Alejandro Diaz-Ortiz

Theory of size mismatched alloy systems: many-body Kanzaki forces

A perturbative approach to determining the strain-induced effective interactions in binary alloys with large atomic size mismatch is presented. Using the chemical energy as the reference state, the strain-induced energy of the alloy is cast into a many-body (Kanzaki) force expansion that depends on both the configurational and displacive degrees of freedom. It is shown that the k-space energy expansion is valid for all wavelengths. The theory is then applied to the Cu3Au alloy where, due to the large difference between atomic sizes, considerable relaxations are observed from first-principles calculations. We found that the inhomogeneous contribution () dominates the strain energy in Cu3Au, whereas the homogeneous part (k = 0), notwithstanding its configurational dependence, contributes only a few per cent.

Cluster expansions in multicomponent systems: precise expansions from noisy databases

We have performed a systematic analysis of the numerical errors contained in the databases used in cluster expansions of multicomponent alloys. Our results underscore the importance of numerical noise in the determination of the effective cluster interactions and in the expansion determination. The relevance of the size of and information contained in the input database is highlighted. It is shown that cross-validatory approaches by themselves can produce unphysical expansions characterized by non-negligible, long-ranged coefficients. A selection criterion that combines both forecasting ability and a physical limiting behavior for the expansion is proposed. Expansions performed under this criterion exhibit the remarkable property of noise filtering. A discussion of the impact of this unforeseen characteristic of the cluster expansion method on the modeling of multicomponent alloy systems is presented.