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

Two types of global space-group optimization (GSGO) problems can be recognized in binary metallic alloys A(q)B(1-q): (i) configuration search problems, where the underlying crystal lattice is known and the aim 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 are given and the aim is finding energetically favorable lattice vectors and atomic occupations. Here, we address the second, lattice-type search problem in binary A(q)B(1-q) metallic alloys, where the constituent solids A and B have different lattice types. We tackle this GSGO problem using an evolutionary algorithm, where a set of crystal structures with randomly selected lattice vectors and site occupations is evolved through a sequence of generations in which a given number of structures of highest LDA energy are replaced by new ones obtained by the generational operations of mutation or mating. Each new structure is locally relaxed to the nearest total-energy minimum by using the ab initio atomic forces and stresses. We applied this first-principles evolutionary GSGO scheme to metallic alloy systems where the nature of the intermediate A-B compounds is difficult to guess either because pure A and pure B have different lattice types 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 intermediate compound has lattice sites belonging simultaneously to a few types (fcc, bcc) (PdTi3). The method found the correct structures, L1(2) type for Al3Sc, D0(19) type for AlSc3, 'CdPt3' type for CdPt3, B2 type for CuPd and AlSc, and A15 type for PdTi3. However, in such stochastic methods, success is not guaranteed, since many independently started evolutionary sequences produce at the end different final structures: one has to select the lowest-energy result from a set of such independently started sequences. Interestingly, we also predict a hitherto unknown (P2/m) structure of the hard compound IrN2 with energy lower than all previous predictions.