Stochastic theory of diffusional planar-atomic clustering and its application to dislocation loops

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Abstract
Atomic clustering into circular planar disks is an important process responsible for interstitial- loop formation in the bulk of irradiated materials, and the evolution of atomic planes during thin-film growth. We develop a stochastic theory for the formation of planar-atomic clusters by atomic diffusion. The theory accounts for the transient coupling between master equations representing small-size atomic clusters and a Fokker-Planck (FP) equation for larger ones. The FP equation is solved self-consistently, together with the master equations by the moments method. Equations for the rates of change of atomic species and for the nucleation rate of atomic clusters are simultaneously solved with appropriate equations for the average size and various moments of the distribution function. An application of the theory is given by comparing the results of calculations with experimental data on interstitial-loop formation in ion-irradiated nickel.