A spacmc HEM 3mm er (:32 Mnm 4 «2+: 2 o m A magazine FIELD The-sis for tha Degree af Ph. D. MEWGAN STATE UNWERSITY NORhfiAN E‘faéjABéE LOVE 1967 [mummn 91ng magma!“ AXE/21817 THESIS This is to certify that the thesis entitled A Specific Heat Study of CszMnC14.2H20 in 3 Magnetic Field presented by Norman Duane Love has been accepted towards fulfillment of the requirements for Ph D degree in M. A %W«/ 7540/ Major professor Date May 15’ 1967 O~169 ABSTRACT A SPECIFIC HEAT STUDY OF CszMnCl4-2HZO IN A MAGNETIC FIELD by Norman Duane Love 4 3 Adiabatic calorimeters for studies at He and He temperatures, and the measuring electronics have been described. Specific heat studies of single crystals of CszMnCl4-2H20 have been made in zero and non-zero mag- netic fields. The zero field specific heat study: 1) compares well with the calculated specific heat from the magnetic susceptibility, 2) gives the Néel temperature as 1.84° i 0.01°K, 3) indicates that 25 percent of the en- tropy is recovered above the Néel temperature due to short range ordering, and 4) gives a sublattice magnetization curve as a function of reduced temperature which agrees with the measured magnetization curve from an nmr study and with the curve computed for a f.c.c. lattice using a three dimensional Ising model. Specific heat studies for several external magnetic fields in each of three orientation A, B, and C which are approximately the (O I I), (1 I I), and (I I I) directions respectively, have been made. They show that the transition temperature are reduced, in agreement with the calculations A SPECIFIC HEAT STUDY OF Cs °2H O 2 4 2 IN A MAGNETIC FIELD MnCl By Norman Duane Love A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1967 ACKNOWLEDGMENTS I would like to express my appreciation to all of those people who have made this study possible, to my thesis advisor Dr. H. Forstat for his time, assistance and many fruitful discussions, to Dr. J. A. Cowen who allowed me to use two of his single crystals of CsZMnC14-2H20 and his unpublished susceptibility results, to Dr. R. D. Spence and Mr. John A. Casey for the use of their unpublished nmr results and their assistance in determining the crys- tal orientation, and to Mr. James N. McElearney whose programming made for accurate and fast data reduction by the computer and whose assistance with the experiments was invaluable. Acknowledgment is also made to the U.S. Air Force Office of Scientific Research for their support of this study. ii TABLE OF CONTENTS ACKNOWLEDGMENTS I. INTRODUCTION II. THEORY A. Thermodynamics of Specific Heats III. IV. . Magnetism . Magnetic Susceptibility for Antiferro- magnetism Transition Temperature Spin- flop EXPERIMENTAL APPARATUS AND PROCEDURE ’TIITUUOW> G. Helium Dewar . He4 Calorimeter He3 Calorimeter Electrical Measurement Apparatus Preparation of Sample Experimental Procedure Pre— cooling . Adding Exchange Gas Liquid- -Helium Transfer . . The Calibration of Sample Thermometer Specific Heat Measurements Voltage- Calibration Data Shut-down . . . . DMNH \IONU'I Data Reduction 1. Calibration of Thermometer 2. Voltage-Calbration 3. Specific-Heat Data RESULTS AND DISCUSSIONS A. B. Description of Crystal Zero-Field Results 111 Page ii \ILN 16 22 25 28 28 30 35 38 42 45 45 48 SO 51 54 SS 55 55 56 61 63 63 63 C. Magnetic-Field Results D. Phase Diagram. . . E. Conclusion REFERENCES APPENDIX I APPENDIX II iv Page 69 82 90 95 97 100 LIST OF TABLES TABLE Page 1. Temperature-Calibration—Curve Parameters from an Experiment made January 13, 1967. . 56 2. One-Millivolt-Voltage Calibration-Curve Parameters for an Experiment made January 13, 1967. . . . . . . . . . . . . . . . . . 59 3. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 2, September 16, 1966, Zero Field. . . . . . . . . . . . . . . . . . . 100 4. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 3, September 21, 1966, Zero Field. . . . . . . . . . . . . . . . . . . 102 5. The Specific Heat of CsZMnC14-2HZO for Sample 2, Run 1, October 5, 1966, Zero Field. . . . . . . . . . . . . . . . . . . 104 6. The Specific Heat of CsZMnCl4-2H20 for Sample 2, Run 2, October 17, 1966, Zero Field. . . . . . . . . . . . . . . . . . . 106 7. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 5, December 23, 1966, 8150 Gauss, Orientation A. . . . . . . . . . . . 107 8. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 6, January 12, 1967, 8150 Gauss, Orientation A. . . . . . . . . . . . 108 9. The Specific Heat of CsZMnC14-2H20 for Sample 1, Run 7, January 13, 1967, 5150 Gauss, Orientation A. . . . . . . . . . . . 110 V Table 10. 11. 12. 13. 14. 15. l6. l7. 18. 19. 20. The Specific Heat of CszMnCl4-2H20 for Sample 1, Run 8, January 18, 1967, 5150 Gauss, Orientation A. The Specific Heat of CszMnC14-2H20 for Sample 1, Run 9, January 20, 1967, 3500 Gauss, Orientation A. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 10, January 23, 1967, 3500 Gauss, Orientation A. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 12, February 11, 1967, 8400 Gauss, Orientation B. The Specific Heat of CsZMnC14'2HZO for Sample 1, Run 13, February 13, 1967, 8400 Gauss, Orientation B. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 14, February 16, 1967, 6050 Gauss, Orientation B. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 15, February 16, 1967, 6050 Gauss, Orientation B. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 16, March 1, 1967, 8400 ' Gauss, Orientation C. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 17, March 3, 1967, 8400 Gauss, Orientation C. The Specific Heat of CsZMnC14-2H20 for Sample 1, Run 18, March 18, 1967, 6050 Gauss, Orientation C. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 19, March 10, 1967, 9830 Gauss, Orientation C. vi Page 111 112 114 116 118 120 122 124 126 127 128 Table 21. 22. 23. 24. 25. 26. 27. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 20, March 14, 1967, 6050. Gauss, Orientation C. The Specific Heat of CsZMnCl4~2HZO for Sample 1, Run 21, March 22, 1967, 8900 Gauss, Orientation C. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 22, April 5, 1967, 9830 Gauss, Orientation C. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 23, April 5, 1967, 3500 Gauss, Orientation C. The Specific Heat of CsZMnC14°2HZO for Sample 1, Run 24, April 5, 1967, 8900 Gauss, Orientation C. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 25, April 7, 1967, 3500 Gauss, Orientation C. The Temperature Changes from an Adiabatic Magnetization Experiment on Sample 1, Orientation C, April 21, 1967. vii Page 129 131 132 133 134 135 136 FIGURE 1a. 1b. 10. 11. 12. 13. 14. LIST OF FIGURES Magnetization Curve Calculated from the Molecular-Field Theory. Shape of Specific Heat Curve Calculated from the Molecular-Field Theory The Susceptibility of an Antiferromagnetic Material as a Function of Temperature in Reduced Units A Magnetic Dewar. . Scale Drawing of Lower Portion of He4 Calorimeter Front and Side View of Top of He4 Calori— meter Photograph of Unassembled Calorimeter The Needle Valve. . . Schematic of He3 Calorimeter. Electrical-Measurement Circuit Diagrams A Photograph of Total System. Schematic Diagram of TOp of Dewar Sample Recorder Chart A Cross—Sectional View of CszMnC14-2HZO Perpendicular to the Elongated Axis with an Arrow Indicating the Direction of Easy Magnetization . . Specific Heat Curve in Zero Magnetic Field. viii Page 15 15 21 29 31 32 33 36 37 39 46 47 52 64 65 Figure 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. Sublattice Magnetization Curves Specific Heat 3500 Gauss. Specific Heat 5150 Gauss. Specific Heat 8150 Gauss. Specific Heat 6050 Gauss. Specific Heat 8400 Gauss. Specific Heat 3500 Gauss. Specific Heat 6050 Gauss. Specific Heat 8400 Gauss. Specific Heat 8900 Gauss. Specific Heat 9830 Gauss. Curve Curve Curve Curve Curve Curve Curve Curve Curve Curve for for for for for for for for for for Orientation Orientation Orientation Orientation Orientation Orientation Orientation Orientation Orientation Orientation EntrOpy Curves for Orientation A. Entropy Curves for Orientation B. Entropy Curves for Orientation C. EntrOpy, Field, and Temperature Surface for Orientation A. Entropy, Field, and Temperature Surface for Orientation B Entropy, Field, and Temperature Surface for Orientation C O o 0 ix and and and and and and and and and and Page 70 72 73 74 75 76 77 78 79 8O 81 83 84 85 86 87 88 Figure Page 32. Phase Diagram for Orientations A, B, and C. 89 33. Temperature vs. Angle from Easy Direction for an Adiabatic Rotation of a Constant External Magnetic Field of 8000 Gauss . . . 92 34. Circuit Diagram for a Simple Potentiometer. 98 LIST OF APPENDICES Page APPENDIX I . . . . . . . . . . . . . . . . . . . . . 97 APPENDIX 11. . . . . . . . . . . . . . . . . . . . . 100 xi I. INTRODUCTION Some nmr studies by Spence1 and susceptibility mea- surements by Cowen2 indicated an antiferromagnetic-para- magnetic transition at about 1.8°K in CszMnC14-2HZO. Since 1.8°K is easily attained by He4 calorimetry, a mea- sure of its specific heat in a zero magnetic field would be of interest and would provide a check on the transition temperature, and a comparison with the molecular-field theory for the sublattice magnetization and magnetic sus- ceptibility. After the zero-field study was completed, studies in an external magnetic field were begun. These studies show that the transition temperatures are reduced as the external magnetic field is increased, in agreement with the molecular-field theory. The magnetic phase dia- gram indicated which of the three crystal orientations is sufficiently close to having its sublattice magnetization direction parallel to the external magnetic-field direction. This study has three purposes: 1) to construct He4 and He3 calorimeters for use in specific heat measurements for the temperature range 0.4°-4.2°K, 2) to report the results of the specific heat study on CsZMnC14-2HZO in both zero and non-zero external fields, 3) to search for a possible spin—flop magnetic region by a calorimetric method. The study is divided into three sections. The first section describes the theories pertinent to the present study. Section two describes the apparatus and the step- by-step procedures for measuring the specific heat. The last section discusses the results, using the theories and equations developed in section one. It is hoped that the present study may provide suffi- cient information concerning the magnetic transition in Cs MnCl ~2H O, that additional problems which have been 2 4 2 raised from these experiments may be pursued fruitfully. II. THEORY A. Thermodynamics of Specific Heats?”4 When energy, as heat, is absorbed by a substance, a temperature change will be observed except for first-order phase transitions. The function which related this tem- perature change to the amount of heat absorbed by the sub- stance is called heat capacity or specific heat, if divided by the mass of the material. This can formally be written as d'Q = chT (1) where d'Q is an increment of heat measured in calories, dT is the change in temperature measured in Kelvin degrees, and CX is the heat capacity measured in calories/degree. The First Law of Thermodynamics, more commonly known as the conservation of energy, can be written for a revers- ible process as dU = d'Q - d'W. (2) The function U is the internal energy and dU is an exact differential, the reason for the absence of the apostrophe. d'Q has already been defined and d'W is d'W = PdV - HdM + other forms of work (3) where P is pressure, V is volume, M is magnetization, and H is the magnetic field. This study deals with solids at low temperatures, and dV will be essentially zero for all of the measurements. The Second Law of Thermodynamics defines another func- tion with an exact differential, called entrOpy, which can be used as a measure of a material's disorder. d'Q may now be written for a reversible process as d'Q = TdS Now the First Law becomes TdS = dU - HdM. Consider S and U functions of T and M only and write ds=§—%)dr+%—%)dM M ‘T and 8U 3U dU = ) dT + ——) dM BI M 8M T Substituting into equation (5), rig—g5.) dT + T%%) dM = 3%) dT + [31%) - H]dM M 1T M T But as) T—— = C . 3T M M Therefore EU) (3 =—— , M 3T M and (4) (5) (6) (7) (8) (9) (10) (11) Now consider S and M functions of H and T, and U a function of M and T. Using the results (10) and (11) write, as) as as) [3M) aM) ] T dT + T—— dH = C dT + T—— dT + ~— dH (12) ET H 3H T M 3M T 3T H 8H T But BS _ TEM)H — CH (13) then _ BS 8M CH - CM - Tgfi) 5T) . (14) T H Using Maxwell's equation, 3.3.1) = _) , (15) M T write 8H 3M C — C = -T——) ——- . (16) H M 3T M 8T H It follows that for low temperatures, CH z CM. From equa- tions (10) and (13), one may write, T 5(T1) - S(T2) = jr 2 CX/T dt (17) T1 where x is either M or H. Statistical mechanics defines entropy5 as the natural logarithm of the volume of phase space or of the total number of states available. If a mole of substance has a quantum number J then there are 2J + 1 states and AS = R in (2J + 1) (18) where AS = jr CX/T dt. (19) 0 Energy may be absorbed by a solid in a variety of ways,6 such as, through an increase in the oscillations of the atoms about their lattice sites (UL); an increase in the kinetic energy of the free electrons (Ue); by the presence of a magnetic exchange energy (UH); by the ex- citation of atoms (Us) and nuclei (Un) to higher energy levels. The internal energy can thus be written as a sum of terms, UT = UL + UH + Un + - - - (20) Therefore the specific heat of the solid may be written as, N _ L C‘—""a‘r“ 3U 3U T 8T EU “1 ) + §T_ + . . . (21) where the appropriate variables are kept fixed during the process. Consequently, CT = CL + CH + Cn + . . . (22) can be written and specific heats are additive. CL and CD need only be measured or calculataiand subtracted from CT to give CH’ B. Magnetism Magnetism has been a curiosity for centuries, as it revealed itself in the form of magnets called lodestones or magnetite. The formal study of magnetism did not begin until the beginning of the 17th century by Gilbert. It was not until the advent of quantum mechanics that a reason- able eXplanation for the origin of magnetism was forthcoming. It was first thought that magnetic effects could be explained on the basis that different paramagnetic ions coupled to- gether through a magnetic dipole-dipole interaction. For most substances this interaction is too weak to account for high internal fields observed, 100 gauss calculated, com— pared to 10,000 gauss measured. 