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, we proposed new analytical expressions of cluster sink-strengths (CSS) indispensable to any complete parameterization of rate equations cluster dynamics accounting for reaction between defect clusters populations having a 1D-mobility. In this second paper, we first establish simulation setup rules for truly converged estimates of effective CSS by Kinetic Monte-Carlo, and then we grid on a wide set of radii, rotation energies, diffusion coefficients and concentrations of both reaction partners. Symmetric roles of some parameters are used to infer a generic form for a semi-analytical expression of CSS depending on all these interaction parameters: it is composed of the various analytical limiting cases established and 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 discrepancies are located and this is due to the asymmetry of the actual transition functions. The expression can be easily extended to temperatures at least a few hundred degrees around the reference. But further extending the CSS evaluations to much smaller diffusion coefficients ratios, we see that the domain for 1D-1D mobility is very extended: for a $10^{-3}$ ratio the computed CSS is still not correctly described by the 1D-CSS with respect to a fixed sink (1D-0), but rather by the established 1D-1D expression. For our typical sets of conditions, it is only when approaching a ratio of $10^{-6}$ that the 1D-0 CSS starts to become more relevant. This highlights the counter-intuitive fact that the growth kinetics of moderately trapped 1D mobile loops, whose effective mobility is greatly reduced, may not be described by 1D-0 kinetics but rather by appropriately corrected 1D-1D CSS which have completely different order of magnitude and kinetic orders.