Thermodynamic properties of the generalized Murnaghan equation of state of solids

In the Murnaghan approximation, an isothermal relation between pressure (P) and volume (V) for solids is derived from the assumption that the isothermal bulk modulus (B) is a linear function ofP. This paper presents a thermodynamic analysis of a generalized form of the equation, based on treating all its various parameters [viz., V, B, and (B/P)_T atP=0] as functions of temperature. Extending a previous study, the effect ofT upon (B/P)_T is accounted for by using a dimensionless parameter introduced by us, which is used in formulating general expressions for the volume dependence of various thermophysical quantities,viz., the thermal expansion coefficient (), the productB, and the Grüneisen and Anderson-Grüneisen parameters. Some combinations of these parameters are identified, which show a simple dependence uponP. The new expressions are used in analyzing current approximations and the behavior of the solid in the low-compression range. In particular, an expression for at highP is reported which generalizes the Anderson equation and previous results by us.