Dislocations in cubic crystals described by discrete models

TL;DR

This paper introduces discrete models for dislocations in cubic crystals that incorporate elasticity, lattice periodicity, and thermodynamic effects, validated through simulations of dislocations in GaAs and Si.

Contribution

It presents a novel discrete modeling approach for dislocations in cubic crystals, including thermodynamic and damping effects, bridging atomistic and continuum descriptions.

Findings

Models recover linear anisotropic elasticity in the continuum limit

Simulations successfully reproduce static screw and 60° dislocations in GaAs and Si

Inclusion of thermodynamic forces and fluctuation terms enhances model realism

Abstract

Discrete models of dislocations in cubic crystal lattices having one or two atoms per unit cell are proposed. These models have the standard linear anisotropic elasticity as their continuum limit and their main ingredients are the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. For these models, conservative and damped equations of motion are proposed. In the latter case, the entropy production and thermodynamic forces are calculated and fluctuation terms obeying the fluctuation-dissipation theorem are added. Numerical simulations illustrate static perfect screw and 60$^\circ$ dislocations for GaAs and Si.