Elastic anisotropy and extreme Poisson's ratios in single crystals

Abstract

The relationship between elastic anisotropy and extreme Poisson’s ratio behaviour (either positive or negative) in single-crystalline materials has been investigated using experimentally determined single-crystal elastic constants for a wide range of solid materials. This makes use of a recently proposed elastic anisotropy index that is applicable to all crystal symmetries. For many real materials we find a striking correlation between the value of the elastic anisotropy index and the magnitudes of maximum and minimum Poisson’s ratios this is independent of crystal symmetry. This structure–property relationship provides new examples of auxetics and shows that negative Poisson’s ratios are actually not uncommon among many classes of inorganic (and organic) materials, including elemental metals, alloys, ionic solids, molecular solids and giant covalent networks.