8 Heisenberg7 suggested a quantum mechanical exchange interaction (between electrons of different paramagnetic ions) which gave internal fields of the order of those measured. Two atoms each with one unpaired electron in similar potentials are considered. They are labeled ”1” and "2" with coordinates r1 and r2. The Hamiltonian8 can be written as, 2 2 2 + VT(r1,r2,r12) (23) 1 - (fiz/ZM) v H(1,2) = -(fi2/2M) v where VT(r1,r2,r12) = V1(r1) + V2(r2) + V(r12) (24) and r12 is the radius vector between the electrons. Assume the electrons to be independent, then V(r12) = 0, and Hw(r1,r2) = ET w(r1.r2) (25) Equation (23) is then separable into, -(fi/2M)v12 wa(r1) + v1(r1) wa(r1) = E, w(r1) (26) -(fi/2M)v22 w8(r2) + v2(r2) (8(r2) = EB ((rz) (27) where 0a and we are the normalized wave functions of the separated equations and a and B designate the energy state. Thus there exist two possible solutions w(r1,r2) wacrl) (8(r2) (28) or ((r1,r20 = wa(r2) wB(r1) (29) to equation (25) with the same energy ET = Ea + EB' To keep the identical electrons indistinguishable when considering probability densities, two linear combinations, a symmetric wS and an anti-symmetric 0A, of the above solutions must be used, ws(rl,r2) = J—[waup 112802) + wa(r2) vamp] (30) V5 wACr1,r2) = éhaul) 428(1‘2) - VJQCI‘Z) $801)] (31) Spins have so far not been considered. All electrons have spin angular momentum i’fi/Z. Thus a magnetic field applied along the z-direction would orient the magnetic moment p2, with magnitude of one Bohr magneton, either parallel or antiparallel to this field. The Pauli princi- ple limits the total wave function for the electrons to be only anti-symmetric. Thus the two total wave functions including the spin wave functions (x) may be written as, $1 = BI ws[xa(l) XB(2) - xa(2) xB(1J] (32) xa(1) XBCZ) VII BII WA XGC1) XB(Z) + xa(2) xB(l) (33) xa(2) XB(1) where WI represents the singlet state and WIT represents the triplet state, and where B and BI are the normaliza- I I tion factors. Adding the interaction between the electrons V(r12) and applying first order perturbation theory the energies are, E = B 2(A + J ) (34) I I 12 12 and E = B 2(A - J ) (35) II II 12 12 where A12 =f‘4’a*(r1) wB*(r2) V(r12) Maul) ((1802) ch, ch, (36) 10 and (37) A12 is the average value of V(r12), and J is called the 12 exchange intergal. If J12 is positive the ground state is EII and the spins are parallel; but if J12 is negative, BI is the ground state and the spins are antiparallel. If this process is applied to an assembly of electrons in a solid, such as the 3d electrons in a transition element, and J12 is positive, the internal magnetic moments add and may be detected ex- ternally as a magnetic field. J12 being positive results in a mechanism for ferromagnetism. If J12 is negative, the spins are coupled antiparallel, and there is no external field possible; this is called antiferromagnetism. Néel9 and Van Vleck,10’ll’12 using two interpenetrating sublat- tices and the molecular field theory, calculated some pro- perties that characterized an antiferromagnet. It was not until the development of neutron diffraction techniques that antiferromagnetism was directly verified, completing the exchange interaction picture. In the above discussion on exchange, the interaction potential is assumed spin independent. But the spins are coupled with a scaler potential proportional to El - :2. Keeping only the spin—dependent part, the exchange energy may be written as, (38) 11 Considering two atoms which have more than one un- paired electron the exchange energy becomes, 3 . 3 (39) E = -2J 1 2 ex 12 where S is the total spin of the atom. All electrons are assumed to have the same exchange integral. If the exchange integral is assumed isotrOpic (Je) and is negligible except for nearest neighbors, then for all of the atoms in a crys— tal the exchange energy is t EeX = -2Je EEj 3i - §j (40) The summation is taken over all of the atoms in the crystal. The prime means i = j is not included. Solving this Hamiltonian should give the properties of magnetism. This has not been possible without making 13,14,15 method further assumptions. The Bethe-Peierls-Weiss assumes a model where a central atom and its interaction with its nearest neighbors is calculated from (40) but the nearest neighbors are assumed to interact with an internal field due to their neighbors. Instead, if the assumption is made that the interac- tion 2Je(S .S .) may be neglected, where Sx’ S .+SS 9 X1 X3 Yl YJ Y and 52 are the components of S, the exchange energy is then written as, E = -2Je .21 s . - s . (41) The above assumption amounts to replacing the instantaneous 12 spin values with their time averages and is called the Ising16 model. There is an extensive literature on the 17,18 calculations made with the Ising model, but these will not be discussed here. 10 Following Van Vleck, the quantum mechanical justi- fication will be made for the Weiss19 molecular-field ap- proximation. Since the interactions are only for the z nearest neighbors, 2 E = 4.18: s.zi . n2 s (42) Z E = 1382 szi - (Ne/gs) Z 3'21, (43) 1 n=1 where g is the gyromagnetic ratio, 8 is the Bohr magneton, and gzn is the average of the neighboring spin. An inter- nal field Hi may be defined, 2 __.. Hi = (Ne/gang1 szn (44) Then, BeX = -g8 gjszi - Hi (45) The magnetization of a specimen with N atoms is M = NgBS (46) Thus Hi = (ZJez/NgZBZ)M = )M (47) where X is Weiss' molecular-field constant. 13 The problem of magnetism has now been reduced to solv- ing for the case of N independent atoms with a permanent moment (gBS) in an applied magnetic field H. According to statistical mechanics the magnetization is, M = N S -S S (48) ZIe-gBSH/kT -S where k is Boltzmann's constant, and S is the spin. Let x = gBH/kT and using the formula for the sum of the geo- metric progression, the reduced equation becomes, M = NgBS Bs(y) (49) where _ ZS + 1 ZS + l 1 1 and is called the Brillouin function, and y = (gBS/kT)H (51) Substituting Hi for H in (49), (50), and (51) gives the solution for the magnetization of a ferromagnet. The sublattice magnetization for an antiferromagnet is found in a similar matter. Divide the lattice into two interpenetrating sublattices such that the next nearest neighbors of an atom in sublattice, a, all lie in sublat- tice, b, and vice versa. The molecular field acting on an atom at site, a, is 14 Hia = yMb (52) and the molecular field acting on an atom at site, b, is Hib = yMa (53) where y corresponds to the Weiss molecular—field constant and is assumed to be the same for both sublattices; but a distinction is made with A for the ferromagnetic case, since now only one-half of the atoms contribute to each of the molecular fields. If [Mal = IMbI = [MOI and M3 = -Mb then, M0 = M5 Bs(y) (54) and y = (ng/kT)YMO (55) where M5 = ENgBS. The 8 appears because each sublattice contains only half the atoms. The solution for M0 is found by solving equations (54) and (55) graphically. The curve in Figure la shows the reduced magnetization Mo/Ms as a function of the reduced temperature T/Tn for S = 5/2 and TH is the Néel temperature about which more will be said later. Since, 8X 1 . YMO (56) E = -gBZSZ. 1 then __ 2 Eex — 2yMO (57) where M0 = ENgBS and S is the average spin. ' 15 WM, 1.0 0.0 - 0.6 - 0.4 - 0.2 - __ I ' 111;, 0 0.2 0.4 0.6 0.8 1.0 Fig. la. Magnetization Curve Calculated from the . Molecular-Field Theory. Tn: awn/MM Tl ' F 3.0 *- #- 2.0 |.0 To Content Value of 4.7-9 0 0.2 0.4 0.6 ‘ 0.0 l.0 ' . Fig. 1b. Shape of Specific Heat Curve Calculated from the Molecular-Field Theory. 16 Now, c = ex ~ M ——9 (58) where CH is the magnetic specific heat. Since MO was deter- mined graphically, equation (58) will have to be solved numerically. Figure 1b shows the curve which is pr0por- tional to the specific heat calculated from equation (58) using points on Figure la. C. Magnetic Susceptibility for Antiferromagnetism The susceptibility curve is separated into parts by the Néel temperature, i.e. the region above the Néel tempera- ture which is the normal paramagnetic state, and the region below the Néel temperature which is the antiferromagnetic state. All the calculations are based on the molecular— field theory and follow the method outlined in the text by Morrish.20 For temperature well above the Néel temperature there are no exchange forces and thus no molecular—field. If a small external field is applied at high enough temperatures, only the first term in the expansion of the Brillouin func- tion need be considered for the calculation of the suscepti— bility. The expansion of the Brillouin function is, Bs(y) = gig—l y + % B;"(0)y3 + . - . (59) where B"'(0) = —6(S + 1)[(s + 1)2 + 521/9053 (60) 17 Now, 7 = (gBS/kT)Hex (61) where Hex is the external field instead of the internal molecular-field. M may be written using the first term of (59), Hex] (62) M . Ngssg _S_S + 1 (2%.; Then 2 2 _ = Ng B S(S + 1) X _ M/Hex 3k 1 C T) = r (63) where C is the Curie constant. Equation (63) is called the Curie Law. For temperatures near the Néel temperature Ma and Mb must be considered since there is usually some short range ordering. Now, :1: u Ta Hex I YMa (64) and H = H - yM Tb ex (65) b and notice that the magnetization vectors are both in the direction of the applied field because of the absense of the long range exchange forces. Again using the first term of the expansion of the Brillouin function and the total magnetization M, as the sum of the two sublattices magneti- zations, write, M = NgBS(S + 1 2 3s $%%[2 Hex ' Y(Ma + Mb)] (66) 18 M = % C/T(2 Hex - yM) (67) Cy C Hex M(1 + 7T) --—ar—— (68) x = T E e (69) where 0 = %CY (70) Equation (69) is the Curie-Weiss Law and 0 will turn out to be the Néel temperature. Below the Néel temperature two cases must be con— sidered, the case with external field parallel to the sub- lattice magnetization and the case with the external field perpendicular to the sublattice magnetization. Consider the parallel case first. Now the internal field will in- clude the external and molecular fields; and, y, (g68/kT)(H + yMb) (71) and yb (gBS/kT)(-H + yMa) (72) At H = 0, Ma = rMb = M0’ and ya = -yb = yo. Now expand the Brillouin function about yO and keep only first order terms, Bs(yo) = Bs(yo) + B;(yo)[H+-Y(Mb - M04 3%; (73) and BSCYb) = BSO’O) - B;(YO) [11+ HMO - 143)] $183? (74) _ ' BS BSO'a) - BS(YO) - BSCYO) [-H - YCMb - 140di 19 l where Bs(y0) is the derivative of the Brillouin function with respect to its argument. Now Ma and Mb are computed from equation (54) and M the total magnetization is M = M8 - Mb (75) Thus, M = 6.6.6.) (H + 6. - M.) + (6 + m. - M.) as] (76) 1 N 28282 ' M = 2 _g_RT__ B5(yo)[2H - YM] (77) Ng262526;(y0) X = 1 2 Z 1 (78) ” kT + 7Ng B s Bs(yo)v ! Now Bs(yo) goes to zero exponentially as T goes to O; and since x = Ngzezsz. , (79) // gNgzszszY+ kT BSCYO) then X / goes to zero as T goes to zero. / The applied field when perpendicular to the sublattice magnetization will cause each of the magnetization vectors to rotate through a small angle 0. At equilibrium the torque on the sublattice magnetization must be zero, therefore, + YMb)| = 0 (80) or sin 26 = 0 (81) MaH cos 0 - yMaMb 20 2Mb sin 0 = H/y (82) and since M3 = Mb then M = (M8 + Mb) sin ¢ = 2Mb sin ¢ (83) Thus, XL = 1/Y (84) Figure 2 shows the qualitative plot of the susceptibility for an antiferromagnetic material. Fisher21 has also worked out a relationship between the parallel susceptibility and the specific heat. He calculates, CM(T) 2 2R f(l — %0)5%I}TX//)/(TX//)w] (85) where f is a slowly varying function of T and is equated to 1, a is a measure of the anisotrOpy of the interaction (equal to zero for pure isotr0pic interactions), 0 is T/Tn’ and (TXHQm is the value of (TX//) extrapolated to high tempera- tures. Assuming an isotropic interaction, T 3(TX//) __ 11 CM ‘ 2R(TX/l)oo aT (86) is the form of Fisher's equation which may be used to com- pare the zero field specific heat with the parallel sus- ceptibility. 21 .muficz wouspom :H oASHmhomEoH mo :ofluoesm m mm Hmfluopmz oflposmmEOHpowfiuc< cm mo xuflafinfipmoomsm one .N .wflm 0.0 o . 