Temperature dependence of thermal pressure for NaCl and KCl crystals

In the present study we proposed the empirical relationships for temperature dependence of thermal pressure at atmospheric pressure for NaCl and KCl solids. It is found that the thermal pressure is a complex function of temperature and deviates from linearity in high-temperature region. The temperature dependence of volume expansion ratio is also established with the help of the thermal pressure. A close agreement between theory and experiment reveals the validity of the present work.     

Analysis of thermoelastic constants of solids and minerals at high temperatures

In the present communication, the thermoelastic constants of ionic solids NaCl and KCl and the minerals MgO, CaO and Mg₂SiO₄ are analyzed using the tabulated data compiled by Anderson and Isaak. It is found that there exists a precise linear relationship between the thermoelastic constant and the thermal pressure. The proposed empirical relationship provides a method to estimate the thermoelastic properties out side the experimental data range.     

Analysis of thermoelastic behaviour of MgO at high temperatures and high pressures

The thermoelastic behaviour of MgO has been studied for the temperature range (300-3000 K) under different compressions down to V/V₀=0.3. It has been shown that a comprehensive study of the thermoelastic properties of MgO can be made with the help of the Anderson-Isaak equation for thermal expansivity and the Vinet equation of state taken together. We have estimated the values of thermal expansivity α, isothermal bulk modulus K_T, their variations with pressure and temperature, the Anderson-Gruneisen parameter and the change in entropy with compression for MgO along isotherms at different temperatures. The results have been discussed and compared with the corresponding values reported in the recent literature.     

The temperature dependence of the equation of state at high pressures revisited: a universal model for solids

A general method to include temperature effects into the equation of state (EOS) of solids is discussed. A universal model based on a pseudo-spinodal approach is used to predict the pressure and temperature dependencies of the thermodynamic properties for a variety of solids: n-H₂, Ar, Kr, Xe, NaCl, LiF, NaF, KCl, CsCl, Li, Na, K, Rb, Cs, Al, Fe, Cu, Zn, Ag, Cd, Pt, Au, and Pb. The predictive capabilities of the complete EOS are discussed and compared with available models.     

Analysis of structural properties of refractory compounds at high temperature and pressure using a potential model

In this paper we focused on the structural and elastic properties of four transition metal mononitrides (TMNs) (M=Ti, Nb, Hf and Zr) by using realistic three body interaction potential (RTBIP) model, including the role of temperature. These TMN compounds have been found to undergo NaCl (B1) to CsCl (B2) phase transition, at a pressure quite high as compared to other binary systems. We successfully obtained the phase transition pressures and volume changes at different temperatures. In addition, elastic constants of TMNs at different temperatures are discussed. The present theoretical results have been compared with the available experimental data and predictions of LDA theory.     

Elastic constants of solids at high pressures

The isothermal and adiabatic nth-order (n ?? 2) elastic constants of a loaded crystal are defined. These constants fully determine the behavior of solids at an arbitrary load and are controlled by both an interatomic interaction and an applied load. Expressions that relate these constants (of the second, third, and fourth order) to Brugger elastic constants of the corresponding order, which are only determined by an inter-atomic interaction, are found for cubic symmetry crystals under hydrostatic pressure. These expressions are used to calculate the equation of state and the second- and third-order elastic constants of bcc tantalum at T = 0 K over a wide pressure range (0?C600 GPa) using an electron density functional method. The results of calculating the equation of state and the second-order elastic constants agree with available experimental data and the calculation results obtained in other works.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Thermodynamics of ice at high pressures and low temperatures

A new equation of state of ice Ih recently proposed by Feistel and Wagner [J. Phys. Chem. Ref. Data 35 (2006) 1021-1047] is used to study the phenomena related to the equilibrium isentropic compression of an ice-water mixture and dynamic loading of solid ice. New results are presented concerning the properties of the new equation of state, equilibrium solid-liquid phase transitions and Hugoniots of low-temperature (100 K) and temperate (263 K) shock-compressed ice.     

Explicit Gibbs free energy equation of state for solids

Semi-empirical equations of state (EOS) are used for interpolation and extrapolation of experimental data and/or electronic structure calculations. For calculation of phase equilibria, it is preferable to use an explicit Gibbs free energy EOS, that is, to express the Gibbs free energy directly as a function of the pressure and temperature. Existing explicit Gibbs free energy EOS formulations often give unphysical predictions at high pressures. The origins of these problems are internal inconsistencies and uncontrolled extrapolations. A set of conditions is put forward, that should be fulfilled by semi-empirical EOS formulations in order to constrain them to known physical behaviour, e.g., to the Thomas-Fermi and quasi-harmonic models at high pressures. A new alternative integration path is devised that eliminates the need for the problematic extrapolation of the heat capacity to high temperatures at low pressures. Based on these developments, a new explicit Gibbs free energy EOS is formulated which is suitable for computational applications. The new EOS may be fitted to represent the thermophysical properties of solids with a reasonably small number of adjustable parameters. A sample application for MgO is presented.     

Thermoelectric properties of Ge-doped Bi85Sb15 alloys at low temperatures

Bulk polycrystalline Bi₈₅Sb_15−xGe_x (x=0, 0.5, 1, 1.5, 2) composites were prepared by mechanical alloying followed by pressureless sintering. The thermoelectric properties were studied in the temperature range of 77–300 K. The results indicate that increasing the Ge concentration causes the Seebeck coefficient to change sign from negative to positive. Moreover, it is found that the maximum value of the Seebeck coefficient can be precisely controlled with the Ge concentration. The maximum dimensionless figure of merit reaches 0.07 at 140 K. These results suggest that the preparation of p-type Bi–Sb alloys is possible by using the Ge-doping approach.     

