Specific heat of the Hf2Fe,Hf2Co,and Hf2Rh intermetallic compounds

The specific heat under constant pressure, C _p, of intermetallic compounds Hf₂Fe, Hf₂Co and Hf₂Rh with the Ti₂Ni structure was obtained by means of differential thermal analysis in the temperature range 275–740 K. The results differ significantly from the Debye theory, even when a correction for optical phonons in Einstein approximation is considered, which indicates existence of a defect contribution to the specific heat. Relative entropy has been determined and the obtained results were fitted and analysed. The anomalous temperature behaviour of C _p is discussed, having in mind results of previous investigations of these and similar systems, obtained by other methods.     

Thermodynamic and transport properties of UPt3

In the normal phase of UPt₃, the magnetoresistivity is large and positive with the striking feature of a quasi-independence of the temperature and magnetic field terms; the thermoelectric power has aT ² dependence and the susceptibility is almost constant up to 4 K. The superconducting transition is broadened and the specific heat jump is weak due to the strong anisotropy of its normal phase. FromT _c to 146 mK (the lowest experimental temperature), a largeT ² contribution is observed in the specific heat, but the thermal conductivity has the same dependence only below 150 mK. These results are compared with the predictions given for polar odd-pairing superconductivity.     

Low-temperature magnetic properties of HoRh4B4

The low-temperature magnetic properties of HoRh₄B₄ have been studied by means of measurements of the magnetic susceptibility, magnetization, specific heat, thermal expansion, and magnetostriction. The ferromagnetic phase transition at T _M= 6.7 K shows almost ideal S = 1/2 mean field behavior in the specific heat. Crystal field effects due to the splitting of the J = 8 Hund's rule ground state of the Ho³⁺ ions result in Schottky anomalies in the specific heat and the thermal expansion and are also revealed in the low-field magnetic susceptibility and the magnetostriction. Information on the ground state doublet of the 4f electrons has been obtained from the nuclear contribution to the specific heat below 1 K and the high-field magnetization below T_M.This research was supported by the Schweizerische Nationalfonds zur Forderung der wissenschaftlichen Forschung (HRO), by the Department of Energy under Contract No. EY-76-S-03-0034-PA227-3 (LDW, MBM), and by the National Science Foundation under Grant No. NSF/DMR77-08469 (DCJ)     

Critical-region thermal expansion in CuK2Cl4 · 2H2O

The Curie-point anomaly in thea-axis linear thermal expansion coefficient of CuK₂Cl₄ · 2H₂O (T _c=0.88° K) has been observed using the three-terminal capacitance technique. Length changes of the 3.8-mm single-crystal sample were determined to within approximately 0.1 Å. In the critical region our data suggest a logarithmic singularity as found previously for the specific heat. However, imperfections in the sample limit the divergence of the expansion coefficient at temperatures closer than 0.01T _c to the transition. From a comparison of the linear expansion coefficient with the specific heat in the critical region, the stress dependence of the Curie temperature is calculated. We find that the temperature derivative of the spin-correlation function describing nearest neighbor magnetic ions is not proportional to the temperature derivative of the spin-correlation function describing next nearest neighbors. Furthermore, the exchange parameters characterizing nearest and next nearest neighbor interactions do not have equal stress dependences. Between 1.5 and 2.5° K the thermal expansion coefficient is proportional to the inverse square of the temperature. Comparison of the expansion coefficient with the specific heat in this temperature range indicates that the temperature derivative of both spin-correlation functions is proportional toT ^–2. The stress dependence of the Curie temperature calculated from data in this region agrees within experimental error with the value found from different considerations using data in the critical region.Work supported by National Science Foundation.     

Specific heat of superconductor-normal metal composites

The specific heat of Th-Nb composites has been measured to determine the extent to which a dense array of Nb rods will enhance the superconducting energy gap of the surrounding Th matrix at temperatures well belowT _c of the Th. A directional solidification technique has been used to prepare an acicular composite having a triangular array of 500-nm-diameter Nb rods in a Th matrix with a center-to-center spacing of 1500 nm. At low temperatures, where both metals are superconducting, the specific heat indicates that the Th matrix has an energy gap about 10% larger than bulk Th, so there is some enhancement by the Nb rods. BetweenT _c of Nb andT _c of Th there is clear evidence of an induced energy gap in the Th, but as yet there is no theory for the specific heat in this regime. A field as small as 20 mT will quench all evidence of proximity-induced superconductivity in the Th, indicating a strong field dependence of the Cooper pair decay lengthK _N ^–1 .This work has been authored by a contractor of the U.S. Government under contract No. W-7405-eng-82. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so for U.S. Government purposes.Operated for the U.S. Department of Energy by Iowa State University under contract No. W-7405-Eng-82. This research was supported by the Director for Energy Research, Office of Basic Energy Sciences, WPAS-KC-02-02-02.     

