Equilibrium faceting shape of auasicrystals at low temperatures: cluster model

Abstract

We calculate the zero-temperature eauilibrium crystal shape (ECS), in a model specialized for the atomie structures of known icosahedral alloys such as Al-Cu-Li and Al-Cu-Fe. We use the approximations of assuming a cluster model of the atomie structure, taking a lattice-gas description of the interface and representing the non-periodic structure by a large cubic celi (rational approximant) of 32 clusters. We find that the facets normal to the fivefold and twofold icosahedral symmetry directions dominate the ECS, with additional smaller facets normal to the threefold directions.