An equivariant graph neural network for the elasticity tensors of all seven crystal systems

Abstract

The elasticity tensor is a fundamental material property that describes the elastic response of a material to external force. The availability of full elasticity tensors for inorganic crystalline compounds, however, is limited due to experimental and computational challenges. Here, we report the materials tensor (MatTen) model for rapid and accurate prediction of the full fourth-rank elasticity tensors of crystals. Based on equivariant graph neural networks, MatTen satisfies two essential requirements for elasticity tensors: independence of the frame of reference and preservation of material symmetry. Consequently, it provides a unified treatment of elasticity tensors for all seven crystal systems across diverse chemical spaces, without the need to deal with each separately. MatTen was trained on a dataset of first-principles elasticity tensors garnered by the Materials Project over the past several years (we are releasing the data herein) and has broad applications in predicting the isotropic elastic properties of polycrystalline materials, examining the anisotropic behavior of single crystals, and discovering materials with exceptional mechanical properties. Using MatTen, we have found a hundred crystals with extremely large maximum directional Young's modulus and eleven polymorphs of elemental cubic metals with unconventional spatial orientation of Young's modulus.