ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR HEAT CAPACITIES AT LOW TEMPERATURES, ENTROPY AND ENTHALPY INCREMENTS OF FOUR NICKEL ZINC FERROSPINELS By Edgar F. Westrum, Jr., and D. M. Grimes MOLECULAR FIELD FLUCTUATION EFFECTS IN MIXED NICKEL ZINC FERRITES By D. M. Grimes, S. Legvold, and Edgar F. Westrum, Jr. LOW TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF ZINC FERRITE By Edgar F. Westrum, Jr., and.D. M. Gi(mes Technical Report No. 34 Electronic Defense Gioup Department of Electrical Engineetring Approved by: H. W. Welch, Jr Project 2262 TASK ORDER NO. EDG-6 CONTRACT NO. DA-36-039 sc-63203 SIGNAL CORPS, DEPARTMENT OF THE ARMY DEPARTMENT OF ARMY PROJECT NO. 3-99-04-042 SIGNAL CORPS PROJECT NO. 194B February, 1957

TABLE OF CONTENTS Page FOREWORD iii ABSTRACT iv PAPER I: HEAT CAPACITIES AT LOW TEMPERATURES, ENTROPY AND ENTHALPY INCREMENTS OF FOUR NICKEL-ZINC FERROSPINELS 1 I. INTRODUCTION 1 II. PREPARATION AND PURITY OF SAMPLES 2 III. CRYOGENIC TECHNIQUE 4 IV. HEAT CAPACITY RESULTS 4 V. THERMODYNAMIC FUNCTIONS 8 REFERENCES 12 PAPER II: MOLECULAR FIELD FLUCTUATION EFFECTS IN MIXED NICKEL ZINC FERRITES 13 REFERENCES 17 PAPER III: LOW TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF ZINC FERRITE 18 I. INTRODUCTION 18 II. EXPERIMENTAL 19 2.1 Preparation of the Zinc Ferrite 19 2.2 Cryogenic Technique 20 III. RESULTS 21 IV. DISCUSSION 23 ACKNOWLEDGEMENT 29 REFERENCES 29 APPENDIX 30 DISTRIBUTION LIST 36 II

FOREWORD This report is actually three related reports bound under one cover. They are copies of manuscripts submitted to the Journal of Physical Chemistry, Physical Review and the Journal of Physics and Chemistry of Solids respectively. It is expected that the appendix will be filed with the American Documentation Institute. iii

ABSTRACT The heat capacity and the magnetic moment versus temperature of ZnxNilx Fe24 has been measured from about 40K to 300 K where x =.9,.8,.7, and.6. The heat capacity has been measured over the same temperature range for Zn Fe204. An antiferromagnetic cooperative transition at about 9.50 K was observed in ZnFe204 which gradually becomes more rounded and contributes less entropy as x decreases. The magnetic moment decreases gradually with increasing temperature and for the larger values of x goes slowly towards zero in marked contrast to the usual Curie temperature behavior. The results are interpreted as being due to molecular field fluctuations. Predicted thermal effects due to triangular-ferrimagnetic transitions were not found. This result is also interpreted in terms of molecular field fluctuations. iv

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN HEAT CAPACITIES AT LOW TEMPERATURES, ENTROPY AND ENTHALPY INCREMENTS OF FOUR NICKEL-ZINC FERROSPINELS BY Edgar F. Westrum, Jr., and D. M. Grimes I. INTRODUCTION Spinel materials are fairly common and include important ores. Synthetic ferrospinels (ferrites) possess interesting electromagnetic properties and are technologically significant components of high frequency electrical circuits. Despite these facts, thermal data extending to liquid helium temperatures, which permit a more accurate evaluation of the thermodynamic properties of the ferrites are available probably only for zinc ferrite (ZnFe204).1 Heat capacity data above 0 2 50 K. have, however, been published for more than twelve others, and measurements on magnetite over the range 1.8 to 4.2~K. have recently been published.3 The gross magnetic properties of the ferrospinels have been explained 4 by Neel in terms of the parallel and antiparallel alignment of the magnetic moments of the ions on two sublattices. For instance, in nickel ferrite (NiFe204) the net spin of the zinc ion is zero and the iron atoms are paramagnetic at this temperature. Mixed nickel-zinc ferrites are ferrimagnetic with a magnetic moment increasing with nickel content over the range studied. For certain ratios of intel to intra-sublattice interactions, it is anticipated by Yafet and Kittel5 that the moments of two sub-sublattices composing one of the sublattices will be oriented neither parallel nor antiparallel with each other, but at some intermediate angle. The existence of such a triangular configuration would give rise to the possibility of transitions between triangular and ferrimagnetic or antiferromagnetic states

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN and hence to singularities analogous to Curie and Neel points. Utilizing an experimental evaluation of the exchange interactions by Neel and Brochet6 for mixed nickel-zinc ferrites (NilxZnxFe204), Yafet and Kittel5 predicted the possible existence of such multiple transitions in mixed nickel-zinc ferrites with x > 0.7. Such transitions should be readily detected at low temperatures by precise heat capacity determinations, for the discontinuities associated with the various types of transitions are well within the range of measurement of modern adiabatic, cryogenic calorimetry. The thermal method has the advantage of avoiding the spurious effects in magnetic measurements occasioned by ferromagnetic impurities, To test the theory of Yafet and Kittel, determination of the heat capacity of Ferramic E, a commerically available ferrite with x approximating 0.6, was first measured. Although no evidence of the anticipated spectrum of transformations was observed, the composition was indeed outside the range specified by Yafet and Kittel5. A ferrite of composition x = 0.8 was then fabricated and its heat capacity determined. An anomalously high heat capacity in the vicinity of 100K. provoked further measurements on additional samples over the range x = 0.6 to x = 1.0. In conjunction with neutron diffraction data7 it has been established that this anomaly arises as a consequence of an antiferromagnetic-ordering which 2 occurs in pure zinc ferrite. Although resolution of the magnetic and lattice components of the heat capacity is not yet possible, the thermodynamic data are presented as a contribution to the thermodynamics of solid solutions. II. PREPARATION AND PURITY OF SAMPLES Mixed nickel-zinc ferrites, the composition of which may be represented by the empirical formula NilxZnfFe204, with x = 0.6, 0.7, 0.8 and O.9 were prepared by milling a slurry of weighed quantities of chemically pure oxides in _____....._____......... 2,,

