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.     

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 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.     

The structural, elastic and thermodynamical properties of zinc-blend structure InN from first principles

A theoretical study of the structural, elastic and thermodynamic properties of the cubic zinc-blende (ZB) structure InN are presented in this paper by performing first principles calculations within local density approximation. The values of lattice constant, bulk modulus and its pressure derivatives and elastic constants are in excellent agreement with the available experimental data and other theoretical results. It is found that the ZB structure InN should be unstable above 20 GPa mechanically. The pressure and temperature dependencies of the bulk modulus, the heat capacity and the thermal expansion coefficient and the entropy S, as well as the Grüneisen parameter are obtained by the quasi-harmonic Debye model in the ranges of 0-1500 K and 0-25 GPa.     

The structural, elastic and thermodynamic properties of thorium tetraboride

The structural, elastic and thermodynamic properties of thorium tetraboride (ThB₄) have been investigated by using first-principles plane-wave pseudopotential density functional theory with generalized gradient approximation. The behaviors of structural parameters under 0-70 GPa hydrostatic pressure are studied by means of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) geometry optimization scheme. By using the stress-strain method, single crystal elastic constants are calculated to test the mechanical stability of the crystal structure and to determine mechanical properties such as bulk modulus at each pressure. However, in order to study the thermodynamic properties of ThB₄, the quasi-harmonic Debye model is used. Then, the dependencies of bulk modulus, heat capacities, thermal expansions, Grüneisen parameters and Debye temperatures on the temperature and pressure are obtained in the whole pressure range 0-70 GPa and temperature range 0-1500 K.     

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.     

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.     

Analysis of P-V-T relationships and thermodynamic properties for some alkali halides

In this paper, Pandey approximation for the volume dependence of Anderson-Grüneisen parameter at fixed pressure, Anderson approximation for the temperature dependence of thermal expansivity, the equations of thermal expansivity along isobars derived by Shanker et al., and the presented approximation for the volume dependence of Anderson-Grüneisen parameter along isobars, have been used to study and predict the pressure-volume-temperature (P-V-T) data and the variations of the volume expansion coefficient and isothermal bulk modulus with temperature and pressure for NaCl, CsCl, LiF, NaF crystals, up to 30 GPa and in the temperature range 298-1073 K. The calculated values are compared with each other. It is found that these equations-of-state are valid and present good agreement with the available experimental data.     

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.     

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     

Elastic properties of Se and As2Se3 glasses under pressure and temperature

The sound velocities and their pressure and temperature variations of Se and As₂Se₃ glasses have been determined by means of a pulse superpositions method, and other elastic constants and their pressure and temperature derivatives were calculated from these data. The bulk modulus was found to be 94·6 kbar for Se glass and 143·7 kbar As₂Se₃ glass, both of which are higher than the values calculated from the previous compression data. No anomaly was observed in any of the pressure and temperature dependence of elastic behavior of these glassses. Furthermore, the comparison of the pressure and temperature derivatives of the bulk modulus indicates that the thermodynamic self-consistency is satisfied on these materials. The bulk moduli of these glasses and crystalline As and Se were used to obtain an empirical bulk modulus-volume relationship for compounds in the As?Se system. The acoustic Grüneisen parameter was calculated and compared with the thermal Grüneisen parameter.     

Elastic, thermal and structural properties of platinum

The thermal equation of state (EOS) for platinum has been calculated to 300 GPa and 3000 K using ab initio molecular dynamics employing the local density approximation (LDA) and the projector augmented-wave methods (PAW). Direct ab initio molecular dynamics avoids the simplifying assumptions inherent in empirical treatments of thermoelasticity. A third-order Birch-Murnaghan equation EOS fitted to the 300 K data yielded an isothermal bulk modulus of B_T0=290.8 GPa and a pressure derivative of B_T′=5.11, which are in better agreement with the measured values than those obtained by previous calculations. The high-temperature data were fitted to a thermal pressure EOS and a Mie-Grüneisen-Debye EOS. The resulting calculated thermal expansion coefficient, α₀, temperature derivative of the isothermal bulk modulus, (∂B_T/∂T)_V, and second temperature derivative of the pressure, (∂²P/∂T²)_V, were 1.94×10⁻⁵ K⁻¹, −0.0038 GPa K⁻¹, and 1.7×10⁻⁷ GPa² K⁻², respectively. A fit to the Mie-Grüneisen-Debye EOS yielded values for the Grüneisen parameter, γ₀, and its volume dependence parameter, q, of 2.18 and 1.75, respectively. An analysis of our data revealed a strong volume dependence of the thermal pressure of platinum. We also present a qualitative analysis of the effects of intrinsic anharmonicity from the calculated Grüneisen parameter at high temperatures.     

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.     

