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.

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 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.

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.