A Rate-Theory Approach to Irradiation Damage Modeling with Random Cascades in Space and Time

Abstract

A modification of the “rate theory” approach to point defect balance modeling is considered in which the production term is written to explicitly capture the discrete occurrence of distinct displacement damage cascades. The constant production rate density is replaced with a pulsed source that operates for very short periods at randomly selected points in time and space to produce new defects. In addition, dislocation sinks are modeled as discrete regions with perfect crystal in between instead of being uniformly distributed in space. Simulations reveal that under conditions of high sink strength, fast diffusion, and lower production rate (cascade frequency) defect populations liberated in any given cascade can be completely eliminated by absorption and recombination well before any new defects are introduced into the same region of space. Populations from distinct cascades may not have the opportunity to intermingle and overlap with each other to approach the bulk average values predicted by standard theory driven by a constant, average production term. Due to the large difference between vacancy and interstitial diffusivities, absorption of defects at microstructural sinks can occur in rapid pulses of interstitials followed by a much delayed influx of vacancies over a longer period. This is in stark contrast to the typical picture of a reasonably constant, perhaps slightly biased flow of one species of defect over the other. Expansion of the model to two spatial dimensions allowed for more explicit treatment of dislocation microstructure through informed dislocation arrangement and the use of proper boundary conditions at the edge of the dislocation core.