Low-temperature structure ofξ′-Al-Pd-Mn optimized byab initiomethods

Abstract

We have studied and resolved occupancy correlations in the existing average structure model of the complex metallic alloy ${\ensuremath{\xi}}^{\ensuremath{'}}$-Al-Pd-Mn [Boudard et al., Philos. Mag. A 74, 939 (1996)], which has approximately 320 atoms in the unit cell and many fractionally occupied sites. Model variants were constructed systematically in a tiling-decoration approach and subjected to simulated annealing by use of both density functional theory and molecular dynamics with empirical potentials. To obtain a measure for thermodynamic stability, we reproduce the Al-Pd-Mn phase diagram at $T=0$ K, and derive an enthalpy of formation for each structure. Our optimal structure resolves a cloud of fractionally occupied sites in pseudo-Mackay clusters. In particular, we demonstrate the presence of rotational degrees of freedom of an Al${}_{9}$ inner shell, which is caged within two icosahedrally symmetric outer shells Al${}_{30}$ and Pd${}_{12}$. Outside these clusters, the chemical ordering on a chain of three nearby sites surprisingly breaks the inversion symmetry of the surrounding structure, and couples to an Al/vacancy site nearby. Our refined tiling-decoration model applies to any structure within the $\ensuremath{\varepsilon}$-phases family, including the metastable decagonal quasicrystalline phase.