0. a»: p) '0. o ESE» 22 D. Transition Temperatures As Figure 1a shows, the sublattice magnetization drops to zero at some transition temperature Tn, commonly called the Néel temperature to distinguish it from the Curie tem- perature for a ferromagnet. This value of Tn can be cal- culated by expanding Bs(y) in powers of y, equation (59); then allowing M0 to approach zero, which means that T goes to Tn and y becomes small, so that in the first approximation one may write, w. = at g 1),, 66 Now combining equations (55), (87), and the definition for M , one obtains, s NngZS(S + 1) -1 _l Tn ‘ 2 3k Y ‘ ZCY (88) This result neglects any external field. Comparing the calculated specific heat curve in Figure 1b with the zero field measured curve in Figure 14 indicates that the molecular-field theory can only give qualitative results. The following discussion will consider the case for H ¥ 0, and its effect on the transition temperature. The 12 method of Kubo will be used, although several calcula- tions, using other methods, have been performed. These have 22 been, (1) calculations of the phase diagram by Gorter, who used the molecular-field theory to find the Gibb's energy, 23 (2) the calculations by Garrett who obtained a graphical solution for the field parallel to the magnetization using 23 using the molecular-field theory, (3) the method used by Temperley24 to calculate a phase diagram for pure dipole 25 to calculate interactions, and (4) the technique of Callen the phase diagram using spin waves with a Green's function method. The transition temperature for the case of the applied field, parallel to the magnetization direction will be cal- culated first. To do this, one starts with, M8 = M5 Bs(ya). (89) Mb = MS Bs(yb), (90) ya = (gBS/kT)(H - YMb), (91) and yb = (gBS/kT)(H + yMa) (92) where the field is the total field and Ma is parallal and Mb is antiparallel to the applied field H. As the tempera- ture is raised Mb first decreases in magnitude, becoming zero, then it becomes parallel to H and finally coincides with Ma' The temperature at which this occurs will be de- noted by Tn(H). Now writing from (92), (aMa/ayb) = (kT/gBS)Y (93) H and from (89), (ama/aya)H = MS 5%; [65(yafl (94) 24 The slopes in (93) and (94) become equal as T approaches Tn(H) in (93) and as Mb+Ma which become zero as T goes to Tn(O) in (94). Now expanding the Brillouin function, ne- glecting all terms of yMa and powers of H/T greater than 3, the combination of (93) and (94) may be written as, k T (H) 2 2 2 2 n _ 1 s + 1 3 '*' s s H 2 k Tn (O) (95) Now, 2 2 2 ,,, 2 2 2 2 we— HTS”) (21.)) n (96) Applying the definition of C, equation (63), (96) reduces to, 4 4 4 2 _ 1 + 1 "' N a s H TncH) - :- Cv z B. (0) i123— (T1803) (97) Multiplying and dividing the last term on the right by C3 one gets, 3 3 2 _ 1 1 "' 3 C Sy H T (H) — — Cy + — B (O) _ n 2 4 s (S + 1)3NZg282 Tn(0)) (98) 3 3 2 1 1 "' 3S yC H = — Cy + — B (0) —— 2 4 s (S + 1) NzngZSZ Tn(0)) (99) 3 yo 3 _ 1 1 "' 35 3 (2‘) 2 H 2 Y Tn(0) (100) 25 Applying the definition of Tn(O) and vi the final result is 2 2 T (H) - T (0) 3 x H n n _ 1 "' 38 _L Tn(O) "'2 Bs (0)(s—:_TJ ‘;;7r‘ (101) S Kubo goes on to do a calculation for the case of the field perpendicular to the direction of magnetization. He gets results similar to those for the parallel case (101), Tn(H) - Tn(O) Tn (9) -1

X// when T evacuation line / Solder joint (ii'i'allay) Epoxy halt ahaild atd terminal block no at 92V container ... § 1w \I' ‘7 P Hf .— I Elatrleei leede / Sample with heater and thermometer A\\\\— a .F I an”). holder / .......__.J L Inner calorimeter can h- somr Joint (In elm) Fig. 4. Scale Drawing of Lower Portion of He4 Calorimeter. 5:. D 0 0 ’e'e’ ’ O 0 O 0 0 ' O O 0 O O 0 0 0" O C ' 0.9%.? ".A.A.A‘ V "4 e s, 0.0 32 Biol" 314' a- 32 stainleee areal ~ I Allen head ecreue\ s\\ \s tieat 'aaeild ‘ «7 K) éA c23;.n N/ r M am m" 4.40 Allen need eareue Fig. 5. Front and Side View of Top of He4 Calorimeter. 33 Fig. 6.—-Photograph of Unassembled Calorimeter. 34 All evacuation lines in contact with room temperature must have some means of trapping the radiation flowing down them. This was achieved by having the lines turn right angle corners in the outer liquid helium bath where the radiation is absorbed. Any reflected radiation is reduced by radiation shields at the mouth of the outer can evacua- tion line, and the calorimeter can evacuation line. The bottom of the outer can is removable to allow the calorimeter can to be centered while it is being soldered into place. Once this has been determined the outer can is tightened, the nylon spacer is positioned, and the bottom is soldered into place. The outer can and its evacuation line are sealed by lead o-rings. ~Care must be taken to tighten the o-rings uniformly. When the o-ring grooves, which are little more than a scratch, were machined, a deeper groove of the same diameter was cut into a die. A three ampere Buss Fuse Wire is laid in the groove on the die and is cut to fill the groove. A low flame of an oxygen-gas torch is passed over the junction of the ends until they fuse to make an o-ring. A proficiency of nearly 70 percent in making good o-rings can be achieved with practice. The fourteen formex coated 0.0031—inch diameter manga- nin electrical leads enter by means of kovar seals mounted in flanges sealed by rubber o-rings at the top of the system. They extend down the calorimeter evacuation line inside a length of teflon Spaghetti, and make a twist around the tip 35 of the He4 container. A small amount of G. E. #1202 varnish is applied to hold them in place and to make good thermal contact with this temperature. Eight of the leads go to one side of the epoxy therminal block. Four leads go to the 56 ohm, 1/10 watt Allen-Bradley resistor used as a bath thermometer. The resistor is glued into a hole cut in the tip of the He4 container with G. E. #1202 varnish. The re- maining two leads go to the 120 ohm, l/lO watt Allen-Bradley resistor used as the bath heater which is glued into a similar hole. Since the needle valve is a critical part of the sys— tem, Figure 7 shows the working parts. It allows liquid helium to be drawn into the innerHe4 container. The needle valve must be closed, isolating the inner He4 container from the outer dewar. The smallest leak through this valve in- creases the lowest temperature that could be attained. C. He3 Calorimeter The advantage of using liquid He3 is that temperatures as low as O.4°K can easily be attained as compared to l°K for He4. Figure 8 shows a schematic of a He3 calorimeter used for one of the zero field experiments. It is similar to the He4 calorimeter except that the He3 section is com- pletely isolated from the He4. It also has an additional line for measuring the He3 vapor pressure. All removable cans are soldered using Cerrolow 117 alloy. The electrical leads enter the system at the t0p by means of a kovar seal, reaching the interior of the outer can by means of its Ia-l/4'-I| Stainloee . Scale ' Stool ouran can evacumou —--—"'—*‘ L'NE ‘—'.==I: ll? OOLDER JOINT H ...—i IIJJII L] fi—OUTER CAN muen cALonmsran evacunriou LINE ~~e , vnpon ancaaunl f ruanuoue'rzn m3 couumnn 9 ii? SOLDII JOINT L iuuen cALonmarcn ~~4~ “up“ 1 aurmuu-euaa 4f out titaotoan JOINT 1 Fig. 8. Schematic of He3 Calorimeter. 38 evacuation line. Any thermal conduction down these leads is minimized by having the leads make good thermal contact to the liquid He4 bath, and then to the liquid He3 bath. The leads enter the calorimeter through the bottom by means of a platinum-glass seal. These seals are made from ten 0.010-inch diameter platinum wires about six inches long, a %-inch diameter tubing, and soft-glass tubing. The platinum tube has one end feathered, i.e. a very sharply ground edge. The fea- thered end of the platinum tube is fused to the soft glass tubing. Each platinum wire is individually fused inside two inches of glass capillary tubing, and the ten are fused together. This bundle is fused inside the glass of the glass-platinum tube. If constructed pr0per1y with the pro- per glass, these seals are He II tight. Any well equipped glass blower can produce these seals. It has later been 28 method of sealing manganin discovered that Wheatley's wires inside metallic tubing using epoxy is also satisfac- tory at He II temperatures. D. Electrical Measurement Apparatus The four separate circuits which are used to make the specific heat measurements are the bath heater, the bath thermometer, the sample thermometer, and the sample heater. The sample thermometer and sample heater circuits are dia- grammed in Figure 9. There are three boxes labeled "Pot." Two of them are Leeds and Northrup K-3 potentiometers, and the one across R is a Leeds and Northrup K-Z potentiometer. I: (f Pot. A ‘0‘ ' 39 THERMOM ETER CIRCUIT .6 A Rafi Thermometer R p 0. C. Ampl. Recorder T Vt I ._...I POI. _‘_..... 60V. HEATER CIRCUIT I IHeoter RH -—— .. 69E -0t Pot. *l'l'l'l'l — .1—d D. c. Ampi. — Precision i l T Iooofi Recorder Recorder ““i Fig. 9. Electrical-Measurement Circuit Diagrams. 40 The "D. C. Ampl.” boxes are Leeds and Northrup D. C. Vol- tage Amplifiers. The two boxes marked "Recorders" which connect to the D. C. amplifiers represent a single variable range card, Leeds and Northrup 2-pen Speedomax G recorder. The remaining recorder is a Leeds and Northrup single pen Speedomax G recorder. ”Gav." is a Leeds and Northrup box type galvanometer. The precision resistors are all manu- factured by General Radio. The bath heater is the simplest of the four circuits. It consists of a 120 ohm, 1/10 watt Allen-Bradley resistor in series with a 10,000 ohm rheostat. These are across a 0-115 volt Variac. The a. c. heater current is controlled by both the rheostat and the Variac. The voltage measurement across the bath thermometer is identical to the one shown in Figure 9. Since the bath thermometer is used only for control, the precise tempera- ture is not required and the tolerances on the current supply need not be so stringent. A transistorized constant current supply is used and will not be discussed since it is not pertinent to the experiment. The bath thermometer, supplied with a current of ten microamperes, gives adequate sensiti- vity for a 56 ohm, 1/10 watt Allen-Bradley resistor. In the sample thermometer circuit VT is a pair of Mallory 28 volt mercury batteries connected in series, RA is a 50 megohm resistor in series with a 10 megohm variable resistor for adjusting the current, and Rp is a 0.1 megohm precision resistor with a tolerance of 0.01 percent. The galvanometer will read null when the potentiometer across 41 Rp is set for 0.1 volt and RA is adjusted to allow one mi- croampere of current to flow through the circuit. The current is monitored continually and can be kept constant manually. However, adjustments were found unnecessary be- cause the thermometer resistance changes were small compared to RA' The multiplying scale factor of the D. C. amplifier, the range of the recorder, and the thermometer current all determine the sensitivity of the recorder in measuring the emf across the thermometer. The range of each pen in the 2-pen recorder can be changed to 10, 5, or 1 millivolt full scale with zero left by using different range cards. The thermometer current cannot be adjusted freely since the greater the current the more power dissipated by the ther- mometer. It is set to give the maximum tolerable power, and any further sensitivity increases must be attained electronically. The heater voltage is measured by the same techniques applied to determine the thermometer voltage. A recorder measures the voltage across a precision resistor which de- termines the heater current. Several different precision resistors are available to keep the voltage within the range of the recorder. The heater current is controlled by vary- ing a resistor in series with the heater (RV in Figure 9) and by adjusting the voltage through the number of cells selected from the battery SUpply. When switch A makes con- tact to the right, current is bypassed through RH’ the substitute heater which has the same resistance as the heater. 42 The current is allowed to pass through the heater when switch A makes contact to the left. At the same time switch C is closed allowing the potentiometer to monitor the heater voltage. A timer operates both switches and measures the time that current flows through the heater for energy mea- surements. The timer can be programmed either to shut off after a predetermined time or to be stopped manually. The use of the substitute heater for balancing purposes is to eliminate a pulse of unknown current in the heater due to the unbalance of the measuring recorder. The heater circuit potentiometer is also used, by appropriate switching, to measure the bath thermometer voltage, voltage across a pre- cision resistor in either the bath circuit or in the heater circuit, or across any external potential. B. Preparation of Sample There are six steps in the preparation of a sample for an experimental run: 1) the selection of a single cry- stal of adequate size, 2) deciding on the proper resistor to be used for the thermometer, 3) connecting manganin leads to the thermometer and the heater, 4) gluing the heater and the thermometer to the crystal, 5) mounting the sample in its holder, and 6) orientating the crystal in the field. CszMnCl4°2HZO crystals were grown from an aqueous solution at room temperature of a mixture of CsCl2 and MnClZ-ZH O.* Two crystals about one inch long and 0.25 cm.2 2 in cross section area weighing about one gram each were used. it Crystals were kindly SUpplied by Professor J. Cowen. 