The time dependence of an atom-vacancy encounter due to the vacancy mechanism of diffusion

Abstract Expressions are obtained for the continuous time development of several properties associated with an atom-vacancy encounter due to atomic diffusion at low vacancy concentrations. These are the waiting-time distributions for the next jump of an atom following a given jump, the probability of eventual return of a vacancy, the mean number of atom jumps in an encounter and the atom displacement probability. All these quantities are expressed as summations or integrals which can be computed numerically using as input the probabilities P k(I) of a random walker being displaced by I in k steps for I the origin and a nearest-neighbour site. The probability of return of the vacancy and the mean number of atom jumps in an encounter have the asymptotic form a - b/t 1/2. Numerical results are presented for the sc lattice.