. Rev., Vol. 73, 1948, pp. 1460-1462. Hayakawa, M., "Measurement of Longitudinal and Transverse Wave Velocities of Dunite, Peridotite, and Some Other Rocks in Hidaka Area, Hokkaido (Laboratory Experiment)," in Geophysical papers dedicated to Professor Kenzo Sassa, Kyoto, Japan, Kyoto University Geophysical Institute, 1963, pp. 25-32. Hearmon, R., "The Elastic Constants of Anisotropic Materials," Rev. Mod. Phys., Vol. 49, 1946, pp. 409-440. 171

WILLOW RUN LABORATORIES Hearmon, R., "The Elastic Constants of Anisotropic Material." Advan, Phys., Vol. 5, 1956, pp. 323-382. Hearmon, R., An Introduction to Applied Anisotropic Elasticity, Oxford University Press, London, 1961, pp. 1-136. Hess, H. H., "The Am. Soc. Hole to the Earth's Mantle," Trans. Am. Geophys. Union, Vol. 40, 1959, pp. 340-345. Hubbard, J. C., and A. L. Loomis, "The Velocity of Sound in Liquids at High Frequencies by the Sonic Interferometer," Phil. Mag., Series 7, Vol. 5, 1928, pp. 1177-1190. Huffman, D. R., and M. H. Norwood, "Specific Heat and Elastic Constants of Calcium Fluoride at Low Temperature," Phys. Rev., Vol. 117, 1960, pp. 709-711. Hughes, D. S., "Elastic Wave Velocities in Sedimentary Rocks," Trans. Am. Geophys. Union, Vol. 32, 1951, pp. 173-178. Hughes, D. S., and C. E. Cooke, Jr., "The Effect of Pressure on the Reduction of Pore Volume of Consolidated Sandstone," Geophysics, Vol. 18, 1953, pp. 298309. Hughes, D. S., and J. H. Cross, "Elastic Wave Velocities at High Pressures and Temperatures," Geophysics, Vol. 16, 1951, pp. 577-593. Hughes, D. S., and H. J. Jones, "Variation of Elastic Moduli of Igneous Rocks with Pressure and Temperature," Bull. Geol. Soc. Am., Vol. 61, 1950, pp. 843-856. Hughes, D. S., and J. L. Kelly, "Variation of Elastic Wave Velocity with Saturation in Sandstone," Geophysics, Vol. 17, 1952, pp. 739-752. Hughes, D. S., and C. Maurette, "Variation of Elastic Wave Velocities in Basic Igneous Rocks with Pressure and Temperature," Geophysics, Vol. 22, 1957, pp. 23-31. Hughes, D. S., and R. G. McQueen, "Density of Basic Rocks at Very High Pressures," Trans. Am. Geophys. Union, Vol. 39, 1958, pp. 959-965. Hughes, D. S., and T. Nishitake, "Measurements of Elastic Wave Velocity in Armco Iron and Jadeite under High Pressures and High Temperatures," in Geophysical papers dedicated to Professor Kenzo Sasso, Kyoto, Japan, Kyoto University Geophysical Institute, 1963, pp. 379-385. Ide, J. M., "Some Dynamic Methods for Determination of Young's Modulus," Rev. Sci. Instr., Vol. 6, 1935, pp. 296-298. Jamieson, J. C., and H. Hoskins, "The Measurement of Shear-Wave Velocities in Solids Using Axially-Polarized Ceramic Transducers," Geophysics, Vol. 28, 1963, pp. 87-90. Kammer, E. W., T. E. Pardue and H. F. Frissel, "A Determination of the Elastic Constants for Beta-Quartz," J. Appl. Phys., Vol. 19, 1948, pp. 265-270. Kataoka, A., and M. Oguri, "Some Dynamic Properties of Rocks at Room Temperatures," Zisin, Series 2, Vol. 12, No. 3, 1959, pp. 91-100. Knopoff, L., "Seismic Wave Velocities in Westerly Granite," Trans. Am. Geophys. Union, Vol. 35, 1954, pp. 969-973. 172

