Temperature-dependent "phason" elasticity in a random tiling quasicrystal

TL;DR

This study measures temperature-dependent phason elastic constants in a random-tiling icosahedral quasicrystal model via Monte Carlo simulations, revealing a sign change in K2 and potential instability, with implications for real quasicrystals.

Contribution

It provides the first detailed temperature-dependent analysis of phason elasticity in a realistic quasicrystal model, connecting simulations to experimental observations.

Findings

K2 elastic constant changes sign at low temperature

K2/K1 approaches -0.7 near the canonical-cell limit

Results suggest a phason-mode modulation instability

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 K2 changes sign from positive to negative with decreasing temperature; in the ``canonical-cell'' limit, K2/K1 appears to approach -0.7, about the critical value for a phason-mode modulation instability. We compare to the experiments on i-AlPdMn and i-AlCuFe.