THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE ELECTRICAL RESISTIVITY OF MOLTEN METALLIC MATERIALS Gary E. Kleinedler A section of a CM 210 report submitted to Professor R. E. Balzhiser on 9 June 1961. Edited for the Industry Program report by J. D. Verhoeven. March, 1962 IP - 557

TABLE OF CONTENTS Page LIST OF TABLES......................................... iv LIST OF FIGURES..................................V... viii NOMENCLATURE.......................................... ix I. INTRODUCTION................................ II. HISTORICAL REVIEW................................... 3 III. THEORETICAL REVIEW............................... Theories of Resistivity of Pure Metals,...7....... 7 Drude-Lorentz Theory............................ 7 Electric Transport Theory.........9......... 9 Resistivity Ratio Group Theories................ 10 Latent Heat-Vibration Theory..................... 12 Extensions of the Latent Heat-Vibration Theory.... 17 Perturbation Theory........................ 19 Electron Scattering Models of Resistivity....... 21 Theories of Resistivity of Binary Molten Alloys...... 26 Theories of Resistivity of Liquid Metallic Amalgams.. 28 IV.. RESISTIVITY APPARATUS REVIEW...................... 31 Electrode-Type Measuring Devices..................... 31 Tube Resistivity Devices.......................... 31 Bath Resistivity Devices..................5.... 35 Electrodeless-Type Measuring Devices............... 37 Liquid Wire Measuring Apparatus..................... 40 V. CALIBRATION OF RESISTIVITY APPARATUS REVIEW...... 41 Electrode-Type Measuring Apparatus.................. 41 Electrodeless-Type Measuring Apparatus............. 42 VI. RESISTANCE IN MAGNETIC FIELD REVIEW................. 45 VII. RESISTIVITY UNDER PRESSURE REVEW................... 47 VIII. RESISTIVITY AT CONSTANT VOLUME REVIEW............... 49 ii

TABLE OF CONTENTS CONT'D Page IX. RESISTIVITY DATA COMPILATION........................ 51 Discussion of Literature Resistivity Presentation.... 51 Form of Data Compilation......................... 52 Data Compilation.................................. 55 Pure Molten Metals..........................55 Molten Binary Alloys............................. 69 Liquid Amalgams............................... 95 X. BIBLIOGRAPHY....................................... 103 Form of Bibliographic Entries....................... 103 Bibliography Entries.............................. 104 iii

Table I II III IV V VI VII VIII X XII XIII XIV XV XVII XVIII XIX XX XXI XIII XXIV XXV XXVI XXVII LIST OF TABLES Early Reports on Resistivity of Molten Metals,.... Wagner and Perlitz Classifications of Resistivity Ratio Groups.................................... Resistivity Ratios Using Mott's Vibration Theory.. Theoretical Resistivity Ratios of Gerstenkorn..... Resistivity of Silver Ag..................... Resistivity of Aluminum Al.................... Resistivity of Gold Au.......................... Resistivity of Bismuth Bi.................... Resistivity of Cadmium Cd................... Resistivity of Cesium Ce...................... Resistivity of Copper Cu.................... Resistivity of Iron Fe........................ Resistivity of Gallium Ga........................ Resistivity of Germanium Ge...................... Resistivity of Mercury Hg...................... Resistivity of Indium In........................ Resistivity of Potassium K..................... Resistivity of Lithium Li........................ Resistivity of Magnesium Mg............ Resistivity of Sodium Na......................... Resistivity of Nickel Ni........................ Resistivity of Lead Pb........................... Resistivity of Rubidium Rb.................... Page 5 13 18 26 57 57 58 58 59 59 59 60 60 60 61 62 62 63 63 64 64 65 66 66 Resistivity of Antimony Sb...................... iv

LIST OF TABLES CONT'D Table XXVIII XXX XXXI XXXII XXXIII XXXV XLI XLVI XLVIII XLIX LI LV LVI LVII LVIII LIX LX LXI LXIII LXV LXVI LXVIII LXIX IX XI Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity of of of of of of of of of of of of of of of of of of of of of of of of of Selenium Se................ Tin Sn...................... Tellurium Te.................. Thallium Th...................... Zinc Zn...................... Silver-Copper Ag-Cu......... Aluminum-Copper Al-Cu.......... Bismuth-Cadmium Bi-Cd............ Bismuth-Lead Bi-Pb............... Bismuth-Antimony Bi-Sb............ Bismuth-Tin Bi-Sn......... Carbon-Iron C-Fe.................. Cadmium-Copper Cd-Cu............ Cadmium-Sodium Cd-Na........... Cadmium-Lead Cd-Pb............ Cadmium-Antimony Cd-Sb,.......... Cadmium-Tin Cd-Sn................. Cadmium-Zinc Cd-Zn.............. Copper-Nickel Cu-Ni.............. Copper-Lead Cu-Pb................ Copper-Antimony Cu-Sb............. Copper-Tin Cu-Sn........... Copper-Zinc Cu-Zn................ Gallium-Indium Ga-In........... Gallium-Tin Ga-Sn............... Page 66 67 68 68 71 72 72 73 74 75 75 76 77 78 78 79 80 80 81 81 82 84 85 86 86 v

LIST OF TABLE CONT'D Table LXXIV LXXV LXXVI LXXVIII LXXX LXXXI LXXXII LXXXIII LXXXV LXXXV I LXXXIX XCI XCII XCV XCVII CII CIII CIV CVII CIX CX CXI CXII CXV Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity Resistivity of Potassium-Sodium K-Na............ of Potassium-Lead K-Pbo............ of Potassium-Rubidium K-Rb.......... of Potassium-Thallium K-Th......... of Sodium-Lead Na-Pb............... of Sodium-Antimony Na-Sb.......... of Sodium-Tin Na-Sn.............. of Sodium-Thallium Na-Th.......... of Lead-Antimony Pb-Sb........... of Lead-Tin Pb-Sn.................. of Lead-Zinc Pb-Zn,................ of Antimony-Tin Sb-Sn,.............. of Antimony-Zinc Sb-Zn.............. of Tin-Zinc Sn-Zn.................. of Aluminum Amalgams Al-Hg......... of Calcium Amalgams Ca-Hg.......... of Cadmium Amalgams Cd-Hg......... of Cerium Amalgams Ce-Hg........... of Copper Amalgams Cu-Hg........... of Germanium Amalgams Ge-Hg........ of Indium Amalgams In-Hg............ of Potassium Amalgams K-Hg.......... of Lithium Amalgams Li-Hg.......... of Sodium Amalgams Na-Hg........... Page 86 87 87 87 88 88 88 88 89 90 91 91 92 95 97 97 97 98 98 98 98 99 100 100 vi

LIST OF TABLES CONT'D Table Page CXVIII Resistivity of Antimony Amalgams Sb-Hg.......... 101 CXXIV Resistivity of Yttrium Amalgams Y-Hg........... 101 CXXVI Resistivity Data for Run 7....................... 101 vii

LIST OF FIGURES Figure Page 1 Typical Tube Resistivity Device................. 32 2 Typical Electrical Measuring Circuit............ 34 3 Typical Bath Resistivity Device................. 36 4 Electrodeless Resistivity Device................. 39 viii

Nomenclature a = lattice constant ao = first Bohr orbit radius A = constant b = radius of cell to which an atom motion is restricted B = constant c = ionic constant of the metal Cb = atomic fraction of component b C = constant d = atom group diameter e = electronic charge EF = kinetic energy of an electron at the maximum Fermi distribution point E = mean energy of vibration per atom m Eo = rest position energy E' = lowest atom energy value 0 E = (potential) energy in x-direction f = partition function fl = liquid state partition function fs = solid state partition function f' = functional relationship f" = functional relationship ix

f(r) = function of container radius g = dimensionless factor determined by the ionic structure arrangement g(h') = structural factor relationship g(h')l = structural factor relationship for the liquid state g(h')s = structural factor relationship for the solid state G = constant h = Plank's constant h' = dimensionless number i = modified Plank's constant H' = magnetic field intensity Hoo = electron constant at infinite dilution I = electric current j = scattering coefficient of one atom and a unit solid angle, J = scattering coefficient of a unit volume and unit solid angle k = Boltzmann's constant K = wave number of an electron at the maximum Fermi distribution point 1 = electron mean free path L = latent heat of fusion L' = resistance ratio of lead to material m = electronic mass M = torque dM = increment of torque x

M = atomic mass n = number of electrons per unit volume n' = number of free electrons per atom nf = number of free electrons per unit volume N = total number of atoms f = constant ND = ionic density (number of free electrons per atom) N1 = total number of atoms in the liquid state Ns = total number of atoms in the solid state p' atom concentration of solute P = denotes constant pressure qa = resistivity constant at infinite dilution Q = effective scattering cross-section r = a dimension measured radially outward from the container center ro = separation distance of two atoms (potential energy minimum) R = container radius s = distance s' = dimensional scale factor (length) s' = average distance of separation between atom groups t = time t = average time between electron collisions T = absolute temperature T' = denotes constant temperature xi

Tmp = melting temperature uoo = viscosity constant at infinite dilution v = electron velocity v' = final electron velocity v = average electron velocity V = volume V' = denotes constant volume Vrs = potential energy at the surface of the atomic sphere w = atomic cross-section for all-directional electron scatter w = number.of individual atom group contacts W(v,v')df = probability that an electron of initial velocity v is scattered x = displacement in one direction from the equilibrium position x = screening constant 2 xI = mean square atom displacement in the x-direction in the liquid 2 xs = mean square atom displacement in the x-direction in the solid z = apparent electron charge number a = temperature coefficient of resistivity aT = coefficient of thermal expansion = temperature coefficient of resistivity A' = isothermal compressibility coefficient y = temperature coefficient of resistivity = viscosity xii

G = coordinate G' = scattering angle at an inclination to the motion of the electron =" = scattering angle GD = Debye characteristic temperature GE = (Einstein) characteristic temperature XF = electron wave-length at the Fermi surface = average frequency of group contacts'1 = attenuation coefficient v = oscillation frequency v1 = atom oscillation frequency in the liquid s = atom oscillation frequency in the solid p = resistivity Pa = resistivity of pure component a Pb = resistivity of pure component b P1 = resistivity of the liquid Po = resistivity at 0~K Ps = resistivity of the solid PT = resistivity at a temperature T (absolute) Pab= resistivity of an a-b alloy a = conductivity 0 = coordinate X =(constant) rotary field angular velocity xiii * * Xlll

cf = angular velocity of the rotary field 2 = solid angle for scattering = resistance Xn = total resistance increase xiv

I. INTRODUCTION At the present time the literature contains a considerable amount of data on the resistivity of liquid metals and alloys. The dataare scattered rather uniformly over the past seventy years and have never been summarized in a comprehensive survey. Consequently, it is quite difficult to locate specific data which may be available. This report is presented in an effort to offer a fairly complete survey of liquid metal resistivities. It presents a compilation of published data and summarizes existing theories. It includes the following material: a review of the historical background in the resistivity field; theoretical derivations for liquid state resistivity; major experimental techniques used in liquid resistivity investigations; and a complete compilation of metallic resistivity data for liquid elements, binary alloys, and amalgams. The last section includes some tabular data on the temperature-resistivity-composition relationship. -1

II. Historical Review1 It had been noted in the 19th century that when a metal passed through a change of state the various physical properties underwent a discontinuous change. Early investigators of this discontinuity were primarly interested in the breakdown of the solid structure upon melting; thus, the variation of the physical properties, including electrical resistivity, were first studied in much detail at temperatures near the melting point. The first recorded investigator was Matthiessen in 1857. He reported a sharp change in electrical resistivity near the melting point of potassium and sodium. In 1872, Matthiessen (with Vogt) made the first report on the resistivity of an amalgam in the liquid state. These two studies were soon followed by those of de la Riva (1863), who studied a few of the common metallic elements. For all metals investigated de la Riva noted resistivity increases through the solid-liquid transformation, except for bismuth and antimony which displayed decreases. In the years 1884-1887 Weber made rather extensive studies on several liquid pure metals and liquid amalgams. Vicentinni and Omodei, investigating tin, bismuth, thallium, cadmium, and lead found that the liquid resistivity of these metals at their melting temperatures were proportional to the atomic weight. They observed a relationship between 1 This subsection was taken from several sources: (26, 30, 69, 76, 101, 111, 113-117, 139, 147-148). Numbers refer to ref. in the bibliography. - 3

-4 the resistivity and the specific volume at the melting temperature: those metals which expanded upon melting showed increases in resistivity; those which contracted showed resistivity decreases. A few additional observations on pure metals were made before 1902, the most well-known and useful being those of Vassura and Guillaume, both in 1892. A complete listing of all investigations on the resistivity of molten metals published before 1902 is given in Table I. The first extensive and systematic data obtained for pure molten metals and for liquid binary alloys, was reported in a series of papers by Bornemann, Muller, et al. (14-16, 83) in 1910-1914. The accurate investigations of Northrup (87-94) on pure metals and binary alloys followed shortly thereafter. Northrup developed a theory of liquid metallic resistivity based upon the Drude-Lorentz electron theory of metals (87). The first studies conducted on the resistivities of molten metals at high pressures were carried out by Bridgeman (20-22) in great detail between 1907 and 1921. Three Japanese investigators, Tsutsumi (139), Konno (69), and Matsuyama (76), did considerable research on binary alloy resistivities over the years 1918 to 1927. Skaupy (129-132) continued the work done by Bornemann on liquid amalgams. He presented both experimental data and the first theoretical interpretations in this field in a series of papers, published from 1916-1920. Basing experimental work on Skaupy's theories, Williams and Evans, et al. (26, 30, 147-148) reported extensive data for amalgams in the 1920's. This group also made initial investigations of the effect of magnetic fields on resistivity, following up some preliminary work

-5Table I. Early Reports on Resistivity of Molten Metals Investigator Year Material Matthiessen Siemens Matthiessen and Vogt de la Riva Benoit Michaelis Weber Cailletet and Bouty Batelli Grimaldi Vicentini and Omodei Jaeger and Kreichgauer MIller Vassura Guillaume Cattaneo von Schweidler Dewar and Fleming Willows Larsen 1857 1861 1862 1863 1873 1883 r 1884 1885 1887J 1885 1887 1887 1889 1892 1892 1892 1892 1893 1895 1896 1899 1900 K, Na Sn Ag, Au amalgams Bi, Cd, Pb, Sb, Sn, Zn Hg Cu amalgams Bi, Hg; Ag, Bi, Cd, Pb, Sn amalgams Hg Ag, Au, Cu, Cd, Na amalgams Na amalgams Bi, Cd, Pb, Sn, Th; Cd amalgams Hg Hg Bi, Cd, Sn Hg amalgams Cd amalgams Hg Cd amalgams Cd amalgams

-6 by others (85, 98-99). Braunbek (17-19) constructed the first practical apparatus for obtaining resistivity data by indirect measurements involving sample rotation in a magnetic field. The next 15 years produced relatively little experimental work; however, in 1934 Mott (82) presented a useful theory on resistivity changes at the melting point. In addition, Harasima's later theory (48-49) for alkali metal resistivities attempted to extend Mott's analysis to more fundamental metal properties. A third extensive theory of metallic resistivity at the melting point was offered by Gerstenkorn (40-41) in two papers about 10 years ago. These investigators were among the first to recognize atomic scattering influences on resistivity and to mention the micro-crystalline structure in the liquid state. Soviet scientists, among them Mokrovski and Regel (78-81, 109), have made many investigations in the last 10 years, particularly on semiconductor elements and compounds. These authors have also theorized on a quasi-crystalline structure in liquids (5). Recent research in the resistivity field includes the efforts of Roll and his co-workers (111-117) who redeveloped and improved the indirect magnetic apparatus for resistivity determinations. They have also presented much material on molten pure metals and binary alloys at high temperatures. Scala and Robertson (121) recently reported data on metals and binary alloys.

