The scattering of x rays from nonideal multilayer structures
A general theory is developed for the scattering of x rays from a single nonideal interface between two dielectric media. It is then extended to describe the scattering of x rays from a multilayer structure composed of many nonideal interfaces. The most unique feature of this theory is that there are no constraints on the physical structure of the interfaces; the interfaces can have any form of roughness or compositional inhomogeneity. A simple analytical expression is derived for both the near and far radiation field to first order, assuming that the scattering is weak. The theory is valid for arbitrary polarization and at all angles of incidence (measured from the normal) less than the critical angle for total external reflection. Finally, the results are applied to study the effect of different interface structures on the performance of multilayer x‐ray optics.
Abstract A layer of random defects in the simple cubic Ising model with nearest neighbor ferromagnetic interactions of strength J is considered. Using the real space renormalization group method we calculate defect free energy in the whole temperature range. Specifically, we analyze: the layer of diluted defects, the layer of spin-glass type defects, and the layer of mixed defects. The free energy is strongly dependent on the value of couplings between the defect and the bulk.