Wavelet analysis of white beam x-ray fluorescence holograms: determination of lattice sites and imaging of local atomic structure

Abstract

The prospects of atomic structure imaging with the continuous spherical wavelet transform (CSWT) as applied to white beam x-ray fluorescence holograms (XFH) are discussed. Recording of XFH with a white x-ray beam eliminates holographic twin images and minimizes extinction effects. However, the lack of these parasitic effects is accompanied by a limited radial resolution. In this work, by introducing an approximation of the white x-ray spectrum based on the Gumbel distribution, we propose an improvement both in generation of white beam XFH and in data analysis. Using approximate analytical models and realistic numerical simulations, we give a detailed description of the properties and resolution of local structure projections directly obtained from XFH by using wavelet analysis. It is demonstrated that the CSWT and, in particular, its windowed inversion can be effectively used to enhance and speed up reliability factor (R-factor) analysis of the data, which enables precise fully threedimensional localization of multiple lattice sites of dopants. For this, an exact analytic formula for the inversion is given, enabling its fast calculation in a single step. As an example system, we consider magnetic ions in wurtzite GaN.

Single-Crystal Model of Highly Efficient Water-Splitting Photocatalysts: A KTaO3 Wafer Doped with Calcium Cations

“…The local structure around metal cations in perovskite-structured metal oxides, SrTiO 3 and Pb­(Mg 1/3 Nb 2/3 )­O 3 , were analyzed. The application to guest-element atoms in a host lattice was examined in a numerical simulation of magnetic ions in wurtzite GaN . The application to photocatalyst materials is experimentally examined in this study.…”

Element sensitive holographic imaging of atomic structures using white x rays

“…In order to retrieve the structural information from the measured holograms, two approaches were used: wavelet analysis 16,25 and a linear regression approach. 18 The first method is model free and allows one to obtain projections of the local atomic structure.…”

“…In this work, r 0 was set to the smallest possible value of 2Å, determined by specific limitations of the wavelet transform. 16 The r c parameter was used to adjust the depth of the view of the projection, r ∼ r c (1 + k/k 0 ). Therefore, signals from atoms located at distances larger then r will be strongly suppressed in the projection.…”

X-ray fluorescence holography studies for a Cu3Au crystal

“…Their reconstruction and direct local structure imaging for disordered systems seems to be possible with tunable synchrotron radiation by means of multiple energy algorithms. The applied methodology could be also implemented for more complex systems such as multilayer samples and, after modification, to analysis of white-beam X-ray holography [21,22]. Efficient recording of XFH data using polycapillary optics and low-power laboratory sources denotes the possibility to perform XFH at low-energy synchrotron radiation facilities such a Solaris [23].…”