Applications of a L₁‐Regularized Linear Regression to X‐Ray Fluorescence Holography Data of Functional Materials

Abstract

To clarify atom‐resolved structural characterizations of materials, X‐ray fluorescence holography (XFH) technique is employed for drawing three‐dimensional (3D) atomic images around a specific element emitting fluorescent X‐rays. By taking the angle dependences of the fluorescent X‐ray intensity (hologram), 3D images of the surrounding atoms can be, in principle, obtained via simple Fourier transform‐like approaches with no special atomic models. In reality, however, an infinite number of the holograms with different incident X‐ray energies are necessary to reproduce the artifact‐less atomic images at the correct positions. Instead, here an inverse problem is applied using a sparse modeling approach of a L 1 ‐regularized linear regression to solve such statistical problem of a small data size. The excellent results of this approach are presented on complex crystals of some functional materials, such as Mn doped Bi 2 Te 3 topological insulator, Fe 65 Ni 35 Invar alloy, and Fe chalcogenide high‐temperature superconductor.