Complete characterization of sink-strengths for 1D to 3D mobilities of defect clusters: Bridging between limiting cases with effective sink-strengths calculations.

Abstract

In a companion paper, new analytical expressions of the cluster sink-strength (CSS) for two one-dimensional diffusers were proposed. These expressions are indispensable to any complete parameterisation of rate-equations cluster dynamics intending to model mobile interstitial clusters such as dislocation loops. Indeed, simulating the long-term microstructural evolution in systems with fast diffusing species such as self-interstitial atom (SIA) clusters relies on establishing the CSS for rate-equation cluster dynamics which critically depends on the complex mobilities of clusters. In this second paper, we will estimate effective CSSs by object kinetic Monte-Carlo (OKMC) on wide ranges of radii, rotation energies, diffusion coefficients, and concentrations of both reaction partners. The symmetric roles of some parameters are used to infer a generic form of a semi-analytical expression of the CSS depending on all these interaction parameters. It is composed of, on one hand, the various analytical expressions established as limiting cases and, on the other hand, of fitted transition functions that allow a gradual switching between them. The analysis of the residuals shows that the overall agreement is reasonably good: it is only in the transition zones that some significant discrepancies are located. This semi-analytical expression answers our practical need for CSSs evaluation in our typical range of conditions, but further extending this range to much smaller diffusion coefficients ratios, it is quite striking to see that the domain for 1D-1D mobility is very extended. It is only when approaching a ratio of 10−6 that the 1D-0 CSSs start becoming more relevant than the adapted 1D-1D CSSs which have completely different orders of magnitude and kinetic orders. Finally, the semi-analytical CSS expression is validated by comparing its implementation in rate-equation cluster dynamics to OKMC simulations of interstitial clusters aggregation. Companion paper: [1]