Finding the lowest-energy crystal structure starting from randomly selected lattice vectorsand atomic positions: first-principles evolutionary study of the Au–Pd, Cd–Pt, Al–Sc,Cu–Pd, Pd–Ti, and Ir–N binary systems

Abstract

Two types of global space-group optimization (GSGO) problems can be recognized in binary metallicalloys AqB1−q: (i) configuration search problems, where the underlying crystal lattice is known and theaim is finding the most favorable decoration of the lattice by A and B atoms and (ii)lattice-type search problems, where neither the lattice type nor the decorations aregiven and the aim is finding energetically favorable lattice vectors and atomicoccupations. Here, we address the second, lattice-type search problem in binaryAqB1−q metallic alloys, where the constituent solids A and B have different lattice types. We tacklethis GSGO problem using an evolutionary algorithm, where a set of crystal structures withrandomly selected lattice vectors and site occupations is evolved through a sequence ofgenerations in which a given number of structures of highest LDA energy are replaced bynew ones obtained by the generational operations of mutation or mating. Each newstructure is locally relaxed to the nearest total-energy minimum by using theab initio atomic forces and stresses. We applied this first-principles evolutionaryGSGO scheme to metallic alloy systems where the nature of the intermediate A–Bcompounds is difficult to guess either because pure A and pure B have different latticetypes and the (i) intermediate compound has the structure of one end-point(Al3Sc,AlSc3,CdPt3), or (ii) none of them (CuPd, AlSc), or (iii) when the intermediatecompound has lattice sites belonging simultaneously to a few types (fcc, bcc)(PdTi3). The method foundthe correct structures, L12 type for Al3Sc, D019 typefor AlSc3,‘CdPt3’ typefor CdPt3, B2 type for CuPd and AlSc, and A15 type forPdTi3. However, in such stochastic methods, success is not guaranteed, since manyindependently started evolutionary sequences produce at the end differentfinal structures: one has to select the lowest-energy result from a set of suchindependently started sequences. Interestingly, we also predict a hitherto unknown(P 2/m) structure of thehard compound IrN2 with energy lower than all previous predictions.