Influence of the roughness profile on the specular reflectivity of x rays and neutrons

Abstract

For the calculation of specular x-ray and neutron reflectivity from rough surfaces two expressions exist, which are valid under different circumstances. Another expression is derived using the second-order distorted-wave Born approximation, which smoothly connects the two existing expressions. The shape of the reflectivity curve depends not only on the average roughness, but also on the lateral correlation of the roughness profile.