Thermal Vinet Equation of State and Its Applications

Based on the Einstein model, the universal equation of state for solids proposed by Vinet et al. is extended to include the thermal effect. Employing the nearest neighbor generalized Lennard-Jones potential to describe the effective interaction between the ions, the lattice part of potential energy per atom is expanded as quadratic function of displacement of ion to derive the Einstein temperature and Debye-Grneisen parameter as a function of the volume. The theory contains four potential parameters except for the three parameters in the Vinet EOS, but only five of them are independent, and as the temperature being higher than the Debye temperature, the number of independent parameter can be further reduced to four. The theory is applied for 23 metallic solids, to predict Debye-Grneisen parameters and compressibility coefficients at chamber temperature. The predicted results are in good agreement with the experimental data. The predicted variation of compressibility and thermal expansivity coefficients with temperature for gold, copper, xenon and sodium chloride also are in good agreement with the experimental data.