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To achieve large population transfer to high vibrational levels in a selected ground-state mode of a polyatomic molecule [Cr(CO)6], we apply chirped femtosecond mid-infrared laser pulses at 2000 cm−1 to optimize vibrational ladder climbing as an energy deposition mechanism, which in turn controls the outcome of a unimolecular dissociation process. Its dependence on excitation parameters (frequency, intensity, chirp) is investigated and found to be in excellent agreement with a theoretical calculation. In particular, it is shown that optimizing vibrational ladder climbing allows for coherently controlled excitation even in a polyatomic molecule.

In this article we present two algorithms that provide optimal control pulses directly applicable in experiment. These are, namely, the optimal control algorithm, in which we incorporated spectral pressure during optimization, and complementarily a theoretical variant of the learning loop based on an evolutionary algorithm. With these tools a productive dialog between theory and experiments on optimal control is imaginable. The implementation of these pulses is assured by calculating the optimal mask pattern, that serves as an interface between theory and experiment.

The electronic ground and excited states of the vanadium monoxide (VO) molecule were studied in detail. Electronic absorption spectra for the molecule isolated in Ne matrices complement the previous gas-phase spectra. A thorough quantum chemical (multi-reference configuration interaction) study essentially confirms the assignment and characterization of the electronic excitations observed for VO in the gas-phase and in Ne matrices and allows the clarification of open issues. It provides a complete overview over the electronically excited states up to about 3 eV of this archetypical compound.

Fully quantum state selected and resolved inelastic scattering of NO(X) by krypton has been investigated. Initial Λ-doublet state selection is achieved using an inhomogeneous hexapole electric field. Differential cross sections and even-moment polarization dependent differential cross sections have been obtained at a collision energy of 514 cm(-1) for both spin-orbit and parity conserving and changing collisions. Experimental results are compared with those obtained from quantum scattering calculations and are shown to be in very good agreement. Hard shell quantum scattering calculations are also performed to determine the effects of the different parts of the potential on the scattering dynamics. Comparisons are also made with the NO(X) + Ar system.

The magnetic and thermodynamic properties of a 3.700 cm diam spherical single crystal of CuSO4⋅5H2O have been investigated from 0.02 to 0.5 °K with various constant fields from 0 to 33 000 G along the γ axis. Heat introduction was used at fields of 0, 1000, 3000, 5000, 10 000, 20 000, 30 000, and 33 000 G, in combination with previously measured entropy references, to determine the thermodynamic temperature, enthalpy, internal energy, and heat capacity in the several fields. Measurements of magnetic moment along isentropes were correlated with temperature in the region below 0.5 °K. It has been known for some time that CuSO4⋅5H2O consists of two relatively independent magnetic systems, each of one‐half mole. The linear chain system loses its entropy in a Schottky curve with a maximum near 1.5 °K. We have found that the lower system has a lambda transition with a heat capacity maximum at 0.027 °K. At temperatures below this maximum the enthalpy change (H–H0 °K) is proportional to S6/5. A consequence of thi...

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...

The heat capacity of a 3.930 cm diam spherical single crystal of neodymium ethyl sulfate 9 hydrate (NES) 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. This axis is in the isotropic ab plane which is perpendicular to the c axis. The temperature range was from 0.5 to 4.2 °K. After small adjustments were applied for the nuclear polarization of the protons, plus 143Nd (12.20%) and 145Nd (8.30%) isotopes, an effective zero of electronic and lattice entropy was found at 1.25 °K and 90 000 G. These isoerstedic entropy changes derived from the heat capacity series were interconnected by 43 series of adiabatics corrected to isentropes. The heat capacity in zero magnetic field was found to be CH=0=2.27×10−3/T2 −8.45×10−5/T3+1.13×10−3T3+2.15×10−5T5 gibbs/FW below 4 °K, where the first two terms are due to the hyperfine states of 143Nd and 145Nd. The magnetic moment was measured by the potentiometric method at the above ...

