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.

The cell-cluster expansion theory is analytically expanded with the anharmonic and the lowest order correlation effects taken into account. The thermodynamic quantities for the all-neighbor and the nearest-neighbor Lennard-Jones models are calculated. The results show that the agreement of the analytic approximate theory with the complete one and the computer simulation is quite good. The comparison also shows that the contributions of the non-nearest neighbors to the thermal parts of thermodynamic quantities are larger than the second-order correlation modification. The ignorance of second-order correlation modification is a reasonable and practically convenient approximation. A simple method is proposed to extend the analytic approximate theory to the quantum case. Considering the quantum effect is remarkable only at low temperature, and tends zero at high temperature, the potential energy of an atom is harmonically expanded to consider the quantum effect of solids within the harmonic oscillator framework. The anharmonic effect is remarkable only at high temperature, and tends zero at low temperature, it is disposed using a classical approximation. The results for the quantum theory are in good agreement with the experimental data of solid xenon.

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.