Three equations of state for solids considering thermal effect

 The Einstein model to consider thermal effect in universal equations of state (UEOS) is modified. It is proposed that the zero-point vibration term should be deleted in a thermal UEOS, and the parameters cannot be directly taken as experimental data at a reference temperature, V_R, B_R, and , but their values at absolute zero temperature, V₀, B₀, and . An approach is proposed to solve V₀, B₀, and from V_R, B_R, and . The approaches are applied to three typical universal EOSs, including the Baonza, mGLJ and Morse EOSs. The numerical results show that the solved values of parameters are almost identical for different EOSs. And the thermo-physical properties predicted through different EOSs are almost identical at zero- and low-pressure conditions, once the same approach and input experimental data are used to solve the parameters. It is concluded that the prediction of thermo-physical properties at zero- and low-pressure conditions cannot be taken as the criteria to judge the applicability of a universal EOS.