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN a steel ball mill for six hours. After drying, the mixture was pressed into 50 gram slugs and fired at 1200~C. for four hours in air and the temperature then reduced 60~C./hr. to about 400~Co in an oxygen atmosphere. The slugs were fragmented in a hardened-steel "diamond mortar," annealed in an oxygen atmosphere and cooled at a rate of 60~C./hr. Because of the strong dependence of the heat capacity in the vicinity of 10~K. upon composition as x approaches unity, especially great care was taken in the preparation technique to obtain a stoichiometric, homogeneous, non-inverted sample of zinc ferrite. The details of the fabrication procedure utilized are described elsewhere. Gravimetric chemical analyses for iron and zinc and spectrochemical analyses were made. Stannous chloride redox titrations were made to determine the ferrous iron content of the samples. X-ray diffraction photographs were taken to establish the phase purity of the samples. The analytical data are presented in Table I. TABLE I PREPARATIVE AND ANALYTICAL DATA ON FERRITE SAMPLES Sample Annealing Percent Iron Percent x = Temp. (~C.) Detected Theoretical Fe+ (0.6)a - 46.9 + 0.1 0.0 + 0.1 0.6 900 46.8 + 0.1 46.84 0.0 + 0.1 0.7 (1200) 0.1 + 0.1 0.8 1200 46.7 + 0.1 46.59 0.0 + 0.1 0.9 (1200) 0.0 + 0.1 1.0b 1100 46.24~ 0.1 46.33 0.0 + 0.1 a Ferramic E, General Ceramic and Steatite Corp. b Percent zinc found = 27.2 + 0.1 (theoretical, 27.12). _ 3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN III. CRYOGENIC TECHNIQUE The design and adiabatic method of operation of the Mark I cryostat8 9 10 and calorimeters W-5 and W-9 have been described. A calorimeter was in turn loaded with sample, evacuated, and 2 to 4 cm. of gaseous helium then added at o 25 C. to aid in the establishment of thermal equilibrium. Lubriseal stopcock grease was used on calorimeter W-5 for thermal contact between heater, thermometer and calorimeter for determinations on samples with x = 0.6 and 0.8 and on Ferramic E. Calorimeter W-9 with Apiezon T grease was employed for the balance of the runs to allow measurements to 350~K. Separate determinations of the heat capacity of the empty calorimeters were made with their respective conductivity greases. The following masses (vacuo) of samples were employed in the measurements: x = 0.6, 203.434 g.; x = 0.7, 164.515 g.; x = 0.8, 191.862 g.; x = 0.9, 180.265 g. Temperatures were determined with a capsule-type platinum resistance thermometer (Laboratory Designation A-3) contained in a central well in the calorimeter. It was calibrated by the National Bureau of Standards from 10~ to above 373~K. Below this temperature range a provisional scale was employed. It is considered that the thermometer reproduces the thermodynamic temperature scale within 0.10 from 4 to 100K., within 0.030 from 10 to 900K., and within 0.050 above 90~K. The ice point was taken as 273.16~K. Calibrated instruments were used in the determination of all the measured quantities including the timing of the energy input. IV. HEAT CAPACITY RESULTS The experimental heat capacity determinations for the four samples of errospinels synthesized in this laboratory are presented in Table II in ~~~~__________~_________________ 4..____________

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE II MOLAL HEAT CAPACITIES OF NICKEL ZINC FERROSPINELS (in calories degree'1 gram-mole-l) T,~K. Cp T,~K. C T,~K. Cp Nio 4ZnO 6Fe204 (Mol. Wt. = 238.404 gm.) Series I 219.59 29.73 10.00 0.2317 228,65 30.61 11.11 0.2569 63.23 6.324 237.58 31.41 12.38 0.2950 69.11 7.354 246.56 32.19 13.77 0.3415 75.83 8.556 255.62 32.91 15.27 0.4018 83.16 9.900 264.65 33.62 16.86 0.4653 91.49 11.418 273.70 34.30 18.52 0.5393 90.54 11.255 282.71 34.92 20.28 0.6274 98.30 12.613 291.70 35*52 22.17 0.7363 106.78 14.100 300.83 36.09 24.37 0.8862 115.28 15.589 26.80 1.073 123.12 16.933 Series II 29.37 1.304 130.70 18.189 32.14 1.591 138.60 19.456 4.50 0.068 35.29 1.956 147.06 20.77 4.87 0.066 38.67 2.394 155.74 22.06 5.65 0.085 42.16 2.879 164.52 23.30 4.75 0.070 46.10 3.468 173.47 24.51 5.58 0.082 50.74 4.204 182.58 25.65 5.49 0.080 55.57 5.003 191.87 26.77 6.66 0.105 60.34 5.818 201.18 27.83 7.87 0.142 65.57 6.376 210.40 28.83 8.96 0.184 Ni0.3ZnO 7Fe204 (Mol. Wt. = 239.073 gm.) Series I 237.48 31.21 335.70 37.43 247.58 32.07 345.83 37.84 35.79 2.522 257.62 32.86 39.51 2.997 267.72 33.59 Series III 48.00 4.276 277.94 34.29 53.47 5.202 288.21 34.92 5.71 0.142 58.77 6.093 298.73 35.55 6.58 0.188 64.43 7.079 309.38 36.16 7.59 0.300 70.56 8.133 319094 36.77 8,56 0.376 77.46 9.330 9047 0.444 84.48 10,608 Series II 10.33 0.4923 91.47 11.826 11.30 0.5186 99.32 13.162 173.08 24.45 12.41 0.5713 5 -

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE II (CONTINUED) 107.50 14.567 182.60 25.62 13.65 0.6353 115.56 15.917 192.25 26.75 15.10 0.7055 123.76 17.273 201.97 27.81 16.75 0.7946 132.32 18.646 211.82 28.84 18.55 0.8878 140.88 19.962 221.95 29.81 20.42 1.0014 149.47 21.25 232.37 30.76 22.32 1.1307 158.52 22.52 242.87 31.68 24.43 1.2913 168.10 23.82 253.32 32.51 27.06 1.5209 177.84 25.07 263.78 33.29 30.05 1.8177 187.66 26.25 274.26 34.02 33.43 2.208 197.62 27.38 284.62 34.70 36.94 2.660 207.21 28.38 294.90 35.34 40.31 3.132 207.31 28.38 305.22 35.93 44.10 3.690 217.42 29.38 315.47 36.48 48.11 4.324 227.23 30.32 325.60 36.94 Nio02Zno.8Fe204 (Mol. Wt. = 239.742 gm.) 4.95 0.152 33.87 2.581 156.53 22.17 5.45 0.154 37.27 3.023 165.21 23.31 5.94 0.269 41.13 3.561 174.01 24.46 6.55 0.438 45*42 4.196 182.75 25.48 7.49 0.578 49.92 4.913 191.53 26.46 8.70 0.721 54.87 5.728 200.38 27.42 9.91 0.846 60.66 6.694 209.27 28.30 11.17 0.8773 67.19 7.809 210.47 28.41 12.50 0.9387 73.80 8.934 219.36 29.23 14.02 1.010 80.35 10.086 228.17 30.00 15.66 1.091 87.37 11.326 237.02 30.73 17.35 1.174 95.11 12.623 245.89 31.46 19.15 1.266 103.38 14.045 254.64 32.08 21.05 1.383 112.09 15.437 263.23 32.71 23.15 1.529 121.39 16.956 271.68 33.23 25.46 1.705 130.54 18.392 280.14 33.76 27.98 1.932 139.40 19.736 288.75 34.25 30.76 2.218 148.06 21.01 297.66 34.71 Nio01Zno. Fe204 (Mol. Wt. = 240.411 gm.) Series I 12.56 1.6665 94.52 12.191 13.71 1.6839 101.80 13.372 6.22 0.330 15.33 1.6961 109.70 14.646 6.48 0.494 17.28 1.7102 118.99 16.123 7.08 0.688 19.34 1.7375 128.10 17.544 7.76 1.29 21.37 1.7923 136.30 18.770 8.54 1.53 23.49 1.8782 144.47 19.950 9.29 1.62 25.88 2.008 153.07 21.15 10.00 1.7283 28.31 2.175 162.33 22.37 - 6~~~~~~~~~~~

