The Newton-Laplace (NL) formula of sound velocity is shown being invalid at high pressure, and a modified formula is derived based on the Rankine-Hugoniot relations. The derivation shows that the transmission of sound should be a process satisfying the energy conservation condition instead of the adiabatic condition in the NL formula. The agreement of equations of state for metallic liquids deduced from sound velocity data through the modified formula with the direct experimental P-V data is evidently improved as compared with that deduced through the NL formula.

In this letter, it is pointed out that an ideal universal equation of state (EOS) of solids should have four merits. The EOS corresponding to the generalized Lennard-Jones (GLJ) potential is derived. It is pointed out that the GLJ EOS is not volume analytic, as the exponents contained in the potential function take arbitrary values. On making the exponents satisfy a relationship, the GLJ EOS becomes volume analytic with two parameters (mGLJ EOS), and has all four merits. By applying six EOSs in investigating 50 materials, it is shown that the mGLJ EOS gives the best results.

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.

The approximate method to treat the practical quantum anharmonic solids proposed by Hardy. Lacks and Shukla is reformulated with explicit physical meanings. It is shown that the quantum effect is important at low temperature, it at be treated in the harmonic framework; and the anharmonic effect is important at high temperature and tends to zero at low temperature, it can be treated by using a classical approximation. The alternative formulation is easier for various applications, and is applied to a Debye-Gruneisen aolid with the generalized Lennard-Jones intermolecular interaction. The expressions for the Debye temperature and Grunelsen parameter as a function of volume are analytically derived. The analytic equation of state is applied to predict the thermodynamic properties of solid xenon at normal pressure with the nearest-neighbour Lennard-Jones interaction, and is further applied to research the properties of solid xenon and krypton at high pressure by using an all-neighbour Lennard-Jones interaction. The theoretical results are in agreement with the experiments.

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.