The Tricritical Point

Analysis of critical phenomena in bodies with the tricritical point, based on the Gibbs equations for the critical state, is performed. The generalized Gibbs equations allow for the difference in the symmetry of the phases, which is characteristic of bodies with the tricritical point. Successive analysis enables one to clarify all characteristics of the critical state of the class of bodies being treated, whose singularity is that their phase diagram contains regions of phase transitions of both the first and second kind, and to establish the regularity of variation of the properties in the vicinity of the tricritical point. In particular, it is demonstrated that the specific heat C _V goes to infinity at the tricritical point following the logarithmic law (along the critical isochore), and the sound velocity vanishes. In the regions of phase transitions of the second kind, the specific heat C _p reaches an infinitely high value at the transition point T _s at p = const also following the logarithmic law. The line of phase equilibrium is a cubic parabola. In the critical state, the second variation of the internal energy ₂ E(S, V) is zero; and, in the vicinity of the line of phase transitions of the second kind, it varies as (T – T _c)². In the critical state, the heat conductivity goes to infinity, etc.     

Anomalous specific heat of liquid 3He above the superfluid transition temperature

The contribution to the specific heat due to order parameter fluctuations in liquid ³He just above the superfluid transition temperature T _c is calculated exactly within a Landau theory approach. The effect turns out to be unobservably small and thus cannot explain the large (9%) rise in specific heat above the normal state value at the saturated vapor pressure in a recently reported experiment. We do not find the divergence of the specific heat at T cobtained earlier by Thouless from a microscopic calculation and indicate how the difference can be reconciled.     

Supersolidity and the Thermodynamics of Solid Helium

The specific heat of solid helium in the temperature range below about 1.2 K has been found to contain a term varying as T ⁷, in addition to the usual T ³ contribution always found in a crystalline dielectric solid. It has been proposed by Anderson, Brinkman and Huse, (Science 310, 1164 (2005)) that the existence of this T ⁷ term supports their theory of supersolidity. However, in this paper we show that corrections to the phonon specific heat arising from phonon dispersion are much larger than expected based on simple order of magnitude estimates and, as a consequence, it is very unlikely that the existence of this T ⁷ term can be considered as evidence for supersolidity.      

Specific heat studies in Ho-Ba-CuO superconductors: Fermionic and bosonic contributions

The specific heats of superconducting HoBa₂Cu₃O_7-δ (T _c≅ 92 K) have been theoretically investigated in the temperature domain 70 ≤T ≤110 K. The bosonic (phonons) contribution to the specific heat is estimated from Debye model in the harmonic approximation for high temperature expansion (T > θ_D/2π) using the moments of the phonon density of states. The fermionic constituent as the electronic specific heat is deduced using a suitable trial function above and belowT _c. As a next step the contribution of specific heat by charge oscillations (plasmons) are obtained. The theoretical results from bosonic and fermionic terms are then compared with the experimental results. We find that the specific heats from electronic as well as plasmon term are only a fraction of lattice specific heat and in particular, plasmons do not influence the thermal conduction significantly. The implications of the above analysis are discussed.     

Phase diagram and concentration susceptibility of 3He-4He mixtures near the tricritical point

The inverse concentration susceptibility (/\x) _T of ³He-⁴He mixtures has been calculated from high-resolution vapor-pressure measurements and in situ measurements of the dielectric constant very close to the tricritical point. The measurements have been fitted to a scaling-law equation of state. In the normal fluid a logarithmic correction term was necessary to obtain a good fit. In the superfluid a regular correction term, proportional to (x – x _t)², was evaluated. New measurements of the phase-separation curve confirm our earlier measurements on the ³He-rich side and extend the measurements much closer to the tricritical point on the ⁴He-rich side. The tricritical point is at temperature T = 0.8669 ± 0.0005 K and mole fraction x = 0.6716 ± 0.0014.Work performed under the auspices of the U. S. Department of Energy.     