The magnetic moment of a 3.920 cm diam spherical single crystal of Nd(C2H5SO4)3⋅9H2O has been measured below 0.5 °K after cooling by demagnetization from fields of 25, 15, 10, and 5 kG along the c axis. Small amounts of irreversibility, measured by ’’entropy gain,’’ enabled correction to true magnetic moments on isentropes. Equilibrium between the lattice and electron systems was lost at fields above about 40 kG and temperatures below 0.5 °K. Entropy gain values were recorded for 0, 1000, 2500, and 5000 G on isoerstedics. An ’’adiabatic demagnetization–sample isolation calorimeter’’ was used to measure enthalpy as a function of entropy by means of electrical heating, thus enabling the determination of the thermodynamic temperature scales along the above constant and zero fields as a function of entropy. The temperature dependent component of the initial susceptibility (χ0−χT−ind) obtained from the magnetic moment data leads to the relation (χ0−0.00341) =1.2114 [1+0.0135/ T −2.69×10−4/T2+1.02×10−6/T3] cm3/...

The heat capacity of a 3.700‐cm‐diam single crystal of CuSO4·5H2O has been measured by means of heat introduction over the range 0.4°–4.2°K with magnetic fields of 1 and 3 kG parallel to the α magnetic axis. These data supplement the previous observations of Anderson and Giauque (A and G) over the range 0–90 KG. A series of 29 adiabatics has been used to evaluate the temperature, heat capacity, and other magnetothermodynamic properties without heat introduction in the range 0.021°–0.4°K. The magnetic irreversibility study reported by A and G on copper sulfate pentahydrate has been extended and indicates that reversible thermodynamic methods may be used when the electronic entropy is as low as 0.05 gibbs/mole provided the field has not been reduced below 1 kG. When the entropy is about 0.1 gibbs/mole or more the field may be reduced to zero reversibly.

The heat capacity and magnetic moment of a 4‐cm‐diam single crystal of α‐NiSo4·6H2O have been measured with stabilized fields 0‐90 kG along the bisector of the a, b axes. The temperature range was about 0.4 to 4.2°K. Magnetic saturation was not reached even at 0.4°K and 90 kG although there was no temperature coefficient of the magnetic moment below 0.7°K and any field. The heat capacity approached zero at the lower temperatures and all fields. Although idealized calculation indicates a nuclear‐spin contribution to the heat capacity in a field of 90 kG between 0.4 and 1°K, there was no evidence that this component was in equilibrium with the lattice, such as was observed when the field was directed along the c axis. The rapid decrease of electronic heat capacity to zero near 1°K at 90 kG indicates that the electron system was unable to serve as a mechanism to bring the nuclear spins into equilibrium with the lattice at temperatures where the nuclear‐spin heat capacity should have made a substantial contribution. With the assistance of temperature observations during adiabatic magnetization the entropy was evaluated over the experimental region. The entropy and its change with field, the isentropic change of temperature with field, the differential magnetic susceptibility, the internal energy, enthalpy, and magnetic work are tabulated.

A discussion of the potentiometric method of measuring magnetic induction has been given for isothermal, isentropic, and isoerstedic processes. The magnetic properties of CoSO4·7H2O have been investigated over the range 1.2° to 78°K and in fields up to 93 kgauss. Values of the differential isothermal magnetic susceptibility and intensity of magnetization as a function of field have been given. Within the limits of error, the system may be considered to consist of a major component which is a function of H/T, and a small temperature independent component with a negative field dependence. The entropy of magnetization calculated from the temperature coefficient of the magnetic work has been compared with the previously published directly determined values. The saturation value of powdered CoSO4·7H2O has been found to be 11800 gauss cm3 mole—1, and the Curie constant, Tχα,m(initial)=1.964 deg cm3 mole—1, each for the magnetic component which is a function of H/T. The temperature‐independent susceptibility inc...

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.

Values of magnetic moment, isothermal differential susceptibility, magnetic work and free energy change of single‐crystal MnCl2 have been obtained by means of a digital voltmeter integrating the dc potential on a sensing coil surrounding a spherical sample. This substance becomes antiferromagnetic near 2°K. The sample was moved vertically along the measuring coil axis which coincided with the field direction in an accurately stabilized field in a long solenoid. The observations cover the range from 1.3° to 4.2°K and fields to 95 kG. The measurements show no signs of irreversibility over the above region. The sample was high purity anhydrous MnCl2 with its b magnetic axis (a crystallographic axis) parallel to the field. The saturation value of MnCl2 was found to be 27 988 G·cm3/mole corresponding to a g=2.004 for a 6S52 state. Problems connected with the accurate use of digital integrators for such measurements are discussed and illustrated by means of various experiments. Magnetic effects due to air, shou...

