Local atomic structure of Fe/Cr multilayers: Depth-resolved method

A depth-resolved method for the investigation of the local atomic structure by combining data of X-ray reflectivity and angle-resolved EXAFS is proposed. The solution of the problem can be divided into three stages: 1) determination of the element concentration profile with the depth z from X-ray reflectivity data, 2) determination of the X-ray fluorescence emission spectrum of the element i absorption coefficient μia(z,E) as a function of depth and photon energy E using the angle-resolved EXAFS data Iif(E,ϑl), 3) determination of partial correlation functions gij(z,r)as a function of depth from μi(z,E). All stages of the proposed method are demonstrated on a model example of a multilayer nanoheterostructure Cr/Fe/Cr/Al2O3. Three partial pair correlation functions are obtained. A modified Levenberg-Marquardt algorithm and a regularization method are applied. •A depth-resolved method for investigation of the local atomic structure is proposed.•We combined data of X-ray reflectivity and angle-depended EXAFS.•The regularization method and Levenberg–Marquardt (L–M) algorithm are used.•Mathematical algorithm comprises three process steps.•This general mathematical scheme cannot be interrupted.