Analysis of thermodynamic identities for materials under extreme compression

Some basic relationships for materials under extreme compression are analyzed with the help of the calculus of indeterminates. The analysis presented here provides an understanding of the origin of identities and constraints at infinite pressure which are satisfied by all physically acceptable equations of state. These identities involve the bulk modulus and its pressure derivatives, the Grüneisen parameter and its volume derivatives, the thermal expansivity, and the Anderson-Grüneisen parameter. The identity for the third-order Grüneisen parameter in terms of the pressure derivatives of the bulk modulus at extreme compression is valid even if the free-volume parameter changes with pressure.     

Second order and third order Grüneisen parameters at extreme compression

On the basis of the free volume theory of Grüneisen parameter (γ) and using the calculus of indeterminates, it is found that the second order Grüneisen parameter (q) and the second pressure derivative of bulk modulus (KK″) change in a similar manner in the limit of extreme compression. The ratio of q and KK″ becomes finite at infinite pressure. This finding has been used further to obtain a relationship for the third order Grüneisen parameter λ in terms of pressure derivatives of bulk modulus up to the third order. The results are found to be consistent with the identities obtained recently by Shanker et al. [14] using the free volume theory.     

Pressure and volume dependence of Grüneisen parameter of solids

Using the assumption δ_T=δ_T0(V/V₀)^k and the Grüneisen parameter γ macroscopic definition expression, we obtained a relationship for the volume dependence of the Grüneisen parameter γ. We have calculated the Grüneisen parameter γ with this relationship for NaCl and ε-Fe at high pressure under study. The calculated values of γ are found to show fairly in good agreement with available experimental data.     

Equation of state and thermodynamics of fcc transition metals: A pseudopotential approach

A simple pseudopotential model is used for the calculation of the phonon spectra at the equilibrium volume and under pressure. The model is based on the secondorder perturbation theory with the local pseudopotential acting on thes electrons while thed electrons contribution is simulated by the repulsive Born-Mayer interatomic potential. Pressure influence on the lattice properties was studied for small compressions (mode Grüneisen parameters) as well as for ultrahigh pressure (equation of state up to 1 TPa). Results of the lattice dynamics calculations were used for determining temperature dependence of the lattice heat capacity and of the macroscopic Grüneisen parameter. The Kohn anomaly at the small wave vectors obtained previously in palladium, platinum and rhodium affects strongly the temperature dependence at low temperature.     

Formulation of the third-order Grüneisen parameter at extreme compression

We present a direct method using the basic principles of calculus to derive the expression for the third-order Grüneisen parameter in terms of the pressure derivatives of bulk modulus at extreme compression. The derivation presented here does not depend on the assumptions regarding the values of free-volume parameter and its variation with pressure. The identities used in the present analysis are valid at extreme compression for all physically acceptable equations of state.     

Thermal expansion behavior of silicon at low temperatures

Lattice parameters, thermal expansion coefficients and Grüneisen parameters of silicon are determined by an X-Ray diffraction method in the temperature range of 180–40 K without the use of liquid gases. Thermal expansion of silicon becomes negative below 120 K which is discussed in terms of its lattice vibrations and crystal structure.     

Electronic and thermal properties of B2-type AlRE intermetallic compounds: A first principles study

The ground state electronic structure and thermal properties of B₂-type intermetallic compounds AlRE (RE: Pm, Sm, Eu, Tb, Gd and Dy) have been studied using a self-consistent tight-binding linear muffin-tin orbital (TB-LMTO) method at ambient as well as at high pressure. These compounds show metallic behavior under ambient condition. The band structure, total energy, density of states and ground state properties like lattice parameter, bulk modulus are calculated in the present work. The Debye-Grüneisen model is used to calculate the Debye temperature and the Grüneisen constant. The calculated results are in good agreement with the reported experimental and other theoretical results. The variation in the Debye temperature with pressure has also been reported. We present a detailed analysis of the role of f electrons of RE in the AlRE system.     

Lattice properties in the vicinity of the martensitic transformation in TiNi

A pronounced peak in the thermal expansion coefficient — and thus in the Grüneisen parameter — has been found at the temperature corresponding to the martensitic transformation in TiNi. This finding, together with results of ultrasound wave propagation studies, attests to anomalous lattice-dynamical behaviour in the vicinity of the phase transition. Ultrasonic wave attenuation and velocity data are interpreted on the basis of Akhieser-type, phonon viscosity damping. Results obtained are consistent with the hypothesis that a soft phonon mode plays a dominant role in the lattice properties of TiNi near the transition.     

