A unifying mathematical framework was presented, for such correlation factors, which used the principles of functional analysis. Collective correlation factors were first introduced and were represented in terms of the cosines of angles between atomic jumps. The relationships between the correlation factors were considered by using the Onsager relationships. Additional relationships were then considered by using a sum rule. Finally, further relationships between the correlation factors were introduced on physical grounds. The results of the analysis were applied to a number of previously derived relationships between tracer correlation factors and collective correlation factors, or between tracer diffusion coefficients and phenomenological coefficients. It was found that the analysis provided a particularly convenient method for comparing the relationships. The analysis was then applied to a dilute binary alloy and to the asymptotic behavior of the relevant diffusion coefficient.

I.V.Belova, G.E.Murch: Philosophical Magazine A, 1996, 73[1], 101-15