Dislocation climb models from atomistic scheme to dislocation dynamics

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.Comment: 38 pages, 7 figure

Dislocation dynamics formulation for self-climb of dislocation loops by vacancy pipe diffusion

“…In this paper, we show that our self-climb formulation derived in Ref. [1] is able to quantitatively describe the properties of self-climb of prismatic loops that were observed in experiments and atomistic simulations. For small circular prismatic loops, our formulation is able to recover the available models in the literature based on linearly mobility relation driven by the interaction force between the loops and an external stress gradient.…”

“…In this section, we briefly review the dislocation climb formulation that we derived in Ref. [1] from atomistic schemes and discuss its physical implication. In this formulation, the dislocation climb velocity consists of contributions from both the climb due to vacancy diffusion in the bulk and the climb due to vacancy pipe diffusion along the dislocations, i.e.…”

“…It has been shown in Ref. [1] that the formulation in Eq. (2.2) is able to successfully predict the conservation of the enclosed area of a prismatic loop during the self-climb process.…”

“…We first review the property shown in Ref. [1] that following the formulation of dislocation self-climb given by Eq.…”

“…See Ref. [1] for detailed derivation, which also accounts for dislocation climb assisted by vacancy bulk diffusion.…”