Rapid Geometric Screening of Low-Energy Surfaces in Crystals.

A high-throughput approach to determine the equilibrium shape of a crystal by brute force is impractical due to the vast number of density functional theory (DFT) calculations required along just a single crystallographic direction. We propose a screening method that allows the bypass of performing DFT calculations for each candidate surface. Using a series of physically-motivated simplifications, we are able to consider the relative surface energy of each of the large number of candidate surfaces required to solve the surface energy minimization problem in 3 dimensions. Application of this technique to calculate the surface energy landscapes of a set of well-known crystal structures demonstrates high accuracy in the prediction of stable planes and validates its potential as a valuable tool in ab initio determination of equilibrium crystal shapes.