Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Abstract

In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the extended defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where, under a sufficient driving stress and vacancy supersaturation, vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.

Insights into dislocation climb efficiency in FCC metals from atomistic simulations

“…While they did apply a large climb stress (around 1 GPa, while keeping the hydrostatic stress equal to zero), our results are consistent with theirs in the sense that we find that it takes a similar number of vacancies to form a jog-pair (4 in our study, 4 in [25]) with a similar potential energy cost (at 4 vacancies, our jog-pair formation energy is around 1.1 eV, and an estimate of the summation of the first 4 points in Fig. 4 in [25] leads to 1.2 eV). It would be of interest for future work to employ the multiscale methodology to other regimes of temperature and supersaturation to investigate whether the transition between low and high climb efficiencies matches the predictions from the present approach.…”

“…8a), we include with the solid point a result from the multiscale simulation study of Baker and Curtin [25], where they find an edge dislocation in Al to become a fully efficient sink at a supersaturation around 145 at a temperature of 600 K. Even though a different potential was used, the results of Baker and Curtin are near our predictions of where the transition to a high climb efficiency at the same temperature and supersaturation conditions occurs. While they did apply a large climb stress (around 1 GPa, while keeping the hydrostatic stress equal to zero), our results are consistent with theirs in the sense that we find that it takes a similar number of vacancies to form a jog-pair (4 in our study, 4 in [25]) with a similar potential energy cost (at 4 vacancies, our jog-pair formation energy is around 1.1 eV, and an estimate of the summation of the first 4 points in Fig. 4 in [25] leads to 1.2 eV).…”

“…This qualitatively agrees with experimental observations [4,5] The jog-pair formation energy values were taken from the annealed pathways. The black dot in a) represents a c(R) c 0 ratio of 146 and a climb efficiency of 1 at a temperature of 600 K, which is meant to mimic the result in [25].…”

“…Sarkar et al used diffusive molecular dynamics (MD) to study the evolution of a jog-pair in FCC Cu [24], and a displacive-diffusive path associated with climb was identified. In further atomistic studies, Baker and Curtin employed a mixture of accelerated MD simulations and solutions to a discrete diffusion equation to investigate jog-pair formation in FCC Al [25]. Lau et al investigated the jog structure and vacancy attachment energies for a mixed dislocation in BCC Fe using the nudged elastic band (NEB) method [26].…”

Relative relevance of mobility and driving force on edge dislocation climb by the vacancy mechanism

“…These results show that the main source of bias in α-Fe as described by the interatomic potential used in this study comes from the probability of defect absorption or emission such that work is performed. 1 Anisotropic diffusion induced by local stresses [15][16][17] , lattice effects [12][13][14] or second order coupling between the external and dislocation fields 18 play a lower order role.…”