Modelling Quasicrystal Growth

TL;DR

This paper reviews current theoretical research on quasicrystal growth, highlighting the challenges posed by quasiperiodic order and the necessity of incorporating disorder to model real samples.

Contribution

It provides a comprehensive overview of various approaches and results in understanding quasicrystal growth, emphasizing the role of disorder in the process.

Findings

Quasiperiodic order complicates local growth algorithms.

Allowing disorder helps model real quasicrystals.

Various theoretical approaches have been developed with differing results.

Abstract

Understanding the growth of quasicrystals poses a challenging problem, not the least because the quasiperiodic order present in idealized mathematical models of quasicrystals prohibit simple local growth algorithms. This can only be circumvented by allowing for some degree of disorder, which of course is always present in real quasicrystalline samples. In this review, we give an overview of the present state of theoretical research, addressing the problems, the different approaches and the results obtained so far.