Mesoscale Field Theory for Quasicrystals

TL;DR

This paper develops a mesoscale field theory for quasicrystals that unifies growth, elasticity, and dislocation dynamics based on density-wave amplitudes, providing insights into defect behavior and interface formation.

Contribution

It introduces a free energy functional for complex amplitudes in quasicrystals, enabling self-consistent modeling of elasticity and defect dynamics from symmetry principles.

Findings

Predicts formation of semi-coherent interfaces

Describes dislocation nucleation and motion

Self-consistent elasticity including phononic and phasonic deformations

Abstract

We present a mesoscale field theory unifying the modeling of growth, elasticity, and dislocations in quasicrystals. The theory is based on the amplitudes entering their density-wave representation. We introduce a free energy functional for complex amplitudes and assume non-conserved dissipative dynamics to describe their evolution. Elasticity, including phononic and phasonic deformations, along with defect nucleation and motion, emerges self-consistently by prescribing only the symmetry of quasicrystals. Predictions on the formation of semi-coherent interfaces and dislocation kinematics are given.