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.

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.

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.

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.

The generalized free volume theory is applied to the soft-core multiple-Yukawa solid, and the hard-core multiple-Yukawa is included in as a special case. The expressions for equation of state and internal energy are derived. The formalism developed is applied to the C60, C76, and C84 solids. The effective diameter of C60 molecule is taken as the experimental value; the parameters of the double Yukawa (DY) potential for carboncarbon atoms are determined through fitting the experimental data of cohesive energy, the lattice constant, and the compression curve of C60 solid at ambient temperature. The effective diameter of C76 and C84 molecules are determined through fitting the experimental lattice constants at ambient temperature. The numerical results of C60 solid from the soft-core DY potential are in good agreement with the experiments, including the lattice constant and compression curve. The lattice constant versus temperature relationship for C76 and C84 solids calculated from the DY potential is qualitatively in accordance with experimental data as same as the Girifalco potential. The compression curve of the C84 solid calculated from the DY potential deviates from and is softer than the experimental data available. The reason for deviation is discussed, and it is concluded that the influence of compressibility of fullerene molecules to thermophysical quantities is important at high-pressure conditions.