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.

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.

The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized selfconsistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature.

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 analytic mean-field potential sAMFPd method proposed by Wang et al. sWAMFPd is verified to be equivalent to the free-volume theory. A generalized analytic mean-field potential sGAMFPd is established in terms of the free-volume theory and the nearest-neighbor pairwise interaction assumption. The GAMFP contains an integral. By using numerical integrated formula to approximately evaluate the integral, the GAMFP is transformed to the WAMFP or other forms of the AMFP, and the WAMFP can be seen as an approximate analytic version of the GAMFP. The GAMFP is exact for nearest-neighbor Lennard-Jones sNN-LJd model solid. The numerical results for thermodynamic quantities of NN-LJ solid from the GAMFP is compared with the WAMFP and other AMFP’s with slightly different forms. The comparison shows that the numerical results from the WAMFP are almost completely in agreement with the GAMFP and are better than several other approximate AMFP’s. The GAMFP and WAMFP with quantum modification have been applied to Vinet-type solids. The numerical results show that the theoretical values of Grüneisen γG and Debye temperature ΘD for three type solids are qualitatively in agreement with experiments, but the agreement is not satisfactory quantitatively. The predicted values of bulk thermal expansivity are too large for rare-gas solids, too small for alkali halides, and for metallic solids the agreement is slightly better but also is not satisfactory. Especially the predicted variations of bulk thermal expansivity and compressibility versus temperature are fairly bad; except for copper, the prediction is fortunately acceptable. It is shown that the fundamental spirit of the GAMFP and WAMFP to use all cold energy to evaluate thermal properties is in contradiction with embedded-atom model sEAMd. It is necessary to improve the GAMFP and WAMFP in terms of the EAM by the replacement of all cold energy with only cold energy from interaction between metallic atoms.