A random-walk approach was developed for tracer diffusion via a point-defect mechanism in grain boundaries with a periodic structure. Such boundaries were characterized by a finite spectrum of possible atomic jumps. The macroscopically measured diffusion coefficient was expressed in terms of the various jump frequencies and associated partial correlation factors. The latter factors were calculated by using a matrix method, in which the matrix elements (next-jump probabilities) were deduced from Monte Carlo simulations of individual point-defect/tracer encounters. In such simulations, the walk of the point defect was followed until it caused a tracer jump or randomized after performing a large number of jumps. Together with the tracer jumps which were caused by the same defect as the previous jump, the possibility of the next tracer jump being caused by interaction with a different defect was taken into account. The method was applied to the calculation of tracer self-diffusion via a vacancy mechanism parallel or perpendicular to the [100] tilt axis in a  = 5 (310) grain boundary in Ag.

J.Mishin: Philosophical Magazine A, 1995, 72[6], 1589-607