Symmetry-driven sampling of atomic geometries for alloy nanocrystal simulations

Simulations of alloy nanocrystals present unique challenges compared to their bulk material counterparts due to the absence of periodic boundary conditions: a size dependence in the material properties due to the varying surface-to-volume ratio and many substitution sites compared to the bulk results in an exponential increase in the number of unique configurations with nanocrystal size. Current implementations of random alloy models, such as special quasi-random structures (SQS) or cluster-expansions, rely on the cell’s periodic boundary conditions to produce unique alloy representatives that describe the bulk material’s properties. While similar approaches can be applied to nanocrystal simulations, representative alloys fail to capture the variance presented by a large configuration space.



In this talk we present a sampling process centered on using symmetric structures that preserve the point-group symmetry of the bulk lattice. We describe the lattice structure by a cycle decomposition of each orbit of the nanocrystal under the point-group symmetry operations. We then examine how pair-wise substitutions of lattice sites transform distinct representations. We propose such substitutions can expand the number of structures encoded by each representative structure while minimizing the change in the material properties. We compare this process to random sampling alone, paired with Bayesian optimization with the material optical response as the objective function.