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE II (CONTINUED) 11,32 1.6868 30.90 2.400 172.04 23.58 33.91 2.706 181.55 24.70 Series II 37.40 3.111 190.90 25.73 41.55 3.650 200.43 26.72 5.66 0.353 46.25 4.319 210.27 27.67 5.93 0.543 51.44 5.109 220.43 28.59 6.27 0.584 56.87 5.958 230.85 29.48 6.59 0.647 61.98 6.800 241.44 30.32 6.98 o.764 67.43 7.686 252.14 31.10 7.43 1.000 73.39 8.662 262.75 31.82 7.89 1.21 80.18 9.809 273.26 32.48 8,28 1.37 87.50 11.050 283.77 33.10 8.73 1.50 95.15 12.296 294.16 33.68 9.23 1.63 304.19 34.20 9.75 1.72 Series III 314.78 34.74 10.33 1.7323 324.97 35.15 10.90 1.6768 80.54 9.866 335.16 35.59 11.61 1.6651 87.37 11.023 345.44 35.98 TABLE III MOIAL ENTROPY AND ENTHALPY INCREMENTS OF NICKEL-ZINC FERROSPINELS T,~K. x = 0.6 x = 0.7 x = 0.8 x = 0.9 in calories degree gram ole (in calories degree-1 gram-mole-l) 10 0.077 0.156 0.196 0.737 15 0.197 0.388 00574 1.419 25 0.507 0.880 1.243 2.322 50 1.995 2.701 3.283 4.438 100 7.501 8.544 9.298 10.317 200 21.392 22.533 23.275 23.929 300 34.362 35.416 35.960 36.291 298.16 34.140 35.196 35.746 36.082 Ho o H H0 - H0 (in calories gram-mole'1) 10 0.58 1.50 2.87 5.42 15 2.09 4.40 7.58 13.84 25 8.39 14.30 20.92 31.63 50 66.59 84.65 99.18 112.15 100 489.11 531.2 557.7 559.8 200 2579.0 2632,6 2655,3 2602.8 300 5806.5 5837.0 5809.0 5675.9 298,16 5740,3 5771,5 5745.0 5613.5 7 -

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN chronological sequence so that the temperature increments of the individual runs can be estimatedfrom the adjacent mean temperatures. Corrections for curvature (occasioned by the finite temperature increments employed in the measurements) and for the slight differences in the amounts of helium and solder in the measurements on the empty and the full calorimeters have been applied. The data are presented in terms of the defined thermochemical calories of 4.1840 absolute joules and the formula (molal) weight in grams using 1953 International Atomic Weights. Heat capacities below 50~K. are presented in Fig. 1. Figure 2 compares the heat capacities at higher temperatures with the smooth curve for zinc ferrite1 in order to amplify the small differences between these curves. On both plots the points indicated represent the individual determinations, and the heat capacities of Ferramic E and zinc ferrite1 have been included for comparison. The significant features are: (1) the sharp transition due to antiferromagnetic ordering in zinc ferrite at about 9.50K. which obviously persists in the mixed ferrospinels at approximately the same temperature, but decreases in intensity with increasing nickel content; and (2) the absence of other peaks or fluctuations in the curves. No singularities of the type predicted by Yafet and Kittel5 were observed. The ferrimagnetic contributions to the thermal properties cannot at present be quantitatively resolved from those of the lattice. V. THERMODYNAMIC FUNCTIONS The entropies and enthalpy increments computed by numerical quadrature from large scale plots of the heat capacity are provided at selected temperatures in Table III. Nuclear spin and isotope mixing contributions have not been included in the entropy. Extrapolation below about 5~K. was made with the Debye limiting law. The estimated probable error in the entropy increment is + 0o06 e.u., and.____8..

6 1. FIG. 1. HEAT CAPACITY VS TEMPERATURE FOR NilxZnx Fe204 0 5 — -~ X=-I.O 04 /9 To o /o? -D ^1 0.9 / ^ i / / < - ~! ~,o- T,~K 9 T,~K

3.0 — X0. 6 FERRAMIC \,,0/I.. E o / v(-A Cp CPFerrospine-CPZnFe4 50 100 150 2002500 400 7L _/ _ \ U 1.0 6 0.\ o 4 0.9 0 C5 _d ^.FIG. 2. DEVIATION OF THE HEAT CAPACITY __'ii^/~~ ~OF Nil_ Zn xFe204 FROM THAT /D OF ZniFe2O SMOOTH CURVE. (A cp = CpFerrospinel= CpZFe2Q04) 50 100 150 200 250 300 T,~K 10

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN in the enthalpy increment is + 0.1%. More extensive tabulation of the temperature dependence of the thermodynamic functions of these four ferrites have been 11 prepared. If the nickel ions occupy B sites and zinc ions occupy A sites, then the configuration entropy resulting from mixing zinc and iron ions at random on the A sites is given by: SA = -R In xX(l-x)lx and the configurational entropy resulting from mixing zinc and iron atoms at random on the B sites is given by: l-x l+x SB = -R in 4-1 (l-x) (l+x). The sum of these two expressions represents an upper bound to the zero-point entropy and amounts to 0.72 R, 1.15 R, and 1.46 R and 1.67 R for x = 0.9, 0.8, 0.7 and 0.6, respectively. The actual entropy at 0~K. will be less than the above due to the mutual ordering effects of the A and B sublattices by the electrical interactions between them. ___________________......._ 11

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN REFERENCES 1. E. F. Westrum, Jr. and D. M. Grimes, (Paper submitted to Physics and Chemistry of Solids). 2. E. G. King, J. Chem. Phys., 60, 410 (1956). Cf. the references to other works contained therein. 3. J. S. Kouvel, Phys. Rev., 102, 1489 (1956). 4. L. Neel, Ann. Phys., 3, 137 (1948). 5. Y. Yafet and C. Kittel, Phys. Rev., 87, 290 (1952). 6. L. Neel and P. Brochet, Compt. rend., 230, 280 (1950). 7. J. M. Hastings and L. M. Corliss, Phys. Rev., 102, 1460 (1956); Rev. Mod..Phys., 25, 114 (1953). 8. E. F. Westrum, Jr. and A. F. Beale, Jr., (to be published). 9. G. A. Burney and E. F. Westrum, Jr., (to be published). 10. E. Greenberg and E. F. Westrum, Jr., J. Am. Chem. Soc.., 78, 4526 (1956). 11. Extensive tabulation of the heat capacities, enthalpy and entropy increments and enthalpy function of these four ferrospinels in addition to heat capacity data on Ferramic E are listed in the Appendix. 12____________________________

