Surface Roughness by X-ray and Neutron Scattering Methods

We discuss how the roughness and morphology of surfaces and interfaces can be characterized by the nondestructive techniques of X-ray and neutron scattering. We first discuss the mathematical description of rough surfaces in terms of correlation functions and then discuss the various kinds of rough surfaces which exist. These fall into the category of self-affine (Gaussian) surfaces, surfaces with capillary wave fluctuations, stepped surfaces, and surfaces with islands or pits. We then discuss how the scattering from such surfaces may be described and which types of information are available from specular reflectivity, off-specular (diffuse) scattering, and grazing incidence reflection experiments, including a comparison with results obtained by other surface techniques. We then discuss multiple rough interfaces and the scattering from thin films and multilayers. Finally, we shall discuss scattering of neutrons by magnetically rough surfaces and multilayers.