A General Lattice and Basis Formalism Enabling Efficient and Discretized Exploration of Crystallographic Phase Space

Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for systematically exploring crystallographic phase space. Coupled with ab-initio techniques, such as density functional theory, this algorithm offers a new approach for exploring and tuning materials behavior, with a broad range of potential applications: polar and magnetic transitions, martensitic phase transformations, and generally materials stability.