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 $L{1}_2$-ordered structures with composition ${\mathrm{Au}}_3\mathrm{Pd}$ and $\mathrm{Au}{\mathrm{Pd}}_3$ and $L{1}_0$ 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 ${\mathrm{Au}}_3\mathrm{Pd}$ is stable in $D{0}_{23}$ structure and and AuPd in chalcopyritelike ${\mathrm{Au}}_2{\mathrm{Pd}}_2$ (201) superlattice structure, whereas thin films are seen in the $L{1}_2$ and $L{1}_0$ structures; (iii) $\mathrm{Au}{\mathrm{Pd}}_3$ $L{1}_2$ is stable and does not phase separate, contrary to the suggestions of an earlier investigation; (iv) at compositions around ${\mathrm{Au}}_3\mathrm{Pd}$, we find several long-period superstructures (LPS’s) to be stable, specifically, the one-dimensional LPS $D{0}_{23}$ at composition ${\mathrm{Au}}_3\mathrm{Pd}$ and two two-dimensional LPS’s at compositions ${\mathrm{Au}}_{13}{\mathrm{Pd}}_4$ and ${\mathrm{Au}}_{11}{\mathrm{Pd}}_4$; (v) Au-Pd has a number of unsuspected ground states, including the structure ${\mathrm{Au}}_7{\mathrm{Pd}}_5$ 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.

• Received 24 September 2005

DOI:https://doi.org/10.1103/PhysRevB.74.035108