Dislocation climb models from atomistic scheme to dislocation dynamics

TL;DR

This paper develops a mesoscopic dislocation climb model derived from atomistic mechanisms, integrating vacancy diffusion, exchange, pipe diffusion, and jog kinetics, enabling more accurate dislocation dynamics simulations.

Contribution

It introduces a comprehensive mesoscopic model that incorporates microscopic vacancy mechanisms into dislocation climb, bridging atomistic and dislocation dynamics scales.

Findings

Quantitative description of prismatic loop translation at low temperatures.

Analytical formulas for climb velocity of straight edge dislocations.

Model implementation in dislocation dynamics simulations.

Abstract

We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of pipe diffusion and the jog structure on dislocations are incorporated by a Robin boundary condition near the dislocations for the bulk diffusion equation and a new contribution in the dislocation climb velocity due to vacancy pipe diffusion driven by the stress variation along the dislocation. Our climb formulation is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Using this new formulation, we derive analytical formulas for the climb velocity of a straight edge dislocation and a prismatic circular loop. Our dislocation climb formulation can be implemented in dislocation dynamics simulations to incorporate all the above four microscopic mechanisms of dislocation climb.