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN MOLECULAR FIELD FLUCTUATION EFFECTS IN MIXED NICKEL ZINC FERRITES By D. M. Grimes, S. Legvold, and Edgar F. Westrum, Jr. Both nickel and zinc ferrites have spinel structures; the lattice constants are not greatly different and the two ferrites are completely soluble in each other. Each zinc cation in zinc ferrite (ZnFe204) carries zero net electronic spin and is situated at the center of a tetrahedron of oxygen ions. The array of all such sites occupied in the perfect lattice is called the A sublattice. The iron cations occupy sites surrounded by an octahedron of oxygen ions. The array of octahedral sites occupied in the perfect lattice forms the B sublattice. For nickel ferrite (NiFe2O4), the nickel carries two net spins and occupies the B sites while the iron occupies all the A sites and one-half of the B sites. For the case of mixed nickel zinc ferrites it is presumed that the nickel goes always on the B sites and the zinc always on the A sites. The questions of the distribution of the nickel on the B sublattice and, in the case of mixed ferrites, of the distribution of the zinc on the A sublattice have been discussed by Nell and Smart,2 and it is concluded that the nickel probably is randomly 2 arrayed on the B sublattice and that the zinc on the A sublattice is also randomly arrayed for the mixed ferrites. However, electrical charge considerations would tend to establish some correlation on the atomic scale between local A and B sublattice populations. The magnetic properties of the ferrimagnetic ferrites (e.g. mixed nickel zinc ferrites) are usually explained by stating that the exchange interactions can be described in terms of effective molecular fields which have their origin in the net spins of the constituent atoms. Each sublattice ~~____~_______________~ ~13 -------------

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN is treated as a homogeneous unit and the problem is considered solved when the constant molecular field coefficients corresponding to the A-A, B-B and A-B interactions are known. For a small concentration, (l-x), of NiFe204 in ZnFe204, there will be (l-x) iron ions on the A sites among the nonmagnetic zinc ions. This can be considered as a basically nonmagnetic lattice with interspersed regions of high magnetic intensity. For such a model the concept of only three applicable molecular field coefficients is no longer valid and the portion which can be retained will depend upon the smallest defineable unit of a particular ferrite., Thus when (l-x) is zero the material will obviously be zinc ferrite, but as (l-x) increases the regions surrounding the A site iron will be a mixed ferrite, the rest a mesh of zinc ferrite. The magnitude of (l-x) for which this heterogeneous model is valid will depend upon the smallest defineable unit of zinc ferrite. Since regions rich in iron would be ferrimagnetic while other regions poorer in iron would not, ferrimagnetic regions immersed in an antiferromagnetic or paramagnetic mesh would result. As the temperature is lowered the fraction of the material in the ferrimagnetic regions increases at the expense of the fraction in the nonmagnetic mesh. Thus the concept of a single Curie temperature becomes meaningless. Although the magnitude of the smallest units of volume which can be considered to be zinc ferrite, or can be considered as a given mixed ferrite, can not be unambiguously resolved; the assumption of particular smallest units involving only nearest neighbor interactions permits a calculation to be made. The qualitative effect of such regions can be seen from the temperature dependence of the magnetic moment of mixed nickel zinc ferrites for ferrites rich in zinc. Figure 1 shows data taken on material of the composition 2nxNilxFe204 where x has the values of 0.9, 0.8, 0.7 and 0.6. Note that as the temperature increases the

IN --- A H=18.4 K Oe o —-— o H= 12.0 K Oe 100 -- -'"XX=.60 80 o 00 140^ 182X.0 -,.. e0 60^'~ 40 2'0 - —.... X=.90 0 100 140 180 220 260 300 T, ~K FIG. 1 MAGNETIC MOMENT VS. TEMPERATURE FOR ZnxNilxxFe2O4 15

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN magnetic moment decreases gradually for the larger values of x. The experimental technique for obtaining the magnetic data has been described.3 A complementary effect can be seen in the heat capacity of the same materials. Zinc ferrite undergoes a type of antiferromagnetic ordering just below 100 K.4 Thus for the case of the mixed ferrites, if some smallest unit of zinc ferrite can be considered, then any larger units of zinc ferrite will contribute to the anomalous heat capacity but material in the neighborhood of A site iron ions will not undergo this transition. The variation in the heat capacity as a function of temperature for several values of the variable x has been presented. It was shown by Yafet and Kittel6 that the two sublattice model for describing the magnetic properties of the ferrimagnetic ferrites, under certain conditions, violates the so-called third law of thermodynamics. They showed that this violation would no longer occur if each of the sublattices were further subdivided into two sub-lattices. They also pointed out, from extrapolation of existing data for the molecular field interaction coefficients of mixed nickel zinc ferrites of high nickel content, that the four sublattice model should give rise to magnetic transitions, for about the composition Ni 2Zn Fe204 not predicted by the two sublattice model. Although they should be observable by modern cryogenic techniques, existing heat capacity data5 show no such transitions. It must be expected, however, that even if such transitions did take place the molecular field fluctuations would result in transition temperatures which vary throughout the material. Hence the heat capacity effect would be spread over a temperature range and, as such, probably not observable. It must be expected that the distribution of effective molecular fields would affect other structure insensitive magnetic properties such as the effective anisotropy. This would in turn affect the relaxation frequency of the material, 16

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN which is proportional to the effective anisotropy field in many cases, and give rise to a relaxation frequency varying from spot to spot in the material. Such effects are, of course, observed.8 However many other factors such as magnetic interactions among grains also produce differing relaxation frequencies so the experimental measurement of this relaxation spread is not considered to be necessarily a verification of fluctuations in the molecular fields. REFERENCES 1o L. Neel, Ann. I'Inst. Fourier 1, 163 (1950). 2. J. S. Smart, Phys. Rev. 94, 847 (1954). 3. Elliott, Legvold, Spedding, Phys. Rev. 91,?8 (1953). 4. E. F. Westrum, Jr. and D. M. Grimes, Submitted to J. Phys. Chem. Solids 5. E. F. Westrum, Jr. and D. M. Grimes, Submitted to J. Phys. Chem. 6. Y.Yafet and C. Kittel, Phys, Rev. 87, 290 (1952). 7. L. Neel and P. Brochet, Compt. rend. 230, 280 (1950). 8. D. Park, Phys. Rev. 97, 60 (1955); 98, 438 (1955). 17

