A novel theoretical technique for quantitative analysis of x-ray diffraction data

A novel technique for quantitative analysis of x-ray diffraction data has been formulated. Comparisons of this new technique are presented which illustrate an excellent agreement with kinematical theory throughout the extended tails of the reflectivity as well as an excellent agreement with dynamical theory at the exact Bragg position. An extension of the fundamental equations provided in this work, allow theoretical modeling of x-ray scattering from layered systems a single monolayer at a time. This layering technique allows for the analysis of a variety of layered systems which range from surface roughness and homogeneous distortions to heterostructures. In order to test the utility of this new technique, an ultra high vacuum triple crystal diffractometer was designed, and constructed. Using this instrument, data was gathered on two types of crystalline systems: a Al$\sb{x}$Ga$\sb{(1-x)}$As/GaAs heterostructure, and a distorted Ge single crystal. The results of the experiments and analyses are presented. The analyses provide proof of the broad utility of this technique