WILLOW RUN LABORATORIES Koga, I., and M. Aruga, "Theory of Plane Elastic Waves in a Piezoelectric Crystalline Medium and Determination of the Elastic and Piezoelectric Constants of Quartz," Phys. Rev., Vol. 109, 1958, pp. 1467-1473. Kravets', V. V., "On the Velocities of Elastic Oscillations and Anisotropy of Certain Metamorphic Rocks," Akad. Nauk. Ukrayin, RSR Dopovidi, No. 3, 1961, pp. 295-298. Mayer, W. A., and E. A. Heidman, "Corrected Values of the Elastic Moduli of Sapphire," J. Acoust. Soc. Am., Vol. 32, 1960, pp. 1699-1700. Madelung, E., and R. Fuchs, "Kompressibilitatsmessungen an festers Korpers," Ann. Phys., Vol. 65, 1921, pp. 289-309 (in German). Mason, W. P., Piezoelectric Crystals and Their Applications to Ultrasonics, Van Nostrand, 1950, 508 pp. Mason, W. P., "Quartz Crystal Applications," Bell Systems Tech. J., Vol. 22, 1943, p. 178. Mason, W. P., Physical Acoustics and the Properties of Solids, Bell Laboratories Series, Van Nostrand, 1958. Matsushima, S., "Variation of the Elastic Wave Velocities of Rocks of the Process of Deformation and Fracture Under High Pressure," Disaster Prevention Res. Inst. Bull., Kyoto, Japan, Vol. 32, 1960, pp. 1-8. McSkimin, H. J., "Ultrasonic Measurement Techniques Applicable to Small Solid Specimens," J. Acoust. Soc. Am., Vol. 22, 1950, pp. 413-418. McSkimin, H. J., "Propagation of Longitudinal Waves and Shear Waves in Cylindrical Rods at High Frequencies," J. Acoust. Soc. Am., Vol. 28, 1956, pp. 484-494. McSkimin, H. J., "Ultrasonic Pulse Technique for Measuring Acoustic Losses and Velocities of Propagation in Liquids As a Function of Temperature and Hydrostatic Pressure," J. Acoust. Soc. Am., Vol. 29, 1957, pp. 1185-1192. McSkimin, H. J., and W. L. Bond, "Elastic Moduli of Diamond," Phys. Rev., Vol. 105, 1957, pp. 116-121. Nagaoka, H., "Elastic Constants of Rocks and the Velocity of Seismic Waves," Phil. Mag., Vol. 50, 1900, pp. 53-65. Papadakis, E. P., "Attenuation of Pure Elastic Modes in NaCl Single Crystals," J. Appl. Phys., Vol. 34, 1963, pp. 1872-1876. Peselnick, L., "Elastic Constants of Solenhofen Limestone and Their Dependence upon Density and Saturation," J. Geophys. Res., Vol. 67, 1962, pp. 4441-4448. Peselnick, L., and W. F. Outerbridge, "Internal Friction in Shear and Shear Modulus of Solenhofen Limestone over a Frequency Range of 107 Cycles per Second," J. Geophys. Res., Vol. 66, 1961, pp. 581-588. Peselnick, L., and R. A. Robie, "Elastic Constants of Calcite," J. Appl. Phys., Vol. 34, 1963, pp. 2494-2495. Petkevich, G. I., "Contribution to the Study of Elastic Properties of Rocks in CisCarpathia," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 2, 1959, pp. 210-213. 173

WILLOW RUN LABORATORIES Petkevich, G. I., "On the Study of Velocities of Longitudinal Elastic Waves on Perforated Models Saturated with Fluids," Akad. Nauk Ukrayin, RSR Dopovidi, No. 11, 1963, pp. 1470-1473. Petkevich, G. I., and T. Z. Verbitsky, "Investigations of Longitudinal Elastic Wave Velocities in Rocks Saturated by Liquids," Akad. Nauk Ukrayin, RSR Dopovidi, No. 5, 1962, pp. 605-608. Prasado Rao, G. H. S. V., "Anisotropy in the Elastic Behavior of Rocks," Proc. Indian Acad. Sci., Sect. A, Vol. 25, 1947, pp. 238-246. Pros, Z., and J. Vanek, "Experimental Study of a Pulse Method for Measuring Elastic Parameters of Rocks in Samples," Ceskoslovenska Acad. Ved. Studia Geophys. et Geod., Vol. 4, 1960, pp. 338-349. Pros, Z., J. Vanek, and K. Kli'ma, "The Velocity of Elastic Waves in Diabase and Greywacke Under Pressures up to 4 Kilobars," Eeskoslovenska, Akad. Ved. Studia Geophys. et Geod., Vol. 6, No. 4, 1962, pp. 347-368. Ramachandran, G. N., and