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The Einstein model to consider thermal effect in universal equations of state is modified, and an approach to solve parameters at absolute zero temperature from experimental data at a reference temperature is proposed and applied to the Baonza equation. The thermal Baonza equation is applied to study thermo-physical properties of α, β and γ-Si3N4. Through analyzing experimental data in literature, the input data-set for the three phases are determined. The results calculated from the thermal Baonza equation is in agreement with available experimental data.

The analytic mean field potential approach is applied to α-, β-, and γ-Si 3 N 4 . The analytic expressions for the Helmholtz free energy, internal energy, and equation of state were derived. The formalism for the case of the Morse potential is used in this work. Its six potential parameters are determined through fitting the compression experimental data of α-, β-, and γ-Si 3 N 4 . The calculated compression curves of α-, β-, and γ-Si 3 N 4 are in good agreement with the available experimental data. This suggests that the analytic mean field potential approach is a very useful approach to study the thermodynamic properties of Si 3 N 4 . Furthermore, we predict the variation of the free energy and internal energy with the molar volume at several higher temperatures and calculate the temperature dependence of the molar volume, bulk modulus, thermal expansion coefficient and isochoric heat capacity at zero pressure.

A five-parameter equation of state (EOS) is proposed to correctly incorporate the cohesive energy data in it without physically incorrect oscillations. The proposed EOS is applied to 10 selected metals. It is shown that the calculated compression curves are in good accordance with the experimental data. The values of the bulk modulus and its derivative with respect to pressure extracted from the proposed EOS remain almost unchanged while the data range used is varied.

Abstract:The analytic mean-field approach (AMFP) was applied to study the thermodynamic properties of Zirconium (Zr). The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The formalism for the case of the Morse potential is used in this work. The four potential parameters are determined by fitting the molar volume of the three phases of Zr. The calculated molar volume of α, β and ω Zr are in fairly good agreement with the available experimental data. The results presented in this paper verify that the AMFP is a useful approach to study the thermodynamic properties of Zr. Furthermore, we predict the variation of the relationship of free energy and internal energy versus the molar volume at various temperatures and the dependence of the bulk modulus, the thermal expansion coefficient and the heat capacity on temperature at zero pressure of α, β and ω Zr.