The effect of trapping on the annihilation of a diffusing particle

Abstract

The theory of stochastic processes is applied to annihilation processes of lattice defects in the presence of traps. If the transport equations for a diffusing particle are given, the analytical expression for the mean first passage time for a given site (mean life time) can be derived by inverting the corresponding jump probability matrix. As an immediate application of the theory, diffusion of dislocation kinks in the presence of a trap or a high potential barrier is considered. The method is extended to three-dimensional diffusion problems. Decomposition and formation of impurity-vacancy complexes are considered for an f.c.c. lattice. The effect of the change in the saddle point energy for vacancy jumps near a substitutional solute atom is examined in detail to find significant influences on the rates of both formation and decomposition processes.