Electronic structure,elastic and thermodynamic properties of α-phase Na3N under pressure from first principles

The structural, electronic, elastic and thermodynamic properties of α-phase Na₃N under pressure are investigated by performing first principles calculations within generalized gradient approximation. The elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio dependencies on pressure are also calculated. The thermodynamic properties of the α-phase Na₃N are calculated using the quasi-harmonic Debye model. The dependencies of the heat capacity and the thermal expansion coefficient, as well as the Grüneisen parameter on pressure and temperature are investigated systematically in the ranges of 0–1 GPa and 0–100 K.     

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.     

Thermodynamic characteristics of the alkali metals (particularly sodium) in the quasiharmonic approximation

The Grüneisen parameters are calculated for several alkali metals. The dependences of the Grüneisen, Slater, and Dugdale-MacDonald versions of this parameter on the relative compression (or extension) of the lattice and on the temperature are derived. A comparison shows that the theoretical isotherms for the sodium equation of state agree satisfactorily with experiment.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 49–52, November, 1969.     

Valence force field theory, elastic, acoustic and thermodynamic properties and a potential function of TeO2 glass

A short survey has been made on the extensive work that is being done on the pressure derivatives of the second order elastic constants (SOEC) to ascertain various properties of substances. Hence an attempt has been made to correlate the pressure derivatives to some properties of the substances. Thus some equations have been derived to correlate the Grüneisen parameter which is evaluated from Schofield's equations and Bhatia-Singh's (BS) parameters. They have been used to compute the longitudinal (γ_g^L) and transverse (γ_g^T) Grüneisen constants. γ_g^L calculated by different methods agree well with experiment. γ_g^T obtained from BS parameters gives rather higher value while Schofield's equations give results in agreement with experiment. The DeLaunay-Nath-Smith (DNS) equation has been used to derive a relation to compute γ_g^el (elastic). A method has been extended to calculate the third order elastic constants (TOEC) and it is found to give excellent values of TOECs in agreement with experiment. The absorption band position of TeO₂ has been predicted to occur at 276 cm⁻¹. The phonon dispersion curves have been calculated through BS equations for TeO₂. Several other properties of TeO₂ have been computed such as thermal Grüneisen parameter γ_g^th, its pressure derivatives (γ_g^th)′≡(dγ_g^th/dP), the pressure variation of bulk modulus C₁≡(dK_T/dP)_T and its pressure derivatives that is (dC₁/dP)_T which is in turn related to (γ_g^th)′, the heat capacity at constant volume C_V, and the second Grüneisen constant Q. In some cases we calculated these quantities by different methods and the agreement between them is good. Besides we evaluated δ_T^AG the Anderson Grüneisen parameter. Another important aspect of the present investigations is the formulation of the potential function (PF) of TeO₂ from which we calculated SOECs and these are found to be in excellent agreement with experiment. All other properties mentioned already have also been calculated through the use of the newly formulated PF and the calculated values obtained through various other equations are in good agreement with those obtained from PF. According to valence force field (VFF) all atomic forces can be resolved into bond bending β and bond stretching α forces. It is shown that TeO₂ does not satisfy Martins unity rule. Hence it is concluded that there is an effective dynamic charge on Te in TeO₂. Using the experimental elastic constants the bond bending force β and bond stretching force α and also their pressure derivatives have been evaluated. In addition the reststrauhlen optic frequency ω has been calculated. A self consistent check has been made by evaluating C₄₄ through the calculated values of α and β.     

Extreme compression behaviour of equations of state

The extreme compression (P→∞) behaviour of various equations of state with K′_∞>0 yields (P/K)_∞=1/K′_∞, an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K^′=dK/dP, and K′_∞, the value of K^′ at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch–Murnaghan equation, Poirier–Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ_∞, the third-order Grüneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.     

Structural, electronic, elastic and thermal properties of Mg2Si

First-principles calculations of the lattice parameter, electron density maps, density of states and elastic constants of Mg₂Si are reported. The lattice parameter is found to differ by less than 0.8% from the experimental data. Calculations of density of states and electron density maps are also performed to describe the orbital mixing and the nature of chemical bonding. Our results indicate that the bonding interactions in the Mg₂Si crystal are more covalent than ionic. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the plane-wave pseudopotential method, is applied to study the elastic, thermal and vibrational effects. The variations of bulk modulus, Grüneisen parameter, Debye temperature, heat capacity C_v, C_p and entropy with pressure P up to 7 GPa in the temperature interval 0-1300 K have been systemically investigated. Significant differences in properties are observed at high pressure and high temperature. When T<1300 K, the calculated entropy and heat capacity agree reasonably with available experimental data. Therefore, the present results indicate that the combination of first-principles and quasi-harmonic Debye model is an efficient approach to simulate the behavior of Mg₂Si.