III. Theoretical Review Most of the experimental resistivity studies before 1900 were of limited accuracy due primarily to inaccurate measuring devices and the lack of suitably pure metals. The theoretical interprelations of this period were of very little value. However, with the discovery of the electron and the introduction of the DrudeLorentz theory of "electron gases" in metals an elementary interpretation of resistivity became possible. The devolopment of a theory for molten metals has been slow. At the present time only the change in resistivity upon melting has been treated theoretically; there is no theory which adequately explains the effect of either temperature or composition on the resistivity of molten alloys. In the three subsections below, a brief description of most of the more important theoretical treatments of resistivity of molten pure metals, binary alloys, and liquid amalgams is given. Theories of Resistivity of Pure Metals Drude-Lorentz Theory2. After the discovery of the electron, various theories of metals were put forth, culminating in what is now known as the Drude-Lorentz theory. A theoretical relation for the electrical conductivity of metal was developed from this theory. 2 From Northrup (87). -7

-8 Although derived for solid metals, it should also apply to liquid metal systems. If there are a number of "free electrons" in a unit volume of metal in the absence of an external applied field, the average velocity of the electrons is identical in all directions. Applying a field introduces a perturbation upon electrons and acceleration occurs: d2s/dt2 = F'e/m (1) Collisions between electrons occur, and after each such collision, the electrons involved lose all velocity in the direction of the field. Assuming the electric field is applied at time zero, integration of Equation (1) gives: v = ds/dt = F'et/m (2) The average velocity between two electron collisions is then: v = F'et/2m (3) The current is a function of the number of electrons present and their velocity: I = nev = ne tF'/2m (4) Application of Ohms's Law to Equation (4) gives for the resistivity: p = 2m/ne t (5) By defining the mean free path, i, as the average distance traversed by the electrons between collisions Equation (5) may be written as:

-9 p = 2vm/lne2 (6) Although the derivation of Equation (6) was more or less rigorous within the framework of the assumptions of the Drude-Lorentz theory, some objections were stated: 1. No explanation was given for the change in resistivity through a change in state. 2. No explanation was given for the different experimental resistivities of different metals at the same temperature. 3. The temperature dependence of the resistivity was difficult to explain. 4. Experimental changes of resistivity with external pressure were not explained correctly. Electric Transport Theory. Northrup, in his experimental studies on the resistivities of materials, had rejected the original Drude-Lorentz theory for some of the reasons offered above, and attempted (87) to explain the experimental behavior of resistivity on the basis of the empirical form: Tmp T PT = o po(l + QT + PT2) + T (T - Tp) (7) Northrup's reasoning is based on the assumption that at reasonable temperatures all electrons are normally attached to atom groups. Under ordinary applied electric fields, electrons can only be detached from their groups when the groups approach each other due to heat motion or pressure application. This idea results in the concept of perfect conductor atom groups surrounded by perfect insulator

-10 spaces. Under an electric potential, the atom groups move within "contact distance" of each other and a transferrence of electrons takes place in such a manner to produce an electric field opposite in direction to the applied field. A result of Northrup's derivation is generalfor both solids and liquids: p OC l/wde (8) Upon further assumption that the material is a metal in the liquid state, the resistivity can be written as: p OC (' - d)m/nd3eIT (9) Equation (9) maintains that at constant volume, the resistivity decreases with temperature3 Although some experimental verification of Equation (9) was possible, no explanation was given for metals which did not have linear temperature dependencies in the liquid state, as assumed by Equation (7). Resistivity Ratio Group Theories. One of the early attempts to consolidate in a regular fashion the various data on resistivity was initiated by Wagner (144) in 1910, and extended (independently) by Perlitz (101) in 1926* Although these efforts were comprised of experimental observation rather than purely theoretical interpretation, 3 A result experimentally verified later (44, 70).

-11 they represent the first work done on the systematic change of resistivity at the melting point. This change in resistivity, usually expressed as a ratio of the resistivity of the liquid to that of the solid, has dominated most of the theoretical interpretations of molten resistivity to date. It was first noted experimentally by Vicentini and Omodei about 1890 that the change in resistivity at the temperature of melting was such that the state of matter with the larger specific volume possessed the larger resistivity. Wagner, collecting experimental data on resistivity ratios, classified various pure elements into four groups by showing that these resistivity group numbers were in the ratio of small integers. A further extension was made by assuming that the resistivity ratios were proportional to the number of "structural" atom groups in both the solid and liquid states (see Table II, page 16). Bridgeman in 1921 reiterated Vicentini and Omodei's observations in his work with metals at high hydrostatic pressures (20). Noting the observations made by these previous researchers, Perlitz (101), investigating the disappearance of the regular crystalline lattice, sought to obtain a relation between the (solid) crystalline structure of a metal and the change in resistivity during melting. Examining some 19 metals for crystalline structure (lattice classification) and resistivity ratio at the melting temperature, Perlitz observed that the values for the ratios were not uniformly distributed numerically, but tended to cluster about several mean values (see Table II, page 16). At the time of Perlitz's observations,

-12 not all of the 19 metal lattice structures had been determined. Even so, Perlitz identified the first group (1/2) as those metals of the rhombohedral-hexagonal solid type; the second group (3/2) as structures of the BCC metals; and the (4/2) group as the close-packed types (FCC and HCP). On this basis Perlitz then postulated that certain given structural lattice groups would have approximately the same resistivity ratio at the melting point. Perlitz noted only one exception to his rule, namely, that aluminum should have possessed a BCC-type structure (mercury was classified separately and hence was not included as an exception). Although the postulate held reasonably well at the time it was stated, it can be seen (Table II, page 16) that with more information available on lattices, other discrepancies are introduced. Latent Heat-Vibration Theory. One of the most important theories of the resistivity change in the solid-liquid transformation was proposed by Mott (82) in 1934 and is still used by many experimenters to interpret results. In this theory an expression is derived which holds reasonably well for most metals. The results can also be extended by various hypotheses to account for!the resistivity ratio anomalies in bismuth and mercury. Mott's derivation is as follows: from the electron theory of metals, the solid state is characterized by atomic vibrations occuring about fixed positions. Similar vibrations occur in liquid which are superimposed upon the shifting mean atomic positions. This shifting is of much smaller magnitude than the oscillation-vibration

Table II. Wagner and Perlitz Classifications of Resistivity Ratio Groups Metal Resistivity Ratio5 Wagner Group Structural Classification6 Resistivity Ratio7 Perlitz Group Bismuth Gallium Antimony Sodium Lithium Potassium Rubidium Aluminum Cesium Silver Cadmium Lead Thallium Copper Zinc Tellurium Tin Gold Mercury 0.465 0.476 1.37-1.70 1.44-1.62 1.58 1.7 1.92 1.92 2.0 2.0 ~2.10 2.17,4.07 } I 1/2 3/2 Rhombohedral (Orthorhombic) Rhombohedral Body-centered cubic Body-centered cubic Body-centered cubic (Body-centered cubic) Face-centered cubic (Body-dentered cubic) Face-centered cubic Hexagonal close-packed Face-centered cubic Hexagonal close-packed Face-centered cubic Hexagonal close-packed Rhombohedral (hexagonal) (Tetragonal) Face-centered cubic Hexagonal (rhombohedral) o.48 0.55 0.69 1.45 1.48 1.50 1.54 1.65 1.71 1.86 1.91 1.97 2.0 2.03 2.05 2.1 2.13 2.28 4.23 } 1/2 3/2 I!-!J } 8/2 From (101, 144). 5 Tabular data from (144). 6Lattice structures in parentheses are from L.S. Darken and R.W. Gurry, The Physical Chemistry of Metals, p. 50-7. The other structures are from (101). 7Tabular data from (01). Tabular data from (i01).

-14 velocity; the average distance of movement of the mean position is about one percent of the interatomic distance. Neglecting this mean position motion in liquid metals, each atom oscillates with a certain frequency. Mott assumes that the frequencies for all atoms are identical, and that the characteristic temperature for the solid is given by Einstein's model as: GE = hvs/k (10) If the melting temperature satisfies the condition, Tmp > hvs/k (11) the work required to move one atom (initially at rest) in the solid to an equilibrium position in the liquid is given by the latent heat of fusion for the metal. Using a statistical mechanical approach, Mott finds the free energy for a given number of atoms as: F = N(kT lnf + Eo) (12) If the total number of atoms is constant and is distributed in some manner between the solid and liquid states, the free energy in Equation (12) becomes: F = Ns(-kT lnfs) + Nl(-kT lnfl + Eo) (13) At the melting temperature, the free energy in Equation (13) is minimized to zero and hence: kTm lnf = kTmp lnfl - E mp s mp o (14)

-15 Equation (14) may be expressed as: (fl/f)exp (-Eo/kTmp) = 1 (15) The partition functions used in Equation (13) are of the form: f = A(kT/v)3 (16) A substitution of Equation (16) into Equation (15) yields: Vl/Vs = exp (-Eo/3kTmp) (17) Mott, noting the relations developed above between the work required for movement across the solid-liquid boundary and the latent heat of fusion, substituted numerical values into Equation (17) and obtained the result: vl/Vs = exp (-40L/Tmp) (18) Mott next develops a relation between the vibration ratio Vl/v and the resistivity. From Block's theory of conductivity in solids, perfect crystallinity produces ideal solids impervious to electronic motions. The ideal conductivity is modified for real bodies, however, since these structures possess irregularities due to either thermal atom motion or the presence of foreign atoms. In addition, resistivity depends upon the freedom of electronic motion from atom to atom. A resistivity equation in the solid state, due to Berthe, is: PT = 1/a = (2mhnKaOT/2n'gMkD2)(c dEF/k dK)2 (19) Considering the possible changes in the variables of the last equation upon melting, Mott concludes that:

1. M, m, aO, c, n' remain constant. 2. K is a function of the specific volume and should not change greatly. 3. dE/dK, while a structural factor, is a function of the Fermi distribution energy and as such is dependent only upon the specific volume, and should not change greatly. Thus, Mott concludes that only the variation in atomic vibration is influenced greatly upon melting. From the characteristic temperature term in Equation (19), and from Equations (10) and (18), the resistivity ratio becomes: Pl/ps = (Vs/l)2 = exp (80L/Tmp) (20) The derivation of Equation (20) relies on Equation (11); however, if this is not justified, i.e., if: Tmp = h vs/k (21) which is especially true for the alkali metals and aluminum, Mott replaces Equation (10) by: (22) (exp [h vs/kTmp] - l)/(exp [h vl/kTmp] - 1) = exp (Eo/3kTmp) A comparison between Mott's theory and experimental values of various resistivity ratios may be found in Table III, page 23. In the table are included the original calculations of Mott from Equation (20) and his values of experimental ratios. Also included are the writer's "Abnormal melts" or those in which an increase of dE/dK exhibits itself in the disappearance of diamagnetism, are expected in this connection.

-17 recalculated values of resistivity ratios using recent thermodynamic data on the basis of Equation (20). Mott considered his theoretical calculations in reasonable agreement with experimental resistivity ratio values, except for mercury, antimony, bismuth, and gallium. He explains this discrepancy by assuming that in these particular cases the factor dE/dK does not remain constant during the liquid-solid phase change. For mercury, a decrease occurs; for the other metals above, an increase of about 10 takes place. (Note that the only metals which undergo contraction upon melting are the latter three: bismuth, antimony, and gallium. Cf. Perlitz theory of groups, page 10.) This theory requires that the additional resistivity in the liquid state is due mainly to the greater atomic oscillation amplitude and not to any great irregularity of the atomic structure. Hence, Mott introduces the important concept that over large distances (in comparison to the atomic distance), the atoms in a liquid possess regularity of position. Extensions of the Latent Heat Vibration Theory. Harasima (48-49), in an attempt to extend the Mott theory of resistivity ratio to more fundamental quantities than the heat of fusion, has derived equations for the ratio in the alkali metals. A brief description of the derivation follows; Harasima postulated that from a knowledge of the mechanism of melting, the atomic distribution, and the state of motion the resistivity ratio can be calculated. This derivation assumes that the electrons in the melt can be considered to be identical to "free" electrons in the solid, and that the atom distribution remains un

Table III. Resistivity Ratios Using Mott's Vibration Theory9 Metal Theoretical Experimental Resistivity Ratios10 Ratios Bismuth 5.0 5.04 0.43 Gallium 4.5 4.24 0.58 Antimony 5.6 5.94 0.67 Sodium 1.58 1.77 1.45 Potassium 1.67 1.761.55 Rubidium 1.76 1.75 1.61 Aluminum 1.8 1.55 1.64 Cesium 1.75 1.74 1.66 Lithium 1.57 2.58 1.68 Silver 2.0 2.08 1.90 Cadmium 2.3 2.46 2.0 Thallium 2.3 1.82 2.0 Copper 1.97 2.42 2.07 Lead 1.87 1.98 2.07 Zinc 2.3 2.17 2.09 Tin 3.0 3.07 2.1 Gold 2.22 2.14 2.28 Mercury 2.25 2.22 3.2-4.9 9 From (82). 10 The first set of calculations are from Mott: data on aluminum, lithium potassium, and sodiumare based upon Equation (22); all other calculations are from Equation (20). The second column contains calculations from Equation (20) using data from Selected Values of Chemical Thermodynamic Properties.

-19 changed upon melting. Hence, Harasima states that the ratio of resistivities is related to atom displacements by: P1/Ps = ( )/(2 (25) To develop the idea of a potential energy-distance relationship, Harasima notes that a potential curve is quite different in the liquid than in the solid state; the curve has a flat portion in the former. Thus, the deviation of an atom from an equilibrium position in the liquid is larger than a similar deviation in the solid. There is one general relation for the atomic displacements: x2 = I x2exp (-Ex/kT)dx/Jfexp (-Ex/kT)dx (24) o o Further reduction of Equation (24) yields expressions for both the liquid and solid states of the form: -2 2 2 (x )1 = 1.81B2ro (25) -2 22 (x )s = 1.24B rO (26) By substitution of Equations (25) and (26) into (25), the resistivity ratio for alkali metals is found to be: pl/Ps = 1.81/1.24 = 1.46 (27) The result is reasonably close to the experimental resistivity ratio values for lithium, potassium, and sodium (see page 18). Perturbation Theory. In addition to the work done onthe resistivity ratios of the alkali metals, Harasima (49) employed a different approach

-20 for the calculation of an absolute resistivity of molten sodium at its freezing point. In this calculation for resistivities, Harasima considers that the resistivity arises from the scattering of electrons in the interior of the metal. This scattering is due to atom displacements in a periodic lattice —the displacements caused either by thermal activity or by foreign atom presence. In employing this basis for calculation, a perturbation method is selected for the electron scattering coefficients, with the assumptions that an atom motion is independent of other such motions, and that the potential-distance relation remains constant with changing atom displacement. Using an analysis similar to that by Mott and Jones,l the resistivity of sodium is derived to be: p = 2.06m2 2(Vr - E?)2/ne 5 (28) Where, the mean square atom displacement is given by: (29) -2 b 2i cos 9)2r2 s dr x = ff J 3(r sin G cos )2r2 sin 9 drd O d0/4tb3 = b2/5 0 00 Substitution of numerical equivalents in Equations (28) and (29) gives a resistivity for molten sodium at its freezing point of 7.1 x 10 -ohm-centimeters. This is slightly less than the experimentally observed value. Harasima found that this calculation on the basis of electron scattering in a periodic lattice gives a value in better agreement with that observed than does the previous derivation based on Mott's analysis 1N. Mott and H. Jones, The Theory of the Properties of Metals and Alloys, p. 249ff.

-21 (page 17). Harasima cautioned, however, that this second analyses uses experimental values to fit a cell distribution function, while previous models have no such dependency. Electron Scattering Models of Resistivity. In general, theories of resistivity of liquid metals based upon the scattering of electron waves in a metal body are extensions of similar theories developed for the solid state. Schubin (124), in 1934, was one of the first to apply this concept of scattering to liquid state resistivity. He considers that the scattering proceeds without loss of energy and that the nature of the ion changes during the process. By analogy with an "almost free electron", Schubin investigates behavior in both constant and varying potential fields. He concludes that the probability of both the scattering process and the ionic change is independent of temperature. Similar to a conclusion of Mott's (see page 17)Schubin states that the resistivity of a liquid metal as compared to that of a solid is scarcely influenced by a change from the ordered crystalline state to a (supposed) disordered liquid condition. This implies that a quasicrystalline state exists in the liquid. Two Indians, Krishnan and Bhatia (72), further extended the points outlined above. They define an attenuation coefficient as being that fraction of the electron wave scattered in all directions in a given unit volume. The coefficient is hence the reciprocal of the electron mean free path. Thus, according to the electron theory of

-22 metals, the resistivity is: p = h'/nn'e2 (30) Furthermore, it can be shown that for the solid alkali metals, the wavelength in Equation (30) is sufficiently large so that the scattering coefficient can be obtained from the following: Jo = en'j (31) where = n'kT' (31a) For Equation (30) and (31) to hold, the absolute temperature in Equation (31a) is assumed to be much greater than the characteristic temperature. By integrating J4 over a solid scattering angle, the attenuation coefficient becomes: A' = 2itf"JtsinG'dGT (32) w = 2itosi Also: w = 2~JE jpsin'd' (33) o From Equations (31), (32), and (33), the scattering coefficient is: i' = en'w (34) Application of the last equation to the alkali metals gives results for the wave length in Equation (30) larger than the wave-length for the

-23 first diffraction maximum occurring in the backward direction. The diffraction in these instances is diffuse compared to the solid diffraction, and the scattering angle is less than 90~. This causes additional scattering in the back plane besides that given in Equation (31). Thus Equation (34) gives a greater scattering coefficient and, according to Krishnan and Bhatia, this is observable through the resistivity increases of the alkali metals at the melting point. For other metals, an analogous treatment of X-ray scattering data,intensity distributions, and atomic structure factors can yield values of resistivity. In these cases, the diffraction pattern of the liquid must be studied. The intensity majority included in the inclination angle 0<G'<K completely determines the attenuation coefficient and, hence, the resistivity. In the derivation of Equation (34) for alkali metals, the intensity majority is limited by Equation (31). This majority, however, being a function of the valency, is only partly included in the given range for other metals. The attenuation coefficient in polyvalent metals is much larger than given in Equation (34). It is given by: I = n'w (35) Krishnan and Bhatia state that the above calculations have been checked with the "abnormal" metals, and that Equation (35) gives reasonable explanation for experimental resistivities. Gerstenkorn (40) has recently published a detailed article on the change of electrical resistivity at the melting point, which was based on free electron scattering probability and a structural influence.