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN LOW TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC PROPERTIES OF ZINC FERRITE By Edgar F. Westrum, Jr. and D. M. Grimes I. INTRODUCTION Zinc ferrite, ZnFe204, crystallizes in the normal spinel structure. A well-tempered zinc ferrite is, therefore, characterized by having the iron atoms located at the centers of octahedra of oxygen atoms and the zinc atoms centered in tetrahedra of oxygen atoms. Conversely, an inverted spinel contains the divalentcation on octahedral sites; since there are twice as many octahedral sites as tetrahedral sites in the spinel structure, half of the trivalent iron atoms also occupy octahedral sites. Typically, the inverted.spinels are ferrimagnetic and the normal spinels are paramagnetic at room temperature. Since the exchange interactions between cations on octahedral sites are antiferromagnetic in nature, some type of antiferromagnetic ordering may take place in zinc ferrite at low temperatures. Although the fairly complex magnetic properties of ferrospinels have been extensively investigated by various techniques, few of these measurements have extended below 10~K. Utilization of low temperature adiabatic calorimetry permits both the detection of magnetic transformations and the evaluation of the thermodynamic parameters associated with these phenomena. This calorimetric technique is relatively sensitive, precise and, compared to more direct magnetic measurements (e.g., susceptibility), less subject to being masked by traces of ferromagnetic impurities. 18

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The study of the low temperature thermal properties of a series of nickel-zinc ferrites1 of empirical formula Nil xZnxFe204 over the range x = 0.6 to x = 0.9 revealed an anomalously high heat capacity in the vicinity of 9 K, the magnitude of which increases rapidly as x approaches unity. Recent measurements by Friedberg, et al.2 on a sample approximating zinc ferrite in composition confirmed the obvious extrapolation to x = 1 in revealing the existence of an anomalous peak in the heat capacity of zinc ferrite (ZnFe204) with a maximum near 9~K and a prominent "tail" on the high temperature side. Low temperature neutron diffraction studies by Hasings and Corliss3 confirm the existence of this transitin and strongly suggest that it results from an antiferromagnetic type of ordering. 4 However, the thermal anomaly reported by Friedberg in zinc ferrite is considerably rounded and broadened compared to other cooperative transformations and reveals no evidence of a discontinuity in the derivative of the heat capacity with respect to temperature. Such deviation from the usual behavior of cooperative transitions might be expected as a consequence of partial inversion of the "normal" spinel structure, of inhomogeneity on the atomic scale, or of deviation from exact stoichiometry in the sample utilized in these measurements. Further investigation of the thermal properties of this substance was, therefore, considered relevant to the understanding of the ordering phenomenon. II. EXPERIMENTAL 2.1 Preparation of the Zinc Ferrite Preliminary investigation revealed the strong dependence on composition of the heat capacity of nickel-zinc ferrites in the vicinity of 100K. For reasons already indicated, great care was exercised in the preparative technique to obtain, as nearly as possible, a stoichiometric, homogeneous, non-inverted sample Cf zinc ferri te - 19

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Equimolal quantities of weighed, anhydrous, chemically pure ZnO and Fe203 were milled in a hardened-steel ball mill using a thin acetone slurry. After passing the slurry through a magnetic separator, the bulk of the acetone was decanted and the remainder evaporated. Cylindrical slugs of about 50 g mass were pressed; the surface layer was removed, and the slugs were fired in air at 1100~C for 14 hours. After furnace cooling, the slugs were sufficiently fragmented in a hardened-steel "diamond mortar" to pass a 30 mesh screen. These granules were reformed into slugs, fired at 1100~C for 12 hours, and gradually allowed to cool in the furnace to 30~C over a period of 16 hours. The resulting ferrite granules were of a uniform reddish-brown color throughout. Gravimetric chemical determinations showed 46.24 + 0.1% iron (theoretical; 46.33) and 27.2 + 0.1% zinc (theoretical: 27.12). Spectrochemical analyses revealed 0.01 to 0.1% of Al and Mn and 0.001 to 0.01% of Ca, Cu, Mg, Ni, and Si. Stannous chloride redox titration indicates less than 0.1% ferrous iron in the samples. 2.2 Cryogenic Technique The Mark I adiabatic cryostat used for these measurements has been described. Measurements were made in a calorimeter (Laboratory Designation W-9) which is similar in design and dimensions to W-66 except for the following modifications: only four conduction vanes were used, protection against possible corrosion was achieved by a 0.02 mm gold plate on the interior surfaces, and a weighed quantity of Apiezon T vacuum grease was used to provide thermal conduction in the thermocouple sleeve and in the thermometer-heater well. The calorimeter contained 2.0 cm helium pressure to improve thermal dunction in the sample space. Temperatures were measured with a capsule-type platinum resistance thermometer (Laboratory Designation A-3) inserted within the heater sleeve in the well. A 20~~~~~

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 150-ohm glass-fibre-insulated, constantan wire was bifilarly wound in a doublethread groove in the heater sleeve. The thermometer was calibrated by the National Bureau of Standards against the International Temperature Scale above 90 K and by comparison at 19 temperatures with the Bureau's platinum thermometers over the o range 10-90 K. Below 100K we established a provisional temperature scale by fitting the constants in the equation R = A + BT2 + CT5 to the observed resistance of the thermometer at 10~K, the resistance at the boiling point of helium, and dR/dT at 10~K. The temperature scale thus defined probably agrees with the thermodynamic scale to 0.1~ below 10~K, 0.03~ from 10 to 90~K, and 0.050 from 90 to 400~K. Measurements of temperature and of electrical energy were made with an autocalibrated White double potentiometer~ A timer operated by an electrically driven 240-cycle tuning fork and amplifier automatically indicated the duration of the energy input. Three independent determinations of the heat capacity of the empty calorimeter have been made over the entire temperature range. III. RESULTS The experimental values of the observed molal heat capacity of zinc ferrite are presented in Table I. These data include small corrections for the slight differences in the amounts of helium and solder between the full and the empty calorimeter and for the finite temperature increments used in the measurements. Since the data are listed in chronological sequence, the temperature increments of the individual determinations can be estimated from the adjacent mean temperatures. The data are expressed in terms of the defined thermochemical calorie equal to'4.1840 absolute joules. The ice point is taken as 273.15~K, and the gram formula weight of ZnFe204 as 241.08. A sample of 163.397 g was employed. 21 -

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE I MOLAL HEAT CAPACITY OF ZINC FERRITE (in calories degree-1 gram-mole-1) T,~K Cp T,~K Cp T,K Cp Series I 10.18 4.17 36.01 2.341 10.91 3.37 39.61 2.716 184.44 24.00 43.47 3.176 193.52 25.00 Series III 47.72 3.740 203.27 25.99 52.45 4.413 212.90 26.93 5.50 0.58 222.68 27.80 6.24 1.11 Series IV 232.53 28.65 6.82 1.50 242.39 29.43 7.48 2.08 17.04 2.123 252.28 30.16 8.46 3.28 18.69 1.957 262.21 30.85 8.89 5.3 52.37 4.298 272.28 31.44 9.39 (8.7) 58.05 5.246 282.53 32.10 9.75 (8.3) 64.00 6.173 292.86 32.71 10.38 3.86 69.98 7.115 303.14 33.25 11.10 3.272 76.16 8.097 313.31 33-77 11.82 3.034 82.61 9.183 323.41 34.23 12.95 2.787' 89.79 10.335 333.65 34.66 13.66 2.635 97.61 11.608 343.93 35.11 14.70 2.457 105.53 12.900 15.85 2.271 111.99 13.917 Series II 16.97 2.127 120.25 15.232 18.31 1.989 128.58 16.526 7.81 2.6 20.14 1.848 137.08 17.81 8.47 3.9 22.28 1.755 146.07 19.11 8.87 5.9 24.45 1.723 155.56 20.42 9.18 7.9 26.74 1.749 165.25 21.70 9.41 9.2 29.39 1.848 175.00 22.90 9.76 6.5 32.55 2.045 184.94 24.06 22

