Extended Cauchy discrepancies: measures of non-central, non-isotropic interactions in crystals

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Abstract
In cubic crystals not subject to inner displacement, the linear combinations of elastic constants Q3=C12-C44+C144-C456 and Q6=2(C12-C44)-C123+C144+C112-C155 are devoid of contributions from central or isotropic interactions. In HCP crystals the combination Q1=1/2(3C12-C11)-C13+C44 has a similar property but is partly influenced by central interactions via an inner displacement term. A special combination R=C13-C44+1/2(C144+C244)-C113+C133-C344+C366 has the additional property that it is entirely free from inner displacement effects. A systematic derivation of these extended Cauchy discrepancies is given and their usefulness as direct measures of non-central, non-isotropic interactions is discussed with reference to all cubic and HCP metals whose third-order elastic constants have been determined.