R. A. Fisher

Thermal Conductivity and Heat Capacity of 7740 Pyrex below 4°K and in Magnetic Fields to 90 kG

The thermal conductivity of Pyrex 7740 glass has been measured over the temperature range 0.4 to 4°K and in magnetic fields from 0 to 90 kG. As expected, the conductivity was unaffected by the field. The glass had an iron content of 0.02%. The heat capacity of Pyrex, at constant magnetic fields, has been measured over the above range of temperature and field. There was a considerable field effect due to the iron content. The variation of temperature with field was measured on a series of isentropes and this enabled the evaluation of the entropy. The change of temperature of Pyrex during adiabatic demagnetization at various values of the entropy is shown as a graph for this typical sample. A description of the apparatus used for the measurement is included.

Magnetothermodynamics of gadolinium gallium garnet. I. Heat capacity, entropy, magnetic moment from 0.5 to 4.2 °K, with fields to 90 kG along the [100] axis

The magnetic moment of a 2.44 cm diam spherical single crystal of gadolinium gallium garnet has been measured with stabilized fields of 500, 1000, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G along the [100] axis, over the range 0.35 to 4.2 °K. The heat capacity was measured over similar ranges, except that 500 G was omitted and zero field included. The magnetic moment reached saturation at 0.35 °K and 90 000 G. The electronic and nuclear spin components of the heat capacity at 90 000 G could be separated from each other near 1 °K, thus locating a zero of entropy for the electronic system. By means of 34 adiabatics, corrected to isentropes, which crossed most of the isoerstedic heat capacity series, the entropies as a function of field and temperature were evaluated in terms of the zero reference. The sample has (0.4 ± 0.1) mole% excess entropy over the maximum R ln 8 for Gd3+ ion. Thus the sample must have contained 0.4 mole% excess Gd over the stoichiometric amount for Gd3Ga5O12. Usi...

Isotope Sieve for 4He vs 3He. The Low‐Temperature Heat Capacity of SiO2 Glass before and after Contact with 4He and 3He

The heat capacity of two samples of annealed SiO2 glass has been measured over the range 0.5°−4.2°K. The data for a solid cast cylinder are represented by C = 0.33T + 0.271T3 + 0.0220T5μgibbs / g. A hollow cylinder made from tubing gave the result C = 0.26T + 0.234T3 + 0.0165T5μgibbs / g. The heat capacity of each sample was also measured at 90 kG with no detectable change. It has been found that 4He can be sorbed by the glass at temperatures below 4.2°K and cannot be appreciably removed by long evacuation at 4.2°K. This effect has been studied in terms of the temporarily altered heat capacity after the glass has been exposed to liquid and gaseous 4He. Similar experiments with 3He indicate that it is not sorbed in SiO2 glass below 4.2°K, and exposure to liquid or gaseous 3He produces no change in heat capacity. It is suggested that SiO2 glass may be useful in separating 3He and 4He by selective sorption.

Magnetothermodynamics of Antiferromagnetic, Ferroelectric β‐Gd2(MoO4)3. III. Heat Capacity, Entropy, Magnetic Moment of the Electrically Polarized Form from 0.4 to 4.2°K with Fields to 90 kG along the b Crystal Axis

The magnetic moment of a 2.49‐cm diam spherical single crystal of electrically polarized β‐Gd2(MoO4)3 has been measured at stabilized fields of 500, 1000, 1500, 2000, 2200, 2300, 2500, 3500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G along the c crystal axis and over the range 0.3–4.2°K. The heat capacity has been measured at fields of 0, 1000, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G over a similar temperature range. The temperature dependent magnetic moment reached saturation at the higher fields and low temperatures. As expected, any effect of reversing the magnetic field with respect to the electrical polarization was too small to be detected, i.e., less than 0.01% of the magnetic moment. The general character of the magnetic moment and its temperature derivatives vs field at 0.5°K and below indicates the development of an antiferromagnetic system. The fact that the heat of vaporization of momentum (h/2π) from the essentially saturated state exceeds 2MsatH/7, bo...

Magnetothermodynamics of Ce2Mg3(NO3)12· 24H2O. I. Heat capacity, entropy, magnetic moment from 0.5 to 4.2°K with fields to 90 kG along the a crystal axis. Heat capacity of Pyrex 7740 glass in fields to 90 kG

The heat capacity of a 4.023 cm diam spherical single crystal of cerium magnesium nitrate hydrate has been measured with stabilized fields of 0, 1000, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G along the a crystal axis, from 0.5 to 4.2°K. The zero of electronic entropy was reached at fields of 90, 65, and 40 kG and the lower temperatures. The isoerstedic entropy changes derived from heat capacity series were interconnected by 28 series of temperatures vs fields on isentropes. Analysis of the heat capacity data indicated that the first excited doublet is 70.5± 1.0 cal/mole Ce3+ above the ground doublet. The splitting factor of the ground doublet was evaluated at gH=1.8385−5.20× 10−12H2± 0.001. An applied magnetic field introduces an internal energy change of 1.39× 10−15H3 cal/mole Ce3+ (H in gauss) to the ground doublet enthalpy separation. The magnetic moment was measured over the same ranges of field and temperature as the heat capacity. Near 0.5°K, and over the range 40 to 90 kG, t...