A rough translation of this paper is given below. The electrical resistivity results from.the scattering of electrons in motion in the metal interior. Hence, the resistivity in solids as well as in liquid may be represented as: p = m/nfe2T (6) and: 1/T = fW(vv') (l-cosG")da'4 (36a) The scattering angle and the electron wave length are combined to produce a dimensionless variable: h' = 2a/X sin (0"/2) (37) If one considers the maximum Fermi energy level as fixed, the integration variable in Equation (36a) may be replaced by Plank's constant. The wave-length under this substitution becomes: k3 = 8r/3nf (38) The scattering probability in Equation (36a) can also be expressed in the form: W = NdVQg (39) An exact theoretical determination of the effective electron scattering cross-section becomes very complex: Q = (ze2/2mv ) (sin [9G/2] + [V/4,a]2)-2 = (2zme2a2X2/+2)2([2ixh']2 + 1)-2 (40)

-25 With further analysis on the structural factor appearing in Equation (39), Gerstenkorn is able to combine Equations (36), (36a), (37), (38), (39), and (40) to obtain an equation representing the absolute value of the resistivity: p = (Nd/35n2) (4z2m2e2/i6)(4)Iix4 I (41) where: I = (1/16) f2a/g(hf)h'tdh'/([2Txh ] + 1) (41a) 0 The ratio of the resistivities of the solid and liquid at the melting point from Equation (41); all factors except that defined in Equation (41a) cancel: Pl/Ps = Il/Is f2a/x(h) lh'3dh/([2Th]2 + 1) / (42) a/Xg(h') hdh''/([2xh')2 + )2 For high temperatures, the resistivity of pure metals, as seen from Equation (41), is influenced only by an electron scattering probability and a structural factor. This is true for any state of aggregation. It is most difficult to calculate structural factors for liquid metals, and Gerstenkorn deduces some of the needed information from X-ray diffraction results for the alkali metals. In the solid, however, the factor can be obtained directly. The substituted values for both the solid and liquid alkali metals at their melting points agree rather closely with experimental values:

-26 Table IV. Theoretical Resistivity Ratios of Gerstenkorn12 Metal nf = 1 nf< 1 Experimental Lithium 1.62 2.04 1.68-1.96 Potassium 1.61 1.59 1.34-1.6 Sodium 1.74 1.77 1.39-1.56 Gerstenkorn calculates the resistivity ratios for elements with one or less free electrons per atom. As can be seen, the calculated values are not at great variance with the experimental ratios. Theories of Resistivity of Binary Metallic Alloys Although there have been a number of attempts to derive a theory of resistivity for pure molten metals, the lack of literature on similar theories dealing with binary molten alloys suggests little progress. A survey of the published information yields not one theoretical derivation relating resistivity and composition at a given temperature or resistivity and temperature at a given composition, much less a general resistivity-composition-temperature relationship. The reason probably stems from the lack of understanding of liquid state, particularly of the liquid state in alloys. The small number of experimental investigations relating to binary alloy resistivity presents a restriction to the development of theoretical conclusions. The few experimental-theoretical observations of binary alloy resistivities noted by various experimenters are discussed below. One of the earliest experiments with liquid alloy resis 12 From (40).

-27 tivities, that of Bornemann and van Rauschenplot (15), produced some original observations. These workers noticed that if the solute added had a strong tendency to form an intermetallic compound with the solvent metal, the resistivity decreased over that of the pure solvent. In general, resistivity-temperature curves were found to be linear at a given concentration. Resistivity-composition curves, however, were in most cases not linear over extended composition ranges. Japanese investigators at Tohoku Imperial University (69) found that simple "series" and "parallel" resistivity-composition relationships held for some of the alloy resistivity data taken. Thus, either of the following relations were approximately obeyed: Pab = Pa + Cb(Pb - Pa) (45) 1/Pab = 1/Pb + Cb (1/Pb - 1/Pa) (4) In a few alloys, the arithmetic mean of Equations (43) and (44) seemed to work well: (45) Pab = (1/2)(Pa + Cb[Pb - Pa] + PaPb)/(Pb - Cb[Pb - Pa]) In a recent investigation of dilute alloy resistivities, made by Scala and Robertson (121), the liquid and solid states were postulated to have almost complete correspondence of thermal, structural, and compositional relationships. With dilute concentrations of various metallic solutes in a copper solvent, the resistivity change for a unit atomic solution was the same as the change found in solid copper solutions. Also, this resistivity change was always an increase,

-28 and the increase per unit of solute concentration was proportional to the difference in electronic charge of the solute and solvent. This relationship was independent of temperature. In the case of solutions of dilute metallic solutes in zinc, however, no resistivity increases were noted in most cases. Theories of Resistivity of Liquid Metallic Amalgams Only one researcher, Skaupy, published articles in the literature on the theoretical derivation of resistivities of liquid amalgams. The theory was presented in a series of papers (129-132) published before and after the advent of the Drude-Lorentz electron theory of metals, and was based upon an analogy to the electrolytic conduction concepts. This viewpoint was adopted for interpretations of liquid amalgam resistivities by most of the subsequent experimenters (26, 30, 147-148). A brief description of this theory follows. The first assumption of Skaupy3 in deriving his theory is that the electrical resistivity of pure substances can be expressed in terms of the electron concentration and the liquid internal friction. Actually, the relation is: n = Cr/p (46) After expressing Equation (46) in logarithmic form and differentiating: An/np = pA(l/p)/p + AT/Rp (47) From Equation (47) Skaupy notes that a substitution of the values for the pure solvent (mercury) could be used, since the A expresses small 13 The following analysis is from (30, 148).

-29 yet finite concentrations. Hence, by setting: An/np = H (48a) pA(l/p)/p = q (48b) Atn/rjp = u (48c) Substitution in Equation (47) gives: H= q +u (49) At infinite dilution, Equation (49) becomes: Hoo = q + uo (50) Although Skaupy first postulated (and showed experimentally) that the resistivity constant at infinite dilution, q., was approximately the same for different amalgams, it was later shown by a co-worker to be only the same order of magnitude. This later conclusion was found in investigations on a number of amalgams.l 14 As for instance, the investigations of (26, 30, 146-148).

IV. Resistivity Apparatus Review In the effort to experimentally determine the resistivity of liquid metals several different types of apparatus have evolved. Early investigators utilized electrode cells to make direct measurements. Later investigations avoid the need for electrodes by employing magnetic fields. Electrode-type Measuring Devices Resistivity, or specific resistance, is defined as the ratio of the voltage to the current for some standardized state. With solid materials, particularly around room temperature, the measurement of resistivity presents no unusual problems. However, obtaining measurements in molten systems introduces such problems as: proper size and shape of container, suitable contact (electrode) and container materials, and uniform temperature distribution. Tube Resistivity Devicesl5 Early investigators, used low melting noncorrosive metals and inert containers in order to minimize the above difficulties. The typical experimental apparatus consisted of a long, narrow-bore tube ending in two large, low resistance contact wells; the molten metal under study filled the interconnected well-tube-well device. Four electrodes, two to serve as current leads and two as voltage leads, were contacted to the bath in the large wells. The tube portion, or more generally the entire device, was either placed 15 Taken from (2-4, 10, 13, 23-24, 26-27, 30, 32, 36, 45-47, 50-51, 53-54, 56, 69, 71, 73, 76, 88-94, 107, 110, 119, 121, 125, 127, 133, 138-139, 142-143, 145, 147-148). -31

CURRENT ELECTRODE MELT HEATING \COIL WELL / 0^ 0 / INSULATION E f/ —VOLTAGE 0 K i M ELECTRODE TUBE ^^^^^'^x*'^"x \ \ \x x x X- x x _ x x x2Q x\ X - x x x X xxxv y*y/ ^y^ \<. \ l, I x x x x x x x \ \\' \ \ \ \\\\\xx\\x\\ -s - z 44 - / - 4 - z / / 4 c/lzA\ a z.11 x x x I.- x x x X —X x x x x x x x N, x - x x x x x N. x x x x x x x x x x x x x x x -u - - I - Figure 1. Typical Tube Resistivity Device.

-33 into a constant temperature region, or surrounded by heating coils. Figure 1, page 32, illustrates a typical resistivity device of early design. In some equipment particularly in work with liquid amalgams the tube portion was varied, being either vertical, U-shaped, or even helical shaped. In a few cases the contact wells were either partially or entirely eliminated, and contact with the material was made through the normal tube sides or ends. The two electrode sets were generally of platium wire, although tungsten, iron, and copper wire or rod have also been successfully employed. The placement of the electrode sets relative to each other and to the contact wells was important to insure measurements in constant electrical density regions. For this reason, the set of voltage electrodes were usually placed far enough inside of the path of current introduced by the current electrodes to be in a region of constant current density. The current electrodes were constructed of larger diameter wire than the voltage electrodes. This procedure reduced the temperature fluctuation in the molten material and gave lower electrical circuit resistance, thereby resulting in more accurate resistivity measurements. The current electrodes were usually connected to a source of direct current such as a battery or small generator. A few experimenters have successfully used alternating current, usually at 60 cycles or less; although withstudies of the resistivity in the semi-metals frequencies of 1000 were not uncommon. The voltage circuits in direct current applications were usually connected to high-precision voltage measuring devices such as Wheatstone or Kelvin

I IIv~-v I X -STANDARD RESISTANCE Figure 2. Typical Electrical Measuring Circuit.

-35 double bridges, or precision potentiometers and galvanometer indicating instruments. In alternating current circuits the voltage was usually measured with either of the devices noted above plus a galvanometer type indicator suitable for use on alternating current. With direct currents provision also had to be made for inclusion of a reverse switch in the current circuit, so that polarization effects could be eliminated by reading the normal and reversed currents and averaging the readings. With alternating current, this procedure was not necessary. Figure 2, page 34,illustrates a typical direct current circuit used for measuring with high precision the current and voltage of resistivity devices. In addition to the associated electrical equipment, either a protective atmosphere or a vacuum was employed when working at high temperatures or with easily oxidizable materials. Provision was usually made in the container tube to permit the introduction of an inert gas. 16 Bath Resistivity Devices. One of the main difficulties experienced with the tube resistivity devices was that the resistivity circuit in the molten material passed through nearly the entire volume of the material. The devices employing this construction were hard to control at a uniform tube temperature. The introduction of the bath resistivity device offered an advance in accuracy and convenience of handling. These devices were based on the concept of immersing a suitable open-ended tube in a large bath of the molten material. Consequently, the resistivity device 16 See footnote 15.

-56 BATH Figure 3. Typical Bath Resistivity Device.

-37 was a unit in itself completely independent of the container and heating units. In most cases the bath resistivity devices consisted of two or more inert open-ended tubes connected together in a rigid manner. Platinum or tungsten electrodes, two to serve as current leads and two as voltage leads, were fastened rigidly to the tubes. This interconnected apparatus was placed into a large bath of molten material. Temperature regulation was accomplished by heating coils surrounding the large bath container. Figure 3, page 36, shows a suitable bath resistivity device. As with the previously described tube device the voltage measuring electrodes were so placed to assure a homogeneous current density. In some cases the current leads were placed in inert tubes, but these were usually left free to contact the bulk of the bath in order to minimize total circuit resistance. The same types of electrical circuits employed with tube resistivity devices were also used with bath resistivity equipment (see above, page 34). Likewise, the methods employed to provide protective atmospheres over molten materials were similar to those used with tube devices (see above, page 35). Electrodeless-type Measuring Devices17 Due to difficulties experienced with the standard types of electrode contact resistivity apparatus the indirect devices were 17 Taken from 17-19, 38, 64-68, 111-117).

-38 developed. With these devices effects such as polarization, localized heating near electrodes, electrode contact problems, extraneous electromotive forces, etc., could be completely avoided. All of the indirect electrodeless methods of resistivity measurement depend upon the interaction of a molten sample with a magnetic field. This interaction produces an eddy currents in the sample; these eddy currents can be examined by studying the "drag" or magnetic friction effect in a rotating magnetic field. Theory shows that such rotation can be related to the resistivity of the molten material by measurements of friction effects, and for similarly shaped molten material masses resistivities may be evaluated. Most of the indirect magnetic apparatus are variations of a basic device consisting of a suitable furnace surrounded with one or more cylindrical coils. The sample, placed in a small crucible, is freely suspended to hang in the center of both the furnace and the coils (see Figure 4, page 39). The application of a rotating magnetic field on the molten sample causes eddy currents to be induced in the mass, and because of internal friction this induction results in a torque transmitted to the free suspension, thus causing rotation. The rotation momentum is obtained through the use of bucking coils or mirror arrangements. With some types of apparatus the molten material is freely suspended in an inhomogeneous magnetic field, and the interaction of the original and produced fields are measured and related to the resistivity.

-39 / I i —I lr x a -11 I I I I w~~ I a 6 a a 6 6 6 6 i * 6 0 0 6 6 6 a fl I 0 0 1 1 1 0 1 1 1 1 1 1 r- I SUSPENSION ROTARY FIELD COILS /....~ ROTAR 6m Ir I I I I 4 4 4 4 4 4 0 0 0 0 0 S S S S S S S S *, *) ////, 1 1115 N SAMPLE IRON CORE - ROTARY / FIELD COIL Kr Figure 4. Electrodeless Resistivity Device.

-40 Liquid Wire Measuring Apparatus An unusual and ingenious device, differing in form from both the direct and indirect apparatus was used in a study on several pure, low-melting metals. Pietenpol and Miley (103-106) first studied a phenomenon noticed earlier: certain metal wires, when suspended in air, could be heated by electric current to temperatures above melting without separation. The conclusion was that an elastic oxide coating was formed on the wire; the strength of the coating being sufficient to support an inner core of molten metal. By conducting measurements of the current and potential drop along the wire, and knowing the volume of the molten zone the resistivity-temperature relationship could be found. The wire to be tested was first heated in air or oxygen to form and strengthen the oxide coating. It was then introduced into an inert atmosphere to prevent further oxidation. Currents, voltage, and temperature reading were taken and a small correction factor was applied for both the wire and coating to account for thermal expansion. Supplementary investigation showed that the current shunting effect through the oxide coating and the thickness of the coating were negligible in calculations of resistivity.

V. Calibration of Resistivity Apparatus Review Electrical resistance is a measure of that property of a material which limits the amount of electrical current it can carry under a given voltage gradient. The unit of resistance is defined as the ratio of the unit of voltage to the unit of current. Resistance is an extensive property and the corresponding intensive property is the specific resistance or resistivity. Resistivity is generally defined as the resistance of a material of a specific shape: the resistivity is numerically equal to the resistance of a material measured between opposite sides of a cube of unit edge of material. With this basic definition, measurements of resistivity are further qualified with increasing temperature as: 1. Resistivity at constant pressure 2. Resistivity at constant mass 3. Resistivity at constant volume. In general resistivity at constant property Z means that Z is held constant with temperature in the volume defined between the measuring electrodes. 18 Electrode-type Measuring Apparatus. In the experimental measurement of resistivity values with electrode devices all values of resistance must be reduced into terms of resistance for a specifically shaped volume; i.e., the unit cube. The actual dimensions of the space between the voltage electrodes may be computed and reduced to that of the unit cube, and this reduction factor applied to all measured values. 18 f See footnote 15. -41

-42 However, it is difficult to calibrate precisely the volume between the electrodes at a given temperature. Thus it has become common to first calibrate the electrode apparatus with a material of known resistivity. The ratio of the resistance values measured on the known material to the resistivity of the known material is a "correction factor" which can be applied reciprocally to experimental data resistances. Mercury has usually been employed for such calibration measurements because of its well-known resistivity-temperature relationship; however, other pure metals such as tin have also served as calibration materials. In addition to the resistance-resistivity correction factor a small correction has sometimes been employed to compensate for the thermal expansion at high temperatures of the measuring cell itself; if the calibration was made near room temperature. Electrodeless-type Measuring Apparatus.19 Braunbek (19) was the first to present a derivation of the theoretical aspects of the indirect magnetic apparatus. He noticed that the torque exerted on the molten material by the magnetic coil of the apparatus causes the crucible and suspension to rotate. The contents of the crucible also rotate, but with less angular velocity. The liquid immediately adjacent to the container walls rotates with nearly the velocity of the rotary field itself, and conducts this motion to the container wall: Df = f(r) (51) 19 See footnote 17.

-45 The eddy current drag on the molten cylinder is: dM - jp(D-of)H' r3dr (52) From the above and from a basic equation in hydrodynamics for frictional liquids, the eddy current torque is also: dM = -2n(d/dr)(r3daf/dr)dr (55) Equating Equations (52) and (53): (d/dr)(r3dwf/dr) = -pH'2(o jf)r3/2r (54) To the first approximation in Equation (54), Clf in the right-hand term can be neglected in comparison to w; the solution of this simplified equation can be formed assuming the following boundary conditions: r =0 dwf/dr =0 } (55a) dwf/dr = J r = R (55b) c)f = 0 (at container wall) as: cf = pH'2(R2 - r )/16( (56) This result in Equation (56), when substituted into Equation (52) and integrated over 0 < r < R, yields as the torque on the cylindrical material: M = (ipDl'R4HT/4) - (itp 1Tl'R6 Ht4/192j) (57)

or: M = M (l - pR 2H'/48r) where: / MO = plI'R4H'2/4 Then since: V = 1R2 by substitution of Equation (59) into Equation (58): (58) (58a) (59) M = M (1 - Mo/12TnV) O (60) Either Equation (60) or Equation (57) is in suitable form to obtain resistivity values from measurements of angular velocity, material viscosity, magnetic field strength, and total torque.

