SCATTERING OF X-RAYS AND NEUTRONS AT INTERFACES

Based on the distorted wave Born approximation we derive a general expression for the kinematic scattering cross-section of X-rays and neutrons impinging on an arbitrary interfacial structure. The scattering intensity is expressed in terms of the two-point correlation function of the atomic number densities. Since our approach takes fully into account the refraction at the corresponding smooth mean interface profile, our results offer the basis for an accurate analysis of the diffuse scattering intensity, which allows one to extract the lateral correlations. As an illustration of this formalism, we discuss applications to particularly interesting systems such as liquid-vapor interfaces, thin films, and multilayers. The systematic separation of the contributions to the scattering intensity which are proportional to the volume of the sample and those scaling with the area of the illuminated surface yields a detailed description of the truncation rod scattering of crystals. In the case of fluctuating interfaces, we provide a systematic derivation for the expression of the scattering cross-section. We show which approximations are necessary in order to recover those formulae which are commonly used to describe the scattering intensity caused by fluctuating interfaces. Therefore, we are able to assess their range of validity and their limitations. Beyond that, we discuss cases in which the vector character of X-rays cannot be ignored or where the atomic form factors and the correlation functions do not factorize.