Magnetothermodynamics of ferroelectric, ferroelastic, antiferromagnetic β‐terbium molybdate. I. Heat capacity, entropy, magnetic moment of the electrically polarized form from 0.4 to 4.2 °K with fields to 90 kG along the c crystal axis

The magnetic moment and heat capacity of a 1.170 cm diam spherical single crystal of electrically polarized β‐Tb2(MoO4)3 have been measured at stabilized fields of 500, 1000, 1500, 2500, 5000, 10 000, 15 000, 25 000, 40 000, 65 000, and 90 000 G, along the c crystal axis, and over the range 0.4–4.2 °K. The heat capacity at zero field was also measured over the same temperature range. The temperature dependent magnetic moment reached saturation at fields of 65 and 90 kG. Its value, 43 050 G cm3/mole Tb3+, corresponds to a splitting factor of gc= 15.41. The small temperature independent magnetic susceptibility χTind = 0.0070 cm3/mole Tb3+ indicates that the upper levels of the 7F6 multiplet are well above the ground doublet. As expected, any effect of reversing the magnetic field with respect to the electrical polarization was too small to be detected. The T3 lattice heat capacity was evaluated at saturating fields of 65 and 90 kG since the electronic heat capacity vanished at these high fields owing to the...

Magnetothermodynamics of Single Crystal CuSO4·5H2O. V. Fields Along the β Axis. Thermodynamic Temperature without Heat Introduction below 0.5°K. A Reference at 0.035°K

The magnetic and thermodynamic properties of a 3.700‐cm‐diam spherical single crystal of CuSO4·5H2O have been investigated down to 0.02°K with fields along the β magnetic axis. Thirty‐eight magnetizations from unknown low temperatures to reference conditions were performed under adiabatic conditions, and 35 were essentially isentropes. These have been used to determine the thermodynamic temperature and heat capacity, both in and out of magnetic fields, without heat introduction. A temperature reference at 0.035°K has been suggested. It has been pointed out that proving a process to be isentropic is no guarantee that “frozen‐in” entropy and energy situations have not developed during the isentropic process, thus conserving nonequilibrium entropy. Entropy conserved in this way cannot be used as an equilibrium variable in determining temperature. It is evident that detailed methods of investigation designed to detect such nonequilibrium magnetic structural situations will be desirable. When “frozen‐in” entro...

Magnetothermodynamics of α‐NiSO4·6H2O. I. Heat Capacity, Entropy, Magnetic Moment, and Internal Energy, from 0.4° to 4.2°K, with Fields 0–90 kG along the c Axis

The heat capacity and magnetic moment of single‐crystal α‐NiSO4·6H2O have been measured over a range of about 0.4°—4.2°K in stabilized fields of 0–90 kG. The field was parallel to the c crystallographic axis of the 4‐cm‐diam spherical sample. Although magnetic saturation was not attained even at 90 kG and 0.4°K, there was essentially no temperature coefficient of the magnetic moment below 0.7°K at any field. The heat capacity approached zero for all fields except for a small calculable contribution due to nuclear polarization at high fields. At 90 kG it was found that the nuclear‐spin heat capacity at 0.95°K and above was in general equilibrium. At 0.90°K equilibrium was quite slow indicating a rather rapid increase in relaxation time with decreasing temperature. Each heat capacity series provided a zero‐entropy reference, above that due to nuclear spin. These references agreed with precise measurements of the temperature change with field on adiabatics joining the various isoerstedic heat capacity series...

Magnetothermodynamic Properties of MnCl2 from 1.3° to 4.4°K at 90 kG. A Zero Entropy Reference. The Magnetomechanical Process at Absolute Zero

The heat capacity of single‐crystal manganous chloride has been measured in a constant magnetic field, accurately stabilized at 90 000 G and parallel to the b magnetic axis (a crystallographic axis), over the range 1.4° to 4.35°K. The heat capacity approaches zero and magnetic saturation occurs near 1°K, thus providing a reference for the zero of electronic entropy which might otherwise be difficult to obtain due to possible irreversible behavior of this antiferromagnetic system below 1°K. It has been established that loss of magnetic moment from the saturated magnetic domain of the crystal occurs with increasing temperature through the loss of individual Bohr units of angular momentum. By extrapolating reversibly measured values of the magnetic moment, on isoerstedic paths to 0°K, the magnetomechanical process of magnetization at the absolute zero has been described in fairly complete detail. The magnetization curve at 0°K consists of two nearly straight lines joined by a small deviation near 10 kG and a...

Heat Capacity and Entropy of NiSiF6·6H2O from 0.35° to 4.2°K with Magnetic Fields 0–90 kG Perpendicular to the c axis. The Use of 3He Gas Conduction in Calorimetry

The heat capacity of nickel fluosilicate hexahydrate has been measured over the range 0.35–4.2°K in stabilized magnetic fields of 0, 1, 5, 10, 20, 40, 60 and 90 kG. The field was perpendicular to the crystallographic c axis of the 3.5‐cm‐diam single crystal. The entropy changes in NiSiF6·6H2O have been accurately tabulated over the ranges 0.35°—4.2°K and 0–90 kG, by combining the heat‐capacity data and the change in temperature with field on isentropics. The temperature was measured by means of a carbon thermometer which was also used to introduce calorimetric heat. The total electronic entropy removed to magnetic saturation was Rln3. The substance gave no indication of hysteresis at any field or temperature. At the higher fields and lower temperatures it was necessary to consider a small entropy change due to nuclear magnetization of the hydrogen and fluorine atoms. As a practical rule it has been shown that a 2 mtorr pressure of 3He, which is sufficient to cause liquefaction near 0.3°K, is acceptable in...