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 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.