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Figure 1 depicts the heat capacity in the vicinity of the observed thermal anomaly. The molal heat capacity and thermodynamic functions derived by numerical integrations of the heat capacity are listed at rounded temperatures in Table II. The heat capacity values were read from a smooth curve through the experimental points and are estimated to have a probable error of 0.1% down to 25~K increasing to 1% at 10~K. The probable error may be 10% below 10~K as a consequence of the sharp dependence of heat capacity on temperature over the region of thermal anomaly and the relatively slow establishment of thermal equilibrium in this region. The deviation of the individual experimental determinations from our smoothed curve are presented in Figure 2. Solid lines represent deviations of + 0.1% and + 1.0% respectively. Below 5~K, a Debye third power extrapolation was used to obtain values of the thermodynamic functions. The probable errors in the entropy, enthalpy, and free energy function are estimated to be 0.1% above 100~K, but for internal consistency one more digit has been retained than is justified by the estimated probable error. The effect of nuclear spin and isotope mixing is not included in the entropy and the free energy function. IV. DISCUSSION After the completion of these measurements, heat capacity data on zinc ferrite from 51 to 298~K were reported by King.9 The deviations of King's data from our smoothed curve are presented in Fig. 2. The data of King trend gradually to higher values toward lower temperatures than do the results of the present research; however, the agreement is good at room temperature. By virtue of compensation of these deviations of opposite sign, the entropy increments (S98.16oK - S~51oK) are in close agreement. Below 51~K, the extrapolated portion _____________________________ - 23 _

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE II MOLAL THERMODYNAMIC FUNCTIONS OF ZINC FERRITE Cp S~ (H~-HP ) -(F~-H)/T T. K. cal/deg cal/deg cal cal/deg 10 4.68 2.2126 17.69 0.4431 15 2.400 3.4473 32.65 1.2705 20 1.857 4.0520 43.11 1.8966 25 1.724 4.4459 51.92 2.3692 30 1.878 4.7701 6.82 2.7427 35 2.248 5.0852 71.07 3.0548 40 2.758 5.4173 83.53 3.3291 45 3.376 5.7766 98.82 3.5807 50 4.059 6.1673 117.38 3.8197 60 5.552 7.0370 165.29 4.2821 70 7.117 8.0095 228.58 4.7441 80 8.721 9.0639 307.7 5.2173 90 10.368 10.1863 403.2 5.7067 100 12.004 11.363 515.0 6.213 110 13.598 12.583 643.1 6.737 120 15.196 13.835 787.1 7.276 130 16.738 15.112 946.8 7.829 140 18.236 16.408 1121.7 8.396 150 19.658 17.715 1311.2 8.973 160 21.01 19.027 1514.5 9.561 170 22.29 20.339 1731.1 10.156 180 23.48 21.648 1960.0 10.759 190o 24.62 22.949 2200.6 11.367 200 25.67 24.239 2452.1 11.979 210 26.65 25.515 2713.7 12.592 220 27.56 26.776 2984.8 13.208 230 28.43 28.020 3264.8 13.825 240 29.25 29.247 3553.3 14.442 250 30.00 30.458 3849.6 15.059 260 30.70 31.647 4153.1 15.673 270 31..34 32.818 4463.4 16.287 280 31.96 33.970 4779.9 16.899 290 32.54 35.102 5102.4 17.507 300 33.08 36.214 5430.5 18.112 350 35.35 41. 93 7143.8 21.082 273.1531.54 33184 62.16.481 298.15 _ _ 32. 00993.00 53..Q

10 8 - FIG. 1. THE MOLAL HEAT CAPACITY OF ZINC FERRITE FROM 5 TO 40~K. The dotted curve represents the measurements of Friedberg et al.2 and the dashed curve approximates (~LU-^iJ — | ||the lattice (vibrational) heat capacity. I I 6 LU) U -,- 0 I I I 0 10 20 30 40 T, ~K 25

FIG. 2. THE DEVIATION OF THE MEASURES HEAT CAPACITIES OF ZINC FERRITE FRO] SMOOTH CURVE, i.e., WCp = Cp(exp't'l det'n.)- C(curve) The open circlerepresent the individual experimental determinations of this work. The solid circles are those reported by King9..10- /.I I I I I. I IL)o \,, O I Ita~t ~ ii 2 T i -05 -\I / i \ II! +0 o/Vo. I, I I 0 / 0 O^' * 0'',I.o o p o U) -0.1% S o I -.05 / \ rr 5 20 50 100 200 300 T,0K 26

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN of King's entropy is in error by nearly four units. This emphasizes the desirability of extending heat capacity measurements to the lowest practicable temperatures when such data are intended for evaluation of chemical thermodynamic functions. Isolated experimental points obtained by Friedberg, et al. over the range 80 to 2000K appear to be at least 5% higher than those reported either in the present work or by King. The existence of a typical cooperative type heat capacity anomaly rising to a sharp maximum greater than 9 cal mole-1 deg-1 at 9.5 + 0.2~K accompanied by a prominent "tail" possibly extending beyond 25 K is characteristic of pure zinc ferrite. However, because thermal equilibrium was so slowly achieved below 10 K, it was desirable to traverse this entire anomaly with a single energy input and then to compare the directly measured enthalpy with that obtained by the integration of the C curve (Fig. 1) over the corresponding range. The results of three such tests are summarized in Table III and indicate good accord with the heat capacity measured with small temperature increments. Table III Comparison of Measured and Integrated Enthalpy Increments o - o Tinitial K-. Tfinal, K. Ameasured Hintegrated 5.16 25.23 52.7 51.7 5.03 14.12 31.6 30.0 5.03 16.07 36.7 36.1 2 The anomaly as, reported by Friedberg, et al., is indicated by the dotted line in Fig. 1. The observed difference is probably due to deviations from exact stoichiometry, from inhomogeneity, and/or from partial inversion 27

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN 2,4 suggested by the mode of preparation and the reported properties of their sample. That the thermal history of the ferrite specimen may have a marked effect on heat capacity over a wide temperature range has recently been demonstrated for lithium10 zinc ferrite. Although it is not yet possible to satisfactorily resolve the magnetic and lattice contributions to the specific heat, a rough approximation may be obtained by fitting the higher temperature data with an empirical equation of the 11 type recommended by Kelley. The Debye and Einstein function sum proposed by King9 was modified to better fit our data. The equation Cp = D(178/T) + 3E(390/T) + 3E(710/T) fits our data to within 0.5% over the range 130 to 300~K. This approximate lattice heat capacity is presented as a dashed curve in Fig. 1. Attempts to make a similar extrapolation from temperatures substantially lower than 130~K resulted in a calculated lattice heat capacity contribution in excess of the measured total value near 40 K. Hence the estimated value of the lattice contribution is almost certainly high over the entire range. If the magnetic contribution is estimated as the difference of this and the experimental curve, the magnetic entropy is 2.2 cal mole-1 deg-1 at 10 K, 4.0 at 25 K, and 4.5 at 150 K. The molal entropy increment between the completely disordered paramagnetic states and the ordered antiferromagnetic state is 2 R in (S + 1) = 7.12 (cal./ mole deg). The discrepancy between the theoretical value and our rough estimate of the magnetic contribution can readily be resolved if we assume the persistence of short range ordering contributions to the thermal properties above 130 K. These data are thus seen to be in accord with the interpretation of Hastings and Corliss3 of the transition from paramagnetic zinc ferrite to an __________-____________________ 28

