On the determination of the volume dependence of Grüneisen parameters in cubic and non-cubic solids

For a material of orthorhombic symmetry under hydrostatic stress, three generalized Grüneisen parameters relative respectively to the three principal directions of the deformation can be defined. Finite strain expressions for these parameters are derived in terms of the Lagrangian strain tensor and the frame-indifferent analogue of the Eulerian strain tensor. The expressions require for their evaluation the thermal expansion coefficients, the elastic moduli and their pressure and temperature derivatives, and the specific heat of the material, so that there are no arbitrary constants or “curve fitting.” In the case of cubic materials, it is possible to determine the unique Grüneisen parameter as a function of volume directly. For non-cubic materials, the volume dependence of the Grüneisen parameters is calculated using a quasi-harmonic finite strain model of equation of state. Numerical applications are given for some cubic and hexagonal metals and the results are discussed.