Structure of Binary Liquid Mixtures. I

An exact solution of the Percus-Yevick equation for the correlation functions ${C}_{\mathrm{ij}}(r)$ appropriate to a binary mixture has been given by Lebowitz. We show that the Fourier transforms ${C}_{\mathrm{ij}}(K)$ lead directly to the structure factors ${S}_{\mathrm{ij}}(K)$, the latter being functions of a total packing parameter $\ensuremath{\eta}$, the ratio of the hardsphere diameters and the concentration parameter $x$ describing the relative amount of each component in the mixture. An expression for the compressibility is also given. The results are applied to a discussion of x-ray scattering from mixtures.