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.

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