Predicting stable stoichiometries of compounds via evolutionary global space-group optimization

Whereas the Daltonian atom-to-atom ratios in ordinary molecules are well understood via the traditional theory of valence, the naturally occurring stoichiometries in intermetallic compounds Ap Bq, as revealed by phase-diagram compilations, are often surprising. Even equal-valence elements A and B give rise to unequal (p,q) stoichiometries, e.g., the 1:2, 2:1, and 3:1 ratios in Alp Scq. Moreover, sometimes different stoichiometries are associated with different lattice types and hence rather different physical properties. Here, we extend the fixed-composition global space-group optimization (GSGO) approach used to predict, via density-functional calculations, fixed-composition lattice types to identify simultaneously all the minimum-energy lattice types throughout the composition range. Starting from randomly selected lattice vectors, atomic positions and stoichiometries, we construct the T=0 "convex hull" of energy vs composition. Rather than repeat a set of GSGO searches over a fixed list of stoichiometries, we minimize the distance to the convex hull. This approach is far more efficient than the former one as a single evolutionary search sequence simultaneously identifies the lowest-energy structures at each composition and among these it selects those that are ground states. For Al-Sc we correctly identify the stable stoichiometries and relative structure types: AlSc2 -B 82, AlSc-B2, and Al2 Sc-C15 in the Nat =6 periodic cells, and Al2 Sc6 -D 019, AlSc-B2, and Al3 Sc-L 10 in the Nat =8 periodic cells. This extended evolutionary GSGO algorithm represents a step toward a fully ab initio materials synthesis, where compounds are predicted starting from sole knowledge of the chemical species of the constituents.