Method of X-Ray Diffraction Data Processing for Multiphase Materials with Low Phase Contents
Keywords:computer statistics, permutation test, statistical methods of analysis, crystalline phases, X-ray lines, X-ray phase and quantitative analysis, lava-like fuel-containing materials, quartz
Amorphous, glass, and glass-ceramic materials practically always include a significant number (more than eight) of crystalline phases, with the contents of the latter ranging from a few wt.% to several hundredths or tenths of wt.%. The study of such materials using the method of X-ray phase analysis faces difficulties, when determining the phase structure. In this work, we will develop a method for the analysis of the diffraction patterns of such materials, when diffraction patterns include X-ray lines, whose intensities are at the noise level. The identification of lines is based on the search for correlations between the experimental and test lines and the verification of the coincidence making use of statistical methods (computer statistics). The method is tested on the specimens of a-quartz, which are often used as standard ones, and applied to analyze lava-like fuel-containing materials from the destroyed Chornobyl NPP Unit 4. It is shown that the developed technique allows X-ray lines to be identified, if the contents of separate phases is not less than 0.1 wt.%. The method also significantly enhances a capability to determine the phase contents quantitatively on the basis of lines with low intensities.
R.V. Arutyunyan, L.A. Bolshov, A.A. Borovoi, E.P. Velikhov, A.A. Klyuchnikov. Nuclear Fuel in the "Shelter" Facility of the Chernobyl NPP (Nauka, 2010) (in Russian).
S.V. Gabielkov, A.V. Nosovskii, V.N. Shcherbin. Degradation model of lava-like fuel-containing materials in the "Shelter" facility. Probl. Bezpek. At. Elektrost. Chornobyl. 26, 75 (2016) (in Russian).
S.V. Gabielkov, I.V. Zhyganiuk, V.G. Kudlai, P.E. Parkhomchuk, S.A. Chikolovets. Crystallization of lava-like fuel-containing materials NBK-OU. Probl. Bezpek. At. Elektrost. Chornobyl. 32, 44 (2019) (in Ukrainian). https://doi.org/10.31717/1813-35188.8.131.52
Phase Identification from Powder Diffraction "Match!". Version 184.108.40.206, Crystal Impact, Bonn, Germany [http://www.crystalimpact.com].
S. Graˇzsulis, A. Merkys, A. Vaitkus, M. Okuliˇc-Kazarinas. Computing stoichiometric molecular composition from crystal structures. J. Appl. Crystallogr. 48, 85 (2015). https://doi.org/10.1107/S1600576714025904
A.D. Scorbun, M.I. Panasyuk. Resolution of low-intensity lines in gamma spectra. Probl. Bezpek. At. Elektrost. Chornobyl. 9, 125 (2008) (in Ukrainian).
D.S. Moore, G.P. McCabe, B.A. Craig. Introduction to the Practice of Statistics (Freeman, 2014) [ISBN: 1464158932].
F. Machatschki. Die kristallstruktur von tiefquarz SiO2 und aluminiumorthoarsenat AlAsO4. Z. Kristallogr. Krist. 94, 222 (1936). https://doi.org/10.1524/zkri.19220.127.116.11
P. Kroll, M. Milko. Theoretical investigation of the solid state reaction of silicon nitride and silicon dioxide forming silicon oxynitride (Si2N2O) under pressure. Z. Anorg. Allg. Chem. 629, 1737 (2003). https://doi.org/10.1002/zaac.200300122
D.J. Hudson. Statistics. Lectures on Elementary Statistics and Probability (CERN, 1964).
H. Tanizaki. On small sample properties of permutation tests: Independence test between two samples. Int. J. Pure Appl. Math. 13, 235 (2004) [ISSN: 1311-8080].
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.