Vibrational and thermodynamic properties of metals from a model embedded-atom potential

This work provides the first systematic test of validity of the embedded-atom potentials of Mei et al. [Phys. Rev. B 43 (1991) 4653], via a complete study of the vibrational and thermodynamic properties of isoelectronic transition (Ni, Pd, Pt) and noble (Cu, Ag, Au) metals. Phonon dispersion curves and thermal properties are studied within the quasiharmonic approximation. Results for the temperature-dependence of the lattice constants, coefficients of linear thermal expansion, isothermal and adiabatic bulk moduli, heat capacities at constant volume and constant pressure, Debye temperatures and Grüneisen parameters are presented. Electronic contribution to the specific heat is included explicitly via density-functional calculation. The calculated phonon frequencies for Ag and Cu agree well with the results from inelastic neutron scattering experiments. Despite less satisfactory agreement between calculated and measured phonon frequencies for the other four metals, isothermal and adiabatic bulk moduli and the specific heats of all metals are reproduced reasonably well by the model, while the Grüneisen parameter and Debye temperature are underestimated by about 10%. The coefficient of linear thermal expansion is underestimated with respect to measured values in most cases except for Pt and Au. The results are good for Pt up to 1000 K and for Au up to 500 K.     

Pressure behaviour and thermal expansion of NiMnSb from first principles calculations

A computational study of the pressure and thermal behaviour of NiMnSb within the framework of density functional theory and the Debye-Grüneisen model is reported. The theoretical values of equilibrium lattice parameter, bulk modulus, its pressure derivative, Debye temperature, Grüneisen constant and coefficient of thermal expansion are estimated from electronic structure calculated by the full-potential nonorthogonal local-orbital minimum basis method (FPLO). The bulk modulus and its pressure derivative have been computed using the Murnaghan form of the equation of states. The volume-temperature dependence was obtained by minimisation of the free energy as a sum of the total energy of the rigid lattice and the free energy of the vibration lattice. The thermal expansion coefficient for the studied NiMnSb, obtained within the Debye theory including anharmonicity, is in good agreement with experimental results.     

Low-temperature lattice thermal expansion of the II-VI semiconductor ZnSe

The low-temperature lattice thermal expansion of the wide gap semiconductor ZnSe is investigated using the quasi-harmonic theory of thermal expansion. The generalized Grüneisen parameters (GPs) of the elastic waves propagating in different directions with respect to the [001] crystallographic axis are calculated using the second-and third-order elastic constants. The values of the generalized GPs γ_j are generally positive except for γ₂ from θ=25 to 65°. The Brugger gamma is calculated and the low-temperature limit of the Grüneisen gamma is determined using the procedure of Menon and Rao. The low-temperature limit has been obtained as 0.46 for ZnSe. The volume expansion is expected to be positive down to absolute zero for ZnSe, since is positive.     

Pressure dependence of the Raman frequencies for the translational mode in ammonia solid II

We study here the translational mode of the ammonia solid II near the melting point by calculating its Raman frequencies as a function of pressure for the fixed temperatures of 230.4, 263.4 and 297.5 K. We perform this calculation of the Raman frequencies using the volume data by means of our Grüneisen relation. The Raman frequency shifts as the volume changes with the pressure, exhibit an anomalous behaviour near the melting point in the ammonia solid II.This anomalous behaviour can be examined experimentally on the basis of our calculations given in this study.     

The influence of pressure on the Mössbauer effect

A study was made of the pressure dependence of the intensity of the Mössbauer line, and the dependence of this quantity on the specific volume of the crystal, which has the same form for all these crystals in the first approximation, was derived for regular atomic crystals in the Grüneisen approximation. The change in intensity of the Mössbauer line due to pressure can be converted, except for a multiplication factor, to a change in intensity of this line caused by a change in temperature.     

Structural and thermodynamic properties of Os from first-principles calculations

We investigate the structural, thermodynamic and electronic properties of Os by plane-wave pseudopotential density functional theory method. The obtained lattice constants, bulk modulus and cell volumes per formula unit are well consistent with the available experimental data. Especially, from our calculated bulk modulus, we conclude that Os is more compressible than diamond. Moreover, the temperature induced phase transition of Os from HCP structure to FCC structure has been obtained. It is found that the transition temperature of Os at zero pressure is 2702 K. However no transition pressure is found in our calculations. The effect of bulk modulus B as well as other thermodynamic properties of Os (including the thermal expansion α and the Grüneisen constant γ) on temperatures have also been studied. Our calculated thermal expansion α=1.510×10⁻⁵ K⁻¹ and the Grüneisen constant γ=2.227 for HCP structure at room temperature agree very well with the experimental data. The density of states for HCP structure at 0 K and FCC structure at transition temperature 2702 K are also investigated in our work.     

