A Self-Consistent Model to Describe the Temperature Dependence of the Bulk Modulus, Thermal Expansion and Molar Volume Compatible with 3rd Generation CALPHAD Databases

Variation of volume with temperature is a significant engineering consideration for numerous applications. In addition, the molar volume is a central property along with the bulk modulus in the scope of developing high pressure Gibbs energy multi-component databases. In this work, a semi-empirical model is proposed to describe the bulk modulus, thermal expansion coefficient and molar volume at atmospheric pressure. It is built based on a multi-frequency Einstein-Gruneisen model. The present methodology has several advantages over the use of polynomial functions. First of all, a self-consistent description of the molar volume and related properties together with heat capacity is achieved. This is an interesting feature in the scope of performing consistent assessments of diverse data in joint optimizations. Second, this description is directly compatible with the 3rd generation CALPHAD framework, as some parameters are shared in common. Therefore, it can be used to develop multi-component molar volume databases. Third, the model is built on physical considerations, enabling to perform reliable extrapolations outside the range of available data. Finally, the proposed description is valid down to 0K, allowing a direct integration of ab initio calculations. The above mentioned features are highlighted in the assessment of alpha-Sn and beta-Sn, for which a critical review of the literature data is provided, as well as of solid CaO. The obtained results suggest that the proposed model can be applied successfully to a large variety of elements and compounds, as it can notably account for unusual features such as a negative thermal expansion at low temperature.