VI. Resistance in Magnetic Field Review20 The influence of a magnetic field on the resistance of pure molten metals and liquid binary alloys has attracted long interest, the first work being done on this subject in 1891. The early workers in this area found that the application of such a field to liquid bismuth and mercury increased the resistance by small amounts. Orginally, this increase was considered to stem from secondary effects and probably due to the heating of the metal by the current passage. Later Berndt and others (6, 85, 118) discovered that the container size affected the change of resistance: the smaller the diameter of the capillary tube used, the smaller the resistance change. It was thought that the observed change was due mainly to unknown effects and that the actual resistance difference was close to zero. Williams (146) has given a theoretical treatment of the problem in which the change in resistance is assumed to be caused by: 1. An actual resistance change. 2. A change dependent upon the energy required to maintain hydrodynamic currents set up in the liquid by the interaction of the magnetic field and the electrical current in the material. An expression for the latter effect was calculated dimensionally, and shown to predominate over true resistance change in all experimental cases except mercury, bismuth, and bismuth amalgams. The variation of the change in resistance with current was found to be due to a 20 Taken from (6, 34-55, 60-61, 85, 98, 118, 146). -45

-46 turbulent motion of the material. In general, the total increase of resistance is: A =G +7 + NT'2stf'(r2/H'Isp)f' "(L)/nT (61) Equation (61) was considered further for cases both of steady and turbulent liquid motion. The experimental equipment for detecting the change of resistance in magnetic fields usually consisted of capillary spiral tubes or even straight tube sections which were placed between the poles of a magnet, and the resistance change noted with and without the field present by a type of standard electrode apparatus. The data were usually reported in terms of this resistance change with no standardized state given for conversion to absolute resistivities.

21 VII. Resistivity under Pressure Review A few early determinations on the resistivity of liquid mercury were conducted at relatively low pressures (under 200 atmospheres) in 1882, 1897, and 1898. Braunbek (18) and Birch (11) also experimented in limited fashion with the resistivity of mercury at various pressures and temperatures. Conclusions by these experimenters as to the nature of the change of resistivity with pressure (a decrease with increasing pressure) were not satisfactorily explained; furthermore, the resistivity-pressure relation did not seem to follow any simple law. Bridgeman (20-22) did the most extensive and accurate work on the resistivity-pressure-temperature relationship of mercury, and also experimented with other molten metals at high pressures: gallium, lithium, potassium, and sodium. Several "abnormal liquids" studied by Bridgeman underwent an increase in resistivity with both increasing temperature at constant pressure and increasing pressure at constant temperature. The normal metals had opposite behavior, similar to that found for mercury. The entire experimental apparatus was generally contained in a pressure "bomb" with resistivity measurements conducted on capillary tubes which were subjected to hydrostatic pressure. Standard electrodetype devices were employed. The data reported are given mainly in terms of relative mass or volume resistivities with the standard taken as the resistivity at 0~C and at 0 atmosphere pressure. 2Taken from (11, 18, 20-22) -47

VIII. Resistivity at Constant Volume Review2 All of the experimental studies reported in the literature have consisted of the determination of resistivity at constant pressure for different temperatures, i.e., the molten material is not constricted but is free to expand in the electrode region. Kraus (70) in 1914 considered the electron theory of metals as applied to the liquid state and calculated temperature coefficients of resistivity for mercury at constant volume from assumptions of the number of conducting charges per atom. He found that at constant volume the resistivity actually decreased with temperature —that the temperature coefficient was negative. Gubar and Kikoin (44) in a recent article also performed calculations on the resistivity of mercury at constant volume. These researchers stated that due to the widespread use of constant volume resistivities in theoretical work, experimental measurements should either be measured directly in terms of constant volume or should be converted from measurements at constant pressure to constant volume by: 1/p = (p/6T)Vt = (p/6T)p/ - (/P/-P)T e/P' (62) These latter investigators also experimentally confirmed Kraus's contention on the negative temperature coefficient in mercury with constant volume. The experimental apparatus (44) consisted of a standard capillary electrode-type device filled completely with the molten material at room temperature and sealed. Under increasing temperature 22 Taken from (44, 70). -49

-50the material was constrained to the capillary bore and the resistivity at constant volume was determined in the usual manner.

IX. Resistivity Data Compilation This section presents a complete listing of most experimental resistivity data from 1902 to the present (early 1961). These data have been taken entirely from the entries in the Bibliography (see pages 243ff) and are presented separately for pure molten metals, molten binary alloys, and liquid amalgams. The experimental data are presented in tabular form whenever possible. Discussion of Literature Resistivity Presentation Among the articles of resistivity of various materials reported in the literature some ambiguity has occurred with the forms of presentation, particularly involving units of measurement. Resistance is an electrical property of a material which is expressed as the ratio of the voltage across a body to the current through it. In the practical system of units, where voltage is expressed in terms of the volt, current as the ampere, resistance has the unit of ohms. The resistivity, or specific resistance, is most commonly used in comparison of resistive properties of different materials. Resistivity is a measurement of the resistance of a substance of unit cross-section area and of unit length at a temperature of 0~C. Under these conditions the resistivity is numerically equal to the resistance offered by a cube of unit edge where the resistance is measured across two opposed faces. Although the unit of resistivity is the ohm-centimeter (resistance times cross-section area divided by length), many -51

-52 hybrid units have been used and reported which are (incorrectly) based upon the above definition. Particularly common is the term "ohm per centimeter cube". In reality this unit is identical to the ohm-centimeter unit. In an analgous manner a system of units based upon conductance and conductivity, the reciprocals of resistance and resistivity, are defined and have received some usage. In consulting references on electrical resistivity the units in which the data are reported must be viewed with care. Most of the data are taken and reported in terms of resistivity at a constant pressure with temperature and composition varying. In a few articles relative resistivities are reported; if the standard value is also given a simple multiplication can yield true resistivities. Form of Data Compilation In each of the following subsections, the literature data are arranged as follows: 1. Pure Metals. Arranged alphabetically according to chemical symbol. 2. Binary Alloys. Arranged alphabetically according to chemical symbol of individual component. 3. Amalgams. Arranged alphabetically according to chemical symbol of non-mercuric component. For each subsection listing, all appropriate sources of data are given in tabular form by reference number (referenced to listings in the Bibliography, pages 243ff). Those sources consulted by the writer and available from the University of Michigan Libraries are

-55 indicated by an asterisk preceeding the number. These tables also contain information on investigator, year of investigation, type of apparatus employed,23 and form of experimental data.24 A tabular listing of most of the available data is also given; each data set is identified by its reference number. In most cases, only reference data obtained from original tabular presentations are included; data taken from graphically-presented sources are enclosed between parentheses. Unless otherwise noted resistivity values are in units of microhm-centimeter (ohm-centimeter x 10-6) at constant pressure, temperature values in degrees Centigrade, and composition values in weight percent. 3 E indicates measurement by a standard electrode-type device; M indicates measurement by an indirect magnetic device; and 0 indicates some other measurement method. 24 T indicates tabular data; G indicates graphical data.

DATA COMPILATION PURE MOLTEN METALS

-57 Table V. Literature Data on Resistivity of Silver Temp *16 *76 *92 *112 *139 960 961 962 18.7 971 978 980 996 1000 19.22 1010 1028 1030 1050 19.86 1083 1100 20.48 1108 1150 21.29 1152 1200 21.67 1220 1235 1250 22.24 1257 1300 22.79 1340 1350 23.30 1400 23. 0 17.3 17.25 16.6 16.2 16.6 17.8 16.7 17.01 17.6 17.9 18.3 17.2 17.8 18.19 18.45 19.2 20.6 19.36 19.35 21.4 19.7 21.7 20.54 21.01 Table VI. Literature Data on Resistivity of Aluminum Temp *16 *76 *87 *112 *139 653 654 658 659 662 670 686 695 700 710 715 735 745 765 774 27.11 20.13 20.1 24.2 25.5 19.6 20.5 26.0 20.9 27.80 24.75 21.0 26,4 21.3 26.8 21.7 26.8

-58 Table VII. Literature Data on Resistivity of Gold Temp *91 *112 1063 30.82 31.25 1077 31.00 1100 31.34 31.8 1140 32.00 1200 32.76 33.15 1217 33.00 1218 33.00 1300 34.76 1400 35.58 1500 37.00 Table VIII. Literature Data on Resistivity of Bismuth Temp 263 269 271 278 279 282 289 300 301 320 324 325 340 350 360 375 376 380 396 400 414 420 440 450 460 500 526 550 590 600 639 650 700 709 750 800 900 1000 *25 *76 *94 *103 *112 *139 127.50 141.7 126.7 130.2 124.430 128. 138. 127. 128.90 125.316 131.9 128. 126.282 128. 130. 127.310 131.55 128.376 133. 129.486 135. 134.20 130.711 137.6 129. 131. 131. 132.000 133.513 136. 137.00 135.224 139.90 143.3 141. 144. 142.50 145.25 149.0 147. 148.00 150.85 154.7 151. 153.55 160.4 166.1 171.8

Table X. Literature Data on Resistivity of Cadmium Temp *16 321 322 33.76 325 350 351 392 400 33.70 419 450 457 494 500 34.12 528 550 596 600 34.82 650 35.26 700 35.78 *76 *94 *112 *121 32.2 34.7 33.76 33.60 33.6 32.8 32.8 33.70 34.7 33.5 33.0 33.90 33.6 33.2 34.7 34.2 33.4 34.2 34.12 35.2 33.8 34.44 34.0 34.82 35.26 35.78 36.3 34.4 Table XII. Literature Data on Resistivity of Cesium Temp *46 28 37.2 30 34 37 59 40.6 *47 36.6 36.6 37.0 Table XIII. Literature Data on Resistivity of Copper Temp *15 *16 *90 *112 *121 *139 1082 1083 1084 1088 1092 1093 1097 1100 1103 1117 1124 1143 1150 1157 1184 1200 1202 1250 1300 1350 1400 1450 1500 1550 12.090 22.0 21.1 20.36 21.38 13.210 22.0 20.45 14.820 16.110 21.52 17.400 19.340 21.270 21.2 22.9 22.2 21.880 20.81 21.19 21.97 24.0 22.4 22.6 22.41 22.1 25.1 22.9 21.59 22.05 22.60 23.15 23.69 24.24 24.80 22.24 23.29 23.29 24.17 26.2 27.3 25.05

-60 Table XIV. Literature Data on Resistivity of Iron Temp *16 1505 1550 1600 1650 131.1 133.3 135.7 138.1 *107 139 139 Table XV. Tenmp *27 0 27.23 18 30 46 Table XVI Literature Data on Resistivity of Gallium *46 28.0 27.2 28.4 *125 25.84 Literature Data on Resistivity of Germanium Temp *28 *62 937 63. 60.

Table XVII. Literature Data on Resistivity of Mercury Temp *15 *19 *30 *57 *76 *83 *139 *147 *148 -39 -35 -32 -25 -23 -19 -18 -11 -6 0 10 12 13 15 17 20 26 30 35 40 44 50 98.54 60 63 70 77 80 90 100 103.32 103 109 129 145 150 108.48 169 184 187 200 114.27 217 221 245 250 123.44 256 258 275 288 297 300 127.70 320 350 389 93.1 85.4 90.1 91.0 92.8 93.2 94.8 93.4 95.2 93.8 94.3 94.074 94.074 94.074 94.920 96.4 94.074 94.074 95.047 97.5 95.328 95.507 95.784 95.6 96.238 96.668 96.6 97.569 100. 98.490 99.429 98.30 99.4 100.387 100.6 101.364 102.359 103.361 103.373 105.7 103.20 103.351 103.361 103.9 103.952 106.415 110.7 108.50 110.863 112.655 112.607 118.0 114.20 116.742 117.194 120.132 120.70 121.797 121.820 121.975 128.8 126.188 127.509 127.876 127.50 127.876 136.7 135.50 145.156

-62 Table XVIII. Literature Data on Resistivity of Indium Temp 154 157 167 182 199 200 220 230 250 261 280 300 350 400 450 500 550 600 650 *112 *121 *133 33.1 29.10 29..28 29.66 30.11 30.84 33.8 35.0 31.87 32.29 33.31 34.87 36.75 39.3 41.9 44.45 36.2 37.4 38.7 39.9 41.2 42.4 43.7 44.9 11 700 47.0 800 49.6 900 52.2 000 54.75 Table XIX. Literature Data on Resistivity of Potassium Temp 63 63 64 64 65 65 68 69 75 81 83 90 90 95 100 105 106 109 115 120 122 129 130 130 150 200 250 300 350 *8 13.3647 13.7534 13.8272 13.4266 13.7317 13.8647 14.2516 13.8926 14.3580 15.1419 15.6052 15.3748 15.0089 *15 *73 *83 *87 13.35 13.16 12.98 14.43 15.49 15.80 15.3 15.5712 16.2528 16.6647 16.7547 16.3675 16.6193 17.6652 17.5475 17.1995 18.70 21.80 25.00 28.20 31.40 18.53 21.78

Table XX. Literature Data on Resistivity of Lithium Temp *7 181 40.5553 181 40.2933 183 40.3368 185 40.6002 186 40.9231 191 41.8586 196 41.8256 200 43.0012 200 42.8753 201 42.2989 208 43.5525 217 44.3250 219 44.4988 229 45.2603 232 45.6321 234 45.8281 Table XXI. Literature Data on Resistivity of Magnesium Temp *112 *121 650 27.4 700 27.7 28.8 750 28.6 800 28.2 28.4 850 28.2 900 28.7 28.0

-64 Table XXIII. Literature Data on Resistivity of Sodium Temp 98 99 100 111 116 125 131 150 200 250 300 350 *9 *15 *47 *83 9.75 *87 9.656 9.60 8.8002 9.0395 9. 345 9.65 9.8 10.2 9.5037 9.3216 11.40 13.18 14.90 16.70 18.44 11.7 13.58 Table XXIV. Literature Data on Resistivity of Nickel Temp 1451 1500 1550 1600 1650 *'15 108.0 108.8 109.9 110.5 111.5

-65 Table XXV. Literature Data on Resistivity of Lead Temp *15 327 94.6 328 329 330 331 332 333 337 338 340 345 346 348 349 350 95.6 358 360 365 373 380 392 400 98.0 404 408 420 433 440 450 100.3 453 460 463 468 468 473 493 500 102.6 510 524 527 536 550 104.9 551 561 577 578 600 107.2 650 109.5 682 700 731 750 776 800 856 900 1000 1100 1200 *16 94.6 *69 *76 *83 95.8 94.6 66.6 50.8 *94 *103 *112 95.0 *139 96.735 67.6 48.7 95.00 96.4 81.5 97.867 83.0 82.9 96.9 101. 100. 99.000 97.6 101. 100.255 85.0 85.2 86.8 87.4 98.0 98.30 101.418 98.2 102. 100. 102.563 103.716 100.55 104. 88.2 87.9 104.878 103. 105. 103. 105. 102.6 102.85 102.9 90.4 106. 105. 107. 105.05 91.8 107. 93.0 111.8 108. 112. 114. 117. 120. 107.2 107.25 109.51 111.8 111.75 114.00 116.4 116.20 121.1 125.7 107.6 112.35 116.4 116.9 121.1 125.7 130.2 134.8 121.6 126.3

-66 Table XXVI. Literature Data on Resistivity of Rubidium Temp *46 40 24.5 43 50 64 26.5 75 100 *47 19.6 20.9 *73 23.15 25.32 27.47 Table XXVII,). Literature Data on Resistivity of Antimony Temp *15 627 630 631 127.80 634 638 650 656 658 690 700 128.98 708 721 746 750 129.88 755 778 800 130.76 808 810 843 850 131.70 900 132.74 910 913 938 9,u 133.86 990 1000 134.98 1009 1050 136.20 1100 137.62 1150 139.07 1200 140.49 *76 *94 *112 *139 117.00 115.0 113.5 111. 110. 111. 117.07 115.5 110. 117.65 115.4 116.1 116.4 111. 118.53 120.31 118.1 113. 112. 113. 115. 117.4 123.54 120.8 119. 120.0 120. 121.9 122.1 Table XXVIII. Literature Data on Resistivity of Selenium28 Data are in ohm-centimeter units. Temp 390 412 437 465 540 582 645 690 *100 76650. 38925. 22340. 12300. 2247. 992. 237. 88.

