1D to 3D diffusion-reaction kinetics of defects in crystals

Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce clusters of self-interstitials performing 1D diffusion.

Changes between equivalent 1D diffusion paths and transversal diffusion result in diffusion-reaction kinetics between one and three dimensions. An analytical approach suggests a single-variable function (master curve) interpolating between the 1D and 3D limiting cases. The analytical result is fully confirmed by kinetic Monte Carlo simulations.