Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method

TL;DR

This paper introduces a transfer matrix method to compute thermodynamic and phason elastic properties of quasicrystal models, enabling analysis of diffuse scattering and entropy in various dimensions.

Contribution

The paper presents a novel transfer matrix approach for calculating thermodynamic and elastic properties of quasicrystals, applicable to any dimension and model.

Findings

Calculated configurational entropy density for the icosahedral phase

Determined two fundamental elastic constants across system sizes

Method demonstrated to be general for other random tiling models

Abstract

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these models, which are related to experimental measurables such as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks. We apply our method to the canonical-cell model of the icosahedral phase, making use of results from a previously-presented calculation in which the possible structures for this model under specific periodic boundary conditions were cataloged using a computational technique. We give results for the configurational entropy density and the two fundamental elastic constants for a range of system sizes. The method is general enough allow a similar calculation to be performed for any other random tiling model.