Prediction of unusual stable ordered structures of Au-Pd alloys via a first-principles cluster expansion

We describe an iterative procedure which yields an accurate cluster expansion for Au-Pd using only a limited number of ab initio formation enthalpies. Our procedure addresses two problems: (a) given the local-density-approximation (LDA) formation energies for a fixed set of structures, it finds the pair and many-body cluster interactions best able to predict the formation energies of new structures, and (b) given such pair and many-body interactions, it augments the LDA set of ``input structures'' by identifying additional structures that carry most information not yet included in the ``input.'' Neither step can be done by intuitive selection. Using methods including genetic algorithm and statistical analysis to iteratively solve these problems, we build a cluster expansion able to predict the formation enthalpy of an arbitrary fcc lattice configuration with precision comparable to that of ab initio calculations themselves. We also study possible competing non-fcc structures of Au-Pd, using the results of a ``data mining'' study. We then address the unresolved problem of bulk ordering in Au-Pd. Experimentally, the phase diagram of Au-Pd shows only a disordered solid solution. Even though the mixing enthalpy is negative, implying ordering, no ordered bulk phases have been detected. Thin film growth shows L1₂-ordered structures with composition Au₃Pd and AuPd₃ and L1₀ structure with composition AuPd. We find that (i) all the ground states of Au-Pd are fcc structures; (ii) the low-T ordered states of bulk Au-Pd are different from those observed experimentally in thin films; specifically, the ordered bulk Au₃Pd is stable in D0₂₃ structure and and AuPd in chalcopyritelike Au₂Pd₂ (201) superlattice structure, whereas thin films are seen in the L1₂ and L1₀ structures; (iii) AuPd₃ L1₂ is stable and does not phase separate, contrary to the suggestions of an earlier investigation; (iv) at compositions around Au₃Pd, we find several long-period superstructures (LPS's) to be stable, specifically, the one-dimensional LPS D0₂₃ at composition Au₃Pd and two two-dimensional LPS's at compositions Au₁₃Pd₄ and Au₁₁Pd₄; (v) Au-Pd has a number of unsuspected ground states, including the structure Au₇Pd₅ with the lowest formation enthalpy and the (301) ``adaptive structures'' in the Au-rich composition range, all of which could not be predicted by other theoretical methods.