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN antiferromagnetic state at 9.50K as a result of the spin interaction of the iron atoms. The anomalously high heat capacity above 9.5~K is consistent with the persistence of short range ordering above the Neel temperature and the interpretation of the diffuse scattering of neutrons observed at liquid nitrogen temperatures as arising from a short-range ferromagnetic interaction. ACKNOWLEDGEMENT The authors appreciate the generous cooperation of Professor E. W. Welch, Jr. of the Electrical Engineering Department, the assistance of James Kuiper in the preparation of the sample, of Dr. Chien Chou and Seisho Tomeoda in the cryogenic measurements and of Te Fu Chang in the calculations. REFERENCES 1. Grimes, D. M. and Westrum, E. F., Jr., (Submitted to J. Phys, Chem), 2. Friedberg, S. A., et al., "Investigation of Thermal and Electrical Properties of Solids at Very Low Temperature, Carnegie Institute of Technology Report (1955). 3. Hastings, J.M. and Corliss, L. M., Phys. Rev., 102, 1460 (1956). 4. Friedberg, S. A. and Burk, D. L., "Low Temperature Heat Capacity of Some Normal Spinels," Conference on Magnetism and Magnetic Materials, Published by A. Inst. Elec. Engrs., New York, (1955). 5. Westrum, E. F., Jr., and Beale, A. F., Jr., J. Am. Chem. Soc. (Submitted). 6. Benjamins, E., and Westrum, E. F., Jr., J. Am. Chem. Soc. 00, 0000 (1956) (In press). 7. Hoge, H. H. and Brickwedde, F. G., J. Research Natl. Bur. Standards, 22, 351 (1939). 8. Osborne, Stimson, Sligh and Cragoe, Bur. Standards Sci. Papers, 20, 65, (1925). 9. King, E. G., J. Phys. Chem.,60, 410 (1956). 10. Westrum, E. F., Jr., and Grimes, D. M., (To be published). 11. Kelley, K. K., Contributions to the Data on Theoretical Metallurgy XI. U. S. Bureau of Mines Bulletin 477. Washington, D. C. (1950). 29

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN APPENDIX The accompanying Tables I through IV list the smoothed values of the heat capacities at selected temperatures of nickel-zinc ferrospinels (NilxZnxFe204) with x = 0.6, 0.7, 0.8 and 0.9, and the values of the thermodynamic functions computed by numerical quadrature of the heat capacities. For the reasons noted in the paper, the zero-point entropies of these materials are unknown and the entropy increments rather than the entropies are tabulated. The estimated probable errors of the entropy increments are + 0.06 e.u. and those of the enthalpy increment are + 0.1%. This precision index includes both the uncertainties in the extrapolation and in the measurements themselves. Molecular weights of 238.404 g., 239.073 g., 239.742 g. and 240.411 g. are taken for x = 0.6, 0.7, 0.8 and 0.9. The data are presented in terms of the defined thermochemical calorie equal to 4.1840 absolute joules and an ice point of -273.15~K. Table V presents the heat capacity of Ferramic E, a commercial ferrospinel produced by General Ceramic and Steatite Corporation. Measurements were made by the technique described in the paper that this document supplements on a 203.454 g. sample of this material fragmented to 4 to 10 mesh. Calorimeter W-5 was used with Lubriseal grease for thermal conductivity and 760 cm. He at 25~C. to improve the thermal contact with the sample. The specific heat of this material (in calories g.-1 deg.-1) represents he fundamental presentation of these data. In addition, primarily for comparison ith the other nickel-zinc ferrospinels, the molal heat capacity of this material as been calculated on the assumption that its formula is Nio.4Zn0 6Fe204 orresponding to the formula weight 238.404 g. This assumption is consistent ith, but not established by, the limiting chemical analysis presented in Table I. 30

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE A.1 MOLAL TEERMODYNAMIC FUNCTIONS OF Nio.6Zno.4Fe204 T, K. Cs S - S~H~ - H (H~ )T -1 cal.deg. cal.deg. cal. cal.deg. 10.232.077.58.058 15.390.197 2.09.139 20.613.338 4.57.229 25.934.507 8.39.336 30 1.367.714 14.10.470 35 1.923.965 22.28.636 40 2.573 1.263 33.49.837 45 3.298 1.607 48.14 1.070 50 4.091 1.995 66.59 1.332 60 5.757 2.891 115.96 1.933 70 7.507 3.910 182.31 2.604 80 9.321 5.031 266.40 3.330 90 11.15 6.235 368.76 4.097 100 12.92 7.501 489.11 4.891 110 14.67 8.814 627.0 5.700 120 16.40 10.165 782.4 6.520 130 18.07 11.544 954.8 7.345 140 19.68 12.943 1143.6 8.168 150 21.21 14.353 1348.0 8.987 160 22.67 15.769 1567.5 9.797 170 24.05 17.186 1801.1 10.595 180 25.34 18.597 2048.1 11.378 190 26.55 20.000 2307.6 12.145 200 27.70 21.392 2579.0 2.895 210 28.79 22.769 2861.5 13.626 220 29.79 24.131 3154.4 14.338 230 30.74 25.477 3457.1 15.031 240 31.62 26.804 3768.9 15.704 250 32.46 28.111 4089.4 16.358 260 33.26 29.400 4418.0 16.992 270 34.02 30.669 4754.5 17.609 280 34.74 31.920 5098.3 18.208 290 35.42 33.151 5449.1 18.790 300 36.04 34.362 5806.5 19.355 273.16 34.25 31.067 4862.3 17.800 298.16 35.95 34.140 5740.3 19.252 31 -

