An integrated thermodynamic approach towards correlating thermal and elastic properties: development of some simple scaling relations

This study presents a detailed thermodynamic analysis of the intricate interrelationship existing between thermal and elastic properties. By invoking only the principles of classical thermodynamics, the multifarious consequences of a possible linear relationship between logarithmic bulk modulus and relative enthalpy at constant pressure are probed. In particular, we identify two linear scaling relations between molar volume and relative enthalpy and between molar volume and logarithmic bulk modulus. These relations are valid at temperatures exceeding the Debye temperature. In addition, certain interesting deductions with respect to the temperature dependences of the Anderson–Grüneisen parameter and the volume thermal expansivity to isobaric specific heat ratio are obtained. In brief, a simple thermodynamic protocol that will be of use in an integrated treatment of the elastic and thermal quantities has been developed. As an illustrative case study, the high temperature bulk modulus of copper is estimated from its thermal properties data using the proposed framework.