Calculation of the generalized Grüneisen parameters for acoustic waves in uniaxial crystals from the third order elastic constants

Abstract

The generalized Grüneisen parameters involved in the theory of thermal expansion of uniaxial crystals are defined. These GP's for the acoustic waves determine the behaviour of the anisotropic expansion at low temperatures. The calculation of these GP's from third order elastic constant data in uniaxial crystals is described. As an example, the third order elastic constants of a h.c.p. lattice with nearest neighbour central interaction are worked out and the GP's of acoustic waves propagating in different directions in the crystal are calculated for the case where this interaction is represented by a (6,12) Lennard-Jones potential.