-67 Table XXX. Literature Data on Resistivity of Tin Temp *15 232 47.6 235 240 250 47.9 255 260 265 270 280 295 300 49.1 320 325 340 350 50.3 360 379 380 385 400 51.4 420 432 440 450 52.6 460 471 485 500 54.0 550 55.5 563 600 56.8 650 58.2 668 700 718 750 783 800 837 61.21 840 61.28 850 61.50 900 987 64.60 1000 1100 1200 1218 69.80 1300 1370 73.20 1390 73.62 1400 1435 74.65 1472 75.49 1500 1600 1617 78.81 *16 *76 47.83 48.1 48.6 *94 *103 *112 47.250 48.0 47.60 47.580 *121 *121 *139 45. 49. 48.3 45.4 48.5 48.331 49.7 49.5 49.142 49.44 49.961 50.782 49.45 49.7 50.1 49.6 46.7 50.5 50.8 47.8 51.506 50.76 52.331 51.3 53.154 52.2 52.0 49.1 52.8 51.60 52.6 52.00 53.980 54.807 55.633 53.30 56.458 52.2 53.2 50.3 54.6 53.85 56.05 58.26 60.45 62.67 54.1 54.62 55.94 56.0 57.22 58.58 59.0 59.88 54.7 54.5 51.5 55.7 52.7 55.5 57.2 59.6 60.0 62.1 61.22 54.0 55.2 56.4 57.7 58.9 60.1 61.3 62.1 64.5 64.98 67.20 69.45 71.70 67.0 69.5 72.0 73.98 76.24 78.51

-68 Table XXXI. Literature Data on Resistivity of Tellurium Temp *31 *46 *71 450 451 460 464 483 500 550 550. 600. 17000 564. 523. 496. 400. Table XXXII Temp *112 302 303 306 309 321 347 356 367 382 400 402 422 500 600 700 800 73.1 Literature Data on Resistivity of Thallium *133 83.38 83.60 83.61 83.89 84.32 84.84 85.35 85.34 85.95 76.25 86.78 87.54 79.1 81.9 84.8 87.75

-69 MOLTEN BINARY ALLOYS

Table XXXIII. Literature Data on Resistivity of Zinc Temp *16 418 419 35.30 420 423 424 425 426 427 432 436 440 445 450 460 484 491 499 500 519 539 540 549 550 555 570 595 600 35.65 601 623 627 650 669 695 700 35.70 750 800 850 900 35.75 I *69 *76 *94 *103 *112 *121 *139 32.8 36.7 33.3 37.0 37.4 23.5 36.955 36.2 36.2 33.8 37.30 33.4 33.7 37.349 37.1 3 3 3 37.08 37.1 37.783 36.9 36.2 33.4 36.60 36.8 36.5 36.2 36.7 33.0 36.2 36.20 32.9 36.5 32.5 35.90 32.4 36.7 36.2 36.3 36.0 35.9 36.4 36.1 36.2 36.7 36.4 36.7 36.2 35.72 36.8 36.6 35.60 35.59 35.60 35.74

-72 Table XXXV Literature Data on Resistivity of Silver-Copper Alloys *16 Temp 1.70Ag 1073 21.16 1100 21.45 1150 21.95 1200 22.46 1250 22.96 1300 23.47 1350 23.97 1400 24.48 Table XLI Literature Data on Resistivity of Aluminum-Copper Alloys *16 *16 *16 *16 *16 *16 Temp 5.OA1 10.OA1 12.3A1 15.OA1 18.OA1 22.3A1 925 73.91 989 1021 1027 1065 1100 1200 1300 1400 72.57 67.57 58.52 43.00 43.18 43.33 43.57 43.81 58.22 57.82 57.40 62.50 66.72 65.67 64.61 63.57 70.08 68.00 66.22 70.27 68.47 66.95 Temp 542 578 592 596 600 638 700 798 800 900 1000 1100 1200 1300 *16 *16 *16 *16 *16 *16 30.OA1 45.OA1 50.OAl 67.2A1 80.3A1 95.OA1 38.21 45.32 48.30 30.82 48.32 45.45 39.03 30.87 26.98 48.59 46.00 40.43 31.68 28.05 65.43 65.44 65.52 65.61 65.70 65.81 65.92 48.85 49.11 49.37 49.64 49.90 50.16 46.57 47.11 47.67 48.22 48.78 49.33 41.83 43.22 44.60 45.97 47.34 48.73 32.52 33.34 34.14 34.95 35.77 36.57 29.78 31.49 33.22 34.96 36.68 38.39

-73 Table XLVI. Literature Data On Resistivity of Bismuth-Cadmium Alloys *76 *76 *76 *76 *76 Temp 10.OBi 30. Bi 50.0Bi 70.OBi 90.OBi 201 224 245 255 264 270 287 295 300 305 325 336 342 350 352 376 378 384 399 400 408 431 438 443 471 474 479 496 108.4 124.9 109.3 125.5 131.0 78.6 127.4 132.2 111.0 78.9 111.1 48.4 128.6 48.5 134.8 79.6 129.5 135.3 48.3 112,5 114.5 48.8 137.0 80.4 49.0 115.4 139.3 133.5 49.6 80.7 134.5

Table XLVIII. Literature Data on Resistivity of Bismuth-Lead Alloys *83 *76 *76 * *76 *76 7 Temp 1.2Bi 10.OBi 30.OBi 50.OBi 70.0OBi 90.OBi 180 213 224 250 264 272 275 285 315 318 325 326 357 358 375 376 397 400 405 421 428 438 471 480 490 498 500 600 700 800 900 1000 111.0 112.9 117.8 108.6 126.7 120.0 116.0 127.9 111.8 118.1 105.5 129.7 131.6 114.1 120.6 124.8 108.8 133.4 97.8 116.0 123.6 112.7 135.0 118.8 115.5 121.5 130.3 116.8 102.4 107.0 111.6 116.2 120.8 125.4

-75 Table XLIX Literature Data on Resistivity of Bismuth-Antimony Alloys *76 *76 *76 Temp 30.OBi 60.OBi 90.0Bi 355 387 425 463 486 519 530 562 563 587 608 614 630 635 664 675 677 126.0 128.4 130.3 132.0 133.5 135.6 136.5 126.6 128.4 122.0 122.8 123.6 124.4 124.8 129.7 130.5 132.4 Table LI. Literature *76 Temp 10.0 202 224 52.2 233 235 244 52.8 260 264 265 270 274 53.1 285 53.5 289 290 291 295 302 305 53.9 320 325 344 352 365 375 55.8 376 392 407 417 455 58.0 515 Bi Data on Resistivity of Bismuth-Tin Alloys *76 *76 *76 *76 30.OBi 50.OBi 70.OBi 90.OBi 62.2 74.6 75.5 P 63.4 96.6 63.8 97.7 76.8 119.2 64.4 120.3 98.6 64.5 77.7 120.7 79.0 99.5 121.7 123.5 67.2 79.6 101.8 124.1 81.1 102.8 71.6

Table LV. Literature Data on Resistivity of Carbon-Iron (Steel) Alloys *16 *16 *16 *4329 *2330 *2331 *2332 Temp 0.2Fe 1.2Fe 3.8Fe 3.3Fe 3.8Fe 3.9Fe 3.9Fe 1060 1090 1115 1123 1132 1135 1137 1140 1150 1155 1170 1180 1190 1200 1240 1250 1300 1310 1350 1400 1416 1450 1495 1500 1550 1600 1650 200. 136. 152. 200. 192. 180 169. 155. 148. 145. 153. 142. 146. 146. 150. 148.0 148.2 150. 146. 148. 150.3 160. 150. 152. 136.4 136.6 138.7 140.8 142.9 149.1 150.1 151.5 154.3 154.3 155.7 152.6 153.7 154.8 157.0 157.0 " Sample 30Sample Sample 32Sample Sample composition: composition: composition: composition: 93.032Fe, 3.337C, 2.752Mn, 0.783Si, 0.061P, 0.035S. 3.8C, 0.2Si, 0.2Mn, 0.1P, 0.02S, remainder Fe. 3.9C, 1.3Si, 0.2Mn, 0.1P, 0.02S,.remainder Fe. 3.9C, 1.3Si, 0.2Mn, 0.1P, 0.0055S, 0.05Mg, remainder Fe.

Table LVI. Literature Data on Resistivity of Cadmium-Copper Alloys *16 * * 16 16 *16 *1616 emp 58.0Cd 63.0Cd 68.5Cd 72.6Cd 76.2Cd 81.OCd 540 43.68 Te 547 549 42.14 559 563 564 600 41.65 650 41.18 700 40.71 42.86 44.65 44.56 42.97 42.35 41.77 45.17 44.45 43.44 42.43 43.89 52.96 42.07 43.97 43.14 42.31 42.42 42.00 41.57 *76 Temp 43.0( 419 466 486 512 525 537 564 568 570 579 580 593 600 601 604 618 619 620 628 629 641 642 645 650 670 672 675 680 33.2 681 692 700 703 35.5 705 719 720 731 36.7 732 745 37.7 757 38.1 812 39.9 850 41.9 *76 *76 *76 *76 *76 *76 Cd 55.0Cd 65.0Cd 75.0Cd 80.OCd 90.OCd 95.0Cd 36.2 36.1 40.0 39.7 35.8 39.7 39.3 42.0 36.0 44.9 41.1 44.6 40.8 44.6 39.1 40.7 42.6 35.8 44.2 39.1 43.6 36.0 40.3 43.4 42.9 42.8 39.7 43.3 42.5 43.3 36.2 39.9 39.8 43.3 42.5 39.8 42.6 43.3 42.3 41.7

-78 Table LVII. Literature Data on Resistivity of Cadmium-Sodium Alloys *15 Temp 4.4Cd 122 150 200 250 300 350 15.30 16.18 17.71 19.25 21.24 23.36 Table LVIII. Literature Data on Resistivity of Cadmium-Lead Alloys *83 *83 *76 *76 *76 *76 *76 Temp 1.4Cd 2.9Cd 10.OCd 30.OCd 50.OCd 70.OCd 90.OCd 300 92.0 302 308 314 315 324 344 350 353 375 390 392 395 400 417 419 420 445 450 454 457 460 484 489 493 500 515 520 521 539 557 600 700 800 68.5 54.2 93.2 92.6 80.9 69.9 93.8 81.8 38,7 55.1 71.2 82.9 38.9 95.7 97.1 96.5 72.0 38.7 55.7 38.8 73.0 97.9 84.6 56.4 56.9 38.7 74.2 101.6 100.9 57.0 85.1 101.7 57.7 102.8 106.1 110.6 115.1 105.4 109.8 114.3

-79 Table LIX. *76 *76 20.OCd 30.OCd Literature Data *76 *76 40.OCd 50.0Cd Temp 378 387 417 428 438 451 462 470 495 496 505 513 515 516 519 524 532 535 541 545 550 553 570 574 585 591 599 600 602 609 610 619 622 625 631 o45 650 653 655 665 690 694 705 706 753 765 on Resistivity of Cadmium-Antimony Alloys *76 *76 *76 *76 60.0Cd 70.0Cd 80.0Cd 90.0Cd 89.9 130.0 128.4 89.6 126.7 89.5 125.7 161.5 90.0 169.6 89.5 149.6 187.5 123.2 153.5 183.6 146.9 62.6 122.7 145.3 160.0 179.7 148.0 141.2 143.3 122.5 63.0 142.2 139.4 172.7 144.9 140.0 64.t 152.9 89.6 139.8 143.2 65.2 167.3 90.8 64.4 149.7 142.4 138.8 139.6 165.2 138.0 149.7

Literatur *76 Temp 10.OC 185 215 228 235 52.2 250 255 52.3 258 276 280 284 53.0 289 295 300 305 320 54.3 330 336 345 356 366 55.6 367 375 384 392 400 407 440 475 Table LX. re Data on Resistivity of Cadmium-Tin Alloys *76 *76 *76 *76:d 30.OCd 50.OCd 70.OCd 90.OCd 52.7 53.8 54.9 54.2 55.6 53.4 56.2 55.6 53.6 56.7 41.0 41.4 56.4 57.6 54.8 56.8 55.6 59.0 41.9 42.2 42.5 43.0 56.5 57.1 Table LXI. Literature Data on Resistivity of Cadmium-Zinc Alloys *76 *76 *76 *76 *76 Temp 10.01 308 320 357 359 361 380 393 406 420 36.4 443 449 463 466 36.2 480 490 502 37.4 509 511 516 538 555 568 576 37.1 588 593 608 618 37.4 627 37.6 Cd 30.OCd 50.OCd 70.OCd 90.OCd 38.1 38.5 38.0 37.9 39.4 37.9 36.1 35.7 35.6 35.0 36.1 37.5 38.4 37.8 37.6 37.1 35.3 36.8 37.8 37.6 36.8 37.8 36.6 36.3 36.8

-81 Table LXIII. Literature Data on Resistivity of Copper-Nickel Alloys *15 *15 *15 *15 Temp 13.8Cu 35.OCu 50.1Cu 81.lCu 1187 1200 1250 1300 1326 1350 1358 1400 1419 1450 1500 1550 1600 1650 53.7 53.8 54.4 55.5 93.0 93.6 57.2 136.7 138.5 94.7 59.2 120.0 120.6 121.7 122.7 123.8 125.0 140.6 142.7 145.0 147.2 95.9 97.1 98.2 99.5 100.6 62.6 66.5 70.0 Table LXIV. Literature Data on Resistivity of Copper-Lead Alloys *16 *16 *16 *16 *16 * *16 16 16 16 Temp 2.0Cu 9.1Cu 11.lCu 60.6Cu 63.7Cu 64.0Cu 83.1Cu 97.1Cu 98.0Cu 657 111.4 700 113.2 800 117.4 900 121.6 1000 125.8 1010 1021 1072 1075 1098 1100 1117 1200 1300 1305 1400 1500 41.26 60.02 24.71 23.74 63.32 130.1 60.82 42.13 25.06 24.0O 134.2 138.5 142.7 118.9 121.3 124.1 124.2 66.69 66.79 126.1 127.1 67.57 68.46 64.29 61.90 43.10 26.21 25.1 65.31 62.98 44.04 27.37 26.; 66.27 67.26 64.05 44.98 45.92 28.53 27..i

-82 Table LXV. Literature Data on Resistivity of Copper-Antimony Alloys *15 *15 *15 *15 *15 *15 *15 *15 *15 Temp 1.2Cu 20.OCu 30.OCu 50.6Cu 60.6Cu 66.7Cu 76.4Cu 83.2Cu 98.1Cu 533 543 600 625 639 650 655 682 700 750 800 815 850 885 900 950 1000 1050 1070 1100 1150 1200 1250 1300 1350 1400 1450 1500 116.44 119.40 118.10 118.40 122.90 123.49 124.70 125.90 127.10 128.31 129.60 130.94 132.36 135.90 140.01 119.30 119.60 147.00 120.50 121.70 122.92 120.80 122.00 123.20 146.64 146.26 145.90 152.20 151.70 150.30 148.97 139.18 138.46 137.79 104.50 124.10 124.40 145.71 147.90 137.10 104.29 125.39 126.70 128.10 129.60 125.59 126.78 127.08 129.17 145.64 145.63 145.68 145.82 146.00 146.39 146.80 146.90 146.14 145.38 144.85 144.39 143.90 143.40 136.40 135.63 134.60 133.60 132.60 131.50 130.50 103.99 103.64 103.39 103.21 103.19 103.19 103.19 84.00 84.09 84.31 84.59 84.79 131.16 130.40 132.70 131/58 132.78 85.08 85.34 85.59 85.84 86.11 29.00 29.24 29.97 30.18 30.62 31.12 31.64 32.16 32.68 33.19 588 589 617 622 627 640 647 651 653 658 659 668 678 *76 *76 10.OCu 30.0Cu 115.5 106.5 115.8 *7676 6 *76 *6 76 *76 *76 40.OCu 50.OCu 60.OCu 65.OCu 70.OCu 80.0Cu 126.5 106.5 127.2 130.0 123.5 107.5 127.5 116.5 136.8 130.5

-85 *76 *76 *76 *76 *76 *76 *76 *76 Temp 10.OCu 30.0Cu 40.0Cu 50.0Cu 60.0Cu 65.0Cu 70.0Cu 80.0Cu 682 142.6 683 108.0 696 124.5 697 128.1 698 117.5 705 141.3 707 135.9 712 124.6 718 140.9 723 129.5 730 128.7 736 135.2 741 125.2 742 109.6 743 140.7 747 118.5 766 129.8 775 118.9 135.0 784 125.5 788 130.0 797 129.4 830 129.7 134.2 836 126.2 854 138.4 856 95.2 861 134.0 880 138.0 886 96.0 902 96.1 924 97.2 941 96.0

Table LXVI. Literature Data on Resistivity of Copper-Tin Alloys * * 16 16 *16 *16 *16 *1616 Temp 20,0Cu 40.0Cu 57.5Cu 61.6Cu 80.0Cu 95.2Cu 98.0Cu 544 58.51 600 59.80 619 66.62 700 61.90 67.40 705 76.02 721 75.00 800 63.98 68.45 74.95 74.02 883 58.50 900 66.02 69.45 74.20 73.05 58.53 1000 68.04 70.50 73.75 72.50 58.72 1054 32.26 1070 25.17 1100 70.08 71.75 73.40 72.22 58.92 32.71 25.51 1200 72.10 73.10 73.40 72.08 59.11 33.63 26.53 1300 74.15 74.50 73.80 72.15 59.30 34.54 27.55 1400 76.20 75.90 73.95 72.32 59.47 35.47 28.57 1500 72.60 59.63 *76 *76 Temp 10.OCu 20.0Cu 411 53.8 435 55.4 505 55.8 545 57.0 548 58.7 587 59.6 594 58.0 602 610 60.2 617 632 637 58.9 648 60.8 667 680 705 708 61.4 717 721 728 733 742 749 753 768 784 63.0 787 790 799 805 807 822 842 858 866 870 871 884 898 908 921 938 941 *76 *76 * * 7 *76 *76 *6 30.0Cu 40.OCu 50.0Cu 60.0Cu 70.0Cu 80.0Cu 63.1 63.3 63.8 68.2 69.3 64.4 69.5 69.7 71.1 70.7 75.4 70.9 69.9 75.5 72.9 66.4 71.1 74.8 66.1 70.6 74.3 70.9 72.4 73.9 70.0 73.6 71.6 71.3 60.2 60.1 60.6 71.1 60.6 70.8 60.6 60.2 70.5 60.6

