Theory of neutron scattering in disordered alloys

A comprehensive theory of thermal neutron scattering in disordered alloys is presented here. We consider in detail the case of substitutional random binary alloy with random changes in mass and force constants; and for all values of the concentration. The cluster CPA formalism in argumented space developed here is free from analytical difficulties for the Green function, performs correct averaging over random atomic scattering lengths and employs a self-consistent medium for the calculations. For easy computation, we describe the graphical representation of the resolvent where the approximation steps can be depicted as closed paths in augmented space. Our results for scattering cross sections, both coherent and incoherent, include new types of terms and these lead to asymmetric line shapes for the coherent scattering. (author)