The heat capacity of nickel fluosilicate hexahydrate has been measured over the range 0.30°—4.25°K in stabilized magnetic fields of 0, 0.25, 0.5, 1, 2, 3, 5, 10, 20, 40, 60, 80, and 90 kG. The field was directed along the crystallographic c axis of the 3.5‐cm‐diam, spherical, single crystal. The variation of temperature with magnetic field has been measured with a carbon thermometer in a calorimetric apparatus at nearly constant entropy. Very minor corrections for entropy leakage and the empty calorimeter have enabled the accurate tabulation of entropy changes in NiSiF6·6H2O with temperature and field over the area 0.30°—4.25°K and 0–90 kG. At the higher fields and lower temperatures it was necessary to consider a small amount of entropy removed by nuclear magnetization of the hydrogen and fluorine atoms. All of the data apply to a sphere in a homogeneous external field uncorrected for the demagnetization effect. The substance gave no indication of magnetic irreversibility. These results will serve as a b...

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, the total moment reaches definite limits at each field. Subtracting the limiting value of the temperature‐dependent moment, 5134−4.36× 10−8H2G·cm3/mole Ce3+, from the total, enabled the evaluation of the differential temperature‐independent magnetic susceptibility as, χT ind=2.221× 10−2−1.71× 10−13H2. Thus MlimitT→ 0=5134+2.221× 10−2H−4.36× 10−3H2−5.7× 10−14H3, where H is in gauss. Smoothed correlated values of the heat capacity, entropy, enthalpy, internal energy, magnetic moment and its isoerstedic temperature coefficient, differential isothermal magnetic susceptibility, and the isothermal work of magnetization have been tabulated over the range 0–90 kG and 0.5 to 4.2°K. The heat capacity of 7740 Pyrex glass has been measured over the same ranges.

An apparatus has been described for the detailed calorimetric measurement of the entropy increase accompanying isothermal demagnetization from high magnetic fields. Integrated automatic heat input controlled by a helium gas thermometer, in thermal contact with the sample, divided by the selected temperature, gives a detailed description of the entropy increase. Investigation of a powdered sample of CoSO4·7H2O has shown that application of fields of the order of 100 kOe near 1°K extracts an entropy of R ln2 as an upper limit from the electronic system of this substance. No irreversible effects were found. The entropy was found to be a function of Hi/T, over the range 1.236 to 4.211°K and from 0 to 94 500 Oe. Hi refers to the magnetic field inside the sample. The resistance of a Pt(91–92%)—W(9–8%) alloy wire used for the noninductively wound calorimetric heater was investigated. The magnetoresistance was positive, very small, and linear with field at all fields. (1/R) (dR/dT) = —5×10—5 deg—1 and (1/R) (dR/dH) = +2.5×10—9 Oe—1, range 1.2 to 4.2°K and from 0 to 95 kOe. Equations for the effect of a magnetic field on the helium gas thermometer are given.

An adiabatic demagnetization−sample isolation calorimeter, in which 3He gas provides equilibrium above 0.3°K, and isolation below 0.2°K as 3He condenses on the sample during demagnetization, has been used to investigate the properties of CZN to 0.8 m°K. The determination of entropy gain during magnetic field changes, for correcting ’’adiabaticas’’ to isentropes, has been discussed. The entropy gain was probably due essentially to heat leak (vibration) arriving at the lower temperatures. The effect of hysteresis at modest rates of field change appeared to be too small to contribute to entropy gain within the limit of error. Heat introduction at zero field has enabled the evaluation of the absolute temperature and heat capacity over the range 0.8−30 m°K. A heat capacity maximum occurred near 1.5 m°K. The heat capacity below 1.4 m°K is given by C = 3.6×1014 T5 gibbs/mole Ce3+. Below 1.7 m°K, the initial magnetic susceptibility is constant at 86.7 cm3/mole Ce3+, which extrapolates to a critical field of 58.5 ...

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. The entropy changes, in combination with the work and free energy of magnetization, enabled the evaluation of the changes of internal energy and enthalpy as a function of field and temperature. With very minor deviations it was found possible to represent the heat capacity data at all fields by means of three state Schottky functions. At zero field the two upper states are degenerate and are 4.74 cm−1 (13.55 cal/mole) above the ground state. The variation of the enthalpy of each of the individual levels with field is given. A detailed description of the magnetocalorimeter is included.

