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.     

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.     

Heat capacity of Heusler alloys: Ferromagnetic Ni2MnSb,Ni2MnSn,NiMnSb and antiferromagnetic CuMnSb

We report the results of the investigation of the specific heat of the ferromagnetic Heusler Ni₂MnSn, Ni₂MnSb, NiMnSb and antiferromagnetic CuMnSb alloys. The low-temperature behaviour of the specific heat may be described as C=γT+βT³ for ferromagnetic compounds and as C=γT+δ T²+βT³ for antiferromagnetic CuMnSb. The values of the density of states from the heat capacity measurements are higher than those from electronic band structure calculations. Debye temperatures are in a good agreement with those obtained from thermal expansion measurements. The Grüneisen parameter is calculated for Ni₂MnSn and CuMnSb from the magnetic contribution to the specific heat in the vicinity of T_C or T_N.     

Coupled temperature dependences of volume and compressibility

We present a new method for understanding the changes with temperature of the volume and compressibility of solids. These changes depend on five parameters: V ₀, B ₀, Θ, γ _G and δ _T. V ₀ and B ₀ are the atomic volume and bulk modulus at T?=?0?K, Θ is the Debye temperature, γ _G is the Grüneisen parameter, and δ _T is the Anderson–Grüneisen parameter. Equations for the temperature-dependent volume, bulk modulus and thermal expansion are given, and examples of the use of these equations are provided, with particular emphasis on the light actinides. For the elements, we examine the relationship between experimental values of γ _G and δ _T, and find no clear correlation. In particular, Swenson's rule, which states that the bulk modulus does not change with temperature if the volume is held constant, is a poor approximation to the data. We reveal a new useful approximate relationship between dB/dP and γ _G. We find that the thermodynamic quantity q, which describes the variation in γ _G with volume, distributes around 2, not around 1, as often assumed. We show that the thermal- expansion behavior of Si and Ge (including negative thermal expansion at low temperatures) are well described with the use of a two-level invar model.     

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.     

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.     

Electronic and thermodynamic properties of B2-FeSi from first principles

The electronic and thermodynamic properties of B2-FeSi have been investigated using the first-principles method based on the plane-wave basis set. The calculated equilibrium lattice constant is in good agreement with available experimental and theoretical data. Our results have shown that B2-FeSi was a narrow gap semiconductor of above 0.055 eV and exhibited metallic characteristics. The density of states (DOS) can also describe orbital mixing. Using the quasi-harmonic Debye model, the thermodynamic properties of B2-FeSi have been analyzed. Variations of the Debye temperature Θ_D, thermal expansion α, heat capacity C_v, entropy S and the Grüneisen parameter γ on temperature T and pressure P were obtained successfully in the ranges of 0-2400 K and 0-140 GPa.     

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.     

Elastic and thermodynamic properties of CaB6 under pressure from first principles

The elastic and thermodynamic properties of CsCl-type structure CaB₆ under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB₆ under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ_B, Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB₆ up to 100 GPa. The thermodynamic properties of the CsCl-type structure CaB₆ are predicted using the quasi-harmonic Debye model. The pressure-volume-temperature (P-V-T) relationship, the variations of the heat capacity C_V, Debye temperature Θ_D, and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0-100 GPa and 0-2000 K.     

On the spectral frequency distribution of translational vibrations in a face-centered cubic lattice of the C60 fullerite

The spectral frequency distribution g(ω) of translational lattice vibrations in the face-centered cubic phase of the C₆₀ fullerite at T = 300 K is calculated by the superposition method. The contribution from the translational vibrations to the heat capacity C _V of the C₆₀ fullerite and the x-ray characteristic temperature gJ_R entering into the exponent of the Debye-Waller factor are determined using the calculated frequency distribution g(ω). The results of the calculations are in good agreement with experimental data. It is noted that the librational and intramolecular lattice vibrations observed in the C₆₀ fullerite do not contribute significantly to the temperature-induced decrease in the x-ray diffraction intensity at T = 300 K. The Grüneisen parameters γ_mod calculated from the x-ray diffraction data are consistent with the thermodynamic Grüneisen parameters γ_lat at temperatures T ≤ 80 K but substantially exceed those at T ≈ 300 K. New x-ray diffraction experiments are proposed for independently determining the anomalously large negative values of the parameter γ₀, which is actually an orientational analog of the Grüneisen parameter.     

