Mean field rate theory and object kinetic Monte Carlo: A comparison of kinetic models

Abstract

Multiscale modeling schemes encompass models from the atomistic to the continuum scale. Phenomena at the mesoscale have typically been simulated using models based on reaction rate theory, such as mean field rate theory (MFRT) or Monte Carlo. These mesoscale models are appropriate for application to problems that involve intermediate-length scales, and timescales from those characteristic of diffusion to long-term microstructural evolution (∼μs to years). Although the MFRT and Monte Carlo models can be used simulate the same phenomena, some of the details are handled quite differently in the two approaches. Models employing the rate theory have been extensively used to describe radiation-induced phenomena such as void swelling and irradiation creep. The primary approximations in such models are time and spatial averaging of the radiation damage source term, and spatial averaging of the microstructure into an effective medium. Kinetic Monte Carlo models can account for these spatial and temporal correlations; their primary limitation is the computational burden, which is related to the size of the simulation cell. Even with modern computers, the maximum simulation cell size and the maximum dose (typically much less than 1 dpa) that can be simulated are limited. In contrast, even very detailed MFRT models can simulate microstructural evolution for doses up 100 dpa or greater in clock times that are relatively short. Within the context of the effective medium, essentially any defect density can be simulated. A direct comparison of MFRT and object kinetic MC simulations has been made in the domain of point defect cluster dynamics modeling, which is relevant to the evolution (both nucleation and growth) of radiation-induced defect structures. Overall, the agreement between the two methods is best for irradiation conditions that produce a high density of defects (lower temperature and higher displacement rate) and for materials that have a relatively high density of fixed sinks such as dislocations.