43 The resistance thermometer selected will depend upon the temperature range to be covered. A 10 ohm, 1/10 watt carbon Ohmite resistorgives the best results for He3 tem- peratures and a 56 ohm, 1/10 watt carbon Allen-Bradley resistor works best for He4 temperatures. The plastic coat- ing on these resistors were not removed, since no problems with thermal equilibrium were noticed previously and the carbon would have to be recoated to prevent the absorption of gas. The sample heater consists of twelve inches (about 450 ohms) of enamel coated Evenohm* wire 0.0014 inch in dia- meter. About one-half inch of the insulation is stripped from both ends of the heater and the ends are tinned using regular solder with a resin core. Eight formex coated man- ganin wires about six inches long (approximately 15 ohms) and 0.0031 inch in diameter are used as leads. They also have their ends stripped and tinned. Two manganin leads are joined to each side of the heater and two leads are soldered as close as physically possible to each side of the thermometer resistor. The excess terminal wire on the thermometer is cut off. The pairs of leads on each side of the heater and the thermometer are wound around a nail to form a coil of about one—quarter inch in diameter. On both the heater and the thermometer two leads provide current flow and two leads allow the voltage to be measured. After the surfaces have been coated with G. E. var- nish #1202, the twelve inches of heater wire are woundas *Trade name for wire supplied by Wilber B. Driver Co., Newark, N.J. 44 non-inductively as possible around the crystal. The ther- mometer is tied to a smooth face of the crystal by means of a nylon thread and is covered by a drop of varnish for better thermal contact. A C—shaped holder (see Figure 4) is made from one— quarter inch german-silver tubing pressed into a metal strip. A nylon thread is looped through two small holes at the top and at the bottom, so that there are two parallel lines across the opening of the holder. The crystal is placed between these threads and held in place by an appli- cation of varnish. The tip of a small brass tack wedged between the loop of thread and the bottom of the holder pulls the sample rigid. A larger hole is drilled in the top to mount the holder to the tip of the inner helium con- tainer. The holder can be rotated about the mounting screw and all orientations of the crystal around this axis of rotation are possible. The crystal is now orientated with respect to the field. The calorimeter system without the outer or inner calorimeter cans is positioned in the dewar. By use of a flashlight and the slit in the dewar, one of the previously placed marks on the epoxy terminal block is chosen to be normal to the magnetic field. The calorimeter system is then removed from the dewar and the chosen fiducial mark is then used to place two other similar indices on the epoxy, such that a line drawn through them is parallel to the field. The orientation of the crystal is made using these two latter 45 indices. It is estimated that there is an error of ap- proximately 5° in this orientation technique. After the above steps have been completed, the leads are soldered to the terminal block, which in turn connect them to the outside through the kovar seals at the top of the system. F. Experimental Procedure After the system has been prepared, the following is the step-by-step procedure necessary for taking data. Figure 10 shows a photograph of the total assembled system. For the name of pumps and valves etc. refer to Figure 11. l. Pre-Cooling.--At least six hours before the trans- fer of liquid helium the outer dewar should be filled, and kept filled with liquid nitrogen. In preparation for this, evacuate the vacuum jacket of the inner dewar for about twenty minutes. In the meantime valve C is closed and the needle valve is opened. Just before the transfer of liquid nitrogen the inside of the dewar is evacuated with the large two inch Kinney pump (pump Y). The inner container is then flushed with helium gas and re-evacuated but care must be taken since pyrex glass is porous to helium gas at room temperature. With pump Y still pumping on the inner dewar, liquid nitrogen is added to the outer container. Shortly after the liquid nitrogen has been transferred, pump Y is closed off and helium gas is added to the inner dewar to act as an exchange gas. This helium gas also keeps liquid oxygen from condensing and frost from clouding the 46 10.--A Photograph of Total System. Fig. a I t . J 4 I Is. ‘i I . I .I I i 0.) .0 V“ on. 47 n I c r r 0 u .... m. m baton 3:... .m M a C m o>_o> r C n m 0 T I 00.69 co. I l < 621m Eaaoo> :2: o... o>_u> W. F: mm > 255 B. an n." . Tc \335252 c... o o>_o> . > 955 0... Sn... 23.. 32.36 .23. Schematic Diagram of Top of Dewar. . 11. F1 48 inner dewar. The largest decrease in pressure of the helium gas due to its cooling occurs during the first hour after it has been added. From then on a three pound per square inch over-pressure will last twelve hours or longer. Valves A and B are closed before or soon after the liquid nitrogen has been transferred. 2. Adding Exchange Gas.--Sometime before the transfer of liquid helium, helium gas for heat exchange must be added to the calorimeter and outer cans. This should be done after the six-hour pre—cooling period, since the calorimeter will be evacuated and if the crystal is not cold enough it may be damaged. Valves A and B are opened to evacuate the cans. After twenty minutes the ion gauge should read about 5 x 10'4 millimeters of mercury; if not, a possibility of leaks in the seals or solder joints may be suspected. If there are no leaks, valves A and B are closed and the pump- ing line is flushed and filled with helium gas slightly above one millimeter of mercury. The pressure should read one millimeter of mercury after the opening of valves A and B. If the pressure is too high carefully pump it down, if it is too low add more helium gas in the same manner as above. Once the desired pressure is obtained valves A and B are closed and the pumping line is evacuated. The system is now ready for the transfer of the liquid helium. 3. Liquid-Helium Transfer.--The needle valve is closed and the vent of the liquid helium dewar is connected to the 49 recovery system by means of a hose. A rubber hose through which there is a slight flow of helium gas is connected to the pressurizing port of the transfer tube. The liquid helium storage container is moved into position and the transfer tube is lowered simultaneously into the storage container and dewar. The transfer tube is sealed from the atmOSphere and pressure is applied to the surface of the liquid helium in the storage container by means of helium gas through the transfer tube's pressurizing port. Liquid helium will be forced over into the dewar and any vapor from the boiling due to the "warm" system is vented and recovered. The liquid level is watched for, using the observa- tion slit and a flashlight. When the level reaches the desired height the pressurizing gas is shut off and the transfer tube is removed. The container is sealed. If the system has been pre-cooled sufficiently a transfer of about six to seven liters will result. The bath thermometer is watched and when its resis- tance has come to equilibrium at a value about ten times its room temperature resistance open the needle valve filling the inner He4 container. Valve B is Opened to evacuate the outer can of exchange gas allowing the isolation of the inner He4 container thermally from the outer bath. The electromagnet is turned on and the field is ad- justed to the desired value. When the sample thermometer comes to equilibrium the first temperature calibration point is taken. 50 4. The Calibration of Sample Thermometer.—-The ther- mometer resistance is calibrated against the helium vapor pressure whose temperatures are listed in the T58 liquid 29 After the thermometer has helium vapor pressure table. come to equilibrium the thermometer resistance, the mercury manometer readings, room temperatures, and height of liquid helium above the sample's position are recorded. The room temperature reading and height of liquid helium are unnec- cessary below the l—point. The needle valve is closed and valve C is opened. Immediately begin to slowly pump on the inner He4 container with pump Y. The pumping speed is manually adjusted by opening and closing a valve, not shown, in the pumping line of Y. The vapor pressure is reduced ten centimeters on the mercury manometer and is manually held at this pressure by watching the bath thermometer and the manometer. This pres- sure is kept constant until the sample thermometer achieves an equilibrium resistance. This takes several minutes at the beginning and up to three quarters of an hour for the final calibration points. The thermometer equilibrium re- sistance and the vapor pressure are recorded. Continue to lower the pressure in ten centimeter steps until four centimeters pressure remain. This calibration point is re— corded and then the oil manometer is connected to the system. This manometer is subsequently used for observing the pres- sure as the pumping valve is adjusted. Below 2.5 centi- meters of mercury, the vapor pressure is read from the McLeod gauge. Continue to pump down in steps of ten centimeters 51 on the oil manometer. This procedure is maintained until all valves are open to pump Y and the lowest possible pres- sure is attained. This will give a temperature of approxi- mately 1°K. Since carbon resistors are used for the thermometers a temperature calibration must be made every time a resistor has had its temperature changed by approximately 20°K. Al- though it has been discovered that a magnetic field as high as 10,000 gauss does not change the temperature calibration within the tolerances of this study. 5. Specific Heat Measurements.--After recording the final temperature calibration point, the bath thermometer is turned off, valve B is closed, and valve A is opened evacuating the calorimeter of exchange gas and thermally isolating the sample. After five minutes the ion gauge should read approximately 10.5 millimeters of mercury and specific heat data can be taken. The sample can never be completely isolated from its surroundings for there are always heat leaks due to radiation, and to thermal conduction along elec- trical leads and nylon threads. These heat leaks constitute the ”background." Since it is not always possible to eliminate the back- ground, some means must be established to measure it or subtract off its heat. A method of subtracting off the background heat is described using the lettered points in Figure 12. The figure shows how a portion of a recorder chart would appear. The 52 Fig. 12. Sample Recorder Chart. 53 lines AB and CD represent the change in resistance due to the background heating. The slopes of these lines can be altered by changing the pumping Speed of the bath or by supplying power to the bath heater which changes the tem— perature surrounding the sample. The 510pe of line BC is due to the background heat and the power added to the cry- stal by the sample heater. The resistance change resulting from the background heat while the sample heater was on can be eliminated in the following manner. Line EF is con— structed midway between points B and C. Lines AB and CD are extended to cross EF. Ds and De represent the resis— tance change due only to the power put into the sample by this heater. The line segment B'DS represents the resis- tance change from the background on first half of heating cycle and DeC' is the resistance change from the background of final half of heating cycle. If the change in the tem- perature of the sample during the heating cycle is small compared to the temperature difference between the sample and its surroundings then B'DS and DeC' are equal. This is usually the case and it is preferred since no assumption is made as to where the background slope changed. These lines are drawn and D5, De’ heater current, heater voltage, and the time that the current flowed through the heater are recorded for each point as the experiment pro- gresses. A specially constructed apron for the recorder, facilitates the drawing of the lines. Before any specific heat data are taken the background heating of the sample is adjusted. When at the desired level 54 the potentiometer setting is changed to move the pen of the recorder to the extreme left. Here the resistance is re- corded. This resistance corresponds to the thermometer resistance at the null position. This resistance is noted whenever the pen is moved from the extreme right to the ex- treme left of the recorder chart. This process is continued until the highest temperature desired is attained. Since the specific heat of the sample may change, the difference between Ds and D8 will change. To obtain minimum scatter in specific heat points the heater current should be adjusted to maintain this difference greater than ten chart divisions in 20 to 30 seconds of heating. 6. Voltage-Calibration Data.- -Voltage calibration data are also taken while the specific heat points are being recorded. When the pen of the recorder reaches the right of the chart (Dr) due to the increase in temperature, the potentiometer setting is changed and the recorder pen moves back to the left (D1), see Figure 12. Two potentiometer settings, in terms of resistances, and the pen position, in chart divisions are recorded. Since neither the change in potentiometer setting nor the pen's movement can be in- stantaneous the slopes of the background heating are extra- polated to give the positions of the pen for an instantaneous movement across the chart. Continue taking this data until the last specific heat point has been recorded. The pen is moved to the left and the final voltage calibration point is taken. 55 7. Shut-down.--By the time the final point has been recorded pump Y may have been closed off and the system vented. To begin shut down, pump Y'is opened to both outer and inner helium baths by opening the needle valve. Valve B is reopened and the diffusion pump on the high vacuum system is turned off allowing the cooling water and forepump to run. All electrical measuring equipment is switched off. Liquid nitrogen is maintained in the outer dewar until it is certain all of the liquid helium has been evaporated. When there is no more liquid helium in the inner dewar, pump Y is shut off, and the outer can, inner calorimeter can, and inner dewar are vented with dry nitrogen gas. When the diffusion pump is cold the forepump and cooling water are turned off. G. Data Reduction 1. Calibration of Thermometer.