Self-Diffusion in Random-Tiling Quasicrystals

TL;DR

This paper demonstrates that phason dynamics in icosahedral Ammann tilings cause self-diffusion, showing subdiffusive behavior at short times and normal diffusion at long times with enhanced diffusion rates.

Contribution

It provides the first explicit evidence linking phason dynamics to self-diffusion in quasicrystals, revealing complex diffusion behavior and potential multiple length scales.

Findings

Short-time transport is subdiffusive with exponent ~0.57

Long-time diffusion is normal and significantly faster than vacancy-assisted diffusion

No simple finite-size scaling suggests anomalous corrections or multiple length scales

Abstract

The first explicit realization of the conjecture that phason dynamics leads to self-diffusion in quasicrystals is presented for the icosahedral Ammann tilings. On short time scales, the transport is found to be subdiffusive with the exponent $\beta\approx0.57(1)$, while on long time scales it is consistent with normal diffusion that is up to an order of magnitude larger than in the typical room temperature vacancy-assisted self-diffusion. No simple finite-size scaling is found, suggesting anomalous corrections to normal diffusion, or existence of at least two independent length scales.