ABSTRACT
The reader has been introduced to the basics of X-ray scattering in Chapter 1, however, only on a very general basis that is not easily applicable in the case of liquid surfaces. In this section, the Fresnel reflectivity of a solid layer system will be introduced as the result is part of the specular scattered signal from liquid surfaces. We will present the calculations and the results briefly. For detailed reviews of reflectivity both from solid state and liquid interfaces, the reader is referred to other articles and text books (see Refs. [6-9]). There are three main approaches to considering reflectivity: (1) From classic optics, the classical Fresnel formulism by considering radiation incident on a planar dielectric interface or discontinuity; (2) the first-order Born approximation or kinetic approximation for which we consider weak interactions of the X-rays with matter; and (3) the distorted-wave Born approximation (DWBA), which is a compromise between the intuitive Born approximation that fails at small incident angles and the exact Fresnel formulism that cannot be extended to describe liquid surfaces. (1) and (2) will be introduced here. The DWBA, first developed by Vineyard in 1982 [10], is based on the kinetic approximations but combines some features of the dynamical treatment such as the transmission function for both the incoming and the scattered radiation. However, this book only gives insight into (1) and (2), and therefore the DWBA will be omitted. For further readings on the DWBA, we recommend more specialized publications [11-14].
