Thermal fluctuations of dislocations reveal the interplay between their core energy and long-range elasticity

Abstract

Equilibrium fluctuations of dislocations are central to the plastic response of metals and alloys because they control the attempt frequency of thermally activated events. We analyze here atomic-scale simulations of thermally vibrating dislocations with the help of an analytical model and show that thermal fluctuations intimately involve both long-range elasticity and short-range core effects. In addition, equilibrium fluctuations of edge and screw dislocations in aluminum are used to derive quantitative parameters that characterize their energetics and dynamics and we discuss how large-scale models such as dislocation dynamics can be parametrized based on these results. In particular, we show that the core parameters found here through fluctuations are transferable and can be used to predict dislocation bow-out under an applied stress.

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]. These transient fluctuations span the entire range of scales, from the very short wavelengths that characterize thermally activated motion of line edge dislocations and prismatic dislocation loops [4,5], to mesoscopic kink-mediated fluctuations of screw dislocations [6,7], up to the almost macroscopic distortions of dislocation lines in dilute alloys or irradiated materials [8,9].…”

“…The linear elasticity theory erroneously predicts that small perturbations of the dislocation line shape are energetically favorable at small wavelengths [2,19], resulting in the ultraviolet catastrophe. In other words, at finite temperature a straight dislocation is predicted to be unstable with respect to short-wavelength fluctuations.…”

“…To apply the local core model to stochastic dislocation dynamics, we require analytical expressions for energies and forces of arbitrary dislocation configurations. Consider the total energy of two closed dislocation loops, labeled by (1) and (2), in an infinite elastic medium, W = W (1) + W (2) + W (1,2) + W (1) core + W (2) core ,…”

“…where W (1) and W (2) are elastic self-energies of the isolated loops and W (1,2) is the elastic interaction energy between the loops. The terms W (1) core and W (2) core represent interfacial energies (1c) in the approximation that the interfacial energy is unaffected by the presence of other dislocations. The elastic interaction energy follows from the bulk Lagrangian (1b),…”

“…[R ,kk ] (1,2) b (1) i b (2) j dl (1) i dl (2) j (1) i b (2) j dl (1) k dl (2) k (1) i b (2) i dl (1) j dl (2) j (1) i b (2) j dl (1) j dl (2) i ,…”