Extreme values of the Poisson’s ratio of cubic crystals

Abstract

The problem of determining the extrema of Poisson’s ratio for cubic crystals is considered, and analytical expressions are derived to calculate its extreme values. It follows from the obtained solution that, apart from extreme values at standard orientations, extreme values of Poisson’s ratio can also be detected at special orientations deviated from the standard ones. The derived analytical expressions are used to calculate the extreme values of Poisson’s ratio for a large number of known cubic crystals. The extremely high values of Poisson’s ratio are shown to be characteristic of metastable crystals, such as crystals with the shape memory effect caused by martensitic transformation. These crystals are mainly represented by metallic alloys. For some crystals, the absolute extrema of Poisson’s ratio can exceed the standard values, which are–1 for a standard minimum and +2 for a standard maximum.