Authors: Jan Grießer, Lucas Frérot, Jonas A. Oldenstaedt, Martin H. Müser, Lars Pastewka

Elastic moduli are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic is complicated by two factors not yet having been concurrently discussed: finite-strain and non-affine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic constants and extend it to explicitly consider non-affine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide and silicon dioxide under hydrostatic compression and dilatation. Based on existing and new results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.

• Publisher’s version (Physical Review Materials, CC-BY): doi:10.1103/PhysRevMaterials.7.073603
• Preprint (arXiv, Open Access): doi:10.48550/arXiv.2302.08754

Cover art: made with Blender with the Atomic Blender addon, amorphous silicon configuration from Matscipy, and assets from ambientCG