Some expressions for the tracer correlation factor f for diffusion by the vacancy mechanism were reviewed and their equivalence justified. In the case of the low-vacancy-concentration limit it was proved that the probability of the second jump of an atom being the reverse of the first was 2/Z where Z was the coordination number of the lattice. This result provided a simple derivation of f in some cases and gave a physical interpretation of the approximation f=1-2/Z. The Monte Carlo evaluation of f was discussed and quantitative estimates made of the number of atoms to be sampled to achieve a given accuracy. Calculated values of the averaged cosines of angles between the direction of an initial jump and the direction of the (k+1)th jump of an atom were presented for the cubic lattices and for the honeycomb lattice. It was deduced that the nature of the correlations in the low-vacancy-concentration limit were different to those at other vacancy concentrations.

Theory and Monte Carlo Calculation of the Tracer Correlation Factor. S.W.Kelly, C.A.Sholl: Journal of Physics C, 1987, 20[32], 5293-304