The Effect of Interfacial Disorder on the X-ray Diffraction of Superlattices

We have generalised our x-ray diffraction results from amorphous/ crystalline multilayers, to include random interfacial disorder of a gaussian type. A general relation is obtained which can be applied to both crystalline/crystalline and crystalline/amorphous multilayers. This gaussian fluctuation or "roughness" can strongly reduce the long-range atomic order along the growth direction of the multilayer. Using classical structure factor calculations, we simulate the evolution of x-ray patterns as a function of the fluctuation amplitude, the superlattice wavelength, and the interatomic distances. Applying this model to the crystalline/ crystalline case we fit the experimental Nb/Cu data, deduce a fluctuation amplitude of about 0.4 A, and relate it to the lattice mismatch between Nb and Cu. For crystalline/amorphous systems (Pb/Ge) this amplitude can be significantly larger (2 A).