Intensities of X-ray scattering from a one-dimensionally disordered crystal having the multilayer averaged structure

A general formula for the intensity of X-ray scattering from a one-dimensionally disordered layer structure is given in matrix form when sharp spots and diffuse streaks are observed along the reciprocal lattice rows. The intensity formula with 'Reichweite'= 1 is expressed in the form I(φ) = I_L(φ) + I_D(φ), where the first term gives intensities of Bragg reflexions due to the 'averaged layer structure' whose period is p times the thickness of one layer, and the second those of diffuse scattering due to the disorder. A solution is given for a model in which each layer site of the p layers is occupied by either of two layers with different structure factors. It is shown that in this model no continuous peak shift occurs regardless of the degree of disorder. Solutions for the cases where each layer site is occupied by one of three or four layers with different structure factors are also given.