W. A. Wooster, "Determination of Elastic Constants of Crystals from Diffuse Reflections of X-Rays," Acta Cryst., Vol. 4, 1951, pp. 335-344. Ramachandra Rao, B., "Elastic Constants of Garnets," Proc. Indian Acad. Sci., Sect. A, Vol. 22, 1945, pp. 194-198. Ramana, Y. V., "Ultrasonic Velocities in Quartzites and Limestones," J. Sci. Ind. Res. (India), Vol. 19B, No. 11, 1960, pp. 446-447. Ramana, Y. V., and Y. Subrahmanyam, "Effect of Texture on Ultrasonic Wave Velocities in Sandstones," Ind. J. Pure Appl. Phys., Vol. 1, No. 5, 1963, pp. 190-191. Rinehart, J. S., J. P. Fortin, and L. Burgin, "Propagation Velocity of Longitudinal Waves in Rocks. Effect of State of Stress, Stress Level of the Wave, Water Content, Porosity, Temperature, Stratification, and Texture," Proceedings of the Fourth Symposium on Rock Mechanics, Bull. Min. Ind. Exp. Sta., Mining Eng. Ser., 1961, pp. 119-134. Riznichenko, Yu. V., and 0. I. Sileava, "Velocities of Elastic Wave Propagation in Rock Samples As a Function of Unilateral Pressure," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 3, 1955. Robertson, E. C., "Experimental Study of the Strength of Rocks," Bull. Geol. Soc. Am., Vol. 66, 1955, pp. 1275-1314. Seshagiri Rao, T., "Elastic Constants of Barytes and Celestite," Proc. Indian Acad. Sci., Sect. A, Vol. 33, 1951, pp. 251-256. Sundaro Rao, R. V. G., "Elastic Constants of Alumina," Proc. Indian Acad. Sci., Sect. A, Vol. 29, 1949, pp. 352-360. Shimozuru, D., H. Seno, and H. Noda, "On the Elasticity of Rocks up to 2000 BarsThe Interpretation of the Velocity Relation," Mem. Fac. Sci., Kyusyu Imperial University, Fukuoka, Japan, Vol. b, 2(3), 1957, pp. 98-103. Simmons, G., and F. Birch, "Elastic Constants of Pyrite," J. Appl. Phys., Vol. 34, 1963, pp. 2736-2738. Somerton, W. H., S. H. Ward, and M. S. King, "Physical Properties of Mohole Test Site Basalt," J. Geophys. Res., Vol. 68, 1963, pp. 849-856. 174

WILLOW RUN LABORATORIES Spangenberg, K., and S. Haussuhl, "Die elastischen Konstanten der Alkalihalogenide vom Steinsalz-typus," Zeit. Krist., Vol. 109, 1957, pp. 422-437. Stephens, D. R., "The Hydrostatic Compression of Eight Rocks," J. Geophys. Res., Vol. 69, 1964, pp. 2967-2978. Subbarao, K., and B. Ramachandra Rao, "A Simple Method of Determining Ultrasonic Velocities in Rocks," Nature, Vol. 180, No. 4573, 1957, p. 978. Sutherland, R. B., "Some Dynamic and Static Properties of Rock," Proceedings of the Fifth Rock Mechanics Symposium, Pergamon Press, 1963, pp. 473-491. Szemeredy, P., "Determination of the Velocity of Propagation of Elastic Vibrations by the Standing-Wave Method," Budapest Tudomany Egyet. Ann. Sec. Geol., Vol. 1, 1957, pp. 89-95. Terry, N. B., and H. J. Woods, "The Measurement of Elastic Wave Velocity in Small Cylindrical Specimens," Brit. J. Appl. Phys., Vol. 6, 1955, pp. 322-325. Toshi, S. K., and S. S. Mitra, "Debye Characteristic Temperature of Solids," Proc. Phys. Soc. London, Vol. 76, No. 12, 1960, pp. 295-298. Tomashevskaya, I. S., "A Study of the Shear Modulus of Rock Samples Under High All-Round Pressures by the Torsion Method," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 3, 1961, pp. 281-284. Verzhbitsky, L. P., "On the Procedure and Accuracy of Determining Longitudinal Wave Velocity in Rocks by Ultrasonic Means," Mosk. Univ. Vestnik, Ser. 4, No. 1, 1964, pp. 43-51. Voigt, W., "Bestimmung der Elasticitatsconstanten