In this paper it is shown that the relationship of bulk modulus with pressure, BZf (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 highpressure 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. © 2004 Elsevier Ltd. All rights reserved.

In this paper it is shown that the relationship of bulk modulus with pressure, BZf (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 highpressure 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. © 2004 Elsevier Ltd. All rights reserved.

A fitting procedure is proposed to establish two analytic approximate expressions for the complicated Rarker-Henderson (BH) diameter with Lennard-Joues potential in two temperature ranges. Considering that the differentiation is a process enlarging the errors and the integration decreasing the errors and that the derivative of BH diameter is important in the calculation of in ternal energy, we propose to tit the derivative directly, instead of usually fitting the original function and subsequently deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively deriving its derivative. The simplicity and precision of two expressions developed are superior to the extensively used expressions in literature. The one with following form only has an average fitting 0.0063% in the reduced temperature range (0.4≤Kt/S≤15), and can be extrapolated to a wider temperature range (0.4≤Kt/S≤50) with an average error 0.13%, which is d/ơ=1.1755+0.02878 In T -0.2072T1/4+0.00643T3/4.

A simple analytic expression with high precision for the radial distribution function of hard spheres is proposed. The form of the expression has been carefully selected to combine the well-known Camahan-Starling equation of state in it and satisfy the limit condition at low density, its simplicity and precision is superior to the well-known Percus-Yevick expression. The coefficients contained in the expression have been determined by fitting the Monte Carlo data for the first coordination shell, and by fitting both the Monte Carlo data and the numerical results of the Percus-Yevick expression for the second coordination shell. The expression has been applied to develop simple analytic equations of state for the hard-core single, double Yukawa fluids, and the hard-core Yukawa mixtures. The comparisons show that the agreement of our model with the computer simulation data is slightly better than the mean spherical approximation and other analytic models.

A simple method is proposed to dispose the quantum effect and anharmonic effect at the same time. Considering the quantum effect is remarkable only at low temperature, and tends to zero at high temperature, the potential energy of an atom is expanded harmonically to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends to zero at low temperature, it was disposed by using a classical approximation. The universal formalism is applied to the generalized Lennard-Jones solid. The comparison shows that the results with and without anharmonic effect are in agreement with cach other at some low temperature, to which the Einstein model is applicable. The results without anharmonic effect become divergent at slightly higher temperatures; however, the results including anharmonic effect are in good agreement with the experimental data of solid xenon. The method proposed in this paper can be extended on other potentials to develop practical molecular thermodynamic equations of state for solids.