The rate equation approach was useful for semi-quantitatively simulating long-term processes of accumulation or recovery of lattice defects in crystalline materials upon irradiation or annealing. This approach was developed and applied to a large number of systems, including three-dimensional or one-dimensional migrating self-interstitial atoms and one-dimensional migrating self-interstitial atom clusters. The dimensionality of the migration of mobile species significantly affects the forms of the reaction rate. For reactions related to one-dimensional migrating self-interstitial atoms and clusters, only their reactions with stationary traps were considered. However, the reactions between one-dimensional migrating self-interstitial atoms (or clusters) could not be ignored, especially for processes in metals, in which the most stable configuration of a self-interstitial atom was the crowdion, under electron and ion irradiations at comparatively high dose rate. The kinetic Monte Carlo method was used here to find the approximate form of the reaction rate between one-dimensionally migrating self-interstitial atoms. For this purpose, the average time for one self-interstitial atom to encounter another self-interstitial atom was examined in systems where the spatial distribution of self-interstitial atoms was kept homogeneous, as a function of the concentration of self-interstitial atoms. The approximate form of the reaction rate between one-dimensional migrating self-interstitial atoms primarily and effectively reflects the two-dimensional migration process. In addition, it was shown that, in the systems composed of all reactive self-interstitial atoms under annealing, the absolute value of the reaction rate by kinetic Monte Carlo became slightly lower than the solution of the derived form after longer times, due to the spatial correlation among self-interstitial atoms.

Reaction Rate Between 1D Migrating Self-Interstitial Atoms: an Examination by Kinetic Monte Carlo Simulation. T.Amino, K.Arakawa, H.Mori: Philosophical Magazine, 2011, 91[24], 3276-89