Grüneisen Gamma from Elastic Data

Abstract

The Gr\"uneisen parameter $\ensuremath{\gamma}$ is commonly used to describe anharmonic properties of solids. It can be determined from thermal data by $\ensuremath{\gamma}=\frac{\ensuremath{\alpha}}{\ensuremath{\kappa}c}$, where $\ensuremath{\alpha}$, $\ensuremath{\kappa}$, 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 $\ensuremath{\gamma}$ and tensorial ${\ensuremath{\gamma}}_{\mathrm{jk}}'\mathrm{s}$ 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 $\ensuremath{\gamma}$ 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.