The rate of proton polarization in α‐NiSO4·6H2O has been measured as a function of magnetic field and temperature by means of the spontaneous heat evolution and change of temperature during polarization. Fields of 90, 65, 40, 25, 15, and 11 kG were directed along the a crystal axis of the 4‐cm‐diam spherical single crystal at temperatures over the range 1.5–0.4°K. The rate observations have been represented by equations of the form, kA = Z exp(− ΔH / RT). The activation enthalpies ΔH were found to correspond to the electron terms, W1–W0, previously derived from the authors' magnetothermodynamic measurements on this crystal. The proportionality factors, Z, in the above equation were field dependent with a minimum near 50 kG. The procedure involved cooling the high‐temperature proton distribution in zero field with subsequent application of the field at temperatures sufficiently low so that the rate of polarization was very small.

Adiabatic measurements on single‐crystal MnCl2 as a function of magnetic field have been tested as isentropics for use with isoerstedic heat capacity data in a ``saw‐tooth'' method of establishing entropy values as a function of field and temperature in the region above 1°K where absolute temperatures are readily available. All measurements were made with the field parallel to the b magnetic axis. Adiabatics with an entropy less than about 0.6 gibbs/mole became irreversible at some unknown temperature below 1°K. However, determinations of the differential magnetic susceptibility on these adiabatics disclosed three high peaks at low temperatures and fields of about 4, 13, and 15 kG. The peaks are evidence of substantial but gradual magnetic structural changes which are much more complex than previously realized. The correction of data obtained during demagnetization for minor heat leak to give true entropy values is discussed.

Values of field and magnetic moment have been measured on 40 magnetic isentropes of NiSiF6·6H2O. The field was directed along the crystallographic c axis of the 3.5‐cm‐diam spherical single crystal. Typical derived values of the magnetic work, differential isentropic susceptibility, relative heat content (enthalpy), and relative internal energy have been tabulated. A principal purpose of the measurements has been to investigate the evaluation of temperature and other thermodynamic properties in the presence of any available magnetic fields without heat introduction below 0.3°K. This avoids the difficulty of distributing heat under small temperature heads in poor thermal conductors. Absolute temperatures from the thermodynamic equation T = (∂H/∂S)H, where H, S, and H are heat content, entropy, and field, respectively, and values of heat capacity CH = T (∂S/∂T)H have been derived at representative fields. At entropies below 1 gibbs/mole and within about ±200 G of zero field, the adiabatic magnetic susceptib...

Detailed magnetothermodynamic measurements have been made on a 3.934‐cm‐diam spherical single crystal of α‐MnCl2·4H2O, at temperatures below 1.7°K and with fields below 25 kG directed along the c crystallographic axis. Forty‐one adiabatics, selected to cross the so‐called boundaries in the magnetic regional diagram of antiferromagnetic MnCl2·4H2O were measured. Values of the temperature and magnetic moment along adiabatics were recorded automatically at very close magnetic field intervals. Equilibrium measurements of magnetic moment between 5 and 10 kG were made after the sample had been stabilized at constant field and temperature. The measurements were made by moving the sample slowly with respect to coils to avoid disturbing the equilibrium moment. Heat capacity measurements, supplementing those of Reichert and Giauque [J. Chem. Phys. 50, 4205 (1969)], were made at close intervals of field and temperature across the magnetic regional boundaries. The combined data made it possible to measure the entropy...

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...

The heat capacity and magnetic moment of a 3.934 cm diameter spherical single crystal of α‐MnCl2·4H2O have been measured with stabilized solenoid fields of 0, 1, 5, 10, 14, 22, 25, 40, 65, and 90 kG, along the [100] crystal axis. The magnetic saturation value, 27 999 G·cm3 mole−1, obtained at both 65 and 90 kG, and 0.46°K, indicates that the temperature independent susceptibility is zero and the saturation moment of the temperature‐dependent system is 27 999 G·cm3 mole−1, equivalent to g[100] = 2.005. At 90 kG the nuclear spins contributed a heat capacity term of 5.6 × 10−3 T−2gibbs mole−1. The amount of enthalpy required to remove quanta of angular momentum from the saturated condition at 90 kG was found to be 20.2 cal mole−1. This is less than gβH = 24.09 cal mole−1, the magnetic work, by 3.9 cal mole−1. This difference is the amount of stored internal energy contributed by the saturated condition to this limiting process, and is consistent with antiferromagnetic interactions. Extrapolation of the magne...

