Crystallographic map: 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 an algorithm for systematically exploring crystallographic phase space. Coupled with ab initio techniques, such as density functional theory, this algorithm offers an approach for exploring and tuning materials behavior, with a broad range of potential applications: particularly martensitic phase transformations and materials stability.