-85 Table LXVIII. Lit Temp 591 665 697 750 762 787 800 818 827 838 840 868 875 877 880 893 895 921 923 927 928 936 940 951 974 984 989 1016 1021 1024 1038 1050 1068 109o 1111:erature Data on Resistivity of Copper-Zinc Alloys *76 *76 *76 *76 *76 *76 10.OCu 30.OCu 40.OCu 50.OCu 60.OCu 79.OCu 40.5 39.8 39.4 39.3 39.0 38.7 48.7 49.9 49.4 49.9 49.5 47.6 49.4 49.2 47.3 48.5 48.3 44.7 45.3 48.0 46.4 48.0 45.0 48.5 47.2 45.6 45.7 37.8 46.0 45.8 44.6 38.7 46.1 38.7 39.1 39.6 *16 Temp 15.OCu *16 *16 *16 *16 *16 *16 *16 *16 34.OCu 39.3Cu 46.2Cu 60.4Cu 80.OCu 85.OCu 96.5Cu 99.1Cu 637 44.83 700 44.04 800 42.78 813 830 850 42.17 900 41.56 994 1000 1017 1069 1080 1100 1200 1300 48.72 49.13 47.87 48.59 46.69 47.35 48.10 46.95 43.90 33.02 44.34 45.53 44.62 42.36 33.03 29.40 22.80 33.44 29.87 23.13 33.83 30.43 24.23 25.33 21.83 22.03 23.03 24.03

-86 Table LXIX. Literature Data on Resistivity of Gallium-Indium Alloys *125 Temp 771.5Ga *125 *125 84.5Ga 92.0Ga 20 27.2 26.7 26.3 Table LXXI. Literature Data on Resistivity of Gallium-Tin Alloys *125 Temp 88.lGa *125 91.8Ga 20 27.3 26.7 Table LXXIV. Literature Data on Resistivity of Potassium-Sodium Alloys *127 *83 Temp 82.1K 6.7K *83 *83 *83 *83 *83 *83 12.9K 37.4K 57.5K 73.3K 85.8K 95.3K -13 7 9 10 35.65 35.75 40.4 40.9 12 41.4 14 41.4 15 17 41.8 32.40 18 42.0 20 42.0 25 42.1 30 42.6 35 43.2 40 43.3 42 50 71 82 100 150 200 28.75 20.82 29.73 38.18 39.00 34.38 21.48 17.25 13.05 13.80 15.90 18.02 18.46 20.55 22.65 32.22 34.72 37.20 40.97 43.73 46.51 41.90 44.80 47.65 37.40 40.70 44.40 24.33 27.50 30.95

Table LXXV. Literature Data on Resistivity of Potassium-Lead Alloys *15 Temp 0.4K 319 350 400 450 500 550 93.60 95.76 99.24 102.72 106.21 109.70 600 113.22 Table LXXVI. Literature Data on Resistivity of Potassium-Rubidium Alloys *73 Temp 10. OK 50 22.57 75 24.57 100 26.39 *73 *73 *73 *73 *73 14.4K 26.OK 45.1K 60.3K 73.3K 22.28 24.15 26.05 21.14 22.28 24.75 19.01 20.75 22.52 16.89 18.42 19.84 17.45 18.98 Table LXXVII. Literature Data on Resistivity of Potassium-Tin Alloys *15 Temp 0.2K 245 49.02 250 49.10 300 50.09 350 51.08 400 52.58 450 54.18 500 56.00 550 57.90 Table LXXVIII. Literature Data on Resistivity of Potassium-Thallium Alloys Temp 110 150 200 250 300 350 *15 94.7K 21.30 26.40 30.36 35.36 40.39 45.40

-88 Table LXXX. Literature Data on Resistivity of Sodium-Lead Alloys *15 Temp 91.8Na 185 24.00 200 24.74 250 27.10 300 29.52 350 31.91 Table LXXXI. Literature Data on Resistivity of Sodium-Antimony Alloys *15 Temp 99.5Na 104 10.24 150 12.04 200 14.02 250 16.00 300 18.00 350 20.10 Table LXXXII. Literature Data on Resistivity of Sodium-Tin Alloys *15 Temp 0.1Na 231 250 300 350 400 450 500 47.61 48.18 49.71 51.20 52.71 54.21 55.75 Table LXXXIII. Literature Data on Resistivity of Sodium-Thallium Alloys Temp 93 100 150 200 250 300 350 *15 92.4Na 20.40 20.48 22.32 24.10 26.00 28.24 30.58

Table LXXXV *76 *76 Temp 30.OPb 40.OPb Literature Data *76 *76 50.OPb 60.OPb on Resistivity of *76 *76 80.OPb 90.0Pb Lead-Antimony Alloys *83 *83 *83 81.6Pb 98.OPb 99.2Pb 253 300 307 315 333 339 380 400 422 459 485 489 494 500 509 519 526 527 531 548 550 551 566 575 588 590 600 602 610 617 618 631 643 647 653 670 684 690 700 717 742 800 900 1000 96.9 93.0 101.7 94.1 106.7 102.3 108.8 102.6 97.6 97.9 104.7 116.0 116.0 116.4 116.0 106.5 102.2 102.5 117.0 108.2 114.9 112.9 115.1 117.6 115.7 118.2 116.7 117.3 114.5 109.4 118.5 110.3 106.8 107.1 117.5 115.3 118.6 116.9 116.2 117.5 120.7 112.5 118.4 118.2 120.7 120.3 114.5 114.1 111.4 111.6 122.5 121.5 118.1 122.3 126.3 115.9 120.1 125.1 116.2 120.8 125.3

-90 Table LXXX *15 *15 Temp 1.7Pb 3.2Pb 224 48.66 228 48.38 243 250 46.90 49.13 254 263 265 285 295 300 50.00 50.48 307 315 325 336 346 350 51.14 51.69 357 363 368 375 376 380 395 399 400 52.30 52.91 404 415 427 446 450 53.45 54.20 457 474 495 500 54.68 55.50 550 56.00 56.80 600 57.50 58.13 650 59.08 59.42 VI. Literature Data on Resistivity of Lead-Tin Alloys *76 *76 *76 *76 *76 10.OPb 30.OPb 50.OPb 80.OPb 90.OPb 50.6 57.1 63.4 64.3 51.2 57.8 52.2 65.8 87.4 59.0 89.5 53.4 66.5 60.1 53.8 67.2 80.0 61.1 92.1 93.0 54.2 81.1 62.3 83.4 94.0 96.2 *83 *83 Temp 10.5Pb 59.9Pb 208 48.0 236 65.8 264 288 300 50.4 67.5 309 321 325 327 400 52.8 70.3 500 55.6 73.2 600 58.4 76.1 700 61.4 78.9 800 64.4 81.9 900 67.4 84.8 1000 70.4 87.7 *83 *83 *83 *83 *83 *83 75.8Pb 88.5Pb 95.1Pb 9F.2Pb 99.3Pb 99.3Pb 73.2 82.3 74.4 82.8 90.7 92.5 93.0 93.7 77.8 86.8 94.6 96.0 96.4 97.1 81.2 90.8 98.8 100.5 100.9 101.7 84.5 94.8 103.1 104.9 105.4 106.2 87.8 98.8 107.3 109.4 109.9 110.7 91.2 102.7 111.5 113.8 114.4 115.2 94.6 106.7 115.7 118.3 11P.9 119.7 98.0 110.7 120.0 122.7 123.5 124.2

-91 Table LXXXIX. Literature Data on Resistivity of Lead-Zinc Alloys *83 Temp 79.6Pb *83 *83 *83 *83 *83 *83 *83 *83 82.3Pb 88.5Pb 92.6Pb 93.6Pb 96.6Pb 97.7Pb 98.6Pb 99.5Pb 235 400 438 500 515 588 600 602 648 700 728 783 800 900 1000 93.2 94.8 96.7 95.6 98.0 101.4 97.5 99.1 99.5 96.9 97.0 101.1 102.2 106.2 97.7 99.7 100.7 103.8 105.3 106.4 108.8 110.8 90.2 87.7 88.1 90.6 92.0 103.5 104.6 108.0 94.55 107.4 108.5 112.2 109.6 110.5 113.5 118.1 122.8 115.5 120.2 124.9 Table XCI. Literature Data on Resistivity of Antimony-Tin Alloys Temp 234 250 277 300 350 360 400 406 415 430 450 470 479 500 509 529 539 550 580 594 600 601 637 638 640 677 687 692 716 738 773 816 855 *15 *76 *76 *76 *76 *76 1.lSb 10.OSb 20.OSb 40.OSb 60.OSb 90.OSb 48.16 46.10 57.0 57.9 49.88 51.16 65.4 59.4 52.40 66.8 60.7 53.69 79.1 80.0 68.6 54.95 94.8 95.1 63.3 69.8 56.28 95.2 71.1 57.62 81.9 115.3 96.0 82.5 84.3 116.0 96.2 116.7 97.7 97.8 118.4 118.4

*76 Temp 10.0 447 48.8 478 48.5 508 48.3 521 527 530 540 550 48.3 556 560 570 571 579 580 584 590 599 600 48.7 605 610 611 612 622 627 630 49.2 647 648 651 653 658 661 678 679 690 691 695 702 708 713 715 720 731 734 742 766 769 770 774 Table XCII. *76 Sb 20.0Sb Literature Data on Resistivity of Anitmony-Zinc Alloys *76 *76 *76 *76 *76 *76 *76 30.0Sb 40.0Sb.55.OSb 60.0Sb 65.0Sb 80.OSb 90.0Sb 107.5 105.6 134.0 133.2 154.7 191.7 68.3 129.9 186.2 163.1 151.9 152.9 104.8 68.3 157.4 104.8 127.2 132.6 68.3 169.5 153.9 149.1 131.8 123.6 163.6 145.9 68.3 159.7 147.4 101.7 133.4 121.5 68.3 142.8 148.9 121.0 154.6 146.9 146.3 145.7 152.0 136.0 136.1 138.9 142.5

-95 Table XCV. Literature Data on Resistivity of Tin-Zinc Alloys *76 * 76 * 76 *15 *15 Temp 10.OSn 30.0Sn 60.OSn 90.0Sn 98.9Sn 99.5Sn 232 250 260 293 300 328 350 369 378 390 397 400 403 423 430 436 441 443 450 480 490 496 500 511 532 545 549 550 569 588 599 600 619 650 47.58 48.02 49.5 50.4 49.36 51.7 50.71 52.2 49.1 43.5 52.9 52.02 49.9 38.6 43.8 53.7 50.3 38.6 53.35 44.0 51.0 38.3 54.15 54.64 44.5 52.4 38.1 44.3 55.29 56.00 44.6 37.8 44.8 56.42 57.30 38.0 57.60 58.61

-95 LIQUID AMALGAMS

-97 Literature *30 Temp 0.01A1 300 127.405 Table XCVII. Data on Resistivity of Aluminum Amalgams *30 0.02A1 126.992 Tc *14P Temp 0.04Au 12 94.9D 100 103.13 217 258 300 127.43 at )le XCVIII. Literature Data on Resistivity *148 *148 *148 *148 *148 0.06Au 0.08Au 0.12Au 0.16Au 0.20Au 94.81 94.75 94.56 94.40 94.27 103.01 102.87 102.64 102.43 102.17 115.77 120.87 127.22 127.04 126.66 126.34 126.02 of Gold Amalgams *148 *148 0.24Au 0.28Au 94.07 93.94 101.97 101.79 114.95 120.07 125.80 125.57 *148 0.32Au 93.81 101.63 125.39 Temp 50 100 150 200 250 300 Table CII. Literature Data on Resistivity of Calcium Amalgams *15. 12Ca 97.02 101.78 106.80 112.50 118.43 126.00 Literature *15 Temp 0.56Cd 50 94.62 100 99.30 150 104.38 200 109.84 250 116.22 300 123.00 Table CIII. Data on Resistivity of Cadmium Amalgams *15 1.72Cd 87.70 91.76 96.10 100.98 107.00 113.70

-98 Table CIV. Literature Data on Resistivity of Cerium Amalgams *30 *30 *30 Temp O.OlCe 0.02Ce 0.03Ce 300 127.720 127.655 127.611 Table CVII Literature Data on Resistivity of Copper Amalgams *148 *148 *148 *148 *148 *148 Temp O.OlCu 0.02Cu 0.02Cu 0.03Cu 0.03Cu 0.04Cu 12 94.93 100 103.18 103.08 300 127.53 127.36 127.21 127.08 126.91 126.80 *148 Temp 0.04Cu 300 126.61 Table CIX Literature Data on Resistivity of Germanium Amalgams *3 3 30 * 30 *30 *30 Temp O.OlGe 0.02Ge 0.02Ge 0.03Ge 302 127.933 127.838 127.762 127.691 250 120.729 Table CX Literature Data on Resistivity of Indium Amalgams *125 *125 *125 *125 *125 *125 Temp 2.9In 6.0In 9.2In 12.5In 16.0In 19.7In 20 79.3 68.6 61.4 55.9 51.8 48.7 *125 *125 *125 *125 *125 *125 Temp 23.6In 27.6In 31.9In 36.4In 41.2In 46.2In 20 46.2 44.0 42.2 40.5 39.0 37.6 *125 *125 Temp 51.5In 57.2In 20 36.3 35.0

-99 Table CXI. Literature Data on Resistivity of Potassium Amalgams *13 *13 *13 *13 *13 *13 Temp 0.01K 0.02K 0.04K 0.04K 0.04K 0.05K 30 97.18 97.77 98.63 98.79 98.33 98.49 *13 *13 *13 *13 *13 *13 Temp 0.06K 0.06K 0.07K 0.09K 0.09K 0.10K 30 98.79 99.31 99.59 100.40 99.10 99.49 *13 *13 *13 *13 *13 *13 Temp 0.11K 0.11K 0.12K 0.14K 0.16K 0.17K 30 99.59 100.10 100.20 100.80 101.20 101.70 *13 *13 *13 *13 *13 *13 Temp 0.18K 0.20K 0.21K 0.21 021K 0.21K 0.23K 30 100.20 101.00 100.90 101.40 101.60 102.00 *13 *13 Temp 0.25K 0.27K 30 102.77 103.57 *83 *83 *83 *83 *83 *83 *83 *83 *83 Temp 1.65K 3.52K 6.56K 8.56K 9.62K 11.92K 21.34K 39.45K 79.35K 57 63 128.80 37.10 88 100 150 162 200 250 256 262 283 287 300 350 400 450 133.95 140.80 165.76 147.80 170.18 155.18 176.38 130.20 132.80 142.50 41.30 46.12 240.25 241.50 243.20 152.75 51.00 163.18 55.85 232.60 197.80 208.50 162.75 170.60 183.95 203.90 192.18 213.45 223.40 233.00 199.90 202.25 211.95 221.50 237.00 244.70 173.60 60.70 242.00 246.18 184.05 65.58 222.00 232.00

-100 Table CXII Literature Data on Resistivity of Lithium Amalgams *13 Temp 0.OOLi 30 100.60 *13 *13 *13 *13 *13 O.OOLi O.OlLi O.OlLi O.O1Li O.OlLi 100.90 100.70 98.79 97.81 98.68 *13 *13 *13 *13 *13 *13 Temp O.OlLi O.O0Li O.OlLi 0.02Li 0.02Li 0.02Li 30 98.04 97.77 103.00 102.80 101.50 101.40 *13 *13 Temp 0.02Li 0.03Li 30 99.20 97.77 *15 Temp 0.OOLi 50 98.82 100 103.80 150 109.21 200 115.40 250 122.18 300 129.54 *15 0.02Li 98.32 103.10 108.32 114.18 120.70 127.70 *15 0.04Li 97.50 101.50 107.00 112.70 119.20 125.90 Literature Data on *15 Temp 0.11Na 50 99.76 56 100 102.74 150 110.20 200 116.56 250 123.60 300 131.40 350 353 400 450 *83 O.llNa Table CXV Resistivity of Sodium Amalgams *83 *83 *83 *8 0.39Na 0.95Na 3.03Na 4.8 100.30 98.10 105.95 102.90 111.65 108.40 117.50 113.80 123.90 119.10 110.70 120.90 124.30 115.00 138.60 129.75 119.25 110 3 5Na 103.75 109.25 115.00 121.50 128.50 135.90.15 123.60 110.15 112.60 115.05 *83 Temp 5.70Na 48 65 100 113 150 200 250 300 321 350 360 122.00 400 123.80 450 126.20 500 *26 Temp 0.04Na 0 94.29 20 96.01 78 101.55 100 103.73 185 113.23 226 118.41 255 122.40 *26 Temp 0.26Na 0 94.81 20 96.64 78 102.34 100 104.56 185 114.41 226 255 302 *83 *83 *83 *83 7.44Na 17.35Na 32.00Na 58.70Na 105.60 50.40 107.40 51.60 122.90 109.10 53.25 127.00 118.00 54.95 129.65 112.55 56.60 132.35 114.30 58.25 126.40 128.05 135.00 116.00 59.95 130.95 117.80 61.62 133.80 136.60 *26 0.05Na 94.38 96.14 101.66 103.87 113.40 118.57 122.65 *26 0.30Na 94.78 96.59 102.35 104.61 114.36 *26 0.08Na 94.48 96.22 101.81 104.05 113.61 118.75 122.93 *26 0.35Na 94.84 96.68 102.43 104.68 114.37 *26 O.llNa 94.57 96.33 101.97 104.21 113.88 *26 0.14Na 94.71 96.48 102.12 104.40 114/17 *26 0.21Na 94.80 96.67 102.36 104.61 114.34 *26 *26 0.46Na 0.60Na 94.66 93.75 96.50 96.22 102.22 101.85 104.48 104.10 113.95 113.39 118.19 122.59 130.21 130.29

