Confirmation of the random tiling hypothesis for a decagonal quasicrystal

TL;DR

This study confirms the random tiling hypothesis for a decagonal quasicrystal by calculating free energy and elastic constants, revealing a phase transition and softening of elastic constants near the transition temperature.

Contribution

The paper provides the first atomistic confirmation of the random tiling hypothesis in decagonal quasicrystals through detailed free energy and elastic constant calculations.

Findings

Confirmation of the random tiling hypothesis in a decagonal quasicrystal

Identification of a phase transition to an approximant at lower temperatures

Observation of softening of a phason elastic constant near the transition

Abstract

Mechanisms that stabilize quasicrystals are much discussed but not finally resolved. We confirm the random tiling hypothesis and its predictions in a fully atomistic decagonal quasicrystal model by calculating the free energy and the phason elastic constants over a wide range of temperatures. The Frenkel-Ladd method is applied for the phonon part and an approach of uncorrelated phason flips for the configurational part. When lowering the temperature, a phase transition to an approximant occurs. Close to the transition temperature one of the phason elastic constants becomes soft.