Ab-initio tiling and atomic structure for decagonal ZnMgY quasicrystal

Abstract

We discover the detailed atomic structure of -MgZnY, a stable decagonal quasicrystal alloy of the layered Frank–Kasper type, and related phases, using the ‘tiling and decoration’ approach. The atoms have invariable sites in the rectangle and triangle tiles of a 10-fold-symmetric planar tiling. To discover the lowest-energy structures, we combine the methods of density functional theory (DFT) total energy calculations, empirical oscillating pair potentials (fitted to DFT), fitting effective Hamiltonians for tilings, and discovering optimum tiling structures using a nonlocal tile-reshuffling algorithm. We find a family of almost stable binary compounds with varying composition, including the decagonal quasicrystal and the known MgZn; in addition, we show the ternary versions can be stable: -MgZnY at high temperature, and -MgZnSc even at .