-101 Literature *30 Temp O.OlSb 302 127.984 Table CXVIII. Data on Resistivity of Antimony Amalgams *3 30 *3030 0.02Sb 0.02Sb 0.03Sb 127.915 127.838 127.761 Table CXXIII. Literature Data on Resistivity of Thallium Amalgams Temp 13 50 100 150 183 200 250 256 295 300 *30 0.06Th 95.083 *30 0.13Th 94.963 *30 0.23Th 94.727 *30 0.38Th 94.492 *30 0.50Th 94. 278 *30 0.75Th 93.820 *30 1.OOTh 93.375 *15 *15 1.03Th 2.91Th 103.216 103.076 102.800 102.517 102.249 101.698 96.58 101.159 101.12 106.22 93.20 97.41 102.10 110.910 111.79 107.00 118.20 112.08 119.788 124.448 125.14 118.20 Temp 20 *125 5.10Th 87.0 *125 *125 *125 10.20Th 15.20Th 20.30Th 80.3 75.5 72.4 *125 25.40Th 70.2 *125 *125 30.40Th 35.40Th 69.0 67.9 *125 40.50Th 67.3 Table CXXIV. Literature Data on Resistivity of Yttrium Amalgams *30 *30 *30 *30 Temp 0.01Y 0.02Y 0.03Y 0.04Y 302 127.943 127.849 127.701 127.494

X. Bibliography This section presents an extensive bibliography on the resistivity of molten metals, molten binary alloys, and liquid amalgams. It is believed that the bibliography is complete over the years 1900 to the present (February 1961). The writer has thoroughly searched the various abstract services (Chemical Abstracts, MetallurZical Abstracts) and has furthermore investigated all cross-references within each reference source consulted. All pertinent references are found below. Form of Bibliographic Entries The individual entries are arranged numerically by author surname; for multiple authorship, surname arrangement is according to article by-line. All entries available from the University of Michigan Libraries are indicated by the appearance of an asterisk preceeding the reference number. A standard form of entry is used. Following this, all nonEnglish articles consulted are indicated by language of origon. With available references from the Libraries, the particular Library and call number are next indicated according to the code: C: Chemistry Library E: Engineering Library GL: General Library Phy: Physics Library T: Transporation Library The call number proper is given in parentheses, preceeded by -105

the code letter. For all entries located through one of the abstract services, this is noted next, by the codes: CA: Chemical Abstracts MA: Metallurgical Abstracts The proper code is followed by the abstract volume number and, separated by a colon, the column (or page) number. Bibliography Entries 1. Baltruszajtis, A. The Electrical Resistance of Liquid and Solid Mercury. Bulletin international de 1' academie des sciences de Craovie -- 888- T1912). CA 8:605.- - *2. Bates, L., and Day, P. The Electrical Resistance of Manganese Amalgams. Proceedings of the Physical Society, 9, 635-41 (1937)..Phy( lPS517 CA 32:57 *3. Bates, L., and Fletcher, W. Electrical Resistance of Ferromagnetic Amalgams. Proceedins of the Physical Society, 51, 778-83 (1939). hyQ. 21) -CA 34: *4. Bates, L., and Prentice, J. The Electrical Resistance of Nickel Amalgams. Proceedings of the Physical Society, 51, 419-24 (1939). - Ph-y(QC 51 A 33 5247. *5. Belashchenko, D. Viscous and Electrical Properties of Liquid Binary Alloys and Their Connection with the Structure of the Liquid. Zhurnal Fizichesk6i Khimii, 31, 2269-76 (1957). RUSSISAN. C(QD1.Z63). 5CA 52:8000. *6. Berndt, G. -v —-. Annalen der Physik, 23, 240- (1907). GERMAN. Phy(QC.A6T1).*7. Bernini, A. On the Effect of Temperature on the Electrical Conductivity of Lithium. Physikalische Zeitschrift, 6, 74-8 (1905). GERMAN. Ph-CQC1.P8').*8. Bernini, A. On the Effect of Temperature on the Electrical Conductivity of Potassium. Physikalische Zeitschrift, 5, 406-10 (1904). GERMAN. PhyTQC.P 8 f). *9. Bernini, A. On the Effect of Temperature on the Electrical Conductivity of Sodium. Physikalische Zeitschrift, 5, 241-5 (1904). GERMAN. Phy(QC1.p55.T5 5T — *10. Bidwell, C. Electrical Resistance and Thermo-electric

-105 - Power of the Alkali Metals. Physical Review, 23, 357-76 (1924). Phy(QC1.P5812). —-- *11. Birch, F. The Electrical Resistamce amd the Crticial Point of Mercury. Physical Review, 41, 641-8 (1932). Phy(QC1.P5812). CA-26 0. 12. Blum, A., Mokrovsii, N., and Regel, A. Electrical Conductivity of Semiconductors and Intermetallic Compounds in the Solid and Liquid State. Izvestiya Akademii Nauk SSR Seriva Fizicheskaya, 16 139-53 (1952). RUSSIAN CA 46:10753.*13. Boohariwalla, D., Paranjpe, G., and Prasad, M. The Electrical Conductivities of Liquid Alkali-metal Amalgams. Indian Journal of Physics, 4, 147-59 (1929). Phy (QClI45). CA 4z:9.. *14. Bornemann, K., and Muller, P. The Electrical Conductiviity of Metallic Alloys in the Fluid Condition. Metallurgie, 7,396-402 (1910). GERMAN. E(TN1.F398). CA 5859 *15. Bornemann, K., and von Rauschenplat, G. The Electrical Conductivity of Metal Alloys in the Liquid State. Metallurie, 9, 473-86, 505-15 (1912). GERMAN. E (TN.398). MA 8:331. *16. Bornemann, K., and Wagenmann, K. The Electrical Conductivity of Metallic Alloys in the Liquid State. Ferrum, 11 276-82, 289-314, 330-43 (1914). GERMAN. E(TN1,F3T). MA 12:287. *17. Braunbek, W. The Electrical Conductivity of Mercury at High Temperatures. Zeitschrift fur Phvsik, 80, 13749 (1933). GERMAN. Phy(QC1.Z4877 CA 27:207. *18. Braunbek, W. The Electrical Conductivity of Mercury at High Temperatures and Pressures. Physikalische Zeitschrift 33, 830-1 (1932). GERMAN. Phy(QClP585 I CA 27*:642. *19. Braunbek, W. A New Method of Electrodeless Conductivity Measurement. Zeitschrift fur Physik, 73, 312-34 (1931). GERMAN.iPhy (QCz). CA 26T7365. *20. Bridgeman, P. Electrical Resistance under Pressure, Including Certain Liquid Metals. Proceedings of the American Academy of Arts and Sciences, 56, 6TW15i (1921)' GL(I1.A'6) — MA3U:455, —*21. Bridgeman, P. The Measurement of High Hydrostatic Pressure. A Secondary Mercury Resistance Gauge. Proceedings of the American Academy of Arts and Sciences, 44_, 2i51-( T909) GL(ll. A46);.. —.

*22. Bridgeman, P. Mercury, Liquid and Solid, under Pressure. Proceedings of the American Academy of Arts and Sciences, 47, 37-T (1911) GL(Qll.A — ). *23. Chernobrovkin, V. Variation in the Electrical Resistance of Cast Iron Brought about by the Graphite Formed in It. Physics of Metals and Metalloraph 4, 153-5 (1957). Phy(l.F73). A 52699. *24. Clay, J. Resistance of Gold Amalgams in the Solid and Liquid State Between -78~ and 100~. Physica, 7, 83844 (1940). Phy(QC1.P578). CA 35:7256. *25. Darmois, G. Variations in the Electrical Conductivity of Metals at the Time of Fusion. Comptes Rendus Academie des Sciences, 244, 174-6 (1957). FRENCH. GL(Q46.A12 C7 ) CA 51:TO80. *26. Davies, W., and Evans, E. The Electrical Conductivities of Dilute Sodium Amalgams at Various Temperatures. Philososphical MaRazine, 10, 569-99 (1930). Phy (QC1.L85). CA 25:13. *27. Dodd, C. The Electrical Resistance of Liquid Gallium in the Neighborhood of Its Melting Point. ProceedinZs of the Physical Society, 63B, 662-4 (1950). Phy(QC1. P5821. CA 45:1401. *28. Domenicali, C. Thermoelectric Power and Resistivity of Solid amd Liquid Germanium in the Vicinity of Its Melting Point. Journal of Applied Physics, 28, 74953 (1957). Phy(QC1.J8637. CA 51:1519-3. *29. Donat, E., and Stierstadt, 0. Liquid Metallic Single Crystals. Annalen der Physik, 17, 897-914 (1933). GERMAN. Phy(QC1lA6T7. CA27:302. *30. Edwards, T. The Resistivity and Conductivity of Dilute Amalgams at Various Temperatures. Philosophical Magazine, 2, 1-21 (1926). Phy(QC1.L85) CA 20: 3119. *31. Epstein, A., and Fritzsche, H. The Electrical Resistivity of Pure Tellurium at the Melting Point and in the Liquid State. Physical Review, 93, 922 (1954). Phy(QC1.P5812). CA 49:9976. *32. Epstein, A., Fritzsche, H., and Lark-Horowitz, K. The Electrical Properties of Tellurium at the Melting Point and in the Liquid State. Physical Review, 107, 412-9 (1957). Phy(QC1.P5812). CA 521704 — -- *33. ---—. Exploring the Conductivities of Molten Metals. Electric Journal, 29, 193 (1932). E(TK1.E27).

-107 *34. Fakidov, I., and Kikion, I. Change of Resistance of Liquid Metals in a Magnetic Field. Zeitschrift fur Physik, 75, 679 (1932). GERMAN. Phy(QC1.Z48). C 26:3968.*35. Fakidov, I., and Kikion, I. On the Influence of a Transverse Magnetic Field upon the Resistance of Liquid Metals. Physikalische Zeitschrift der Sowietunion,, 381-92 (1933), PhyFQC1.P587)*36. Forster, F., and Tschentke, G. Method for Measuring the Influence of Temperature on Electrical Resistance, Specific Heat, of Solid and Liquid Metals. Zeitschrift fur Metallkunde, 32, 191-5 (1940). GERMAN. E(TN3.Z48). CA 35:3935. *37. Fowler, R. The Theory of Liquid Metals of Mott and the Transition Points of Metals and Other Solids. Helvetica Physica Acta 7 (Supplement II), 72-80 (T-"4). FRENCH. Phy(QC.H4). CA 29:3208. *38. Gaibullaev, F., and Regel, A. Characteristics of the Temperature-Resistivity Relation for Liquid Eutectic Systems. Soviet Physics-Technical Physics, 2, 18507 (1957). Phy(QClZ643). CA 52:-7933, 39. Gehloff, G., and Nevmeier, F. Thermal and Electrical Conductivity, Thermoelectric Power and the Wiedemann-Fratz Ratio of Mercury Between -190~ and 150~, and Their Change During Transition for the Solid to the Liquid State. Berichte der deutschen physikalischen Gesellschaft, 2 2T 17 (1919). CA 14:482. *40. Gerstenkorn, H. The Change of the Electrical Resistivity of Pure Metals at the Melting Point. Annalen der Physik, 10, 49-79 (1952). GERMAN. Phy(QC.A6T7. MA 20:8. — *41. Gerstenkorn, H., and Sauter, F. Cheange of Electrical Resistance of Pure Metals at the Melting Point. Naturwissenschaften, 38, 158-9 (1951). GERMAN. Phy(QC1.N3). CA 46:178. 42. Giessen, P. The Discontinuity in Electrical Conductivity Accompanying the Change from the Solid to the Liquid State. Berichte der deutschen physikalischen Gesellscha,, 414-8 (1912). GERMAN. CA 6:2027.. *43. Gin, G. Note on the Electrical Resistivity of Iron and Steel at High Temperatures. Transactions of the American Electrochemical Society 8 287-9-(195). C(QD.-E38). -

*44. Gubar, S., and Kikion, I. Temperature Dependence of the Electrical Resistance of Liquid Metlas at Constant Volume. Journal of Physics USSR, 9, 52-3 (1945). Phy(QC1,587). CA 40:783. *45. Guntz, A., and Broniewski, W. Electrical Resistance of the Alkali Metals and of Gallium and Tellurium. Comptes Rendus Academie des Sciences, 147, 1474-7 (1908). FRENCH. GL(Q47.1l4 C7). CA3:'T983. *46. Guntz, A., and Broniewski, W. Electrical Resistance of the Alkali Metals, Gallium, and Tellurium. Journal de chimie physique, 7, 464-85 (1909). FRENCH. GL 46.A1l4 C7), CA 4:t06. *47. Hackspill, L. The Electrical Resistance of the Alkali Metals. Comptes Rendus Academie des Sciences, 151, 305-8 (1910). FRENCH. GL(Q46.Al Z7)7 *48. Harasima, A. The Change in Electrical Resistance of Alkali Metals on Melting. Proceedings of the Physico-Mathematical Society of Japan, 6,"79-86 (1939). GL(QCI.P5828). CA 32712197. *49. Harasima, A. The Electrical Resistance of Liquid Sodium. Proceedings of the Physico-Mathematical Society, 22, 183-8 ( 1970; GL(QC.P5828). CA 34'3761. *50. Henkels, H. Conductivity of Liquid Selenium 200-5000. Journal of Applied Physics, 21, 725-31 (1950). Phy (Q1i.J8667. CA 44:10420. *51. Henkels, H., and Maczuk, J. Electrical Properties of Liquid Selenium. Journal of Applied Physics, 24, 1056-60 (1953). Phy(QCl.J53). CA 47-:11857. *52. Hering, C. Comparing Electrical Resistivities at High Temperatures. Metallurgical and Chemical Engineerin, 13, 32-8 (1915). E(TN1.3T7). CA:7 8 *53. Hine, T. Electrical Conductivities of Dilute Sodium, Potassium, and Lithium Amalgams. Journal of the American Chemical Society, 39, 8821-95 177. C (QD1.A51237. CAi 11159O - *54. Horn, F. The Change of Electrical Resistance of Magnesium on Melting. Physical Review, 84, 855-6 (1951). Phy(QCl.P5812). CA 46::3 -- *55. Hornbeck, J. Thermal and Electrical Conductivities of the Alkali Metals. Physical Review, 2, 217-40 (1913). Phy(QC 1P5812)..

-109 *56. Ilschner, B., and Wagner, C. The Electrical Conductivity of Liquid Magnesium-Bismuth Alloys. Acta Metallurica, 6, 712-3 (1958). E(TN1.A19). *57. Jaeger, W., and von Steinwehr, H. Change of Resistance of Mercury with the Temperature Between 0~ and 100 Annalen der Physik, 45 1089-1108 (1914). GERMAN. Phy(QCl. A63). CA 9'749. *58. Jaffray, J., and Cariat, J. Some Physical Properties of Nickel Amalgams. Comptes Rendus Academie des Sciences, 231 1128-30 (1950 FRENCH GL(Q47.A14 I. CA 53T4621. *59. Johnson, V. Electrical Conductivity of Liquid Tellurium. Physical Review, 98, 1567 (1955). Phy(QC1.P5812). CA 5 T:105:4_ — *60. Jones, P., and Jones, T. The Effect of a Magnetic Field on the Electrical Resistance of Mercury and Some Amalgams. Philosophical Magazine, 2, 176-94 (1926). Phy(QCl L85). CA 20:324. *61. Jones, T. The Electrical Reistance of Mercury in Magnetic Fields. Philosophical Magazine, 50, 46-60 (1925). Phy(QCl.L85), CA 19:3057. *62. Keyes, R. The Electrical Conductivity of Liquid Germanium. Physical Review, 84, 367-8 (1951). Phy (QC1.P5812). CA 46:80 63. Khalileev, P. Heat Conduction and Electrical Conductivity of Alkali Metals in the Solid or Liquid States. Zhurnal Eksperimental' noi i Teoreticheskoi Fiziki, 10, 40-57(1940). RUSSIAN. -CA 34:7681. *64. Knappwost, A. Electrical Resistance of the Intermetallic Compound Mg2Pb in the Vicinity of the Melting Point. Zeitscrift fur Elektrochemie, 56, 594-8 (1952). GERMANi QD.122). CA 47:2563. *65. Knappwost, A. Entropy of Fusion and the Resistance Ratio of Some Multivalent Metals at Their Melting Points. Monatsthefte fur Chemie und verwandte Teile anderer Wissenschaften, 85, 548-57(1954). GERMAN. C(QD1. M77) CA 48.13317. *66. Knappwost, A. Magnetic and Resistometric Studies of Substances with a Negative Volume Change Near the Melting Point. Zeitschrift fur Elektrochemie, 57, 618-24 (1953). GERMAN. C(QD1.ZSTT-CA 48: 30 8.7 *67. Knappwost, A. A Technique of Measurement of Electrical

