Structure of Binary Liquid Mixtures. I

An exact solution of the Percus-Yevick equation for the correlation functions $C_{\mathrm{ij}}\mathrm{}\left(r\right)\mathrm{}$ appropriate to a binary mixture has been given by Lebowitz. We show that the Fourier transforms $C_{\mathrm{ij}}\mathrm{}\left(K\right)\mathrm{}$ lead directly to the structure factors $S_{\mathrm{ij}}\mathrm{}\left(K\right)\mathrm{}$, the latter being functions of a total packing parameter $\eta$, 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.