Application Of Analytical Mean-field Method Of ¦Å-o <sub> 2 </ Sub> And Of Si <sub> 3 </ Sub> N <sub> 4 </ Sub> Thermodynamic Properties

The equation of state (EOS) gives the relationship of variables for a thermodynamic system under thermodynamic equilibrium, such as pressure, volume and temperature. The study on the EOS is a fundamental problem and an important content in physics.In this paper, we discourse upon the fundamental theory of EOS and some study skills of thermodynamic properties for solids. We mainly introduce the free volume theory (FVT) and the analytic mean field potential approach (AMFP), and further apply the AMFP to study the thermodynamic properties of theεphase of solid oxygen and Si₃N₄, and obtain some useful numerical results. Solid oxygen has many unusual properties and shows successive phase transitions as the pressure and temperature change, therefore this motivates a great current interest of many scientific groups. Silicon nitride (Si₃N₄) is currently one of the most important technical materials, because of its unique mechanical and electronic properties. Silicon nitride has high strength, high melting temperature, high hardness, wear resistance, corrosion resistance. In particular, it has been shown silicon nitride materials exhibit superior mechanical properties at elevated temperatures. Considering these aspects, we will aplly the AMFP to study the thermodynamic properties of theεphase of solid oxygen and Si₃N₄.In this paper, the analytic expressions for the Helmholtz free energy, internal energy and equation of state for theεphase of solid oxygen and Si₃N₄ have been derived by using the AMFP. The potential parameters are determined through fitting the available experimental data of theεphase of solid oxygen and Si₃N₄. The calculated compression curves are fairly good agreement with the available experimental data. This suggests that the AMFP is a very useful approach to study the thermodynamic properties of theεphase of solid oxygen and Si₃N₄. Furthermore, we predict the variation relationship of some thermodynamic quantities for theεphase of solid oxygen and Si₃N₄ at several higher temperatures.