ISSRNS 2012: Abstracts / Synchrotron Radiation in Natural Science Vol. 11, No 1 – 2 (2012) P 15
WAVELET ANALYSIS OF X-RAY ABSORPTION ANISOTROPY:
ACCURACY AND LIMITATIONS OF ATOMIC STRUCTURE IMAGING
D.T. Dul∗ and P. Korecki
Institute of Physics, Jagiellonian University, Reymonta 4, 30–059 Krak´ow, Poland
Keywords: X-ray absorption anisotropy, wavelet transform, atomic structure
∗e-mail : dawid.tadeusz.dul@uj.edu.pl
X-ray absorption anisotropy (XAA) is a holographic-like imaging method that originates from the interference of an incident plane wave with spherical waves scattered from atoms inside the sample. Because of this interference the total x-ray filed at the atomic absorbing sites is modi- fied, and thus the absorption cross section changes with the relative orientation of the incident beam and the sample. The usage of broad-band polychro- matic x-ray radiation enables one to interpret XAA patterns as quasi-real space projections of the local atomic structure.
As a holographic method, XAA solves the phase problem common in the traditional diffractive x-ray experiments and, in principle, allows one to obtain element sensitivity. However, analysis of XAA pat- terns still presents a challenge for experimenters.
Some current reconstruction methods involve direct comparison of data with the geometrical projections of the crystallographic structure or a tomographic algorithm. The first approach gives only qualitative information as projections of atomic planes and di- rections are distorted by remnant diffraction. The second technique is on the other hand limited to cubic samples. Recently, an new approach was pro- posed in [1, 2], where the use of the continuous spherical wavelet transform was presented. This ap- proach is constantly under development.
In this work we present a detailed study of the application of the spherical wavelet transform to the analysis of simulated, white-beam XAA patterns.
Simulations have been performed for the hardest x-ray wigglers in operation. A new approximation to the x-ray spectrum (based on the Gumbel distri- bution) was proposed which accounts for its strongly skewed nature. Analytic formulas were derived for the wavelet filter and the resolution in both the ra- dial and angular directions from the absorber.
As an example, it was shown that the wavelet filter can be effectively used to determine the pro- jections of the local atomic structure in the GaN crystal (Figure 1). Potential applications of XAA
such as polarity determination or imaging of local structure around magnetic ions in the GaN matrix were thoroughly investigated.
Figure 1 : Projection of the local atomic structure around Ga atoms in the GaN crystal obtained with the wavelet transform filter from a simulated XAA pattern (top right), crystal view from the inside (bottom left).
Circles and ellipses mark the nearest surrounding of Ga atoms.
Acknowledgments: This work was supported by the Polish National Science Center (DEC- 2011/01/B/ST3/00506).
References
[1] P. Korecki, D.V. Novikov, M. Tolkiehn, “Projections of local atomic structure revealed by wavelet analy- sis of x-ray absorption anisotropy,” Phys. Rev. B 80 (2009) 014119.
[2] P. Korecki, M. Tolkiehn, K.M. Dabrowski, D. V.
Novikov, “Fluorescence detection of white beam x-ray absorption anisotropy: Towards element sensi- tive projections of atomic structure,” J. Synchrotron Radiat. 18 (2011) 851.
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