Off-Specular Scattering in Neutron Reflectometry

Abstract

When neutrons are scattered at small angles from planar, laterally homogeneous, stratified media, only specular (mirror like) reflection is observed. Sample inhomogeneities, such as interfacial roughness or voids, give rise to off-specular scattering which has been observed in many experiments with neutrons and X-rays. The easiest way to describe this scattering theoretically is based on the distorted-wave Born approximation (DWBA), which uses the neutron wavefunctions that describe reflection from a smooth surface as the basis functions for perturbation theory. From the DWBA one may obtain a number of qualitative results which are supported by experiment. Examples include the Yoneda fringes observed in reflection experiments with microscopically rough surfaces and the constant-q_z fringes observed for multilayers with correlated, rough interfaces. One must, however, use the DWBA with care. When the correlation range within the reflecting interfaces is large – for example, when a surface is composed of misoriented facets – the approximation breaks down. Some authors have also reported a lack of quantitative agreement between versions of the DWBA calculations and the scattering observed with microscopically rough surfaces. A remarkable feature of neutron (or X-ray) reflectometry is the length scales that are probed within reflecting surfaces. These range from a few hundred Ångstrøms up to several microns allowing neutron scattering to probe objects of a size normally visible by optical microscopy! The intent of this paper is to provide a simple description of scattering from rough surfaces that is accessible to a wide audience. Mathematical completeness is sacrificed in favour of intuitive arguments and experimental examples.