--The T58 liquid helium vapor-pressure table lists all of the vapor pressures in microns of mercury at 0°C. The mercury-manometer reading must be normalized from room temperature to 0°C. This cor- rection is unnecessary for the McLeod gauge. The vapor pressure must be corrected for the height of liquid helium above the level of the sample. Below the X-point this correction becomes unnecessary, because He II has a very high thermal conductivity and the temperature is uniform throughout the liquid. The calibration temperatures and their corresponding 30 resistances are fitted to the two parameter Clement—Quinnell equation, 56 1/2 [£9%—3] = a + b log R (116) by the method of least squares. The relative deviations from this curve are then fitted by the method of least squares to a sixth-degree polynomial, [log R]1/2 _ [log R]1/2 T meas. T calc. Cn(log R)n (117) 172 I :5 II 0‘ o 01 log R T meas . where the Cn's are arbitrary constants. The temperature is calculated from the resistance by combining the parameters of these two fitted equations into the following, —2 T = log R a + b 10g R (118) Cn(log R)n P10» no Table 1 shows the temperature calibration, curve fitting results for an eXperiment made January 13, 1967. The maximum deviation is about ten millidegrees at the higher temperatures. This deviation becomes smaller for lower tem- peratures. Temperature changes of the order of one milli- degree or less can be detected but the actual temperature is known only to ten millidegrees. 2. Voltage-Calibration.--The voltage calibration or the volts-per-division data is needed to calculate the ther- mometer resistance (Rt) from the potentiometer reading, when the recorder pen is not at the null position. When the 57 oaao.o- om.o- omewH.H oaewfi.fi o.ooo.om aaao.o OH.H OHN0¢.H o~moe.a N.OHO.OH aoeo.o- ow.o- ooa0k.H oweoa.a o.mmm.m mNHo.o- am.o- soamm.a oeamw.fi a.mom.a mmao.o- mm.fi- meofio.N oaeao.~ a.mam.m ANAH.O mk.e awmma.m ooama.~ o.wmm.a Hooa.o NH.m wm¢HH.m oawfia.m o.maa.a maca.o- ao.m- HNHNa.m oomaa.m N.oea mea.o- mm.s- memao.m omwmo.m o.osw Hosa.o- aa.o- eaaew.m oommw.m o.eoa mafio.o- ma.o- aaoao.e ommoo.a m.aon moH~.o oo.a amaaa.a oeoma.a o.moo monopowwflm mxoififiawev oHSuMWMWEoH oHSHMWMWEoH oocmwmmwom ucoupom oocohommflm poumasunu popzmmoz pohsmmoz mweaaamooo.o- u .meNmHNo.o u mu .wmmeomm.o- u Nu .Nwoawe.fi I He .mwmoam.m- u 00 .mmeoae.o u a .ommmaw.fi u a ome ucoeflpomxm cm Eopm muouoEmgmm o>psuIQOHHHHQHHHUIoHDumthEoH .aeaa .mH snagged .H oanmb 58 thermometer is replaced by a variable resistor, Rt can be calculated from the equation, Rt = _T~:"C;D (119) where RO is the potentiometer reading divided by the ther- mometer current. D is the distance from the pen position to the null position on the recorder chart. This is taken as positive if the pen position is to the right of the null position and negative if it is to the left. Cl and C2 are obtained from a least-squares fit of the voltage-calibration data to the equation, R01 R02 _ c + c (R01 + R02) D1 - D2 1 2 2 0r AR/AD = C1 + C2 R, (121) For the derivation of these equations see Appendix I. When the variable resistor is replaced by the ther- mometer, the plot of AR/AD vs R is fitted best by a third- degree polynomial instead of (121). Table II gives the results of this fit. The necessity for such an analysis for the voltage-calibration curve is due to the off-balance readings of the potentiometer. Since such off-balance readings introduce an error current in the thermometer, the proper correction is necessary. Inserting an amplifier with a high-impedance input would reduce the error current, and 59 mm.o onao.o mmmo.~ mmmo.~ Nwma.m aN.N- ammo.o- eeNV.N mHHm.N momm.e mm.H wamo.o anew.m moaw.~ RNNm.m 0N.H- mamo.o- meefi.m omma.m omko.e mo.H- ammo.o- mama.m maoo.m NHmN.a oa.o mONo.o HNwm.e mmoe.e AHNo.w NN.¢ HHmN.o wwaN.m wane.m oama.oa OH.N- mHNH.o- mmmm.o camc.o HAS¢.NH aa.o- owoo.o- cfiam.a eNom.a m-w.aa as.o Raeo.o maea.m m~wa.w aowm.aa cocoammcaa fl.>fle\mseoe A.>ae\mseov A.>ae\maeov a OH x meeov unoUHom monopommfio Q<\m< poumasoamu Q<\m< onSmmoz m om mH-OH x afiwmmo.auau .m-OH x momaao.m-umu .e-oa x mwmeoo.mumu .H-OH x aooaa.anflu meld + Name + emu + J u mi: .noma .mH Sumscwh owes “coefihomxm am How mgouoEmuwm o>h:o-:oflumpnflamu ommufio>IpHo>fiHHHZIoeo .N oHan 60 om.N Noao.o eomo.o ooeo.o meow.o mm.H Heao.o onmu.o Hamn.o mono.a mw.o whoo.o woew.o wmmw.o oaom.fi No.a moao.o wamm.o Hmoo.a ommm.H Hm.oi oooo.o- ONNH.H BOOH.H mmom.a wm.m- mmeo.o- caem.a ommN.H chom.m «0.0- oooo.o- oeam.a mmfim.H mooo.m na.o- Hmoo.o- Hmwm.a flown.a oNHN.m ouaopommfim n.>fip\menov m.>fi©\menov m.>flw\mecov n OH x menov “coupon ouaohomwfla Q<\m< popmfisunu Q<\m< vohsmmoz m cm fiemseaoeouv .N magma 61 it has been tried with several amplifiers, but the noise level was increased beyond a tolerable level. An empirical formula which gives Rt’ using the cubic fit, R0, and D has been derived by trial and error. This is, 2 3 ‘[C1 - c 2R - 2C3R - 3C4R ]D Rt 2 1 +[c 2 + 2C3R + 3C4R ]D (122) where the C's are the coefficients of the third-degree poly- nomial fit, and Rt in the first approximation, is calculated using R = R0. The calculation is iterated using R = Rt until the previous calculated value differs by 0.1 percent from the final value. 3. Specific Heat Data.--The specific heat of the point ABCD in Figure 12 can now be calculated. The resistance at Ds and De are determined using the voltage-calibration data and the empirical formula. The temperature for these resis- tances are computed using the thermometer calibration equa- tion. The heater current (1h), heater voltage (Vh), the time of heating (t), and the mass of the sample in moles (M) have all been measured. Therefore Cm may be written as, C = Ih x Vh x t (123) e - TS)M The specific heat (Cm) curve is the plot of Cm versus T where T = 2(Te + T5), the average of the temperatures cal- culated from D6 and DS 62 There are several possible sources of errors, but the largest is reading distances on the chart. The scatter caused by this error, as mentioned before, is kept to a minimum by keeping the difference between D8 and Ds greater than ten small divisions, where the chart is divided into 100 of these divisions. Another source of error is the ad- ditional heat capacities of the thermometer, heater wire, and varnish. This error is largest at 4°K and the calcula- tion indicates that it contributes approximately 2.8 percent of the total specific heat at that temperature. IV. RESULTS AND DISCUSSION A. Description of Crystal The samples each consisting of a single crystal of CszMnC14-2HZO were studied. They both are about one inch 2 long with a cross sectional area of 0.25 cm . The mass of sample 1 is 1.353 grams or 0.00272 mole, and the mass of sample 2 is 0.905 gram or 0.00181 mole, using 498.63 grams/ mole as the molecular weight. S. J. Jensen30 has made an x-ray study of CsZMnCl4-2HZO. The crystals are triclinic, of space group PT with one formula unit per unit cell. The parameters are: 0 a = 5.75A a = 67.0° O b = 6.66A B = 87.8° O c = 7.27A Y = 84.3° Figure 13 shows a cross section of the crystal and identi- fies several faces. B. Zero Field Results Four separate specific heat studies were made in a zero magnetic field. Two studies were made on sample 1 in the He4 calorimeter between l.4° - 5.0°K. Sample 2 was studied first in the He4 calorimeter, and then secondly in the He3 calorimeter between 0.6° and 3.0°K. Figure 14 shows these results plotted as a function of temperature, and 63 64 (III) (100) tom . ' ' (0i I) X9”. 85!? / IlOO) (m) Fig. 13. A Cross Sect1ona1 View of CszMnCl4-2HZO Perpendicular to the Elongated Axis with an Arrow Indi~ cating the Direction of Easy Magnetization. 65 .paofim uflpocwmz chow cw o>gsu “no: 0fiwfluomm gov wmahHSU HNQI UHWHUGQW .OH .wfinm .xc mmapmmazm» e x n .~ - .. . Mesa 6339...“. . 4 4 0.83 I...» $3.85 6 533.0 x :25 33 < 5:253 o~:~.¢_o=2~8 ‘72 o. N. I .Ix.~310w/°'Iv0) .LVSH almads ' 73 .mmsmw omHm new < powumpcoflho How o>gsu “we: uflwfioomm » c... $2.25“.sz e n u . . , 4242.61.59...“ _ 4 . _ . _ . vet... ...L. 1 a $350 6 5350 x :25 one 4 5:62.25 09.53.86.290 .NH .mE q 0. N. *— 0|e°310W/"IVOI lVSI-I OIJIOSdS ‘74 .mmsmo omaw new < HOwaucofipo pom o>gso pee: Uwauoam CE mm:hasu poo: uflwfluomm C... wmahdmmmzmh A . n N . ma A. .MHM flUXNYnXWZLWm~XOMv%y%m~vavnonuvkakaxun x8»... a» hm\m.\No o hm\m_\No x 3:00 omom m 5.3.5.5 o~:~.¢_o§~8 I. O. N. .... Ix.-:-I'Iowx'1v0) 1V3H Oldloads 76 .mmsmu oovw new m :oflueucoflho pom o>esu poo: ufimfioomm 3.6. mm:..psu poo: UHMMoon 3... “132.132.“... o . n N ¢ _ .HN .mE menace.“ 915.6.aawamx9w . _ J) . . _v . $.15. are: .. as hw\ho\¢o o hm\mo\¢o .x 3:60 00mm 0 cote—cote 09568:: «8 o. N. v. Ole-310W I'WVOI .LVBH .OIJIOBdS ‘78 .mmsmo omoo can u :oflumucofiho how o>wsu poo: uflwfluomm .NN .wfim .xe_um:busu umoz ufiwfluomm 2L mm:...esu pee: UMMHuomm 3.6. mmahpso poo: dawfioomm 3.6. um..:._.~o o hwxozno x :35 onmm 0 5:62.25 . o~:~.¢_o§~8 .mN .wfim O. N. 0. Ole '3'IOW/"IVOI .LVBI-I Old IOBdS 82 Figures 26, 27, and 28 show the entropy as calculated from the specific heats. The curves in Figure 26 and 27 are normalized by extrapolating the Cm/T curves to 0°K. The curves in Figure 28 are normalized to the zero field entropy curve by an adiabatic magnetization experiment. This experi— ment was performed in the following way. The sample was thenmflly isolated and the temperatures were measured as the field was increased to a maximum and then decreased to zero. Table 27 in Appendix II list these temperatures. The entrOpy remains constant and its value for each magnetization is found from the zero field entrOpy curve. The points shown in Figure 28 are the results of this experiment. Figures 29, 30, and 31 are three—dimensional plots of entropy, magnetic field, and temperature. These results indicate that at low temperatures, adiabatic magnetization may produce cooling by as much as 0.3°K, when the field is increased from zero to 8900 gauss. D. Phase Diagram Figure 32 is a plot of the applied magnetic field against the transition temperature, called the H-T phase diagram. All points to the right and above the curves are in the paramagnetic state and all points to the left and below the curves are in the antiferromagnetic state. The smooth curves were plotted assuming the points of each orientation follow the H2 dependence as given by equation (101). Orientation C is the direction closest to the easy ENTROPY (COL/Mole-‘Kl 83 __R__!n§_________........- .. HID .-—- 'B-ISI. 3 _ / 2 Caz MnCl4-2H20 I . 'I I i l l l O I ‘ 2 *3 ’ TEMPERATURE PK)- Fig. 26. Entropy Curves for Orientation A. (Cal./MoIe-°K)S ENTROPY ‘ 84 Rlns ________ -V-'-‘-'—- "to 'ICOBO 30400 3— :! __ Chfizhln(3h$42FEZC’ . /, F- / | —- 0L.__4 ‘ L__'___.___.I___. I 2 3 . ' TEMPERATURE (’K) Fig. 27. Entropy Curves for Orientation B. 85 CsZMnCl4-2H20 O H= 35009008! x H = 6050 gauss D H= 8400gauss A H= 8900 gauss N ENTROPY (CalJMolc-‘lO o——-—L———-I—___.l____l____| l 2 3 TEMPERATURE PK) Fig. 28. Entropy Curves for Orientation C. 86 .< coauwucofipo How oomwhsm ohspmpomEoH can .wHon .xmopucm 3.83:5 Bur. . _ or. 32.5.2sz c. n mm aw . . _ 09953250 N Durward/100) AdOUlNS fl) . .WHHH 87 .m :oflpmpaoflho How oommpsm ohspwpomEoH can .waoflm .zmoupcm .om .wflm 33.3.8 35... _ O... mmakdmwmgfik v n q . — ouxuboczumo (Mo "ION/199) AdOHLNH 88 .u soapmucoflpo wow oummhsm onnumpomEoH .caoflm .xmopucm .Hm .wwm 72.823 3mm. C... mmak ohsumhomEoH .mm .mflm £332.33: anew S 322:3 =3: 3.3:: 3.22 o < a on. 00 00" 0000 T . . J . a: .. . ad. . . _ 3.. m Au a... u .... 3.. w m m. F.0-l. Mm On_ 0 ...». I .. e . 3.. w 2... . 93 the three different orientations. The curve is drawn assum- ing Z—fold symmetry, although the present crystal has only an inversion axis and the angles between A, B, and C are ap- proximate. This method, however, will still be useful. On the right of Figure 33 are the resistances of the thermometer for the three plottaipoints. Therefore enough sensitivity exists so that by simply rotating the magnet and watching the thermometer, the crystal can be aligned so that the ex- ternal field will be parallel to the direction of magnetiza- tion. This is achieved when maximum resistance is attained on the thermometer. Neutron-diffraction studies would also be useful to help confirm the axis of easy magnetization. Referring again to Figure 33, if a spin-flop transi- tion did occur for a field of 8000 gauss at orientation C the spins would now be ordered in the same configuration as they would be in orientation B. It would appear that the temperatures for these two configurations should be identi- cal for the same entrOpy value. Then if the crystal is adiabatically rotated in constant magnetic field from orien- tation B to orientation C, the temperatures would change as shown in Figure 33 until within approximately 5° of orienta- tion C. Since spin-f10p can only occur within approximately 5° of the easy direction, the temperature in Figure 33 will rise from about 1.20° to 1.34°K, the value of the tempera- ture for orientation B. This is indicated by the dashed curve in Figure 33, and may be another method for detecting 94 the spin-flop transition. Justification for this technique would be evident from the fact that the three-dimensional S-H—T curves would show a depression in their surface. In the above discussion it has been tacitly assumed that the shape of the crystal does not affect the results. To test the affect of the shape of the sample it would be necessary to grow larger crystals and grind them into spheres, etc. and repeat the experiment. In this way it may be possible to determine whether the field is uniform over the entire length of the crystal. The effect of the external magnetic field on the nuclear—spin specific heat has, of course, been neglected, just as it was for the zero-field measurements. Such ef- fects will not appear much before very low temperatures, and in external fields, probably greater than 50,000gauss, since it would involve the further splitting of the nuclear- spin levels. 10. 11. 12. l3. 14. 15. 16. 17. 