-110 Conductivity of Solid and Liquid Metals. Zeitschrift fur Elektrochemie, 55, 598-600 (1951). GERMAN. C D1. Z52). CA 46:330. *68. Knappwost, A., and Thieme, F. The Resistance Discontinuity and Entropy of Melting of Some Metallic Elements. Zeitschrift fur Elektochemie, 60, 1175-80 (1956). GERMAN. C(:.Z52). CA 51:62.7 *69. Konno, S. On the Determination of Electrical Resistance of Alloys Lead-Tin and Lead-Zinc at High Temperatures. Science Reports of the Tohoku Imperial University, 1 57-74 (1921 )T GLQ77S47 A2)*70, Kraus, C. The Temperature Coefficient of Resistance of Metals at Constant Volume and Its Bearing on the Theotr of Metallic Conduction. Physical Review, 4, 159-62 (1914). Phy(QCl.P5812). *71. Kraus, C. and Johnson, E. The Electrical Conductivity of Tellurium and of Liquid Mixtures of Tellurium and Sulfer. Journal of sical Chemist 32, 1281-93 (1928). C(QD.J87. CA 22: 43 2r *72. Krishnan, K., and Bhatia, A. Electric Resistance of Liquid Metals. Nature 156, 503-4 (1945). Phy (QC1.N285). CA W 4-074. *73 Kumrnakov, N., and Nikitinsky, A. Electrical Conductivity and Flow Pressure of Potassium-Rubidium Alloys. Zeitschrift fur Anorganische Chemie, 88, 151-60 (1914). GERMAN. CQDZ5). *74. Lewis, G., and Hine, T. Electrical Conduction in Dilute Amalgams. Proceedins of the National Academy of Sciences, 2 638 (11.5 Lll. N)11. 75. Matsuyama, Y. Electrical Resistance of Molten Metals and Alloys. Kinzoku-no-Kenkyu, 3, 439-55 (1926). *76. Matsuyama, Y. The Electric Resistance of Molten Alloys and Metals. Science Reports of the Tohoku Imperial Univerist, 4477 927). GL(Q77s47 A2). CA 77. Matsuyama, Y. Electrical Resistance of Pure Metlas in the Molten State. Kinzoku-no-Kenkus, 3, 254-61 (1926). CA 22:2309. 78. Mokrovskii, N., and Regel, A. Correlation Between Variations of Density and Electronic Conductivity During Melting of Substances with Diamond or Zinc Blende Structure. Zhurnal Tekhnicheskoi Fiziki, 22, 1281

-111 9 (1952). CA 49:11347. 79. Mokrovskii, N., and Regel, A. The Electrical Conductivity of Copper, Nickel, Cobalt, Iron, and Manganese in the Solid and Liquid States. Zhurnal TekhnichFiziki, 23, 2121-5 (1953). CA 49:8651. 80. Mokrovskii, N., and Regel, A. The Electrical Conductivity of Liquid Silicon. Zhurnal Tekhnicheskoi Fiziki, 3, 779-82 (1953). CA 49:869 81. Mokrovskii, N., and Regel, A. Peculiarities of the Temperature Changes of the Densities and of the Electrical Conductivities of Liquid Te-Se Melts. Zhurnal Tekhnicheskoi Fiziki, 25, 2093-6 (1955). CA 50:3028 *82. Mott, N. The Resistance of Liquid Metals. Proceedings of the Royal Society, 146A, 465-72 (1934). Phy TrcIT888)T. CA 28:70977 *83. Muller, P. The Electrical Conductivity of Metallic Alloys in Fluid Condition. Metalluie 7, 730-40 (1910). GERMAN. E(TN1.F398) CA 5-1391. 84. Nagamiya, T., and Noguchi, T. Electrical Resistance of Metals. Nippon Butsuri Gakkaishi, 2, 23-30 (1947). CA 44:9205. *85. Nielsen, W. The Resistance Change of Mercury in a Transverse Magnetic Field and the Hall Effect in Molten Bismuth. Physical Review, 23, 302 (1924). Phy(QC1. R5812). *86. Norbury, A. The Electrical Resistivity of Dilute Metallic Solid Solutions. Transactions of the Faraday Society, 16, 570 *87. Northrup, E. Electrical Conduction at High Temperatures and Its Measurement. Transactions of the American Electrochemical Soce 25, 373-9 2 4Tl ) C(QD1. E38&). *88. Northrup, E. High Temperature Investigation and a Study of Metallic Conduction. Journal of the Franklin Institute, 179, 621-62 (1915). T7T1.F8343). *89. Northrup, E. Resistivity of Brass; Solid and Molten. Metallurpical and Chemcial Engineerin, 12, 161-2 T1 914) E(TIN.Cl7)T —-- *90, Northrup, E. R8sistivity of Copper in Temperature Range 20 to 1450 C. Journal of the Franklin Institute, 177, 1-21 (1914)- T4(TI..F83...

-112 *91. Northrup, E., Resistixity of Pure Gold in Temperature Range 20 to 1500 C. Journal of the Franklin Institute, 177, 287-92 (1914). T-T1.F834j) *92. Northrup, E. Resistivity of Pure Silver; Solid and Molten. Journal of the Franklin Institute, 178, 85-7 (1914), T(TT.F834 jT *93. Northrup, E. and Sherwood, R. New Method for Measuring Resistivity of Molten Materials: Results for Certain Alloys. Journal of the Franklin Institute, 182, 477-509 (1916). T(T1r.F3 —T. *94. Northrup, E,, and Suydam, V. Resistivity of a Few Metals Through a Wide Range of Temperature. Journal of the Franklin Institute, 175, 153-61 (1913). T T 3lj. F-34j- -. *95. Paranjpe, G., and Buhariwala. Electrical Conductivities of Mercury Amalgams of Potassium and Sodium. Proceedings of the 15th Indian Science Congress, —, 74 (1928)7- GL(QT.I4. CA 25:2902. *96. Parravano, N,, and Jovanovich, P. On Amalgams of Gold Rich in Gold. Gazzetta Chimica Italiana, 49, 1-6 (1919). ITALIAN. C(QDI1.G29)... *97. Parravano, N., and Jovanovich, P. On Amalgams of Silver Rich in Silver. Gazzetta Chimica Italiana, 49, 6-9 (1919). ITALIAN. C(QD1.G29). - *98. Patterson, J. On the Change of the Electrical Resistance of Metals When Placed in a Magnetic Field. Philosophical Magazine, 3, 643-56 (1902). GL(Q1TL5 ). 99. Pavlovitch, P. --—. Journal of the Russian PhysicoChemical Society, 4 7, 29 —-1 T5). *100. Pelabon, H. The Resistivity of Selenium. Comptes Rendus Academie des Sciences, 173, 295-7 (1921)* FRENCH. GL(Q.ATZI 7) *101. Perlitz, H. Apparent Relation Between the Rate of Change of the Electrical Resistance at Fusion and the Crystal Lattice of Metallic Elements. Philosophical Magazine, 2, 1148-52 (1926). Phy(QCl.L85. CA 22: 1880. 102. Perlitz, H. Change in Volumes and Electrical Resistances of Antimony and Arsenic at Fusion. Sitzungsberichte der Naturforscher-Gesellschaft bei der Universtat Tartu, 35, 121-5 (92). CA 2353772.

*103. Pietenpol, W., and Miley, H. Electrical Resistivities and Temperature Coefficients of Lead, Tin, Zinc, and Bismuth in the Solid and Liquid States. Physical Review, 34, 1588-1600 (1929). Phy(QC1.P5812). CA 24:482. *104. Pietenpol, W., and Miley, H. Liquid Wires and Their Surface Films. Physical Review, 30, 697-704 (1927). Phy(QCl.P5812). CA 22:1882. *105. Pietenpol, W., and Miley, H. The Supercooling of Tin and Resistivity Lag in the Solid-to-Liquid Transformation. Journal of the Colorado-Wyoming Academy of Science,, 39 -(1930T GL(Q11.C7 4 CA 26:3417. *106. Pietenpol, W., and Miley, H. The Temperature Coefficients of Low Melting Point Metals in the Solid and Liquid States. Physical Review, 33, 294 (1929). Phy(QC1. P5812). CA 24:4437. *107. Powell, R. Electrial Resistivity of Liquid Iron. Philosophical Magazine, 44, 772-5 (1953). Phy(QC1.L385T CA 51:-716T47. *108. Powell, R., and Tye, R. Thermal and Electrical Conductivities of Molten Metals. British Chemical EnRineering, 2, 596 (1957). E(TP1.B87)..CA 52:43033. 109. Regel, A. The Relation Between the Structure of Liquids and Their Electrical Properties. Stroenie i Fizicheskoi Svoistva Veshchesta v Zhidkom aSostoyaii Sbovnik,-,, 17-31 (1954), ~C 52:2487. - *110. Rodgers, R. Change of Resistance with Temperature of Various Sodium Amalagams. Physical Review, 8, 25977 (1916). Phy(QCl.P5812). CA 106525377 *111. Roll, A., and Fees, G. ------ Zeitschrift fur Metallkunde, 51, 540 —- (1960). GEREAN. -E(TN3. i ). *112. Roll, A., and Motz, H. Electric Resistance of Metallic Melts. I. Methods of Measurement and Electrical Resistance of Molten Pure Metals. Zeitscrift fur Metallkunde, 48, 272-80 (1957). GERMAN. ETNT.748). CA 52:5907. *113. Roll, A., and Motz, H. Electric Resistance of Metallic Melts. II. The Electrcial Resistance of Molten Cu-Sn, Ag-Sn, Ma-Pb Alloys. Zeitschrift fur Metallkunde, 48, 435-44 (1957). GERMANi, ETN37Z8). *114. Roll, A., and Motz, H. Electric Resistance of Metallic Melts. III. The Electrical Resistance of the Solid

Solution Alloys Silver-Gold and Gold-Copper and of the Eutectic Systems Silver-Copper, Tin-Zinc, and Aluminum-Zinc. Zeitschrift fur Metallkunde, 48, 495502 (1957). GERMAN.: E(TN3.Z-). CA 52:5907. *115. Roll, A., and Uhl, E. The Electrical Resistance of Metallic Melts. IV. The Electrical Reistance of Molten Gold-Tin, Gold-Lead, and Silver-Lead Alloys. Zeitschrift fur Metallkunde, 50, 159-165 (1959). GERMAN. E(TN3. Z48T. *116. Roll, A., and Swamy, A. The Electrical Resistance of Metallic Melts. VI. The Electrical Resistance of Molten Binary Alloys of Cadmium with Lead, Mercury, Zinc, of Indium with Gallium, Mercury, and of Antimony with Bismuth. Zeitschrift fur Metallkunde, 52, 11120 (1961). GERMA.E(TN3. Z- ). *117. Roll, A., Felger, H., and Motz, H. Electrodeless Measurement of Electrical Conductivity by a Rotary Field Method. Zeitschrift fur Metallkunde, 47, 70713 (1956). GERMANI E( TN3.Z). CA 51:7986. 118. Rossi, G. ----—. Nuovo cimento, 2, 337 —- (1911). *119. Sato, T., and Kaneko, H. Studies on Selenium and Its Alloys. III. Vapor Pressure and Electric Conductivity of Molten Selenium Alloys. Technology Reports of the Tohoku University, 16, 18-33 (1952) E(T1. St73). CA 47:2111.: 120. Sato, T., and Kaneko, H. Selenium and Its Alloys. VI. Effect of Some Doping and Anti-doping Elements on the Electrical Conductivity of Molten Selenium. Nippon Kinoku Gakkaishi, 16, 309-12 (1952). CA 48:1745. *121. Scala, E., and Robertson, W. Electrical Resistivity of Liquid Metals and of Dilute Liquid Metallic Solutions. Transactions AIME, 197, 1141-7 (1953). E(TN1.A512t). CA 47:117857 - *122. Schleicher, A. Electrical Resistance Measurements on Mixtures of Copper and Mercury. Zeitschrift fur Elektrochemie, 18, 998-1000 (1912). GERMAN. CTQD1. Z52). *123. Schroeder, J. Change in Resistance of Bismuth Single Crystals at the Melting Point; Proceedings of the Iowa Academy of Science, 41, 254 (1934). GL ITT. 641). CA 29: T70. *124. Schubin, S. On the Theory of Liquid Metals. Physikalishche Zeitschrift der Sowjetunion, 5, 81-05 (19 34). Phy(QCI.5. 587Y

-115 *125. Schultz, L. and Spiegler, P. An Experimental Determination of the Electrical Resistivity of the Liquid Alloys Hg-In, Hg-Tl, Ga-In, Ga-Sn, and of Liquid Gallium. Transactions AIME, 215, 87-90 (1959). E (TN1.A512t 2t *126. Schulze, A. The Electrical Properties of Amalgams. Zeitschrift fur Metallkunde, 17 101, 132-3, 170, 203-4 (1925):GERMAN. E(TTN3.Z48). CA 21:3037. *127. Siebel, K. The Change of Thermoelectromotive Force and Electrical Conductivity of a Potassium-Sodium Alloy by Changing form the Solid to the Liquid State. Annalen der Physik, 60, 260-78 (1919). GERMAN. Phy (QC1.A613)l. CA 14:88. *128. Simon, F. On the Electrical Conductivity of Metals. Zeitschrift fur Physik, 27, 157-63 (1924). GERMAN. Phy(QC1.Z488) MIA 34:3987 *129. Skaupy, F. Conduction of Electricity and the Constitution of Liquid Metals and Alloys. Physikalische Zeitschrift, 21, 597-601 (1920). GERMAN. Phy 1. P5852). CA 13T978. *130. Skaupy, F. The Electrical Conductivity of Dilute Amalgams. Zeitschrift fur physikalische Chemie, 58, 560-6 (1907). GERMAN. CAD1,Z56), CA"::067. 131. Skaupy, F. The Electrical Conductivity of Liquid Metals and Alloys in Its Relation to the Electron Concentration and the Viscosity. Verhandlungen der deutschen physikalischen Gesellschaft 18, 252-60 (1916). CA 10:3014. 132. Skaupy, F. The Specific Heat of Liquid Mercury. The Heat Content of Liquids, Especially Metals at the Melting Point, and Its Relation to Specific Heat, Electrical Conductivity, and Internal Friction. Berichte der deutschen hsikal n Gesellschaft, 18, 302-77T916). CA 11:2851. *133. Smith, A. The Electrical Conductivity of Indium and Thallium. Ohio Journal of Science, 16, 244-7 (1916). GL(Q1.03). *134. Somerville, A. Temperature Coefficients of Electrical Resistivity. Physical Review, 23, 77 *135. Sutra, G. Changes in the Electrical Conductivity of Metals During Fusion. Comptes Rendus Academie des Sciences, 234, 2589-91 (152). FRENiCH- GL(Q467f4 C7). CA 44369.

*136. Sutra, G. The Changes in the Electrical Conductivity of Metals During Fusion. II. Comptes Rendus Academie des Sciences, 235, 707-9 (1952). FRENCH. GL(Q. t z 7; 7.-CA 477563. *137. Sutra, G. The Difficulties in the Electronic Theory of Metals. Compte Rendus Academie des Sciences 236 2391-3 (1953)7 -FRENCH,. GL(Q46.AT4TC7 - 47TCA 7 35. *138. Toye, T., and Jones, E. Physical Properties of Certain Liquid Binary Alloys of Tin and Zinc Proceedings of the Physical Society, 71, 88-99 (1958). Phy(QCl. P-8T.. CA 52:198 38. - *139. Tsutsumi, H. On the Variation of Electrical Resistance During the Fusion of Metals. Science Reports of the Tohoku Imperial University, 7, 93-105 (1918), GL (q77.S47 A2). CA 13:88. 140. Tsutsumi, H. The Variation of Electrical Resistance During Fusion. Proceedings of the Tokyo MathematicoPhysical Soc iety9 349 (19T)7-CA 12-2:277 *141. Vanstone, E. Electrical Conductivities of Sodium Amalgams. Chemical News and Journal of Physical Science, 108. 164 (191 T T C(QDl.C51 1). CA 8:6.6 *142. Vanstone, E. Sodium Amalgams: Specific Volume and Electrical Conductivities. Journal of the Chemcial Society, 105, 2617-23 (1914). C (QD1753. CA 9:409. *143. Vanstone, E. Sodium Amalgams. II. Electrical Conductivity. Transactions of the Faraday Society, 9, 2916 (1914). C(QDl.C52T.CA 8:3262. *144. Wagner, E. Systematic Changes in the Electrical Conductivity of Metals at Their Melting Points. Annalen der Physik, 33, 1484-92 (1910). GERMAN. Phy(QC1. 6T3). CA 5T357. *145. Williams, C. Electrical Resistivity of Certain Copper Alloys in the Molten State. Metals & Alloys 2, 240-1 (1931). E(TN1.M58). CA26:2404. *146. Williams, E. The Effect of a Magnetic Field on Electrical Resistivity of Liquid Metals and Alloys. Philosophical Magazine, 50, 27-46 (1925). Phy(QC1.L83~T CA 19:3057. *147. Williams, E. The Electrical Conductivity of Some Dilute Liquid Amalgams. Philosophical Maazine, 50, 589-99 (1925). Phy(QC1.L85). CA 19:340

-117 *148. Williams, E., and Evans, E. The Electrical Conductivity of Dilute Liquid Amalgams of Gold and Copper at Various Temperatures. Philosophical Magazine, 6, 1231-53 (1928). Phy(QCl.L85). CA 231027.There also exist various references on the resistivity of pure metals and metallic alloys compiled from the same data as given in this report: A. International Critical Tables. Volume VI. New York: McGraw-Hil1 Book Company, 129,7 B. Liquid Metals Handbook (2nd Edition, Revised). Washington: US Government Printing Office, 1954. C. Liquid Metals Handbook (Na-K Supplement). Washington: US Government Printing Office, 195?. D. Smithells, C. Metals Reference Book. Volume II. New York: Interscience Publishers, 1955. E. Smithsonian Physical Tables (9th Edition Revised). Washington: - Smithsonian Institution, 1954.

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