Reaction rate between 1D migrating self-interstitial atoms: an examination by kinetic Monte Carlo simulation

Abstract

The rate equation approach is useful for semi-quantitatively simulating long-term processes of accumulation or recovery of lattice defects in crystalline materials upon irradiation or annealing. This approach has been developed and applied to a large number of systems, including 3D or 1D migrating self-interstitial atoms (SIAs) and 1D migrating SIA clusters. The dimensionality of the migration of mobile species significantly affects the forms of the reaction rate. For reactions related to 1D migrating SIAs and clusters, only their reactions with stationary traps have been considered. However, the reactions between 1D migrating SIAs (or clusters) cannot be ignored, especially for processes in metals, in which the most stable configuration of an SIA is the crowdion, under electron and ion irradiations at comparatively high dose rate. In the present study, we use the object kinetic Monte Carlo (KMC) method to find the approximate form of the reaction rate between 1D migrating SIAs. For this purpose, we examine the average time for one SIA to encounter another SIA, in systems where the spatial distribution of SIAs is kept homogeneous, as a function of the concentration of SIAs. The approximate form of the reaction rate between 1D migrating SIAs primarily and effectively reflects the 2D migration process. In addition, it is shown that, in the systems composed of all reactive SIAs under annealing, the absolute value of the reaction rate by KMC becomes slightly lower than the solution of the derived form after longer times, due to the spatial correlation among SIAs.