Two universal equations of state for solids satisfying the limiting condition at high pressure

In this paper it is shown that the relationship of bulk modulus with pressure, B=f(P), should be linear both at low and high-pressure limiting conditions. Because most of present equations of state (EOS) for solids cannot satisfy such linear relationship at high pressure, a new function f(P) is proposed to satisfy the linearity. By integrating the bulk modulus, an EOS with three parameters and satisfying the quantum-statistics limitation is derived. It is shown that the EOS can be reduced to two-parameter EOS approximately satisfying the limiting condition. By applying the two EOSs and other three typical EOSs to 50 materials, it is concluded that for materials at low and middle-pressure regimes, the limiting condition does not operate, the Baonza EOS gives the best results, but it cannot provide analytic expression for cohesive energy. The Vinet and our second EOSs are slightly inferior, both EOSs can provide analytic expression for cohesive energy, and for materials at high-pressure regimes our second EOS gives the best results. The Holzapfel and our first EOSs give the worst results, although they strictly satisfy the limiting condition. For practical applications, the limiting condition is not important because it only operates as V→0.     

High frequency and static dielectric constants of zinc blende structured solids

A correlation is presented for the high frequency ε_∞ and static ε_o dielectric constants of A^IIB^{V I} and A^IIIB^V semiconductors with the zinc blende structure. The high frequency ε_∞ and static ε_o dielectric constants can be represented by an empirical linear relation that is a simple function of melting temperature T_m, atomic volume Ω and product of ionic charges (Z₁Z₂). Values of high frequency ε_∞ and static ε_o dielectric constants of A^IIB^{V I} and A^IIIB^V zinc blende semiconductors exhibit a linear relationship when plotted against the k_BT_m/Ω (k_B=Boltzmann’s constant), but fall on two straight lines according to the product of ionic charges of the compounds. The calculated results are compared with available experimental data and previous calculations based on phenomenological models.     

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.     

Shanker formulation needs modification at high pressures

It is found that the Shanker formulation widely used in the literature to study the thermal expansion of solids (at constant pressure) works under the effect of pressure (at constant temperature) up to a limited range (≈30 kbar). Large deviations occur, when the pressure range is increased, demonstrating the failure of the relation under high pressure (at constant temperature). We, therefore, propose the modification in the formulation on an empirical basis. The modified relation is used to study the compression behavior of ionic solids viz. NaF, NaCl, NaBr and NaI crystals. The results obtained with the modified relation are compared with the experimental data in the light of the results obtained from Shanker formulation and Birch-Murnaghan equation of state. A good agreement between theory and experiment demonstrates the validity of the modification presented in the present note.     

Application of the NRL tight-binding method to the heavy elements Pb and Po

We have applied the NRL tight-binding (TB) method to study the mechanical and electronic properties of the heavy elements Pb and Po. The predicted properties include ground-state structure, electronic band structure and elastic moduli. Phonon-dispersion curves at T=0 K were also determined. As demonstrated in this paper, the results are in good agreement with the full potential linearized augmented plane wave calculations and the available experimental data. In addition, we performed molecular-dynamics simulations to obtain various temperature-dependent quantities of Pb such as the atomic mean-square displacement, Debye-Waller factor and thermal expansion coefficient. With our TB we have also calculated the vacancy formation energy of Pb. Finally, we report on the effects of spin-orbit coupling, through our TB scheme, on electronic structure and energetic properties.     

An apparatus for the measurement of thermal expansion of solids at low temperatures

A dilatometer, using the three terminal capacitance technique, suitable for measurement of linear thermal expansion of solids in the temperature range 1.3–300 K is described. The dialtometer is designed such that the mounting system for the specimen does not undergo any significant changes in dimensions when the specimen is heated. The apparatus, therefore, yields in principle absolute values of α, the coefficient of linear thermal expansion. The performance of the apparatus has been checked by measurements on copper in the temperature range of 77–300 K. Some preliminary results on the behaviour of α for Y₁Ba₂Cu₃O_6.9 compound in the vicinity of superconducting transition temperature,T _c are also described. The system can detect relative changes in length Δl/l ₀ of about 10⁻⁸. Attempts are being made to improve the sensitivity.     

Analysis of thermal expansion coefficients under the effect of high temperature for minerals

A simple and straightforward method for the determination of thermal expansion is investigated and applied for four minerals of geophysical importance. The results obtained for four minerals such as Mg₂SiO₃, Al₂O₃, Grossular garnet and Pyrope garnet at different temperatures are found to be in excellent agreement with the experimental data. The simplicity of the method is discussed in the light of another method in high temperature research on minerals.     

An equation of state for condensed matter; application to solid chemical elements

A particularly simple equation of state derived from the definitions of the compressibility k and the volume thermal expansion β of homogeneous condensed phases is applied to 100 solid elemental species, which are found to show two types of colligative characteristics: typical elements whose compressibility and expansivity depend on the packing coefficient of the crystal structures and isovalent elements whose values of k and β depend on the valence of the element in the solid state.     

Elastic modulus of supercooled liquid and hot solid silicon measured by inelastic X-ray scattering

The dynamical structure factors of supercooled-liquid and hot-solid silicon are measured by inelastic X-ray scattering at the same temperature, 1620 K. Two significant changes in the averaged longitudinal sound velocities and in the longitudinal modulus are observed. First, we observe a different longitudinal modulus in the polycrystalline hot-solid silicon compared to the extrapolated value obtained from the single-crystal measurement. This reduction of the modulus may be a precursor of the semiconductor-to-metal transition. Second, the increase in the longitudinal modulus in the liquid upon supercooling is consistent with an increase in the degree of the directional bonding.