Diffraction from random alloys

We calculate the diffraction from a random alloy, consisting of bonds of different natural lengths. The resulting structure is a distorted crystal with strong correlations between displacements at different sites. The diffraction pattern is dominated by a set of Bragg peaks whose intensity is modulated by a Debye-Waller factor. At the base of each of these Bragg peaks, we find divergent Huang scattering due to the second-order correlations between displacements. Higher-order correlations produce a negligible nondivergent background. Results are obtained in closed form and compared with computer simulations.