Contributions to the heat capacity of solid molybdenum in the range 300–2890 K

An analysis has been made of contributions to the heat capacity of Mo, with a special examination of the effect of the formation of vacancies near the melting point. Literature values of the heat capacity at constant pressure C _P were fitted to a polynomial. Using recent measurements of the velocity of sound at high temperature and literature data of the coefficient of expansion, the dilation correction was made to C _P to obtain the heat capacity at constant volume C _V . This heat capacity was taken to consist only of independent contributions from electron excitations (C _VE), harmonic lattice vibrations (C _VH), anharmonic lattice vibrations (C _VA), and the formation of vacancies (C _VV). Three models of C _VE (free electron, band theory, and electron-photon) have been used to calculate the electronic contribution, and an examination of the results indicates that the electron-phonon model is the best. C _VH is assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity C _VEX= C _V -C _VE -C _VH is taken as equal to (C _VA +C _VV ), where C _VA is linear with temperature (C _VA=A T), and we have fitted the values of C _VEX to determine the values of A and the energy and entropy of formation of vacancies which give the best fit. The anharmonic contribution is positive. The energy of vacancy formation is 100,000 J · mol^–1, in agreement with estimates by Kraftmakher from C _P data. The entropy of formation is 11.6 J · mol^–1 · K^–1. The concentration of vacancies at the melting point (2890 K) is calculated to be 6.3%.     

Specific heat of quench-condensed hydrogen films

The specific heatC(X, T) of quench-condensed films of H₂ has been measured as a function of ortho concentration X with 0.28–2 at temperatures between 0.4 and 3.0 K. The films were condensed on evaporated gold substrates held at several temperaturesT. _cond between 1.0 and 3.5 K. The observed specific heat is attributed to orientational ordering of the ortho-H₂ molecules. For the films withX = 0.74 condensed atT _cond>2.5 K, there is a peak which indicates a bulk-like ordering transition. At temperatures below the peak, there is a large contribution toC, which is not present in bulk H₂, and which we attribute to short-range ordering size effects. AsT _cond is decreased below 2.5 K, the shape of the specific heat curve changes, and the peak at 1.5 K is replaced by a gradual rise with a sharp drop above 2.6 K. Despite this strong dependence ofC onT _cond, the entropy per molecule at 3 K is only weakly dependent onT _cond and comparable to that for bulk H₂. Film annealing at 3.4 K produces a change in the specific heat curve, and a study of this effect is presented. The ortho-para conversion rate of the films condensed at the various temperatures is found to be same as in bulk, well-annealed H₂. As in bulk H₂, the transition temperature inferred from the location of the specific heat peak or anomaly decreases withX. Unlike in bulk H₂, there is no temperature hysteresis inC for any of the quench-condensed films. This implies that the ordering transitions are not accompanied by a martensitic transformation.     

Logarithmic Temperature Dependence of the Sound Speed in Amorphous Silica at Low Temperatures

The tunneling model has enjoyed considerable success in describing the low temperature properties of glasses. However, departures from the tunneling model have been noted in experiments at very low temperatures (below 100 mK). We have measured the change in the sound speed ΔV/V ₀ between 1 and 40 mK in an amorphous silica double paddle oscillator oscillating at 14 kHz. Most importantly, the sound speed displayed the logarithmic temperature dependence predicted by the tunneling model to a lower temperature than in previous experiments on amorphous silica. Below 3 mK the sound speed departed from the logarithmic temperature dependence and began to level off. The leveling off can be explained by either an intrinsic effect or thermal decoupling of the sample from the thermometer. By heating the oscillator with a gamma source to determine the thermal resistance of the oscillator, it was found that a relatively large stray heat input (9×10⁻⁴ nW) would be needed to cause the leveling off. Further work will be needed to determine whether the leveling off is due to stray heat or intrinsic physics.     

Contributions to the heat capacity of alpha (HCP) titanium from 200–1000 K

The heat capacity at constant pressure C _p of alpha (HCP) titanium from 200 to 1000 K has been analyzed for contributions from lattice vibrations and electron excitations. Experimental data in the literature have been used to obtain the heat capacity at constant volume C _V by the dilation correction. From C _V has been subtracted an harmonic lattice contribution C _VH given by the Debye heat capacity using a single Debye temperature and an electronic contribution C _VE . The difference C _V –(C _VH +C _VE ) is positive, and from about 600 to 1000 K it is real in the sense that it is larger than the experimental uncertainty in C _V . This difference is attributed to an anharmonic lattice vibration contribution C _VA . Two models for C _VE have been used. One, which includes electron-phonon enhancement, leads to a C _VA of about 15% of C _V at 1000 K. The other takes into account the shift in the density of states with temperature and leads to a C _VA of about 5% of C _V      

