Grüneisen Gamma from Elastic Data

The Gr\"uneisen parameter γ is commonly used to describe anharmonic properties of solids. It can be determined from thermal data by γ=ακc, where α, κ, and c are the thermal expansivity, compressibility, and heat capacity; or it can be approximated by means of continuum models from elastic data. A scalar parameter γ and tensorial γⱼₖ's are expressed here in terms of second- and third-order elastic coefficients for arbitrary crystal symmetry, and the relations are specialized for isotropic, cubic, and rhombohedral materials. Curves of γ versus temperature for a variety of substances have been calculated on a digital computer on the basis of the nondispersive (Debye) and a dispersive (Born-von Karman) continuum model, and they are compared with curves obtained from thermal data.