A MODIFIED REACTION–DIFFUSION MODEL OF SELF-ORGANIZED STRUCTURES OF RADIATION DEFECTS

Abstract

Radiation damage in metals produces complex spatial and temporal patterns of point defects. These defects strongly influence swelling, creep, and structural reliability in nuclear environments. Classical rate-theory models describe only the average defect concentration. They cannot explain the formation of spatially organized microstructures. Earlier continuum models, such as Selyshchev’s reaction–diffusion model, introduced elastic interactions to describe defect ordering. However, those models were deterministic and relied on oversimplified physical assumptions. In this study, we present a modified reaction–diffusion model that overcomes these limitations. The model introduces three major extensions. First, it includes a spatially resolved temperature field that accounts for heat diffusion and recombination heating. Second, it incorporates stochastic defect generation using multiplicative Ornstein–Uhlenbeck noise to represent irradiation randomness. Third, it introduces nonlocal elastic interactions described by a tunable Fourier kernel that controls the interaction range. Numerical simulations in this study show a noise-induced transition from uniform defect accumulation to persistent periodic structures with alternating defect-rich and defect-poor regions. Fourier analysis results identify a dominant wavelength that scales linearly with the elastic interaction range. Simulations for iron (Fe), nickel (Ni), and tungsten (W) reproduce experimentally observed defect spacings and clustering behaviour. Parameter sweep results yield a state diagram that distinguishes uniform, patterned, and noise-dominated regimes. The results show that stochastic fluctuations play a constructive role in defect self-organization. Elastic interactions determine the spatial scale of the resulting structures. The proposed framework provides a predictive link between microscopic irradiation kinetics and experimentally observed defect patterns in metals.