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Elastic constants are among the most fundamental and important properties ofsolid materials, which is why they are routinely characterized in bothexperiments and simulations. While conceptually simple, the treatment ofelastic constants is complicated by two factors not yet having beenconcurrently discussed: finite-strain and non-affine, internal displacements.Here, we revisit the theory behind zero-temperature, finite-strain elasticconstants and extend it to explicitly consider non-affine displacements. Wefurther present analytical expressions for second-order derivatives of thepotential energy for two-body and generic many-body interatomic potentials,such as cluster and empirical bond-order potentials. Specifically, we revisitthe elastic constants of silicon, silicon carbide and silicon dioxide underhydrostatic compression and dilatation. Based on existing and new results, weoutline the effect of multiaxial stress states as opposed to volumetricdeformation on the limits of stability of their crystalline lattices.

Analytic elastic constants in molecular calculations: Finite strain, non-affine displacements, and many-body interatomic potentials