The equilibrium shapes (ESs) of icosahedral quasicrystals are analyzed for a wide class of lattice models which incorporate finite-range two-body interactions. Completely faceted shapes have been predicted for such models at temperature T=0. We prove that a number of simple shapes cannot be ESs for any model in this class for which the atomic interactions are constrained to be pure-attractive. This extends the result of Ho et al. [Phys. Rev. Lett. 59, 1116 (1987)], who showed that the pentagonal dodecahedron, a shape observed in grains of icosahedral Al-Cu-Fe and Ga-Mg-Zn, is a forbidden shape for pure-attractive models. We then introduce a lattice model for quasicrystals which incorporates mixed attractive and repulsive interactions and show that the possible ESs include the dodecahedron and other previously forbidden shapes.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics