Development of a thermodynamic framework for a combined analysis of thermal and elastic properties based on a linear scaling relation between logarithmic bulk modulus and enthalpy

Abstract

The main objective of this study is to develop a rigorous thermodynamic apparatus for elucidating the temperature and pressure dependencies of thermal and elastic properties in an integrated manner. Towards this cause, an isobaric linear scaling relation or approximation connecting logarithm of adiabatic bulk modulus (lnBS) with enthalpy increment (ΔH=HT−H0) of the formln(BS)=ln(B0)+kS(HT−H0),is invoked in this study. kS is a temperature independent thermoelastic parameter. It is found that this relation is obeyed by a number of solids irrespective of their bonding peculiarities, that includes metals, ceramics and minerals of geophysical and nuclear interest. A rigorous analysis of the thermodynamic implications of this scaling relation is presented in this paper. In particular, useful approximations for the temperature and pressure dependencies of bulk modulus, entropy and enthalpy are obtained. More importantly, the analysis brings out vividly the underlying physical basis for the apparent temperature independence of certain popular thermoelastic quantities like Grüneisen and Anderson–Grüneisen parameters. Besides, as a useful offshoot a new relation connecting the isobaric temperature variation of Grüneisen parameter with the corresponding enthalpy change is also obtained. Further, the possibility that suitably parametrised enthalpy or specific heat data can be made use of in obtaining reliable estimates of thermal expansion or vice versa is also demonstrated in this work. In all, a simple and consistent thermodynamic framework connecting elastic and thermal properties is presented. The applicability of the theoretical framework discussed in the present study towards the cause of estimation, extrapolation, and an integrated assessment of thermal cum elastic property data is exemplified, by taking thoria as the illustrative case study. In particular, a self-consistent estimate of its bulk modulus at high temperatures has been obtained using experimental enthalpy and molar volume data.