Stable dense icosahedral quasicrystals

Abstract

Using lattice sums we show that the dense, monatomic, face-centered, icosahedral quasicrystals can be stable at zero temperature. We compare the energy to other periodic crystals and find it minimal. We create phason strain in this lattice, calculate the energy, and show that this lattice is at least locally stable against such strains. We calculate the two elastic constants associated with this strain. Our calculations indicate that it is also globally stable against phason strains. We argue that it is also stable under elastic strains. We show that the energy as a function of the strain is not described by a simple quadratic expansion as implied by simple phason elastic theory.