von Topas und Baryt," Ann. Physik D. Chemie, Vol. 34, 1888, pp. 981-1029. Voigt, W., "Bestimmung der Elasticitatsconstanten des brasilianischen Turmalines," Ann. Physik, D. Chemie, Vol. 41, 1890, pp. 712-729. Voigt, W., "Bestimmung der Elastizitatskonstanten von Eisenglanz," Ann. Physik, Vol. 22, 1907, pp. 129-140 Voigt, W., "Bestimmung der Elastizitatskonstanten von Aragonit," Ann. Physik, Vol. 24, 1907, p. 290. Volarovich, M. P., and D. B. Balashov, "Study of Velocities of Elastic Waves in Samples of Rock Under Pressures up to 5000 kg/cm2," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 3, 1957, pp. 56-69. Volarovich, M. P., and Ye. I. Bayuk, "Effect of All-Sided Pressures up to 4000 kg/cm2 on the Elastic Properties of Rock Specimens," Dokl. Acad. Sci. USSR (English Transl.) Vol. 135, 1961, pp. 1237-1239. Volarovich, M. P., and A. S. Gurvich, "Investigation of Dynamic Moduli of Elasticity for Rocks in Relation to Temperature," Bull. (Izv.) Acad. Sci. USSR, No. 4, 1957, pp. 1-9. Volarovich, M. P., and Z. I. Stakhovskaya, "A Study of Young's Modulus in Rock Samples Under Isotropic Pressures up to 5000 kg/cm2 by the Bending Method," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 5, 1958, pp. 329-335. Volarovich, M. P., D. B. Balashov, and V. A. Pavlogradsky, "Study of the Compressibility of Igneous Rocks at Pressures up to 5000 kg/cm2," Bull. Acad. Sci. USSR, Geophys. Ser. (English Transl.), No. 5, 1959, pp. 486-492. 175

WILLOW RUN LABORATORIES Volarovich, M. P., D. B. Balashov, I. S. Tomashevskaya, and V. H. Pavlogradsky, "Study of the Effect of Uniaxial Compression on the Velocity of Elastic Waves in Specimens of Rocks Under High Hydrostatic Compression," Bull. (Izv.) Acad. Sci., USSR, No. 8, 1963, pp. 728-732. Volarovich, M. P., E. I. Bayuk, A. A. Zhdana, and I. S. Tomashevskaya, "An Investigation of the Elastic Properties of Rocks from the Kola Peninsula Under Conditions of Multilateral Pressure up to 7000 kg/cm2," Bull. (Izv.) Acad. Sci., USSR (English Transl.), No. 8, 1964, pp. 712-716. Volarovich, M. P., A. I. Levykin, and N. Ye. Galdin, "Study of Longitudinal Wave Velocities in Rock Samples at Pressures up to 20,000 kg/cm2," Dokl. Akad. Nauk SSSR, Vol. 157, No. 6, 1964, pp. 1349-1351. Wackerle, J., "Shock-Wave Compression of Quartz," J. Appl. Phys., Vol. 33, 1962, pp. 922-937. Walsh, J. B., "The Effect of Cracks on the Uniaxial Compression of Rocks," J. Geophys. Res., Vol. 70, 1965, pp. 399-412. Woollard, G. P., and M. H. Manghnani, "Ultrasonic Velocities of Some Hawaiian Basaltic Rocks," Trans. Am. Geophys. Union, Vol. 45, 1964, p. 637. Wyllie, M. R. J., A. R. Gregory, and L. W. Gardner, "Elastic Wave Velocities in Heterogeneous and Porous Media," Geophysics, Vol. 21, 1956, pp. 41-70. Wyllie, M. R. J., A. R. Gregory, and G. H. F. Gardner, "An Experimental Investigation of Factors Affecting Elastic Wave Velocities in Porous Media," Geophysics, Vol. 23, 1958, pp. 459-493. Wyllie, M. R. J., G. H. F. Gardner, and A. R. Gregory, "Studies of Elastic Wave Attenuation in Porous Media," Geophysics, Vol. 27, 1962, pp. 569-589. Zisman, W. A., "Young's Modulus and Poisson's Ratio with Reference to Geophysical Applications," Proc. Natl. Acad. Sci. U.S., Vol. 19, 1933, pp. 653-665. Zisman, W. A., "Compressibility and Anisotropy of Rocks at and near the Earth's Surface," Proc. Natl. Acad. Sci. U.S., Vol. 19, 1933, pp. 666-679. Zisman, W. A., "Comparison of the Statically and Seismologically Determined Elastic Constants of Rocks," Proc. Natl. Acad. Sci U.S., Vol. 19, 1933, pp. 680686. 176

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UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1. ORIGINATIN G ACTIVITY (Corporate author) 2a REPORT SECURITY C LASSIFICATION Willow Run Laboratories, Institute of Science and Technology Unclassified The University of Michigan, Ann Arbor, Michigan 2b GROUP 3 REPORT TITLE SOUND VELOCITIES IN ROCKS AND MINERALS 4 DESCRIPTIVE NOTES (Type of report and inclusive dates) VESIAC State-of-the-Art Report 5 AUTHOR(S) (Last name, first name, initial) Anderson, Olson L., and Liebermann, Robert C., Lamont Geological Observatory, Columbia University, Palisades, New York 6 REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS November 1966 xi + 182 307 8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) SD-78 and DA-49-083 OSA-3137 7885-4-X 7885-4-X b. PROJECT NO. c. 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned this report) d. 10. A V A IL ABILITY/LIMITATION NOTICES Qualified requesters may obtain copies of this document from DDC. 11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Advanced Research Projects Agency, Department of Defense, Washington, D. C. 13. ABSTRACT This state-of-the-art report summarizes experiments and data on sound velocities in rocks and minerals and projects useful lines of research. The report discusses in detail the three common measuring techniques now employed: (1) resonance methods, (2) pulse-transmission methods (time-of-flight), and (3) ultrasonic-interferometric methods. Promising techniques, both direct and indirect, are described, the most important of these is the resonance of small spheres. Methods of estimating elastic constants at high pressure and high temperature are indicated. The data extant on the sound velocities in rocks and minerals are considerable and are tabulated in several appendixes. The lack of systematic coverage and quality of these data is discussed. A method of estimating unmeasured properties in a class of rocks, using data already reported for that class, is reviewed. Techniques of estimating isotropic sound velocities from single-crystal elasticconstant data are reviewed. D i JAN 64 1473 UNCLASSIFIED Security Classification

UNIVERSITY OF MICHIGAN UNCLASSIFIED 3 9015 02499 5295 security Classification. ~~~~~14~~. ~ LINK A LINK B LINK C KEY WORDS ROLE WT ROLE WT ROLE WT Sound velocities Rocks Minerals INSTRUCTIONS 1. ORIGINATING ACTIVITY: Enter the name and address imposed by security classification, using standard statements of the contractor, subcontractor, grantee, Department of De- such as: fense activity or other organization (corporate author) issuing (1) "Qualified requesters may obtain copies of this the report. report from DDC." 2a. REPORT SECURITY CLI,ASSIF ICATION: Enter the over2a REPORT SECUTY CLASSICATION: Enter the over- 2) "Foreign announcement and dissemination of this all security classification of the report. Indicate whether is not "Restricted Data" is included. Marking is to be in accordance with appropriate security regulations. (3) "U. S. Government agencies may obtain copies of this report directly from DDC. Other qualified DDC 2b. 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