Thermodynamic properties of OsB under high temperature and high pressure

The energy-volume curves of OsB have been obtained using the first-principles plane-wave ultrasoft-pseudopotential density functional theory (DFT) within the generalized gradient approximation (GGA) and local density approximation (LDA). Using the quasi-harmonic Debye model we first analyze the specific heat, the coefficients of thermal expansion as well as the thermodynamic Grüneisen parameter of OsB in a wide temperature range at high pressure. At temperature 300 K, the coefficients of thermal expansion α_V by LDA and GGA calculations are 1.67×10⁻⁵ 1/K and 2.01×10⁻⁵ 1/K, respectively. The specific heat of OsB at constant pressure (volume) is also calculated. Meanwhile, we find that the Debye temperature of OsB increases monotonically with increasing pressure. The present study leads to a better understanding of how the OsB materials respond to pressure and temperature.     

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.     

Charge ordering and elastic anomalies in NaxCoO2

We report in-plane resistivity and elastic constant C₃₃ measurements on the Na_0.8CoO₂ and Na_0.5CoO₂ systems. An ordering transition is found at T₀=280 K for Na_0.8CoO₂. The temperature dependence of the elastic constant C₃₃ propagating perpendicular to the CoO₂ layers is interpreted, in a phenomenological approach, as being due to the anharmonicity of atomic vibrations. The effective Grüneisen parameter γ_eff deduced directly from the temperature dependence of C₃₃ exhibits important changes at the charge ordering, magnetic and metal-insulator phase transitions.     

The hydrostatic pressure derivatives of the elastic constants of indium and an indium cadmium alloy

The hydrostatic pressure derivatives of the elastic stiffness constants of indium and indium-3.4 at.% cadmium alloy single crystals have been obtained from pulse echo overlap measurements of the dependence of ultrasonic wave velocities upon pressure. The softest zone centre acoustic phonon mode in indium is a shear mode propagating k along the [101] direction rather than that (k[110], e[11?0]) which drives the ferroelastic phase transition in the indium-cadmium alloys. The derivative δ((C₁₁ – C₁₂)/2)/δP is positive, accounting for the stability of the fct structure of indium under high pressure. Using the quasiharmonic, anisotropic continuum model the acoustic mode Grüneisen parameters have been calculated and are discussed in terms of mode softening. The high temperature limiting value$\text{\$}\text{?}$γ_H (= 2.56) of the mean acoustic mode Grüneisen parameter is found to be close to the thermodynamic Grüneisen parameter γ^th (=2.5).     

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.     

Grüneisen parameter for HCP iron at extreme compression

The Thomas–Fermi approximation gives the Grüneisen parameter γ=γ_∞=1/2 for all materials at extreme compression (P→∞ or V→0). After re-analyzing the existing experimental data of volume dependence of Grüneisen parameter γ of hexagonal close-packed (HCP) iron, we find that γ=1/2+a(V/V ₀)^1/3+b(V/V ₀) ⁿ , where a, b and n are constants. Based on this new form of γ, the second Grüneisen parameter q, the Debye temperature θ_D and the shear sound velocity v _s of HCP iron are discussed in the present work. It is found that the zero pressure second Grüneisen parameter q ₀=0.654, which is consistent with the previously determined value of HCP iron for Earth's core physics from Dubrovinsky et al. The calculations for the Debye temperature and the shear sound velocity are also found to be in good agreement with the experimental data.     

On the Debye temperature and Grüneisen parameters for hexagonal close-packed crystals consisting of p-H2 and o-D2 molecules

The expressions for the Debye temperature Θ as well as for the first (γ = ?[?ln(Θ)/?ln(V)] _T ) and second (q = [?ln(γ)/?ln(V)] _T ) Grüneisen parameters are derived based on the Mie-Lennard-Jones pair atomic interaction potential. The conditions imposed on the Θ(V/V ₀), γ(V/V ₀), and q(V/V ₀) dependences for V/V ₀ → 0 and for V/V ₀ → ∞ are analyzed. Here, V/V ₀ is the ratio of the molar volumes for pressure P at temperature T and for P = 0 at T = 0 K. Calculations are performed for crystals of parahydrogen and orthodeuterium at T = 0 K for V/V ₀ ranging from 1.30 to 0.01. Good agreement is reached between the calculated dependences and experimental data. The behavior of dependences Θ(V/V ₀), γ(V/V ₀), and q(V/V ₀) upon a variation of the isotopic composition of the crystal is analyzed.