18. R. . J. . W. REFERENCES D. Spence (Private communication) A. Cowen (Private communication) P. Allis and M. A. Herlin, Thermodynamics and Statis- tical Mechanics, McGraw-Hill, New York (1952): . W. Sears, Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics, Addison-Wesley, Reading, Mass. (1953) Kittel, Elementary Statistical Physics, John Wiley 8 Sons, New York (1958) Kittel, Introduction to Solid State Physics, John Wiley 8 Sons, New York’(1956) . Heisenberg, Z. Physik 49, 619 (1928) . Merzbacher, Quantum Mechanics, John Wiley 6 Sons, New York (1963) . Néel, Ann. Phys. (Paris) 5, 232 (1936) . H. Van Vleck, J. Chem. Phys. 9, 85 (1941) B. Lidiard, Rept. Prog. Phys. 25, 441 (1962) . Nagamiya, K. Yosida, and R. Kubo, Advan. Phys. 4, l (1955) . R. Weiss, Phys. Rev. 14, 1493 (1948) Li, Phys. Rev. 84, 721 (1951) . Oguchi and Y. Ubata, Prog. Theoretical Phys. 9, 359 (1953) Ising, Z. Physik 31, 253 (1925) F. Newell and E. W. Montroll, Rev. Mod. Phys. 25, 353 (1953) . Onsager, Phys. Rev. 65, 117 (1944) 95 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. C... . Weiss, J. Phys. 9, 667 (1907) . H. Morrish, The Physical Principles of Magnetism, John Wiley 8 Sons, New York (1965) E. Fisher, Phil. Mag. 1, 1731 (1962) . J. Gorter and T. van Peski-Tinbergen, Physica 99, 273 (1956) G. B. Garrett, J. Chem. Phys. 19, 1154 (1951) . A. Sauer and H. N. V. Temperley, Proc. Roy. Soc. (London) 176A, 203 (1940) B. Anderson and H. B. Callen, Phys. Rev. 136, A1068 (1964) S. Jacobs, Bull. Am. Phys. Soc. 99, 285 (1967) . J. Poulis, J. van den Handel, J. Ubbink, J. A. Poulis, and C. J. Gorter, Phys. Rev. 99, 552 (1951) R. Roach and J. C. Wheatley, Rev. Sci. Instr. 99, 634 (1964) ‘ G. Brickwedde, H. van Dijk, M. Durieux, J. R. Clement, and J. K. Logan, J. Research 64A, 1 (1960) . J. Jensen, Acta Chem. Scand. 18, 2085 (1964) . E. Cooke and D. T. Edmond, Proc. Phys. Soc. (London) 1;, 517 (1958) Debye, Ann. Physik 99, 780 (1912) . M. Burley, Phil. Mag. 9, 909 (1960) van den Handel, H. M. Gijsman, and N. J. Poulis, Physica 19, 862 (1952) 96 APPENDIX I Using Kirchoff's Circuit Law for the current 100p Ie in Figure 34 one can write, (Ie - Ip)Rp + IeR + (Ie + It)Rt = 0 (1) where Ip is the potentiometer current, Rp is the potentio- t is the thermometer resistance, It is the thermometer current, R is the lead resistance, and Ie meter resistance, R is the unbalance current. When I = 0 then I R = I R . e p p t t Thus I R = V where V0 is the voltage read from the potentio- p p 0’ meter. Rewriting (1) using V0 one gets, (1 - Ie/Ip)VO = IeR + (1 + Ie/It)ItTt. (2) I8 has been measured and found to be proportional to the recorder-pen deflection from zero, positive when de- flected to the right and negative when deflected to the left. Let D be the deflections measured in chart divisions. Ie has never exceeded 0.1 microampere in any of the experiments to date. Ip is never less than 200 microamperes, therefore, Ie/Ip is always less than 0.0005 which can be neglected com- pared to 1. So that (2) may be written as, VO = aDR + (l + qD/It)ItR (3) where I8 = aD and a is a proportionality constant depending 97 98 Fig. 34.- Circuit Diagram for a Simple Potentiometer. 99 upon the range card and the D. C. amplifier scale factor. The a's of different scales differ by an integral multi- plying factor. Since It is held constant, let R0 = VO/It then (3) becomes, R0 = (d/It)RD + [l + (a/It)D]Rt (4) Keeping Rt and R constant change the voltage setting on the potentiometer, and obtain, R01 - (on/It)RD1 + [l + (a/It)D1]Rt (5) R02 - (a/It)RD2 + [1 + (a/It)D2]Rt (6) Subtracting (6) from (5), gives, R01 - R02 = (a/It)(R + Rt)(Dl - D2) (7) 01‘ ARC/AD = C1 + CZRt (8) where C1 = (a/It)R and C2 = a/It. Solving equation (4) for Rt gives, Rt = [R0 - (a/It)RD1/[1 + (a/It1D] (9) or finally, R - C D _ 0 l Rt ‘ m- (103 APPENDIX II Table 3. The Specific Heat of CszMnCl4-2H20 for Sample 1, Run 2, September 16, 1966, Zero Field. Cm dT T Cm dT T Cm dTfi T 2.959 0.001 1.408 3.719 0.002 1.548 4.573 0.003 1.664 3.032 0.003 1.414 3.831 0.002 1.556 4.495 0.003 1.669 3.026 0.003 1.423 3.664 0.002 1.560 4.506 0.003 1.674 2.904 0.003 1.428 3.550 0.002 1.564 4.706 0.003 1.680 2.947 0.003 1.434 3.804 0.002 1.568 4.982 0.002 1.689 3.147 0.002 1.443 4.045 0.002 1.572 4.885 0.003 1.694 3.118 0.003 1.449 3.789 0.002 1.576 4.845 0.003 1.698 3.091 0.003 1.455 3.848 0.003 1.580 4.909 0.002 1.703 3.299 0.002 1.463 3.856 0.003 1.585 4.825 0.003 1.709 3.239 0.002 1.468 4.052 0.003 1.590 4.890 0.002 1.713 3.269 0.002 1.474 4.094 0.003 1.594 5.188 0.002 1.717 3.322 0.002 1.482 4.053 0.003 1.600 5.200 0.002 1.721 3.293 0.002 1.487 3.929 0.003 1.604 5.212 0.002 1.725 3.265 0.002 1.492 3.936 0.003 1.608 5.766 0.002 1.729 3.383 0.002 1.499 4.179 0.003 1.611 5.301 0.002 1.735 3.321 0.002 1.504 4.297 0.003 1.615 5.246 0.002 1.738 3.324 0.002 1.509 4.250 0.003 1.620 5.748 0.002 1.742 3.500 0.002 1.516 4.113 0.003 1.625 5.333 0.002 1.746 3.468 0.002 1.521 4.088 0.003 1.630 5.663 0.005 1.751 3.508 0.002 1.525 4.134 0.003 1.636 6.091 0.005 1.760 3.664 0.002 1.530 4.537 0.003 1.643 6.230 0.005 1.767 3.401 0.002 1.535 4.505 0.003 1.648 6.293 0.004 1.774 3.441 0.002 1.540 4.309 0.003 1.653 6.764 0.004 1.782 3.633 0.002 1.544 4.320 0.003 1.658 6.786 0.004 1.789 100 101 .Table (Continued) Cm dT‘ T Cm dT' T’ Cm dT T 7.165 .004 .795 .362 0.014 2.091 .573 0.033 3.214 7.525 .004 .801 .399 0.013 2.119 .542 0.035 3.258 7.832 .004 .810 .289 0.015 2.147 .521 0.036 3.311 7.917 .004 .815 .242 0.015 2.182 .502 0.037 3.356 8.440 .003 .820 .122 0.017 2.217 .498 0.038 3.429 9.034 .003 .826 .124 0.017 2.256 .489 0.039 3.485 9.906 .003 .832 .077 0.017 2.294 .472 0.040 3.554 7.022 .004 .837 .041 0.018 2.332 .462 0.041 3.612 3.787 .007 846 .999 0.019 2.369 .449 0.042 3.691 2.798 .010 .860 .960 0.020 2.409 .429 0.044 3.757 2.502 .011 .873 .944 0.020 2.450 .421 0.045 3.837 2.277 .012 .890 .898 0.021 2.496 .412 0.046 3.906 2.151 .013 .905 .872 0.022 2.546 .396 0.048 4.002 1.988 .014 .922 .856 0.022 2.591 .391 0.048 4.078 1.882 .015 .938 .826 0.023 2.641 .377 0.050 4.194 1.809 .016 .955 .763 0.025 2.695 .363 0.052 4.279 1.740 .016 .972 .759 0.025 2.744 .358 0.053 4.391 1.648 .011 .986 .734 0.026 2.795 .342 0.055 4.480 1.603 .012 .997 .701 0.027 2.846 .339 0.055 4.621 1.624 .012 .009 .670 0.028 2.897 .329 0.057 4.716 1.561 .012 .020 .650 0.029 2.949 .325 0.058 4.832 1.606 .012 .032 .629 0.030 3.005 .322 0.058 4.913 1.563 .012 .044 .601 0.031 3.066 .318 0.059 4.986 1.608 .012 .056 .558 0.034 3.119 .315 0.063 5.077 1.481 .013 .068 .573 0.033 3.160 .309 0.064 5.158 102 Table 4. The Specific Heat of CszMnC14-2HZO for Sample 1, Run 3, September 21, 1966, Zero Field Cm dT T Cm dT T Cm dT T 3.019 0.004 1.365 4.348 0.004 1.594 7.128 0.004 1.794 2.774 0.003 1.381 4.492 0.004 1.600 7.462 0.004 1.802 2.953 0.003 1.399 4.454 0.004 1.610 7.613 0.004 1.808 3.089 0.004 1.411 4.535 0.004 1.616 7.948 0.004 1.814 3.093 0.004 1.423 4.048 0.005 1.623 8.060 0.004 1.819 3.252 0.004 1.438 4.998 0.004 1.630 8.594 0.003 1.826 3.414 0.004 1.452 4.932 0.004 1.636 9.289 0.003 1.832 3.390 0.004 1.459 4.951 0.004 1.646 10.010 0.003 1.838 3.501 0.004 1.468 5.028 0.004 1.652 10.410 0.003 1.843 3.473 0.004 1.475 5.063 0.006 1.663 11.057 0.003 1.849 3.597 0.003 1.484 5.217 0.005 1.673 10.347 0.003 1.853 3.621 0.003 1.491 5.292 0.005 1.684 4.981 0.006 1.860 3.594 0.003 1.501 5.442 0.005 1.693 3.399 0.008 1.872 3.655 0.003 1.506 5.569 0.005 1.704 3.036 0.006 1.883 3.724 0.003 1.515 5.857 0.005 1.712 2.598 0.007 1.896 3.766 0.003 1.521 5.811 0.005 1.724 2.478 0.008 1.906 3.820 0.003 1.529 5.916 0.005 1.731 2.313 0.008 1.920 3.911 0.003 1.535 6.080 0.005 1.742 2.198 0.009 1.931 4.015 0.005 1.544 6.166 0.005 1.749 2.058 0.009 1.947 4.062 0.005 1.551 6.216 0.005 1.758 1.976 0.010 1.962 4.165 0.005 1.561 6.382 0.004 1.765 1.899 0.010 1.974 4.123 0.005 1.568 6.718 0.004 1.772 1.864 0.010 1.992 4.252 0.004 1.578 6.834 0.004 1.781 1.788 0.011 2.005 4.325 0.004 1.585 6.736 0.004 1.787 1.703 0.011 2.023 103 Table 4 (Continued) Cm dT T Cm dT T Cm dT T 1.667 0.011 2.037 .071 0.018 .371 .621 0.030 3.140 1.606 0.012 2.055 .044 0.018 .416 .597 0.032 3.214 1.583 0.012 2.070 .958 0.020 .463 .597 0.032 3.300 1.494 0.013 2.088 .924 0.020 .505 .554 0.034 3.382 1.473 0.013 2.104 .915 0.021 .552 .559 0.034 3.474 1.412 0.013 2.126 .832 0.023 .602 .533 0.036 3.570 1.381 0.014 2.144 .861 0.022 .653 .521 0.036 3.682 1.347 0.014 2.161 .819 0.023 .707 .498 0.038 3.782 1.413 0.013 2.178 .768 0.025 .762 .537 0.035 3.849 1.306 0.015 2.195 .727 0.026 .818 .486 0.039 3.955 1.273 0.015 2.223 .725 0.026 .877 .475 0.040 4.063 1.222 0.015 2.253 .711 0.027 .935 .493 0.038 4.127 1.153 0.016 2.293 .694 0.027 .005 .401 0.047 5.015 1.068 0.018 2.329 .659 0.029 .072 .497 0.038 5.207 .496 0.057 5.281 104 Table 5. The Specific Heat of CszMnCl4-2HZO for Sample 2, Run 1, October 5, 1966, Zero Field. CIn dT T Cm dT T Cm dT T 3.322 0.006 1.417 .670 0.009 1.635 10.292 0.004 1.835 3.294 0.006 1.430 .775 0.009 1.650 10.233 0.004 1.840 3.245 0.006 1.442 .959 0.008 1.665 4.624 0.009 1.848 3.418 0.005 1.450 .120 0.008 1.679 3.216 0.009 1.861 3.291 0.006 1.461 .230 0.008 1.692 2.917 0.009 1.872 3.362 0.005 1.475 .520 0.007 1.703 2.529 0.011 1.887 3.477 0.005 1.484 .657 0.007 1.718 2.363 0.012 1.900 3.460 0.005 1.494 .823 0.007 1.727 2.192 0.013 1.917 3.566 0.005 1.509 .902 0.007 1.740 2.065 0.013 1.935 3.658 0.005 1.516 .285 0.007 1.749 1.948 0.014 1.954 3.713 0.005 1.526 .424 0.006 1.762 1.872 0.015 1.972 3.817 0.005 1.535 .280 0.007 1.770 1.772 0.016 1.991 3.679 0.005 1.545 .901 0.006 1.780 1.708 0.016 2.011 3.873 0.005 1.553 .086 0.006 1.788 1.649 0.017 2.032 3.912 0.005 1.563 .351 0.006 1.796 1.596 0.017 2.052 3.994 0.005 1.571 .542 0.005 1.804 1.527 0.018 2.075 4.095 0.004 1.581 .979 0.005 1.811 1.475 0.019 2.098 4.188 0.004 1.588 .271 0.005 1.817 1.430 0.019 2.121 4.170 0.010 1.601 .902 0.005 1.823 1.426 0.019 2.140 4.355 0.009 1.618 .637 0.004 1.830 1.404 0.020 2.159 105 Table (Continued) Cm dT T Cm dT T dT T 1.359 .020 2.190 .853 0.032 0659 .559 0.049 3.421 1.373 .020 2.221 .826 0.033 .723 .587 0.047 3.506 1.288 .021 2.257 .814 0.034 .781 .624 0.044 3.595 1.216 .023 2.300 .746 0.037 .848 .655 0.021 3.665 1.178 .023 2.343 .727 0.038 .910 .492 0.056 3.820 1.101 .025 2.388 .684 0.040 .982 .607 0.023 3.904 1.057 .026 2.437 .646 0.043 .069 .576 0.048 4.006 1.020 .027 2.487 .603 0.046 .147 .413 0.033 4.233 0.972 .028 2.541 .578 0.048 .237 .552 0.025 4.290 0.886 .031 2.601 .563 0.049 .331 .587 0.023 4.395 .519 0.026 4.506 106 Table 6. The Specific Heat of CsZMnC14-2HZO for Sample 2, Run 2, October 17, 1966, Zero Field. Cm dT’ T’ Cm dT T Cm ET 7T 0.856 0.012 0.673 .473 0.014 0.844 2.533 0.036 1.215 0.838 0.013 0.686 .453 0.015 0.855 2.644 0.035 1.227 0.818 0.013 0.701 .522 0.012 0.863 2.665 0.034 1.253 0.928 0.011 0.714 .561 0.012 0.871 2.854 0.073 1.292 0.965 0.011 0.722 .585 0.011 0.880 3.146 0.067 1.350 1.025 0.010 0.732 .609 0.011 0.888 3.494 0.060 1.403 1.061 0.010 0.740 .620 0.025 0.899 3.771 0.056 1.445 1.147 0.009 0.747 .663 0.024 0.916 4.022 0.052 1.483 1.111 0.010 0.752 .734 0.023 0.928 4.142 0.051 1.515 1.151 0.009 0.759 .751 0.023 0.945 4.371 0.048 1.545 1.112 0.010 0.764 .767 0.023 0.961 4.565 0.046 1.569 1.181 0.009 0.768 .819 0.022 0.978 .4.497 0.047 1.585 1.216 0.009 0.772 .846 0.022 0.994 5.074 0.093 1.633 1.263 0.015 0.782 .832 0.022 1.007 6.218 0.076 1.700 1.293 0.015 0.793 .898 0.021 1.019 7.800 0.061 1.749 1.340 0.014 0.802 .924 0.021 1.034 5.328 0.089 1.814 1.332 0.014 0.810 .920 0.021 1.038 2.044 0.232 1.933 1.336 0.014 0.820 .043 0.049 1.064 1.428 0.331 2.143 1.398 0.013 0.827 .159 0.045 1.103 1.185 0.400 2.333 1.425 0.015 0.833 .234 0.041 1.132 0.917 0.516 2.608 1.420 0.009 0.836 .319 0.039 1.162 0.763 0.620 2.926 .428 0.038 1.190 0.639 0.741 3.255 107 Table 7. The Specific Heat of Cs MnC14-2HZO for Sample 2 1, Run 5, December 23, 1966, 8150 Gauss, Orientation A. C dT T C dT T C dT T m m m 1.655 0.004 1.040 2.689 0.018 1.324 1.231 0.059 2.035 1.707 0.007 1.045 2.861 0.017 1.343 1.180 0.062 2.080 1.635 0.008 1.052 2.995 0.026 1.363 1.312 0.055 2.113 1.766 0.028 1.069 3.145 0.024 1.388 1.199 0.061 2.057 1.722 0.016 1.086 3.225 0.024 1.410 1.174 0.062 2.118 1.909 0.014 1.099 3.475 0.022 1.432 1.121 0.065 2.175 1.924 0.014 1.111 3.618 0.021 1.453 1.063 0.068 2.232 1.934 0.014 1.123 4.054 0.019 1.485 1.007 0.072 2.288 1.884 0.014 1.134 4.567 0.024 1.546 1.028 0.071 2.352 1.923 0.014 1.145 4.887 0.022 1.573 0.927 0.078 2.453 2.024 0.013 1.156 5.271 0.021 1.596 0.909 0.080 2.547 2.027 0.020 1.160 5.606 0.019 1.617 0.810 0.090 2.647 2.094 0.019 1.178 6.913 0.016 1.635 0.775 0.094 2.743 2.102 0.019 1.195 7.320 0.015 1.650 0.759 0.096 2.900 2.315 0.017 1.211 11.166 0.019 1.667 0.716 0.102 3.013 2.168 0.018 1.227 15.555 0.014 1.683 0.604 0.121 3.140 2.289 0.017 1.243 3.157 0.129 1.754 0.605 0.120 3.238 2.346 0.017 1.257 1.565 0.053 1.840 0.542 0.134 3.333 2.442 0.016 1.273 1.465 0.050 1.887 0.542 0.134 3.428 2.470 0.016 1.287 1.339 0.054 1.936 0.506 0.216 3.661 2.588 0.019 1.303 1.288 0.056 1.985 0.611 0.179 3.972 0.446 0.245 4.297 108 Table 8. -2H 0 for 4 2 8150 Gauss, Orientation A. The Specific Heat of CsZMnC1 Sample 1, Run 6, January 12, 1967, Cm dT T Cm dT T Cm dT T 2.178 .004 1.186 .124 0.016 1.412 12.112 0.008 1.685 2.166 .004 1.190 .114 0.016 1.429 3.634 0.027 1.708 2.270 .005 1.193 .161 0.016 1.445 2.427 0.023 1.731 2.149 .014 1.200 .654 0.014 1.460 2.059 0.029 1.752 2.289 .013 1.213 .769 0.013 1.474 1.886 0.032 1.779 2.294 .015 1.225 .859 0.013 1.487 1.722 0.034 1.799 2.326 .012 1.237 .976 0.013 1.500 1.761 0.023 1.830 2.417 .012 1.247 .363 0.007 1.510 1.500 0.028 1.863 2.497 .010 1.256 .418 0.026 1.527 1.551 0.019 1.886 2.455 .010 1.265 .656 0.025 1.553 1.531 0.019 1.905 2.520 .011 1.274 .997 0.023 1.576 1.602 0.018 1.923 2.437 .020 1.290 .891 0.023 1.598 1.507 0.019 1.942 2.527 .019 1.309 .860 0.020 1.618 1.508 0.019 1.958 2.802 .018 1.327 .371 0.018 1.637 1.485 0.019 1.977 2.849 .018 1.344 .249 0.016 1.653 1.421 0.020 1.997 2.873 .018 1.383 .807 0.015 1.667 1.475 0.019 2.016 2.887 .012 1.398 .706 0.010 1.678 