Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems

TL;DR

This paper derives clear necessary and sufficient elastic stability conditions for all crystal classes, clarifying previous ambiguities especially in non-cubic materials, serving as a comprehensive reference.

Contribution

It provides the first complete set of closed-form elastic stability criteria applicable to all crystal symmetries, extending beyond cubic systems.

Findings

Unified stability conditions for all crystal classes

Clarification of stability criteria in non-cubic crystals

Pedagogical reference for materials scientists

Abstract

While the Born elastic stability criteria are well-known for cubic crystals, there is some confusion in the literature about the form it should take for lower symmetry crystal classes. We present here closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in non-cubic materials.