The generalized Cauchy relation: a probe for local structure in materials with isotropic symmetry

The elastic properties of the isotropic state of condensed matter are given by the elastic constants ell and c44. In the liquid state the static shear stiffness c44 vanishes whereas at sufficient high probe frequencies a dynamic shear stiffness may appear. In that latter case the question about the existence of a Cauchy relation appears. It will be shown that a pure Cauchy relation can appear only under special conditions which are rarely fulfilled. For all investigated materials, including ceramics, liquids and glasses, a linear relation between ell and c44 called generalized Cauchy relation is observed, which, surprisingly, follows a linear transformation