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 L1‐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 Bi2Te3 topological insulator, Fe65Ni35 Invar alloy, and Fe chalcogenide high‐temperature superconductor.

Temperature‐dependent local atomic structures in the traditional Fe65Ni35 Invar alloy by X‐ray fluorescence holography

“…For the atomic images, the fourfold and threefold rotational symmetries are taken into account around the central atoms. Details of this analytical method are given elsewhere and successfully adopted in recent papers; ie, images down to about 10% of the maximum intensity are obtained with physically reliable results.…”

“…However, the integral by k is replaced by the sum of the limited number of holograms with different k values, ie, incident energies. This is the main reason of the appearance of artifacts in the reconstructed atomic image, and signals up to about 30% of the maximum atomic images hide beneath the noises and artifacts . Thus, this is a typical example of an equation for underdetermined system, ie, too less input experimental data for the requested unknown parameters.…”

Valence-selective local atomic structures in inorganic materials by X-ray fluorescence holography

“…Examples of excellent improvements in atomic images by using L 1 regularized linear regression are given elsewhere. 4,18)…”

Local Structure of the Impurity Site in Nd:LaF3 by X‐Ray Fluorescence Holography

“…X‐ray fluorescence holography (XFH) is a versatile and powerful method that can be applied for this task. [ 1 ]…”

“…The reconstructions can be further improved by a sparse‐modeling approach for the reconstruction. [ 1 ] This technique is suitable for determining impurity sites and their local environments, which cannot be easily detected by usual diffraction methods.…”