Magnetic Specific Heat of Heavily p-Type Doped (Zn,Mn)Te:P

The magnetic contribution to the specific heat of bulk crystals of Zn_1–x Mn _x Te ( x = 0.03) heavily (up to 10¹⁹ cm^–3) p-type doped with P is studied over the temperature range 0.5–15 K and magnetic field range 0–3 T. The magnetic specific heat observed at zero magnetic field indicates that a substantial part of the magnetic ions has the degeneracy of their magnetic ground state lifted by d–d and p–d exchange interactions. The effect increases for doped and annealed samples with higher concentration of conducting holes. We have also carried out a theoretical analysis that takes into account the contributions due to small magnetic clusters, single magnetic ions in crystal field of distorted crystal lattice, and low energy excitations of the p–d exchange-coupled system of local moments and carriers.     

Aluminum. II. Derivation of C v0from C p and comparison to C v0 calculated from anharmonic models

The specific heat at constant pressure, C _p, of aluminum measured by Ditmars, Plint, and Shukla has been reduced to the volume V ₀ appropriate for 0 K employing the Murnaghan equation. The C _v0 thus obtained is compared with the theoretical C _v0 calculated in the harmonic and the lowest-order anharmonic approximation from three different pseudopotentials (Harrison, Ashcroft, and Dagens-Rasolt-Taylor) as well as a phenomenological Morse potential. The higher-order ( ⁴) anharmonic contributions are calculated from the same nearest-neighbor Morse potential as in the lowest-order anharmonic theory. The role of the vacancy and the higher-order anharmonic contributions to C _v0 has been examined and we conclude that the ⁴ contributions to C _v0 are much smaller than the vacancy contribution. After removal of the vacancy contribution, the reduced C _v0 is found to be in excellent agreement with the Ashcroft and Harrison pseudopotentials as well as the Morse potential including the ² and ⁴ contributions to C _v0.     

Experimental investigation of nonuniform heating and heat loss from a specimen for the measurement of thermal diffusivity by the laser pulse heating method

Nonuniform heating effect and heat loss effect from the specimen in the measurement of thermal diffusivity by the laser pulse heating method have been experimentally investigated using an axially symmetric Gaussian laser beam and a laser beam homogenized with an optical filter. The degree of error is theoretically estimated based on the solution of the two-dimensional heat conduction equation under the boundary condition of heat loss from the surface of the specimen in the axial direction and the initial conditions of axially symmetric nonuniform and uniform heating. A correction factor, which is determined by comparison of the entire experimental and the theoretical history curves, is introduced to correct the values obtained by the conventionalt _1,2 method. The applicability of this modified curve-fitting method has been experimentally tested using materials in the thermal diffusivity range 10⁻³ to 1 cm²·s⁻¹. The experimental error due to the nonuniform heating and heat loss was reduced to approximately 3%.     

Thermal and magnetic properties of copper potassium tutton salt below 0.15 K

The specific heat and the ac susceptibility of copper potassium tutton salt have been measured between 0.01 and 0.15 K. The magnetic phase transition from the paramagnetic to the canted ferromagnetic state was observed at 29.5 mK in zero field. From the obtained electronic entropy curve this salt is considered to be a Heisenberg-type ferromagnet. The copper nuclear specific heat of the hyperfine splitting is estimated to beC _N =1.1×10^–5 R/ (T ²/[K²]), which is one order smaller than the value calculated from previous results of the paramagnetic resonance.     

Comment on the specific heat of superfluid 3He

We present numerical results for the specific heat of ³He-B in the weak-coupling-plus model. We find that the full temperature dependence of the specific heat is accurately determined by the specific heat jump at T _c .This provides a test of the T _c /T _F expansion scheme for calculating strong coupling effects in superfluid ³He.     

Contribution of equilibrium vacancies to vanadium caloric properties

For the first time, data have been obtained on the parameters of the contribution of equilibrium vacancies to the caloric properties of vanadium: the vacancy formation energy, E = 1.22 eV, the vacancy formation entropy, S = 26.8 J/(mole K)⁻¹, and the temperature dependence of the vacancy concentration (at the vanadium melting temperature, T _m = 2220 K, the concentration equals to c = 4.2%). These values are determined on the basis of experimental measurements of the average heat capacity of vanadium. From analysis of the interconnection between the vacancy contribution and the limit temperature of superheating of the beginning of melting, T _sh, we found that the most reliable vacancy-free straight line of the average heat capacity corresponds to (T _sh/T _m) ≈ 1.25 and may serve as a reliability criterion for calculation of the vacancy contribution in metals.