General relationship between concentration derivatives and correlation functions for alloys

A general relationship is derived between the concentration derivative of any ensemble-averaged quantity and the correlation function of that quantity with fluctuations in the concentration. This relationship is then used to obtain general formulas for the concentration derivatives of the magnetization $M\left(\overrightarrow{\kappa }\right)$, and of the Warren short-range order parameters, $\alpha \left(\overrightarrow{\mathrm{R}}\right)$, for the case of binary substitutional alloys. The use of these formulas in the analysis of diffuse elastic neutron-scattering data and in the analysis of the effects of short-range order is discussed briefly.