Abstract
A simple matrix expression is derived for the atom jump probabilities due to an interstitial defect moving by an interstitialcy mechanism of diffusion, in terms of the probability generating functions, the defect jump probabilities, and the number Z′ of jump directions available to an interstitial atom. This expression is used to calculate the atom jump probabilities numerically for various cubic systems.
The tracer correlation factor is calculated from the atom jump probabilities. It is shown, using a symbolic mathematics computer package, that for all the systems considered the tracer correlation factor can be expressed in the general form f= 1 - AB2 /[α(αZ′ - AB)], where the A, B and α are linear combinations of the probability generating functions, the defect jump probabilities and the numbers of each jump type respectively. The details of the expressions for A, B and α depend on the structure of the system. The results for some cubic and two-dimensional systems are given.
The atom displacement probability due to a single atom-defect encounter is calculated for various types of interstitialcy mechanism of diffusion in the NaCl structure as an example.