Equilibrium faceting shapes for quasicrystals

Kevin Ingersent, Paul J. Steinhardt

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)980-992
Number of pages13
JournalPhysical Review B
Issue number2
StatePublished - 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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