1.372 0.021 2.037 109 Table (Continued) Cm dT T Cm dT T Cm dT T 1.431 .020 2.057 .762 0.038 .654 .512 0.056 3.444 1.388 .021 2.069 .790 0.040 .719 .506 0.057 3.556 1.150 .025 2.102 .765 0.041 .776 .466 0.061 3.636 1.153 .025 2.139 .748 0.038 .832 .489 0.058 3.706 1.176 .024 2.172 .727 0.039 .900 .478 0.060 3.770 1.067 .027 2.212 .684 0.0424 .956 .508 0.056 3.828 1.035 .028 2.262 .635 0.045 .029 .523 0.055 3.883 0.935 .031 2.315 .638 0.045 .095 .580 0.049 3.935 0.839 .034 2.418 .595 0.048 .200 .656 0.044 3.982 0.889 .032 2.490 .685 0.042 .284 .634 0.045 4.026 0.875 .032 2.560 .545 0.052 .369 .505 0.057 4.066 110 Table 9. The Specific Heat of CsZMnC14-2HZO for Sample 1, Run 7, January 13, 1967, 5150 Gauss, Orientation A. C dT T C THT T C dT T m m m 2.083 0.009 1.190 3.916 0.013 1.496 1.681 0.020 1.954 2.231 0.009 1.198 3.774 0.013 1.509 1.517 0.034 2.005 2.429 0.012 1.206 4.154 0.012 1.522 1.428 0.035 2.053 2.269 0.013 1.215 3.961 0.013 1.534 1.320 0.040 2.105 2.298 0.012 1.227 4.081 0.029 1.554 1.254 0.042 2.151 2.431 0.012 1.238 4.424 0.021 1.580 1.202 0.043 2.195 2.519 0.011 1.246 4.938 0.019 1.600 1.155 0.045 2.239 2.421 0.012 1.256 4.477 0.021 1.618 1.196 0.044 2.284 2.536 0.011 1.266 5.252 0.018 1.637 1.063 0.049 2.321 2.492 0.011 1.277 5.188 0.018 1.655 1.059 0.049 2.363 2.561 0.011 1.289 5.766 0.016 1.673 0.929 0.056 2.434 2.594 0.011 1.300 6.070 0.016 1.689 0.905 0.058 2.537 2.729 0.010 1.309 5.801 0.016 1.704 0.861 0.061 2.632 2.801 0.010 1.319 7.037 0.017 1.720 0.821 0.064 2.770 2.841 0.018 1.333 7.881 0.015 1.736 0.754 0.069 2.876 2.820 0.018 1.350 8.986 0.013 1.750 0.676 0.077 3.019 2.833 0.018 1.366 11.160 0.011 1.761 0.692 0.073 3.130 2.784 0.018 1.379 6.262 0.019 1.777 0.607 0.086 3.280 3.040 0.017 1.395 2.763 0.034 1.803 0.576 0.091 3.405 3.125 0.016 1.421 2.297 0.033 1.834 0.544 0.096 3.523 3.410 0.015 1.435 2.023 0.017 1.857 0.495 0.105 3.695 3.518 0.014 1.454 2.018 0.026 1.869 0.484 0.108 3.809 3.518 0.014 1.468 1.897 0.028 1.895 0.588 0.089 3.907 3.628 0.014 1.482 1.823 0.029 1.920 0.463 0.113 4.026 111 Table 10. The Specific Heat of Cs MnCl ~2HZO for Sample 2 4 1, Run 8, January 18, 1967, 5150 Gauss, Orientation A. C dT T C dT T C dT T m m m 1.796 0.008 1.138 3.465 0.015 1.506 1.480 0.034 2.070 1.824 0.008 1.146 3.461 0.015 1.521 1.257 0.040 2.144 2.121 0.007 1.153 3.500 0.015 1.535 1.224 0.041 2.192 2.153 0.014 1.164 3.493 0.015 1.550 1.132 0.045 2.242 2.144 0.013 1.177 4.075 0.012 1.563 1.097 0.046 2.287 2.134 0.013 1.189 3.809 0.013 1.576 1.095 0.046 2.333 2.172 0.013 1.201 4.368 0.012 1.590 0.981 0.051 2.416 2.257 0.013 1.210 4.639 0.025 1.608 0.868 0.058 2.507 2.277 0.013 1.221 4.949 0.023 1.632 0.788 0.064 2.630 2.297 0.012 1.231 5.185 0.022 1.654 0.709 0.071 2.819 2.316 0.012 1.241 5.313 0.022 1.675 0.682 0.074 2.934 2.398 0.012 1.252 6.233 0.018 1.695 0.628 0.080 3.085 2.666 0.011 1.271 6.847 0.017 1.712 0.537 0.094 3.209 2.806 0.010 1.288 7.355 0.016 1.728 0.626 0.080 3.308 2.853 0.010 1.306 8.341 0.014 1.743 0.533 0.095 3.432 2.646 0.011 1.327 8.864 0.013 1.756 0.489 0.103 3.552 2.860 0.010 1.342 11.579 0.010 1.767 0.488 0.103 3.673 2.851 0.010 1.359 3.957 0.029 1.787 0.514 0.098 3.797 3.033 0.009 1.377 2.482 0.033 1.816 0.449 0.112 3.942 3.239 0.016 1.397 2.112 0.035 1.848 0.423 0.119 4.088 2.795 0.018 1.421 1.919 0.040 1.884 3.490 0.015 1.448 1.719 0.044 1.923 3.674 0.014 1.467 1.520 0.050 1.967 3.718 0.014 1.486 1.563 0.032 2.021 112 Table 11. The Specific Heat of Cs MnCl ~2HZO for Sample 2 4 1, Run 9, January 20, 1967, 3500 Gauss, Orientation A. Cm dT T Cm dT T Cm dT T 1.757 0.011 1.007 2.534 0.011 1.286 3.897 0.013 1.589 1.962 0.010 1.016 2.556 0.011 1.296 4.034 0.013 1.602 1.920 0.010 1.024 2.640 0.011 1.306 4.722 0.011 1.616 1.630 0.012 1.032 2.613 0.011 1.316 4.763 0.024 1.633 1.897 0.010 1.056 2.623 0.011 1.326 5.062 0.023 1.656 2.051 0.009 1.071 2.647 0.011 1.336 5.280 0.022 1.678 2.021 0.009 1.084 2.536 0.011 1.345 6.179 0.018 1.720 1.776 0.011 1.099 3.096 0.009 1.354 6.783 0.017 1.738 1.950 0.010 1.109 2.804 0.010 1.362 6.868 0.017 1.754 2.046 0.009 1.119 2.885 0.010 1.370 7.625 0.015 1.770 1.987 0.009 1.128 2.857 0.010 1.379 10.244 0.011 1.798 2.049 0.009 1.144 2.976 0.017 1.391 6.231 0.018 1.812 2.015 0.009 1.152 2.949 0.017 1.404 3.032 0.022 1.832 2.033 0.009 1.160 3.084 0.017 1.421 2.548 0.022 1.853 2.026 0.009 1.168 3.153 0.016 1.438 2.321 0.025 1.877 2.123 0.009 1.176 3.230 0.016 1.454 1.866 0.031 1.902 2.089 0.013 1.190 3.326 0.015 1.472 1.913 0.030 1.929 2.122 0.013 1.206 3.263 0.016 1.487 2.026 0.017 1.949 2.186 0.013 1.219 3.463 0.015 1.503 1.975 0.017 1.966 2.281 0.012 1.232 3.300 0.015 1.518 1.898 0.018 1.983 2.074 0.014 1.242 3.717 0.014 1.535 1.789 0.019 2.002 2.366 0.012 1.255 3.603 0.014 1.549 1.789 0.019 2.020 2.400 0.012 1.265 3.813 0.013 1.563 1.687 0.020 2.039 2.376 0.012 1.276 4.007 0.013 1.576 1.486 0.023 2.052 113 Table 11 (Continued) Cm dT T Cm dT T Cm dT T 1.417 0.024 2.079 .008 0.034 .400 .675 0.075 2.879 1.329 0.025 2.105 .964 0.035 .441 .624 0.082 3.033 1.349 0.025 2.131 .974 0.035 .494 .597 0.085 3.186 1.268 0.027 2.158 .875 0.039 .534 .534 0.095 3.374 1.182 0.029 2.186 .890 0.038 .575 .498 0.102 3.529 1.280 0.026 2.217 .856 0.040 .616 .478 0.106 3.674 1.198 0.028 2.249 .840 0.040 .655 .461 0.110 3.843 1.145 0.030 2.281 .853 0.040 .696 .508 0.100 3.996 1.125 0.030 2.322 .965 0.035 .734 .403 0.126 4.165 1.047 0.032 2.360 .801 0.063 °783 114 Table 12. The Specific Heat of CsZMnCl4 1, Run 10, January 23, 1967, 3500 Gauss, Orientation A. -2HZO for Sample C dT T C dT T C dT T m m m 1.542 0.012 0.979 2.301 0.008 1.238 3.628 0.014 1.514 1.542 0.012 0.990 2.375 0.008 1.246 4.533 0.011 1.526 1.516 0.013 1.000 2.464 0.014 1.257 4.229 0.012 1.546 1.533 0.012 1.011 2.432 0.014 1.270 4.386 0.012 1.572 1.587 0.012 1.020 2.427 0.014 1.283 4.400 0.017 1.594 1.485 0.013 1.050 2.532 0.013 1.295 4.735 0.016 1.616 1.862 0.010 1.077 2.486 0.014 1.308 4.967 0.015 1.639 1.825 0.010 1.107 2.948 0.011 1.336 5.167 0.015 1.660 2.078 0.009 1.128 2.920 0.012 1.354 5.406 0.014 1.680 2.207 0.009 1.152 3.076 0.016 1.379 5.935 0.013 1.709 1.959 0.010 1.167 3.072 0.017 1.401 6.351 0.018 1.730 2.143 0.009 1.179 2.874 0.018 1.420 7.016 0.016 1.752 1.913 0.010 1.192 2.870 0.018 1.439 7.264 0.016 1.772 1.893 0.010 1.203 3.269 0.016 1.456 7.325 0.016 1.791 2.223 0.009 1.213 3.336 0.015 1.471 9.397 0.009 1.804 2.226 0.009 1.221 3.514 0.014 1.486 5.077 0.014 1.815 2.300 0.008 1.230 3.476 0.015 1.500 2.683 0.013 1.828 115 Table 12 (Continued) Cm dT T7 Cm dT T Cm dT T 2.365 0.024 1.847 .262 0.040 .163 0.765 0.066 2.836 2.421 0.011 1.867 .238 0.041 .204 0.762 0.067 2.952 2.067 0.021 1.892 .176 0.043 .245 0.673 0.076 3.112 1.622 0.021 1.921 .169 0.044 .288 0 625 0.081 3.228 1.813 0.019 1.945 .166 0.044 .332 0.611 0.083 3.332 1.780 0.019 1.970 .118 0.045 .374 0.522 0.097 3.541 1.605 0.021 1.998 .960 0.053 .419 0.594 0.086 3.659 1.583 0.021 2.023 .942 0.054 .457 0.530 0.096 3.791 1.471 0.023 2.051 .932 0.055 .495 0.535 0.095 3.961 1.362 0.037 2.084 .880 0.058 .597 0.493 0.103 4.103 1.280 0.040 2.123 .856 0.059 .702 116 Table 13. The Specific Heat of C5 MnCl -2HZO for Sample 2 4 1, Run 12, February 11, 1967, 8400 Gauss, Orientation B. C dTV T C dT T C dT T m m m 2.421 0.011 1.206 3.320 0.016 1.404 4.476 0.012 1.599 2.762 0.014 1.218 3.152 0.017 1.416 4.595 0.011 1.609 2.719 0.012 1.230 3.401 0.015 1.429 4.799 0.007 1.618 2.700 0.012 1.239 3.366 0.016 1.442 5.096 0.007 1.624 2.710 0.012 1.250 3.428 0.015 1.455 4.807 0.007 1.630 2.730 0.012 1.255 3.492 0.015 1.468 5.143 0.007 1.636 2.700 0.012 1.264 3.639 0.014 1.480 4.926 0.007 1.641 2.719 0.012 1.273 3.532 0.015 1.493 5.362 0.006 1.647 2.736 0.012 1.283 3.692 0.014 1.503 4.890 0.004 1.651 2.741 0.012 1.294 3.924 0.013 1.515 5.149 0.007 1.654 2.688 0.013 1.305 3.852 0.014 1.527 5.968 0.006 1.664 3.099 0.011 1.312 3.949 0.013 1.539 5.620 0.006 1.669 2.936 0.018 1.325 4.013 0.013 1.549 5.642 0.006 1.674 2.843 0.018 1.342 4.176 0.013 1.561 5.374 0.007 1.678 2.907 0.018 1.358 4.184 0.013 1.572 5.627 0.006 1.682 3.073 0.017 1.373 4.329 0.012 1.580 6.127 0.006 1.686 3.093 0.017 1.388 4.289 0.012 1.591 5.614 0.006 1.691 117 Table 13 (Continued) Cm dT T Cm dT T Cm dT* T 6.819 0.005 1.695 .710 0.005 .735 .162 0.045 .152 5.737 0.006 1.700 .196 0.007 .740 .188 0.044 .196 7.195 0.005 1.705 .032 0.007 .745 .224 0.043 .241 8.083 0.004 1.709 .131 0.006 .750 .075 0.049 .287 6.610 0.005 1.714 .312 0.006 .754 .081 0.048 .336 7.093 0.005 1.718 .934 0.006 .758 .063 0.049 .384 6.953 0.005 1.723 .990 0.005 .763 .085 0.048 .432 6.525 0.005 1.726 .313 0.028 .035 .000 0.052 .482 7.320 0.005 1.730 .299 0.040 .069 .722 0.072 .536 6.700 0.005 1.733 .288 0.041 .109 118 Table 14. The Specific Heat of Cs MnCl -2HZO for Sample 2 4 1, Run 13, February 13, 1967, 8400 Gauss, Orientation B. C dT T C dT T C dT’ T m m m .635 0.011 1.598 2.634 0.013 1.196 3.332 0.010 1.377 2.889 0.012 1.207 3.230 0.015 1.390 .607 0.011 1.608 h-b-b 2.832 0.012 1.217 3.134 0.016 1.403 .849 0.010 1.618 2.765 0.012 1.227 3.005 0.017 1.423 5.032 0.010 1.627 2.657 0.013 1.234 3.499 0.014 1.439 5.069 0.010 1.637 2.687 0.012 1.243 3.612 0.014 1.453 5.050 0.010 1.646 2.746 0.012 1.253 3.571 0.014 1.467 5.030 0.010 1.656 2.730 0.012 1.263 3.553 0.014 1.481 4.986 0.010 1.665 2.673 0.012 1.273 3.397 0.015 1.491 5.056 0.010 1.674 2.745 0.012 1.283 4.021 0.012 1.505 5.622 0.009 1.687 2.733 0.012 1.300 3.944 0.013 1.517 6.177 0.008 1.697 2.927 0.011 1.312 4.079 0.012 1.530 5.709 0.009 1.708 2.906 0.011 1.324 4.029 0.012 1.542 5.608 0.009 1.719 2.903 0.011 1.335 4.010 0.012 1.553 6.408 0.008 1.727 2.918 0.011 1.346 4.691 0.011 1.565 6.642 0.008 1.735 2.780 0.012 1.356 4.468 0.011 1.576 7.002 0.007 1.742 3.173 0.011 1.367 4.594 0.011 1.587 7.397 0.007 1.749 119 Table 14 (Continued) Cm dT T Cm dT 7T Cm dT T 8.447 0.006 .755 .329 0.038 .066 .654 0.077 3.018 7.723 0.006 .761 .248 0.040 .124 .624 0.080 3.104 10.091 0.005 .767 .201 0.042 .176 .628 0.080 3.184 8.163 0.006 .772 .143 0.044 .235 .662 0.076 3.262 3.906 0.013 .782 .060 0.047 .299 .573 0.087 3.329 2.772 0.012 .795 .948 0.053 .360 .591 0.085 3.421 2.509 0.013 .807 .944 0.053 .423 .589 0.085 3.506 2.733 0.012 .823 .892 0.056 .503 .564 0.089 3.572 2.212 0.015 .845 .840 0.060 .571 .487 0.103 3.656 2.037 0.025 .876 .801 0.062 .645 .446 0.112 3.799 1.729 0.029 .921 .747 0.067 .742 .456 0.110 3.959 1.537 0.033 .974 .714 0.070 .827 .544 0.092 4.124 1.425 0.035 .022 .903 0.055 .910 .482 0.104 4.312 120 Table 15. The Specific Heat of C5 MnC14-2HZO for Sample 2 1, Run 14, February 16, 1967, 6050 Gauss, Orientation B. Cm dT T Cm dT T Cm dT T 2.221 0.015 .193 .133 0.011 .415 .105 0.010 1.641 2.487 0.014 .207 .159 0.011 .425 .248 0.010 1.651 2.484 0.014 .218 .173 0.011 .451 .510 0.009 1.660 2.448 0.014 .230 .340 0.010 .465 .431 0.009 1.670 2.436 0.014 .241 .453 0.010 .478 .072 0.019 1.706 2.551 0.013 .251 .037 0.011 .490 .690 0.017 1.724 2.620 0.013 .262 .609 0.009 .500 .979 0.016 1.741 2.686 0.013 .272 .586 0.009 .510 .383 0.015 1.756 2.624 0.013 .283 .116 0.016 .523 .825 0.012 1.785 2.634 0.013 .293 .934 0.013 .537 .116 0.019 1.800 2.506 0.014 .308 .102 0.012 .550 .318 0.015 1.817 2.981 0.011 .321 .093 0.012 .562 .710 0.019 1.835 3.002 0.011 .332 .202 0.012 .575 .473 0.020 1.854 2.930 0.012 .343 .620 0.011 .586 .088 0.024 1.875 2.876 0.012 .354 .698 0.011 .610 .046 0.025 1.899 2.758 0.012 .392 .925 0.010 .621 .973 0.026 1.925 3.019 0.011 .404 .065 0.010 .631 .042 0.025 1.946 121 Table 15 (Continued) Cm dT T Cm dT T Cm dT T 1.523 0.033 .004 .763 0.066 .843 .544 0.093 3.705 1.403 0.036 .055 .744 0.068 .935 .582 0.087 3.739 1.354 0.037 .103 .666 0.076 .046 .581 0.087 3.826 1.293 0.039 .162 .641 0.079 .134 .548 0.092 3.886 1.164 0.044 .217 .636 0.080 .213 .531 0.095 3.948 1.115 0.045 .276 .670 0.076 .290 .485 0.104 4.009 1.037 0.049 .358 .701 0.072 .370 .489 0.103 4.070 1.012 0.050 .438 .666 0.076 .445 .505 0.100 4.124 0.892 0.057 .544 .599 0.085 .512 .504 0.101 4.183 0.849 0.060 .635 .596 0.085 .579 .529 0.096 4.238 0.781 0.065 .745 .558 0.091 .648 122 Table 16. The Specific Heat of Cs MnCl ~2HZO for Sample 2 4 1, Run 15, February 16, 1967, 6050 Gauss, Orientation B. Cm dT T Cm dT T Cm dT T 2.612 0.013 1.194 .223 0.010 1.381 4.218 0.012 1.574 2.835 0.012 1.205 .293 0.010 1.396 4.417 0.011 1.581 2.621 0.013 1.216 .209 0.010 1.405 4.498 0.011 1.590 2.646 0.013 1.226 .294 0.010 1.413 4.422 0.011 1.600 2.658 0.013 1.236 .188 0.011 1.422 4.709 0.011 1.610 2.364 0.014 1.251 .978 0.011 1.431 4.774 0.024 1.626 2.710 0.012 1.265 .404 0.015 1.443 4.870 0.023 1.649 2.781 0.012 1.276 .420 0.015 1.456 5.199 0.022 1.665 2.854 0.012 1.288 .515 0.014 1.469 5.877 0.019 1.686 2.732 0.012 1.299 .614 0.014 1.483 5.964 0.019 1.705 2.534 0.013 1.310 .605 0.014 1.495 6.180 0.019 1.723 2.897 0.012 1.321 .655 0.014 1.506 6.187 0.018 1.740 2.889 0.012 1.331 .835 0.013 1.517 7.831 0.015 1.759 2.860 0.012 1.341 .857 0.013 1.529 7.774 0.015 1.773 2.938 0.011 1.351 .107 0.012 1.540 8.762 0.013 1.785 2.945 0.011 1.361 .156 0.012 1.552 9.161 0.012 1.797 2.745 0.012 1.369 .083 0.012 1.563 3.713 0.026 1.815 123 Table 16 (Continued) Cm dT T Cm dT T Cm dT T 2.631 0.019 .835 .440 0.035 .086 .678 0.075 2.959 2.637 0.019 .844 .350 0.037 .136 .537 0.094 3.073 2.354 0.022 .864 .323 0.038 .181 .586 0.086 3.252 2.216 0.023 .886 .201 0.042 .243 .570 0.089 3.374 2.096 0.024 .910 .181 0.043 .306 .508 0.100 3.484 2.021 0.025 .935 .139 0.044 .398 .524 0.097 3.591 1.799 0.028 .960 .994 0.051 .507 .530 0.096 3.687 1.722 0.029 .997 .798 0.063 .668 .534 0.095 3.777 1.598 0.032 .035 .754 0.067 .790 124 Table 17. The Specific Heat of Cs MnCl ~2HZO for Sample 2 4 1, Run 16, March 1, 1967, 8400 Gauss, Orientation C. Cm dT T7 Cm dT T C;' dT T 4.372 0.007 1.396 .276 0.005 .522 1.637 0.021 1.727 5.016 0.006 1.402 .343 0.005 .527 1.555 0.022 1.745 5.293 0.005 1.408 .565 0.005 .533 1.426 0.024 1.821 5.238 0.005 1.413 .709 0.005 .537 1.427 0.024 1.845 5.058 0.010 1.421 .412 0.005 .542 1.435 0.024 1.869 5.031 0.010 1.431 .476 0.005 .547 1.375 0.025 1.889 5.002 0.010 1.440 .589 0.006 .553 1.289 0.026 1.912 5.192 0.010 1.449 .653 0.006 .559 1.265 0.027 1.945 5.077 0.010 1.458 .717 0.006 .565 1.242 0.027 1.981 5.464 0.009 1.466 .593 0.014 .580 1.189 0.028 2.030 5.875 0.009 1.474 .908 0.019 .602 1.177 0.029 2.068 6.202 0.008 1.482 .164 0.017 .622 1.163 0.029 2.102 7.066 0.007 1.490 .048 0.017 .639 1.045 0.032 2.145 7.415 0.007 1.497 .950 0.017 .656 1.007 0.034 2.181 7.288 0.007 1.503 .803 0.019 .673 1.005 0.034 2.215 8.087 0.006 1.510 .699 0.020 .691 1.057 0.032 2.248 8.393 0.006 1.516 .556 0.022 .708 1.196 0.028 2.270 125 Table 17 (Continued) Cm dT T Cm dT T Cm dT T 1.132 0.030 .299 .919 0.037 2.606 0.644 0.079 3.149 1.060 0.032 .330 .811 0.063 2.655 0.587 0.086 3.224 1.086 0.031 .356 .845 0.060 2.716 0.701 0.072 3.302 1.005 0.034 .388 .776 0.065 2.766 0.809 0.063 3.369 1.039 0.033 .421 .768 0.066 2.831 0.581 0.087 3.444 0.912 0.037 .456 .743 0.068 2.898 0.564 0.090 3.533 0.945 0.036 .492 .747 0.068 2.966 0.485 0.104 3.624 0.857 0.039 .530 .731 0.069 3.029 0.535 0.095 3.724 0.890 0.038 .568 .737 0.069 3.098 126 Table 18. The Specific Heat of Cs MnCl -2HZO for Sample 2 4 1, Run 17, March 3, 1967, 8400 Gauss, Orientation C. Cm dT T Cm dT T Cm dT T 4.093 0.012 1.263 5.651 0.009 1.464 1.818 0.019 1.637 4.215 0.012 1.274 5.759 0.013 1.484 .889 0.018 1.657 3.680 0.014 1.295 6.132 0.012 1.500 .743 0.029 1.689 3.585 0.014 1.311 8.489 0.009 1.511 .639 0.025 1.727 4.018 0.013 1.324 9.995 0.008 1.519 .436 0.035 1.782 4.030 0.013 1.336 11.924 0.006 1.526 .371 0.037 1.835 4.245 0.012 1.348 11.822 0.006 1.533 .285 0.039 1.921 4.112 0.012 1.360 10.298 0.007 1.540 .136 0.044 2.010 4.023 0.013 1.369 10.118 0.008 1.547 .077 0.047 2.076 4.394 0.011 1.380 8.391 0.009 1.555 .982 0.051 2.165 4.657 0.011 1.390 6.444 0.012 1.566 .949 0.036 2.238 4.737 0.011 1.400 3.407 0.015 1.578 .810 0.042 2.427 4.717 0.011 1.410 2.605 0.019 1.593 .800 0.042 2.533 4.697 0.011 1.419 2.234 0.015 1.608 .808 0.063 2.625 5.313 0.009 1.436 2.042 0.017 1.621 127 Table 19. The Specific Heat of Cs MnCl °2HZO for Sample 2 4 1, Run 18, March 8, 1967, 6050 Gauss, Orientation C. Cm dT T Cm dT T Cm dT T 3.421 0.015 1.302 5.335 0.009 1.602 1.376 0.037 2.040 3.197 0.016 1.315 5.253 0.010 1.612 1.260 0.040 2.079 3.159 0.016 1.329 5.771 0.009 1.621 1.317 0.038 2.118 3.077 0.016 1.343 6.525 0.008 1.639 1.264 0.040 2.160 3.119 0.016 1.357 6.168 0.008 1.647 1.144 0.044 2.202 3.207 0.016 1.387 6.760 0.007 1.655 1.156 0.044 2.246 3.208 0.016 1.402 6.923 0.007 1.662 1.134 0.045 2.287 3.477 0.015 1.418 6.988 0.007 1.669 1.050 0.048 2.361 3.625 0.014 1.432 7.591 0.010 1.678 0.844 0.060 2.538 3.679 0.014 1.446 8.182 0.009 1.688 0.794 0.064 2.658 3.971 0.013 1.457 8.455 0.009 1.697 0.796 0.064 2.742 4.101 0.012 1.470 4.596 0.017 1.709 0.703 0.072 2.828 4.230 0.012 1.482 2.527 0.020 1.725 0.642 0.079 2.939 4.467 0.011 1.494 2.476 0.020 1.743 0.612 0.083 3.064 4.345 0.012 1.505 2.248 0.023 1.762 0.604 0.084 3.186 4.167 0.012 1.516 2.067 0.025 1.783 0.553 0.092 3.314 4.513 0.011 1.526 1.904 0.027 1.806 0.527 0.096 3.425 4.323 0.012 1.562 1.735 0.029 1.828 0.528 0.096 3.539 5.004 0.010 1.573 1.663 0.030 1.881 0.471 0.108 3.689 4.940 0.010 1.583 1.491 0.034 1.942- 0.514 0.098 3.827 5.374 0.009 1.593 1.507 0.034 1.989 0.412 0.123 3.979 Table 20. The Specific Heat of Cs 128 2 MnCl 4 1, Run 19, March 10, 1967, 9830 Gauss, Orientation C. ~2HZO for Sample Cm dT T Cm dT’ T CIn dT T 4.279 0.012 .314 1.638 .021 1.536 0.806 0.042 2.348 4.441 0.011 .335 1.532 .022 1.561 0.850 0.040 2.438 4.557 0.011 .345 1.422 .024 1.587 0.795 0.042 2.540 4.673 0.011 .355 1.351 .025 1.611 0.759 0.044 2.617 4.789 0.011 .365 1.394 .024 1.636 0.746 0.045 2.677 4.941 0.010 .374 1.352 .025 1.659 0.748 0.045 2.743 5.225 0.010 .382 1.274 .027 1.682 0.677 0.050 2.791 5.967 0.008 .399 1.280 .026 1.702 0.715 0.047 2.821 6.863 0.007 .405 1.266 .027 1.725 0.703 0.072 2.890 7.214 0.007 .413 1.162 .029 1.750 0.590 0.086 3.008 7.800 0.006 .419 1.233 .027 1.775 0.595 0.085 3.130 8.593 0.006 .426 1.250 .027 1.872 0.601 0.084 3.250 9.230 0.005 .431 1.102 .031 1.916 0.598 0.085 3.406 10.123 0.005 .437 1.039 .033 1.954 0.545 0.093 3.523 10.010 0.005 .440 1.030 .033 1.986 0.508 0.099 3.644 14.591 0.003 .444 1.066 .032 2.012 0.501 0.101 3.744 6.324 0.008 .442 0.993 .034 2.045 0.513 0.099 3.876 4.500 0.011 .450 0.982 .034 2.073 0.568 0.089 3.977 3.402 0.015 .462 0.970 .035 2.100 0.568 0.089 4.057 2.115 0.016 .476 1.074 .031 2.148 0.521 0.097 4.089 1.972 0.017 .509 0.982 .034 2.202 129 Table 21. The Specific Heat of Cs MnC14-2HZO for Sample 2 1, Run 20, March 14, 1967, 6050 Gauss, Orientation C. CT dT T ~ C dT T C dT Tr m m m 3.201 0.016 1.308 5.019 0.010 1.568 3.467 0.012 1.714 3.370 0.015 1.321 5.233 0.010 1.578 2.810 0.012 1.726 3.249 0.016 1.334 4.890 0.010 1.588 2.590 0.012 1.738 3.193 0.016 1.347 4.583 0.011 1.599 2.368 0.012 1.750 3.117 0.016 1.360 6.201 0.008 1.608 2.294 0.015 1.762 3.346 0.015 1.378 6.039 0.008 1.616 1.808 0.019 1.777 3.427 0.015 1.393 5.629 0.009 1.625 1.997 0.017 1.794 3.398 0.015 1.407 6.645 0.008 1.633 1.922 0.018 1.810 3.406 0.015 1.420 6.009 0.008 1.642 1.772 0.019 1.825 3.488 0.015 1.432 6.285 0.008 1.650 1.759 0.019 1.833 3.942 0.013 1.476 5.653 0.009 1.657 1.655 0.020 1.851 3.924 0.013 1.493 6.704 0.008 1.664 1.572 0.021 1.870 4.018 0.013 1.507 6.427 0.008 1.671 1.607 0.021 1.891 4.029 0.013 1.524 9.584 0.005 1.685 1.581 0.021 1.911 4.456 0.011 1.536 8.727 0.006 1.690 1.546 0.022 1.932 4.819 0.011 1.547 8.307 0.006 1.696 1.470 0.023 1.953 4.490 0.011 1.557 5.449 0.009 1.704 1.458 0.023 1.960 I l 1 I .1 1 l 130 Table 21 (Continued) Cm dT T Cm dT T Cm dT T 1.449 0.023 1.981 .025 0.049 .330 .579 0.087 3.341 1.457 0.023 2.002 .941 0.054 .449 .585 0.087 3.428 1.353 0.025 2.024 .883 0.057 .542 .583 0.087 3.514 1.347 0.025 2.005 .802 0.063 .669 .529 0.096 3.639 1.432 0.024 2.040 .793 0.064 .770 .502 0.101 3.771 1.369 0.025 2.099 .692 0.073 .922 .461 0.110 3.894 1.295 0.026 2.141 .659 0.077 .022 .511 0.099 3.998 1.226 0.028 2.180 .616 0.082 .114 .561 0.090 4.079 1.094 0.046 2.252 .608 0.083 .244 Table 22. 1, Run 21, March 22, 1967, 131 The Specific Heat of Cs MnCl '2H 4 2 8900 Gauss, Orientation C. O for Sample Cm dT T Cm dT T Cm dT T 3.835 0.013 1.318 13.579 0.004 .494 1.083 0.031 2.039 4.144 0.012 1.331 7.342 0.007 .502 1.064 0.032 2.070 4.422 0.011 1.341 6.827 0.007 .508 1.106 0.030 2.101 4.100 0.012 1.352 4.828 0.010 .515 1.076 0.031 2.128 4.374 0.012 1.363 3.986 0.013 .525 1.050 0.032 2.164 4.367 0.012 1.373 2.800 0.012 .536 1.106 0.030 2.205 4.428 0.011 1.383 2.490 0.014 .539 0.987 0.034 2.251 4.755 0.011 1.393 2.074 0.016 .558 0.922 0.037 2.321 4.901 0.010 1.402 1.856 0.018 .575 0.969 0.035 2.388 5.764 0.009 1.412 1.827 0.018 .593 0.865 0.039 2.515 5.219 0.010 1.421 1.712 0.020 .612 0.751 0.045 2.673 5.654 0.009 1.428 1.718 0.020 .631 0.738 0.046 2.761 5.969 0.008 1.437 1.528 0.022 .651 0.681 0.050 2.907 6.372 0.008 1.444 1.445 0.023 .690 0.670 0.050 3.011 6.592 0.008 1.452 1.407 0.024 .721 0.652 0.052 3.102 7.636 0.007 1.459 1.375 0.025 .766 0.626 0.081 3.236 8.269 0.006 1.466 1.389 0.024 .824 0.655 0.077 3.346 8.774 0.006 1.472 1.422 0.024 .868 0.595 0.085 3.482 10.751 0.005 1.479 1.197 0.028 .922 0.501 0.101 3.680 11.812 0.004 1.483 1.219 0.028 .962 0.496 0.102 3.828 14.589 0.003 1.487 1.155 0.029 .998 0.409 0.124 3.978 10.271 0.005 1.491 132 Table 23. The Specific Heat of Cs MnC14-2HZO for Sample 2 1, Run 22, April 5, 1967, 9830 Gauss, Orientation C. Cm dT T Cm dT T Cm HT TC 3.429 0.015 .271 6.781 0.007 .415 .048 0.032 2.084 3.850 0.013 .284 4.430 0.011 .422 .011 0.033 2.128 3.865 0.013 .296 3.104 0.016 .434 .962 0.035 2.185 3.880 0.013 .308 2.028 0.025 .452 .916 0.037 2.245 3.922 0.013 .319 1.768 0.019 .498 .921 0.037 2.294 3.965 0.013 .330 1.615 0.021 .526 .882 0.038 2.346 3.656 0.014 .340 1.508 0.022 .553 .859 0.039 2.407 3.757 0.013 .350 1.420 0.024 .580 .819 0.041 2.457 4.560 0.011 .360 1.401 0.024 .603 .819 0.041 2.501 4.758 0.011 .369 1.336 0.025 .627 .747 0.045 2.546 5.220 0.010 .377 1.290 0.026 .651 .774 0.044 2.627 5.400 0.009 .385 1.253 0.027 .673 .739 0.069 2.709 5.771 0.009 .392 1.304 0.026 .697 .738 0.069 2.795 6.818 0.007 .399 1.259 0.027 .720 .676 0.075 2.886 6.801 0.007 .405 1.223 0.028 .807 .570 0.089 2.971 7.876 0.006 .411 1.155 0.029 .865 .570 0.089 3.092 7.969 0.006 .409 1.253 0.027 .904 .567 0.089 3.316 9.274 0.005 .414 1.135 0.030 .950 .563 0.090 3.646 13.220 0.004 .418 1.069 0.032 .995 .464 0.109 3.953 13.474 0.004 .426 0.976 0.035 .038 .511 0.099 4.171 Table 24. 133 The Specific Heat of Cs 2 MnCl 4 1, Run 23, April 5, 1967, 3500 Gauss, Orientation C. -2HZO for Sample Cm dT T Cm dT T Cm dT T 2.703 0.019 1.290 .453 0.011 1.623 2.358 0.021 1.859 2.688 0.019 1.306 .706 0.011 1.634 2.087 0.024 1.914 2.458 0.021 1.323 .674 0.011 1.645 1.658 0.032 1.954 2.493 0.020 1.339 .156 0.010 1.656 1.657 0.031 1.985 2.607 0.019 1.355 .460 0.009 1.665 1.505 0.034 2.071 2.671 0.019 1.374 .949 0.010 1.675 1.410 0.037 2.130 3.227 0.016 1.391 .327 0.010 1.682 1.238 0.042 2.199 2.777 0.018 1.406 .701 0.009 1.692 1.171 0.045 2.246 2.801 0.018 1.421 .563 0.009 1.701 1.202 0.044 2.291 3.127 0.016 1.444 .195 0.010 1.708 1.181 0.043 2.336 3.381 0.015 1.459 .342 0.008 1.717 1.111 0.047 2.381 3.583 0.014 1.474 .954 0.009 1.725 1.103 0.047 2.449 3.716 0.014 1.488 .167 0.008 1.731 0.877 0.058 2.553 3.743 0.014 1.501 .800 0.007 1.739 0.855 0.059 2.647 3.250 0.016 1.516 .690 0.007 1.746 0.742 0.068 2.779 3.575 0.014 1.526 .879 0.006 1.753 0.754 0.067 2.887 3.702 0.014 1.539 .583 0.006 1.765 0.681 0.074 3.029 3.713 0.014 1.552 .158 0.006 1.770 0.613 0.083 3.149 3.917 0.013 1.561 .596 0.005 1.776 0.672 0.075 3.298 3.829 0.013 1.573 .553 0.006 1.781 0.544 0.093 3.437 4.011 0.013 1.583 .301 0.010 1.788 0.507 0.100 3.586 3.946 0.013 1.594 .136 0.012 1.798 0.449 0.113 3.800 3.829 0.013 1.605 .813 0.018 1.813 0.434 0.117 3.986 4.716 0.011 1.612 .450 0.021 1.830 0.420 0.121 4.171 134 Table 25. The Specific Heat of Cs MnCl ~2HZO for Sample 2 4 1, Run 24, April 5, 1967, 8900 Gauss, Orientation C. Cm dT T Cm dT 4T7 Cm dT 4T 3.381 0.015 1.266 .995 0.007 1.514 1.063 0.033 2.024 3.449 0.015 1.279 .112 0.010 1.522 1.136 0.031 2.074 3.501 0.015 1.293 .324 0.016 1.535 1.119 0.032 2.119 3.491 0.015 1.305 .170 0.024 1.555 1.097 0.032 2.178 3.525 0.015 1.318 .779 0.020 1.576 1.045 0.034 2.224 3.497 0.015 1.331 .780 0.020 1.596 0.941 0.038 2.310 3.859 0.014 1.343 .682 0.021 1.615 0.856 0.041 2.376 3.787 0.014 1.356 .573 0.023 1.635 0.882 0.040 2.472 3.913 0.013 1.368 .529 0.023 1.655 0.832 0.043 2.546 4.091 0.013 1.378 .516 0.023 1.677 0.809 0.044 2.654 4.203 0.012 1.389 .444 0.025 1.699 0.754 0.047 2.735 4.126 0.013 1.428 .398 0.025 1.721 0.766 0.046 2.851 4.796 0.011 1.440 .458 0.024 1.741 0.720 0.049 2.933 5.246 0.010 1.450 .311 0.027 1.763 0.645 0.055 3.000 6.005 0.009 1.460 .310 0.027 1.787 0.619 0.057 3.094 6.089 0.009 1.468 .259 0.028 1.811 0.750 0.047 3.196 6.985 0.007 1.476 .372 0.026 1.853 0.603 0.059 3.320 8.141 0.006 1.483 .366 0.026 1.894 0.532 0.098 3.468 9.105 0.006 1.489 .157 0.031 1.940 0.571 0.092 3.608 9.629 0.005 1.495 .195 0.030 1.970 0.494 0.106 3.751 11.642 0.004 1.498 .154 0.031 1.997 0.507 0.103 3.851 13.337 0.004 1.508 135 Table 26. The Specific Heat of Cs MnCl -2HZO for Sample 2 4 1, Run 25, April 7, 1967, 3500 Gauss, Orientation C. Cm dT T Cm 3T T CIn dT T 2.713 0.019 1.309 5.155 0.010 1.660 .966 0.026 1.878 2.620 0.019 1.326 5.667 0.009 1.670 .991 0.025 1.905 2.661 0.019 1.342 5.091 0.010 1.679 .794 0.028 1.964 2.625 0.019 1.358 6.253 0.008 1.688 .616 0.031 2.024 2.736 0.018 1.374 5.765 0.009 1.697 .439 0.035 2.098 2.878 0.018 1.392 6.367 0.008 1.705 .411 0.036 2.150 3.025 0.017 1.409 5.867 0.009 1.713 .217 0.042 2.231 3.036 0.017 1.426 7.531 0.007 1.721 .125 0.045 2.300 3.511 0.014 1.481 6.377 0.008 1.727 .018 0.050 2.401 3.097 0.016 1.502 7.101 0.007 1.735 .968 0.052 2.513 3.153 0.016 1.518 7.278 0.007 1.742 .866 0.058 2.640 3.706 0.014 1.534 6.515 0.008 1.749 .830 0.061 2.743 3.575 0.014 1.548 6.378 0.008 1.756 .717 0.071 2.883 3.851 0.013 1.562 6.596 0.008 1.762 .771 0.066 2.983 4.050 0.012 1.575 8.035 0.006 1.768 .639 0.079 3.128 4.618 0.011 1.586 7.365 0.007 1.774 .599 0.084 3.266 3.580 0.014 1.599 8.273 0.006 1.779 .549 0.092 3.470 4.597 0.011 1.611 5.239 0.010 1.786 .544 0.093 3.623 4.518 0.011 1.621 3.222 0.016 1.797 .699 0.072 3.722 4.756 0.011 1.630 2.746 0.018 1.812 .487 0.104 3.821 4.870 0.010 1.641 2.321 0.022 1.832 .479 0.106 3.904 4.722 0.011 1.651 2.315 0 1.854 .022 136 Table 27. The Temperature Changes from an Adiabatic Magnetization Experiment on Sample 1, Orientation C, April 21, 1967. T(0) *Tc3500j* T(6050) T(8400)* T(8900) 1.282 1.244 1.196 1.161 1.154 1.311 1.256 1 202 1.164 1.156 1.298 1.263 1.209 1.166 1.156 1.514 1.471 1.402 1.345 1.330 1.519 1.474 1.406 1.346 1.331 1.516 1.473 1.402 1.345 1.330 1.519 1.477 1.405 1.345 1.330 1.607 1.565 1.485 1.412 1.393 1.607 1.566 1.488 1.413 1.393 1.607. 1.561 1.486 1.412 1.392 1.607 1.565 1.489 1.412 1.392 1.729 1.685 1.601 1.485 1.449 1.728 1.687 1.602 1.486 1.449 1.727 1.671 1.602 1.485 1.447 1.726 1.671 1.603 1.485 1.447 1.798 1.757 1.672 1.573 1.550 1.798 1.756 1.669 1.572 1.550 Table 27 (Continued) 137 T(0) T(3500) T(6050) T(8400) T(8900) 1.857 1.833 1.792 1.755 1.747 1.852 1.828 1.788 1.753 1.747 1.903 1.884 1.853 1.830 1.827 1.894 1.877 1.848 1.828 1.827 1.920 1.902 1.873 1.855 1.853 1.913 1.896 1.870 1.853 1.853 2.068 2.063 2.061 2.076 2.086 2.066 2.059 2.058 2.074 2.086 2.165 2.165 2.176 2.208 2.221 2.156 2.157 2.168 2.203 2.221 2 432 2.449 2.490 2.570 2.595 2.417 2.434 2.478 2.560 2.595 3.028 3.081 3.182 3.313 3.333 2.960 2.993 3.083 3.255 3.333 3.322 3.386 3.531 3.717 3.762 3.224 3.284 3.424 3.660 3.762 "11111111111114"! W 11111111” WIT TITS 3 1293 03162 3411