A complete representation of structure–property relationships in crystals

Whereas structure-property relationships have long guided the discovery and optimization of novel materials, formal quantitative methods to identify such relationships in crystalline systems are beginning to emerge. Among them is cluster expansion, which has been successfully used to parametrize the configurational dependence of important scalar physical properties such as bandgaps, Curie temperatures, equation-of-state parameters and densities of states. However, cluster expansion is currently unable to handle anisotropic properties, a key distinguishing feature of crystalline systems central to the design of modern epitaxial structures and devices. Here, I introduce a tensorial cluster expansion enabling the prediction of fundamental tensor-valued material properties such as elasticity, piezoelectricity, dielectric constants, optoelectric coupling, anisotropic diffusion coefficients, surface energy and stress. As an application, I develop predictive ab initio models of anisotropic properties relevant to the design and optimization of III-V semiconductor epitaxial optoelectronic devices.