Layer thickness variations and x-ray diffraction patterns: A general treatment

Abstract

Using a columnar approximation, the effect of random layer thickness variations in a compositionally modulated material on the x-ray diffraction pattern is expressed in terms of their distribution function. It is demonstrated that the Fourier transform of this distribution function appears in a function describing the effective phase relations between the individual layers. Features of multilayer diffraction patterns, such as the presence or absence of superlattice peaks, are explained. It is also shown that when the Fourier transform of the thickness variation distribution changes sign from positive to negative, the superlattice peaks change position from integral to half-integral order. The effects of thickness variations are compared with those of interface roughness.