Symmetry properties of the collective diffusion correlation factors in the random alloy

In the present study a unifying mathematical framework for collective correlation factors in the random alloy is presented using principles of functional analysis. In the formal part of the analysis collective correlation factors are introduced and represented in terms of cosines of angles between atomic jumps. Relations among the correlation factors are discussed using the Onsager relations. Next, additional relations are considered using a sum rule. Finally, further relations between the correlation factors are introduced on physical grounds. Results of the analysis are applied first to the consideration of a number of previously derived relations between tracer correlation factors and collective correlation factors, or equivalently, between tracer diffusion coefficients and phenomenological coefficients. The analysis provides a particularly convenient way of comparing the relations. Secondly, the analysis is applied to the dilute binary alloy and consideration of the asymptotic behaviour of the relevant diffusion coefficient.