Modelless approach in X-ray reflectivity of multilayer nanoheterostructure Fe/Cr

A new modelless method of determining the element concentration profile of metallic multilayer nanoheterostructures for low-contrast systems is applied to study periodical and aperiodical multilayer Fe/Cr system by X-ray reflectivity. As a special case, we discuss a cluster-layered Fe/Cr film with Kondo-like behavior of the resistance. The method does not require any a priori information on the structure of the multilayer nanostructures, such as position and width of interfaces, as well as, their shape. The method is based on solution of the Fredholm integral equation of the first kind, which relates the reflection coefficient and the concentration profile of the chemical elements of the sample. The ill-posed inverse problem of determination of the element concentration profile is solved by the regularization method. Efficiency of the method is confirmed by model calculations.