Atomic Image Reconstruction from Atomic Resolution Holography Using &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;-Regularized Linear Regression

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X‐ray fluorescence holography (XFH) is typically performed using zero‐dimensional detectors. This makes data acquisition in synchrotron facilities time consuming. Here, we report the first direct imaging of the X‐ray fluorescence hologram of a Fe3O4 sample using a 2D hybrid detector. The apparatus, data acquisition and data processing are described here. The recorded Fe Kα hologram agreed well with simulations, and the atomic images reconstructed using the SPEA‐L1 algorithm showed agreement with the expected Fe and O positions. Furthermore, by tuning the incident X‐ray energy, fluorescence from the Fe3+ cations can be suppressed, allowing the imaging of Fe Kα holograms from Fe2.5+ cations. The valence‐sensitivity of the holograms was confirmed by the appearance of different sets of Kossel lines in the hologram, and in the atomic reconstructions. Reconstructions from the holograms from Fe2.5+ cations show that these emitters are located on octahedral sites, and the reconstruction from the Fe3+ holograms shows emitters on the tetrahedral sites. These results demonstrate that the new 2D hybrid detector‐based apparatus is a good XFH alternative that can be used to clarify structures of multi‐valence materials. Further applications to radiation‐damage sensitive samples, and even time‐resolved XFH experiments can also be achieved using this new XFH apparatus.

“…For the reconstructions done in this work, SPEA‐L1 with type B corrections, (also referred to as “threshold scaling”) . of the atomic distribution function was used.…”

Section: Methodsmentioning

confidence: 99%

λ = β max true[- \partial E true(g true) / \partial g true]

Section: Methodsmentioning

confidence: 99%

Direct Imaging of Valence‐Sensitive X‐Ray Fluorescence Holograms of Fe₃O₄

Ang

Matsushita

Hashimoto

et al. 2018

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“…The recorded X‐ray fluorescence holograms have been used to reconstruct the local atomic environment around the Fe atoms in real space by a scattering pattern matrix extraction algorithm (SPEA) using L 1 regularized linear regression (SPEA‐L1) . The SPEA‐L1 algorithm represents a sparse modeling approach to the experimental data, and the calculations parameters were set as follows: The sparseness of the atomic reconstruction is controlled by the parameter λ , which was set to

λ = β \cdot m a x true(- \partial E (g) / \partial g true),

where E ( g ) is the mean error function and g is the voxel value of the atomic image.…”

Section: Methodsmentioning

confidence: 99%

Local Structure of FeSe_0.4Te_0.6 by Low‐Temperature X‐Ray Fluorescence Holography

Stellhorn

Ideguchi

Kawasaki

et al. 2018

We present low‐temperature X‐ray fluorescence holography experiments to investigate the atomic scale structure of the high‐temperature superconductor FeSe0.4Te0.6. The results present a direct investigation of the local structure around the Fe atoms. Very clear images of the structure are obtained by a sparse modeling approach to the experimental data using a L1‐regularized linear regression. The results are in good agreement with previous findings of XRD and XAFS experiments on the FeSe1−xTex system, but furthermore indicate large fluctuations in the Fe sub‐lattice. The findings also represent a starting point for further discussions on more curious features of the FeSe1−xTex structure.

“…In this section, we introduce three recent experimental results of functional materials analyzed using the L 1 ‐regularized linear regression algorithm …”

Section: Examples Of the Data Analysismentioning

confidence: 99%

“…Thus, a sophisticated analytical algorithm is highly required for obtaining fully reliable 3D atomic images. To solve this problem of an equation for an underdetermined system, Matsushita recently developed a new algorithm, named SPEA‐L1 (the scattering pattern matrix extraction algorithm using L 1 regularized linear regression), which is based on inverse problem and sparse modeling…”

Section: Introductionmentioning

confidence: 99%

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

Hosokawa

Stellhorn

Hayashi

et al. 2018

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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.