It was noted that microstructural features in crystalline solids, which arose from the diffusion-reaction kinetics of mobile components, depended upon the dimension of the underlying diffusion process; which was commonly assumed to be 3-dimensional. In metals, irradiation-induced displacement cascades produced clusters of self-interstitials performing 1-dimensional diffusion. Changes between equivalent 1-dimensional diffusion paths, and transverse diffusion, resulted in diffusion-reaction kinetics for between 1 and 3 dimensions. An analytical approach led to a single-variable function for interpolating between the 1-dimensional and 3-dimensional limiting cases. The analytical result was confirmed by kinetic Monte Carlo simulations.

1D to 3D Diffusion-Reaction Kinetics of Defects in Crystals. H.Trinkaus, H.L.Heinisch, A.V.Barashev, S.I.Golubov, B.N.Singh: Physical Review B, 2002, 66[6], 060105 (4pp)