AIP Advances (Sep 2016)

Elastic anisotropy of crystals

  • Christopher M. Kube

DOI
https://doi.org/10.1063/1.4962996
Journal volume & issue
Vol. 6, no. 9
pp. 095209 – 095209-6

Abstract

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An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.