Surface scattering of x rays in thin films. Part I. Theoretical treatment

Abstract

The diffuse scattering of x rays by thin films limited by rough interfaces is presented theoretically in terms of height–height correlation functions. The method employed, analogous to the use of Green functions, allows a rigourous treatment down to grazing incidences. An expression for the scattered intensity is obtained from the scattering cross section. The results are then discussed using a model correlation function, and the interpretation of x-ray reflectivity experiments is reexamined. We show that off-specular scans yield direct information about the correlations between interfaces which, in case of liquid thin films, can be used to determine elastic parameters. The generalized case of stratified media is examined in an appendix. This theory is compared to experimental results in the case of soap films in a companion article.