Ultraviolet catastrophe of a fluctuating curved dislocation line

Max Boleininger,Laurent Dupuy,Thomas D Swinburne,Sergei L Dudarev

doi:10.1103/physrevresearch.2.032033

Abstract

The authors demonstrate that the line tension expression for dislocation core energy and the regularization of elastic fields near the core fundamentally emerge from the periodicity of the discrete atomic lattice. A continuum model for the dislocation core is presented which addresses the problem of short wavelength instability of dislocation lines inherent to linear elasticity theory, and predicts configurational energies.

Highlights

The motion of dislocation lines, the dominant agents of plastic deformation of crystalline solids, occurs through stochastic thermal fluctuations of the line shape that propagate through the material under the effect of applied stress [1,2,3]
By combining a linear elastic description of displacements at a large distance from a curved dislocation with the aforementioned nonlinear slip condition at the glide surface, we obtain a dislocation dynamics model that predicts a stable spectrum of shape fluctuations over the entire range of scales, with configuration energies quantitatively consistent with atomistic simulations, and containing no adjustable parameters
Based on a variational PeierlsNabarro model, we develop a dislocation dynamics formalism that takes into account the planar spreading of plastic eigendistortion across the glide surface

Summary

Ultraviolet catastrophe of a fluctuating curved dislocation line

The motion of dislocation lines, the dominant agents of plastic deformation of crystalline solids, occurs through stochastic thermal fluctuations of the line shape that propagate through the material under the effect of applied stress [1,2,3]. To understand the fundamental origin of the shortwavelength instability and develop a treatment free from these runaway ultraviolet fluctuations, we introduce a nonlinear description of the dislocation core derived from a minimal model of atomic bonding in a body-centered-cubic (bcc) crystal that accounts for periodicity in the discrete lattice [23,24]. By combining a linear elastic description of displacements at a large distance from a curved dislocation with the aforementioned nonlinear slip condition at the glide surface, we obtain a dislocation dynamics model that predicts a stable spectrum of shape fluctuations over the entire range of scales, with configuration energies quantitatively consistent with atomistic simulations, and containing no adjustable parameters. The model provides an insight into the origin of the commonly used empirical line-tension approximation for the dislocation core energy

Published by the American Physical Society

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