Complete characterization of sink-strengths for mutually 1D-mobile defect clusters: Extension to diffusion anisotropy analog cases

TL;DR

This paper derives and validates new analytical expressions for sink-strengths in systems with mutually 1D-mobile defect clusters, accounting for diffusion anisotropy and extending previous models to more complex interactions.

Contribution

It introduces general formulas for CSS between different 1D-mobile clusters, incorporating diffusion anisotropy and validating them against kinetic Monte-Carlo simulations.

Findings

Derived CSS expressions depend on cluster radii, concentrations, and diffusion coefficient ratios.

Validated formulas match kinetic Monte-Carlo results without multi-sink terms.

Extended understanding of defect cluster interactions in anisotropic diffusion scenarios.

Abstract

Simulating more than seconds of microstructure evolution in systems involving almost athermally or very fast diffusing species such as self-interstitial atom (SIA) clusters currently relies on mean-field or coarse-graining techniques. Rate-equation cluster dynamics (RECD) is the most popular of those when dealing with irradiated microstructure or second phase precipitation. The important input parameters of RECD are the absorption rates, also called cluster sink-strengths (CSS). These quantities crucially depend on the way clusters interact and diffuse and notably on the dimensionality of the involved random diffusion processes. As expected theoretically and experimentally confirmed, SIA clusters migrate in a one-dimensional fashion (possibly with random orientation changes). This complicates the calculation of the related CSS. When involving a 1D-mobile specie and an immobile reaction partner (a "1D-0" reaction) the expressions are quite well known as well as the extension including random rotations (a "1DR-0" reaction). Expressions of CSS for absorptions between identical 1D-mobile species were proposed in the literature, but the general case of 1D-1D absorptions between different cluster classes is unknown. Here we propose such general expressions which turn out to depend on capture radii of interacting clusters populations, concentrations and notably on the ratio of their respective diffusion coefficients through a power-law. The same power-law formulation is found for 1D-3D absorptions but with different exponents, which thus appear as signatures of the dimensionality of the involved random motions. These limiting cases of CSS being established, they are finally implemented in an RECD calculation. The comparison with time consuming kinetic Monte-Carlo simulations completely validates their expression and without any need of multi-sink terms.