Thermoelastic and thermodynamic properties of harzburgite—An upper mantle rock

A number of thermoelastic and thermodynamic properties such as compressibilities, specific heat ratio, specific heat capacities, Grüneisen parameters, Debye temperature, the melting temperature, and their dependence on temperature and pressure have been obtained for the harzburgite rock of Oman ophiolite suite. Debye temperature Θ_D and the ratio of the specific heats are the basic inputs which are determined here by making use of the seismic velocities and the density data. The specific heat capacities C_P and C_V are evaluated from the thermodynamic equations as well as from the Debye theory. These data along with the computed values of compressibilities have been used to evaluate the Grüneisen parameter and its dependence on temperature through thermodynamic and acoustic relations. The computed values of the Debye temperature has also been found very helpful to estimate the melting temperature of the rock whose pressure dependence is analyzed following the Clausius-Clapeyron equation.     

Anharmonic self energy shift of a librational mode

A sizable anharmonic self energy shift of the Raman active librational modes in KN₃ has been found and shown to be a linear function of temperature above the Debye characteristic temperature of the solid (ca. 351°K). The Grüneisen parameter for the librational mode is estimated from the data to be 1.40. The Raman active mode involving the translation of the K⁺ ion shows a negligibly small anharmonic shift.     

Thermodynamic properties of a diluted Heisenberg ferromagnet with interaction anisotropy—Magnetocaloric point of view

The thermodynamics of a site-diluted ferromagnetic Heisenberg model for spin S=1/2 with interaction anisotropy in spin space is investigated. The study is aimed at presenting the magnetocaloric properties of such a model, including the entropy and temperature changes in magnetization/demagnetization processes, generalized Grüneisen ratio as well as the quantities characterizing the efficiency of magnetic cooling cycles. The results are obtained using pair approximation (PA) method and extensively compared with the molecular field approximation (MFA) calculations. The importance of interaction anisotropy and site-dilution is discussed. The inadequacy of the MFA approach (even on the qualitative level) is found for selected quantities, while PA provides the results which are consistent with the experimentally observed behavior.     

一种直接测量W-J参数的实验方法

本文探索了一种直接测量W-J参数的方法. 实验选用NaCl作为试样, 在快速压缩过程中原位测量样品的温度和压力的变化值. 通过温度修正使测量值在原理上更符合等熵压缩过程的结果, 并采用大幅度增压结合中值定理得出中点压力处温度随压力的变化率, 进而根据R=(P/T) (∂T/∂P)_S关系式求出W-J参数, 整个过程没有引入其他参数. 此外, 作为对比, 我们还从相关的物态方程、经验公式和已知参数出发计算了NaCl的W-J参数及其随压力变化的关系. 结果表明: 实验测得的NaCl的W-J参数随压力增加而增加; 实验结果与计算值符合得很好. 这说明快速增压直接测量物质的W-J参数是一种可行且可靠的方法. 关键词： NaCl W-J参数 快速增压 高压     

Low-temperature elastic experiments on glasses at very low frequencies

The Grüneisen parameter and the low-frequency elastic loss of vitreous silica, PMMA, and of the metallic glasses PdSiCu, PdZr, and CuZr have been measured between 0.4 K and 6 K using an elasto-caloric technique. The absorption measurements between 5·10^–3 Hz and 30 Hz give further support for the tunneling model in a hitherto poorly investigated domain of relaxation times. New features of the low-temperature behaviour of glasses are a long-time creep and an absorption peak of the metallic glass PdZr nearT _c.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

Theoretical investigations on structural, elastic and electronic properties of thallium halides

Theoretical investigations on structural, elastic and electronic properties, viz. ground state lattice parameter, elastic moduli and density of states, of thallium halides (viz. TlCl and TlBr) have been made using the full potential linearized augmented plane wave method within the generalized gradient approximation (GGA). The ground state lattice parameter and bulk modulus and its pressure derivative have been obtained using optimization method. Young's modulus, shear modulus, Poisson ratio, sound velocities for longitudinal and shear waves, Debye average velocity, Debye temperature and Grüneisen parameter have also been calculated for these compounds. Calculated structural, elastic and other parameters are in good agreement with the available data.