Calculation of diffusion coefficients and correlation factors in grain-boundary diffusion

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Abstract
A random-walk approach is developed for tracer diffusion by a point-defect mechanism in grain boundaries with a periodic structure. Such boundaries are characterized by a finite spectrum of possible atomic jumps. The effective (macroscopically measured) diffusion coefficient is expressed in terms of the different jump frequencies and the associated partial correlation factors. The partial correlation factors are calculated by a matrix method, the matrix elements (i.e. next jump probabilities) being obtained by Monte Carlo simulations of individual point-defect-tracer encounters. In such simulations, the walk of the point defect is followed until it induces a tracer jump or randomizes after executing a large number of jumps. Together with the tracer jumps induced by the same defect as the previous jump, the possibility of the next tracer jump by interaction with a ‘fresh’ defect is taken into account. The method is applied for the calculation of tracer self-diffusion by the vacancy mechanism parallel and perpendicular to the [001] tilt axis in a σ = 5, (310) grain boundary in silver.