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE A.II MOLAL THERMODYNAMIC FUNCTIONS OF Nio.3Zn0.7Fe204 T, K. Cs S -S HS-H (Hl-)/1 cal.deg.l cal.deg.-1 cal. cal.deg. — 10.470.156 1.504.150 15.700.388 4.40.293 20 974.626 8.57.428 25 1.339.880 14.30.572 30 1.812 1.165 22.14.738 35 2.408 1.487 32.64.933 40 3.079 1.853 46.35 1.159 45 3.820 2.257 63.56 1.413 50 4.618 2.701 84.65 1.693 60 6.308 3.691 139.20 2.320 70 8.039 4.794 210.97 3.014 80 9.791 5.980 300.05 3.751 90 11.57 7.237 406.9 4.521 100 13.28 8.544 531.2 5.312 110 14.99 9.890 672.5 6.114 120 16.66 11.266 830.6 6.922 130 18.28 12.664 1005.4 7.734 140 19.83 14.075 1195.9 8.542 150 21.32 15.494 1401.7 9.345 160 22.73 16.916 1622.0 10.137 170 24.07 18.334 1856.0 10.918 180 25.31 19.746 2102.9 11.683 190 26.49 21.145 2362.0 12.432 200 27.61 22.533 2632.6 13.163 210 28.66 23.906 2914.0 13.876 220 29.63 25.262 3205.5 14.570 230 30.56 26.600 3506.4 15.245 240 31.44 27.920 3816.4 15.902 250 32.27 29.219 4135.0 16.540 260 33.03 30.499 4461.5 17.160 270 33.74 31.760 4795.4 17.761 280 34.41 32.999 5136.2 18.344 290 35.04 34.218 5483.5 18.909 300 35.64 35.416 5837.0 19.457 273.16 33.96 32.154 4902.4 17.947 298.16 35.53 35.196 5771.5 19.357 32

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE A. III MOLAL THERMODYNAMIC FUNCTIONS OF Nio.2Zn0.8 Fe204 Cs S~-S H- H (H~ o)/T T, K. cal.deg.-1 cal. deg. cal. cal.deg. 10.848.196 2.877.288 15 1.057.574 7.580.505 20 1.316.913 13.49.675 25 1.667 1.243 20.92.837 30 2.132 1.586 30.35 1.012 35 2.723 1.957 42.45 1.213 40 3.399 2.365 57.74 t.443 45 4.130 2.807 76.54 1.701 50 4.924 3.283 99.16 1.983 60 6.586 4.327 156.69 2.611 7.0 8.294 5.470 231.06 3.301 80 10.04 6.689 322.63 4.033 90 11.76 7.971 431.60 4.796 100 13.47 9.298 557.7 5.577 110 15.11 10.659 700.7 6.370 120 16.72 12.043 859.8 7.165 130 18.31 13.445 1035.0 7.962 140 19.83 14.857 1225.7 8.755 150 21.28 16.275 1431.4 9.543 160 22.65 17.693 1651.1 10.320 170 23.93 19.106 1884.1 11.083 180 25.15 20.509 2129.6 11.831 190 26.30 21.899 2386.9 12.563 200 27.37 23.275 2655.3 13.276 210 28.37 24.636 2934.0 13.971 220 29.28 25.977 3222.4 14.647 230 30.15 27.299 3519.6 15.302 240 30.98 28.599 3825.2 15.938 250 31.76 29.879 4139.0 16.556 260 32.48 31.138 4460.2 17.155 270 33.14 32.377 4788.3 17.734 280 33.75 33.594 5122.8 18.296 290 34.32 34.788 5463.2 18.839 300 34.83 35.960 5809.0 19.363 273.16 33.33 32.764 4893.3 17.914 298.16 34.74 35.746 5745.0 19.268 33

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE A.IV MOLAL THERMODYNAMIC FUNCTIONS OF Ni0.1Zno.9Fe204 T, K. Cs -1 S-So~H~-1 (H -)/T cal.deg. cal.deg.. -cal. cal.deg. 10 1.747.737 5.42.542 15 1.694 1.419 13.84.922 20 1.752 1.912 22.42 1 121 25 1.956 2.322 31.63 1, 265 30 2.317 2.708 42.24 1.408 35 2.827 3.102 55.06 1.573 40 3.444 3.519 70.69 1.767 45 4.136 3.964 89.62 1.991 50 4.885 4.438 112.15 2.243 60 6.470 5.467 168.82 2.814 70 8.101 6.588 241.73 3.453 80 9.773 7.778 331.04 4.138 90 11.45 9.026 437.2 4.858 100 13.08 10.317 559.8 5.598 110 14.69 11.639 698.7 6.352 120 16.28 12.986 853.6 7.113 130 17.84 14.352 1024.3 7.879 140 19.31 15.728 1210.1 8.643 150 20.73 17.108 1410.3 9.402 160 22.07 18.490 1624.3 10.152 170 23.32 19.866 1851.3 10.890 180 24.51 21.233 2090.5 11.614 190 25.63 22.587 2341.2 12.322 200 26.67 23.929 2602.8 13.014 210 27.65.25.255 2874.4 13.687 220 28.54 26.562 3155.3 14.342 230 29.40 27.850 3445.1 14.979 240 30.20 29.119 3743.1 15.596 250 30.95 30.366 4048.9 16.195 260 31.64 31.593 4361.8 16.776 270 32.28 32.799 4681.4 17.338 280 32.88 33.985 5007.2 17.883 290 33.44 35.148 5338.8 18.410 300 33.97 36.291 5675.9 18.920 273.16 32.47 33.177 4783.7 17.512 298.16 33.88 36.082 5613.5 18.827 34

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN TABLE A.V HEAT CAPACITY OF FERRAMIC E T Spec. Heat C T Spec. Heat C oK. cal. mg cal le Kcal 1 ca cal~mole1 K cal cal4m o e dSege. I- deg0eg.0 deg.37 Series I 63.00 0.02673 6.373 69.23 0.03125 7.450 5.59 0.000364 0.087 75.89 0.03621 8.632 6.36 0.000404 0.096 83.03 0.04164 9.927 7.38 0.000564 0.134 90.35 0.04723 11.26 8.65 0.000816 0.195 97.86 0.05281 12.59 10.00 0.001074 0.256 105.87 0.05.868 13.99 11.45 0.001292 0.308 114.12 0.06472 15.43 12.94 0.001501 0.358 122.47 0.07068 16.85 14.46 0.001755 0.419 131.20 0.07676 18.30 16.04 0.002051 0.489 140.13 0.08276 19-73 17.72 0.002350 0.561 149.01 0.08851 21.10 19.54 0.002739 0.653 158.03 0.09404 22.42 167.25 0.09945 23.71 Series II 168.47 0.10012 23.87 177.45 0.10507 25.05 16.78 0.002226 0.5309 186.57 0.10981 26.18 18.64 0.002599 0.6198 195.75 0.11434 27.26 20.61 0.003038 0.7243 204.81 0.11858 28.27 22.80 0.003617 0.8624 213.75 0.12248 29.20 25.27 0.004320 1.030 222.67 0.12617 30.08 27.97 0.005277 1.258 231.62 0.12974 30.93 30.95 0.006351 1.514 240.59 0.13309 31.73 34.11 0.008154 1.944 249.57 0.13636 32.51 37.47 0.009773 2.330 258.62 0.13934 33.22 41.26 0.011934 2.845 267.81 0.14224 33.91 45.54 0.01457 3.473 276.99 0.14509 34.59 50.25 0.01768 4.215 286.10 0.14756 35.18 55.23 0.02109 5.028 295.17 0.15016 35.80 52.74 0.01937 4.618 304.24 0.15251 36.36 57.47 0.02267 5.405

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