Exploring the configurational space of binary alloys: Different sampling for different cell shapes

In many areas of alloy theory, such as determination of the T=0 ground state structures or calculation of finite-T alloy thermodynamics, one needs to enumerate and evaluate the similar to 2(N) configurations sigma created by different substitutions of atoms A and B on the N sites of a unit cell. These configurations consist of M-ICS "inequivalent cell shapes" (ICS's), each having M-SSS "same-shape structures" (SSS's). Exhaustive evaluation approaches attempt to compute the physical properties P(sigma) of all SSS's belonging to all ICS's. "Inverse band structure" approaches sample the physical properties of all SSS's belonging to a single inequivalent cell shape. We show that the number M-ICS of ICS's rises only as BN alpha, whereas the total number of SSS's scales as Ae(gamma N). Thus, one can enumerate the former (i.e., calculate all) and only sample the latter (i.e., calculate but a few). Indeed, we show here that it is possible to span the full configurational space efficiently by sampling all SSS's (using a genetic algorithm) and repeating this by explicit evaluation for all ICS's. This is demonstrated for the problem of ground state search of a generalized cluster expansion for the Au-Pd and Mo-Ta alloys constructed from first-principles total-energy calculations. This approach enables the search of much larger spaces than hitherto possible. This is illustrated here for the 2(32) alloy configurations relative to the previously possible 2(20). (c) 2006 American Institute of Physics.