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

Abstract

Simulating the long-term microstructural evolution in systems involving 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 one of the most popular of those when dealing with irradiated microstructure or second phase precipitation by thermal aging. Some of the most 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, i.e. rotations of their Burgers vector). 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 a heuristic approach to such general expressions which turn out to depend on the respective capture radii of interacting clusters classes, concentrations and notably on the ratio of their respective diffusion coefficients through a power-law. In the companion paper [1], 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.