Traveling the configurational space of binary alloys

Binary $A_{1-x}B_{x}$ alloys can exist in any of the $2^{N}$ possible configurations on a periodic lattice of $N$ sites. In many areas of the alloy theory one needs to search all lattice configuration. Such a problem arises, for example, when the $T=0$ ground state configurations are sought, or in problems of materials design, where it is desirable to scan all the configurations to find the configuration $\sigma^{*}$ that has specific property. This task is complicated by (i) the huge computational demand for large $N$ and (ii) by the possibility that the $P(\sigma)$ is sensitive to the cell shape. In this talk we present a new computational approach for defining and searching the configurational space, that is based on (i) the exhaustive {\em enumeration} of the ``Inequivalent Cell Shapes'', and, for a given cell shape on (ii) the {\em sampling} of the related ``Same-Shape-Structures'' via a Genetic Algorithm. We apply this procedure to few ground state problems in semiconductor and metal alloys: For (AC)$_{x}$(BC)$_{1-x}$ tetrahedral semiconductor alloys we predict the lattice configurations of minimum bond-bending and bond-stretching strain both in free-floating bulk and under the epitaxial strain. We show that the chalcopyrite structure remains a ground state even under epitaxy. For Au-Pd alloy modelled with the mixed basis cluster expansion Hamiltonian, we determine the ground state structures and compare the convex hull to the one found previously by the direct enumeration approach.