Formulation of the Grüneisen Parameter for Monatomic Cubic Crystals
Abstract
It is found that in the temperatureindependent approximation the DugdaleMacDonald formulation of the Grüneisen parameter differs from the Slater relation only because the former authors have implicitly considered the effect of the variation of Poisson's ratio with volume. The Slater assumption of the volume independence of Poisson's ratio is found to be untenable for any real crystal, and as a result, greater validity is attributed to the DugdaleMacDonald approximation. The DugdaleMacDonald approximation, however, is still found inadequate because of the simplicity of the model on which it must be based. Consequently, a new formulation for the temperatureindependent Grüneisen parameter is presented for all monatomic cubic crystals in which the atomic forces are central. The new formulation includes the effect of the variation of Poisson's ratio with volume and requires only a knowledge of the lattice energy at zero temperature as a function of the lattice parameters.
 Publication:

Physical Review
 Pub Date:
 May 1965
 DOI:
 10.1103/PhysRev.138.A767
 Bibcode:
 1965PhRv..138..767P