Segmented Random Walks and Correlation Factors in Solid State Diffusion

Abstract

Hart's discussion of the measured diffusion coefficient D, for systems in which atom transport occurs via both the vacancy mechanism and along dislocation pipes, has been generalized to include any number of contributing mechanisms. The treatment introduces the concept of uncorrelated segments and shows that the correlation factor associated with each contributing mechanism contains a time independent parameter [Formula: see text] associated with the average number of jumps per segment. The analysis shows that the usual expression for the correlation factors obtained by assuming [Formula: see text] can be corrected for finite values of [Formula: see text]. The error involved in a typical case is less than 1% if [Formula: see text].