Modeling dislocations in quasicrystals through amplitude equations
arXiv:2504.11039 · doi:10.1016/j.cma.2025.118324
Abstract
Quasicrystals (QCs) are a class of aperiodic ordered structures that emerge in various systems, from metallic alloys to soft matter and driven non-equilibrium systems. Within a mesoscale theory based on slowly-varying complex amplitudes for QCs, we track dislocations as topological defects harbored by the amplitudes and characterize their Burgers vectors and induced deformations. We study the formation of dislocations at semicoherent interfaces, particularly those emerging from rotated inclusions, and find a hierarchy of dislocations forming at such interfaces. We further analyze interfaces in strained systems, revealing conditions for the emergence of periodic dislocation arrays and discussing the energetics of dislocations associated with different phonon and phason deformations. The stability, interaction, and motion of dislocation dipoles and quadrupoles are also discussed. These findings provide new insights into the mesoscale modeling of dislocations in QCs and their distinct behavior compared to conventional crystals, while demonstrating a versatile framework for studying dislocations in systems exhibiting quasicrystalline order.
15 pages, 5 figures
References in corpus (18)
- Modeling Elasticity in Crystal Growth
- Potfit: effective potentials from ab-initio data
- How Do Quasicrystals Grow?
- Stability of Quasicrystals Composed of Soft Isotropic Particles
- Controlled self-assembly of periodic and aperiodic cluster crystals
- Effective potentials for quasicrystals from ab-initio data
- Quasicrystalline order and a crystal-liquid state in a soft-core fluid
- Total-energy-based prediction of a quasicrystal structure
- Growth modes of quasicrystals
- Consistent Hydrodynamics for Phase Field Crystals
- Topological grain boundary segregation transitions
- A coarse-grained phase-field crystal model of plastic motion
- A phase field crystal theory of the kinematics of dislocation lines
- Emergent Quasicrystalline Symmetry in Light-Induced Quantum Phase Transitions
- Quasi-crystalline order in vibrated granular matter
- A unified field theory of topological defects and non-linear local excitations
- Generalized dynamics of moving dislocations in quasicrystals
- Mesoscale Field Theory for Quasicrystals