Temperature-dependent phason elasticity in a random tiling quasicrystal

Abstract

Both phason elastic constants have been measured from Monte Carlo simulations of a random-tiling icosahedral quasicrystal model with a Hamiltonian. The low-temperature limit approximates the ``canonical-cell'' tiling used to describe several real quasicrystals. The elastic constant ${K}_{2}$ changes sign from positive to negative with decreasing temperature; in the ``canonical-cell'' limit, ${K}_{2}∕{K}_{1}$ appears to approach $\ensuremath{-}0.7$, about the critical value for a phason-mode modulation instability. We compare to the experiments on $i$-AlPdMn and $i$-AlCuFe.