Values of the magnetic moment of a 3.5‐cm‐diam spherical single crystal of NiSiF6·6H2O have been determined over the range 0.3°—4.25°K and 0–90 kG. The field was parallel to the c crystallographic axis. The observations have been used to give values of the isothermal differential magnetic susceptibility, and the isothermal work of magnetization. The data have been combined with our previous measurements of the heat capacity and entropy in magnetic fields to give values of the internal energy and heat content. The above properties will, with later observations. serve as a basis for extending the determination of the magnetothermodynamic properties of NiSiF6·6H2O into the region below 0.3°K. All of the data refer to a spherical crystal without correction for the demagnetizing effect since this is unnecessary and inconvenient in a thermodynamic treatment. This substance is very completely saturated at the available magnetic fields and temperatures. The saturation value, corrected for diamagnetism, was found to be 12547 G·cm3/mole, corresponding to a g=2.246. Observations of the saturation moment at fields of 60–90 kG indicate that there is no appreciable ``temperature‐independent'' paramagnetic component in the magnetic moment.

The thermodynamically reversible isothermal change of entropy of MnCl2 with magnetic field directed along the b magnetic axis has been measured calorimetrically. At 1.498°K (∂S/∂H)T is positive below 7.5 kG, then negative to magnetic saturation. At 1.333°K, (∂S/∂H)T is negative below 4.5 kG, then positive to 9.25 kG, after which it is negative to saturation. The isothermal entropy change with field has also been measured by a two‐step process, in which: (1) the internal‐energy change was obtained by combining calorimetric measurements with irreversible magnetic work; (2) combining the internal‐energy change with reversible measurements of magnetic work. Measurements of heat capacity in constant fields have been repeated to improve accuracy and to apply a severe test of magnetothermodynamic reversibility by series of measurements made after varied approaches to the starting conditions. The entropy, internal energy, and heat content have been given over the range 0–4.2°K and 0–100 kG, and there are evidently no transition points in the entire area investigated, although gradual changes in magnetic structural types undoubtedly occur. Some values of the heat capacity at constant magnetic moment have been calculated.

Magnetothermodynamic data for α‐NiSO4·6H2O, with magnetic fields along two axes, the c crystallographic axis ([001] direction) and the [110] direction, have been interpreted using a spin‐Hamiltonian–molecular‐field model for the NI(H2O)6+ 2 complexes. Best values for the spin‐Hamiltonian parameters are D = 4.741 cm− 1 (singlet–doublet separation for H = 0); gz = 2.2158, gxy = 2.2495 (principal values for the g tensor of the Ni(H2O)6+ 2 complexes); φ = 39.00° (angle the z magnetic axes of the four Ni(H2O)6+ 2 complexes per unit cell makes with the c tetragonal screw axis—the x magnetic axes are perpendicular to the tetragonal axis); γ = 0.272 mole / cm3 (molecular field constant representing an isotropic combined ferromagnetic exchange and dipole–dipole interaction between Ni+ 2 ions); and λ = − 281 cm− 1 (the spin–orbit coupling constant). For the c axis the temperature‐independent susceptibility α was computed to be 0.75 × 104, while for the [110] direction it was 0.98 × 10− 4 cm3/mole. However, a best f...

The magnetothermodynamic properties of a 3.912‐cm‐diam spherical single crystal of CuK2 (SO4)2· 6H2O have been measured down to 0.007°K with fields along the α magnetic axis. Forty‐four of 49 adiabatic magnetizations from unknown low temperatures and zero field were shown to be isentropes. Measurements with electronic entropies below 0.08 gibbs/mole showed entropy production at low fields. The measurements were combined with available reference data above 0.5°K to determine the thermodynamic temperatures, both in and out of magnetic fields, without heat introduction below 0.5°K. The zero‐field temperatures at entropies below 0.8 gibbs/mole were systematically different from those obtained previously after demagnetization with the field along the γ magnetic axis. It is concluded that an unstable magnetic structure, with an energy of about 0.003 cal/mole above that of the stable structure at 0°K, has been frozen‐in. The instability develops below the lambda region where cooperative effects dominate the prop...

Equations for calculating the magnetothermodynamic properties, under varied conditions of field and temperature, are presented and discussed for a model based on a theory of paramagnetism in the solid state. An averaging technique, making use of a digital computer, is derived for use in evaluating the theoretical equations for randomly oriented crystals of paramagnetic material. These equations are applied to the magnetic system of randomly oriented crystals of CoSO4·7H2O. It was shown previously that after subtracting a small temperature independent term from the measured isothermal differential magnetic susceptibility and magnetization, the data followed an H/T function, where H is the magnetic field within the crystals. (The experimental magnetic entropy measurements were made in the liquid‐helium range of temperature. Magnetic induction measurements were made in the liquid‐helium and liquid‐hydrogen temperature ranges, and at the boiling point of liquid nitrogen.) Since CoSO4·7H2O has two different Co...

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...

Values of the magnetic moment of a 3.5‐cm‐diam spherical single crystal of NiSiF6·6H2O have been determined over the range 0.3°—4.2°K and 0–90 kG. The field was perpendicular to the c crystallographic axis. The differential isothermal magnetic susceptibility and the isothermal work of magnetization are given. The data have been combined with our previous related measurements of heat capacity and entropy to evaluate the changes in internal energy and enthalpy. All of the data apply to a spherical crystal without correction for the demagnetizing effect. The temperature‐independent magnetic moment was estimated as 3.4×10−4H G·cc/mole from the high‐field observations. Using this value to correct the data, ga,b=2.233, and a similar correction of our previous data with H ∥ c axis gives gc=2.241 for the temperature‐dependent moment. Measurements of magnetic moment as a function of field on 40 adiabatics have been used to extend the thermodynamic temperature and heat capacity below the region of heat introduction...

This work is a continuation of our previous magnetothermodynamic measurements on a 3.934‐cm‐diam spherical single crystal of MnCl2·4H2O in which case the field was directed along the c crystallographic axis. Here the heat capacity and magnetic moment have been measured between 0.3° and 4.2°K with stabilized solenoid fields of 0, 1, 5, 7.5, 10, 14, 18, 22, 25, 40, 65, and 90 kG, along the b crystallographic axis. At 0.716°K and fields of 90, 80, and 70 kG. the electron system was magnetically saturated. The derived temperature‐independent magnetic susceptibility was found to be − 1.6 × 10−4 cm3 mole−1 and the saturation moment of the temperature‐dependent system is 27 974 G·cm3 mole−1, equivalent to gb = 2.004. At 90 kG the nuclear spins were found to contribute a heat capacity term of (5.9 × 10−3 / T2) gibbs mole−1. The amount of enthalpy required to remove quanta of angular momentum from the saturated condition at 90 kG was found to be 20.63 cal mole−1 of angular momentum. This is less than gβH = 24.07 c...

A spectroscopic technique is introduced to measure the amount of vapor species appearing from shocked metals upon unloading into vacuum. The degree of vaporization is correlated with the shock wave entropy, from which follows the possibility to determine the equation of state at pressures above 200 kbar.

This is a continuation of our magnetothermodynamic measurements on a 3.913‐cm‐diam spherical single crystal of CuK2(SO4)2·6H2O. The magnetic moment and heat capacity have been measured over the range 0.4–4.2°K, with fields of 0, 0.5, 1.0, 2.5, 5, 10, 15, 25, 40, 65, and 90 kG directed along the α magnetic axis. At 0.5°K the magnetic moment reached limiting values at fields in the range 40–90 kG. Mα(limit) = Mα(sat) + χαH = 6405 − 2.22 × 10−4HG·cm3/mole, where χα is the temperature‐independent susceptibility (diamagnetic), and 6405 G·cm3/mole is the saturation value of the temperature‐dependent paramagnetic system. Thus gα = 2.294. This may be compared with our previously measured gβ = 2.237 (corrected) and gγ = 2.071. No evidence of magnetic hysteresis was observed at temperatures above 0.4°K. Calorimetric measurements near magnetic saturation in the range 40–90 kG and magnetic susceptibility measurements near zero field each indicated weak ferromagnetic (presumably dipolar) interactions. The heat capacit...