Analysis X-ray diffractograms from near-surface layers of monocrystals: development of models, algorithms and software

I.P. Yaremiy; S.I. Yaremiy; O.O. Vlasii; D.V. Vekeryk; Ya.I. Tomyn

doi:10.15330/pcss.25.2.413-420

Authors

I.P. Yaremiy Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
S.I. Yaremiy Ivano-Frankivsk National Medical University, Ivano-Frankivsk, Ukraine
O.O. Vlasii Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
D.V. Vekeryk Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
Ya.I. Tomyn Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

DOI:

https://doi.org/10.15330/pcss.25.2.413-420

Keywords:

computer simulation, algorithm, X-ray diffraction, crystal structure, surface layer, strain profiles, rocking curve, defects

Abstract

An algorithm for analyzing double-crystal rocking curves from the near-surface layers of monocrystals has been proposed, and corresponding software has been developed. It is taken into account that to obtain correct results, both coherent and diffuse components of X-ray scattering need to be considered. The possibility of simultaneous analysis of rocking curves from several reflections is provided. To approximate experimental rocking curves with theoretical ones, an approach that simultaneously uses three different approximation methods has been utilized. The effectiveness of the proposed approach is confirmed by verifying the uniqueness of the obtained results.

References

D.K. Bowen and Brian K. Tanner High Resolution X-Ray Diffractometry And Topography (CRC Press, London, 1998); https://doi.org/10.1201/b12575.

U Pietsch, V. Holy, T. Baumbach, High-Resolution X-Ray Scattering. From Thin Films to Lateral Nanostructures, (Springer New York, New York, 2004); https://doi.org/10.1007/978-1-4757-4050-9.

Ion beam applications in surface and bulk modification of insulators (International Atomic Energy Agency. Vienna, 2008).

I. S. Yakimov, A. N. Zaloga, L. A. Solov’ev, et al., Method of evolutionary structure-sensitive quantitative X-ray phase analysis of multiphase polycrystalline materials, Inorganic Materials, 48(14), 1285 (2012); https://doi.org/10.1134/s0020168512140208.

Web-sourse: Company «Analyzetest» web: https://www.analyzetest.com/2021/03/11/495/.

V. S. Bushkova, S. I. Mudry, I. P. Yaremiy, V. I. Kravets, X-Ray Analysis Of Nickel-Cobalt Ferrite Nanoparticles By Using Debyeв–Scherrer, Williamsonв–Hall And Ssp Methods, Journal of Physical Studies, 20(1/2), 1702 (2016); https://doi.org/10.30970/jps.20.1702.

A.V. Kopaev, V.V. Mokljak, I.M. Gasyuk, et al., Structure ordering in Mg-Zn ferrite nanopowders obtained by the method of sol-gel autocombustion, Solid State Phenomena, 230, 114 (2015); https://doi.org/10.4028/www.scientific.net/SSP.230.114.

V. Penkov, I. Kopylets, M. Khadem, et al., X-Ray Calc: A software for the simulation of X-ray reflectivity, Original software publication, 12, 100528 (2020); https://doi.org/10.1016/j.softx.2020.100528.

G. Vignaud, A. Gibaud, REFLEX: a program for the analysis of specular X-ray and neutron reflectivity data, Journal of Applied Crystallography, 52, 201-213 (2019); https://doi.org/10.1107/S1600576718018186.

S. Stepanov, Transformation of X-ray Server from a set of WWW-accessed programs into WWW-based library for remotecalls from X-ray data analysis software, Thin Solid Films, 515(14), 5700 (2007); https://doi.org/10.1016/j.tsf.2006.12.011.

C. Suryanarayana, M. Grant Norton, X-Ray Diffraction: A Practical Approach (Springer New York, New York, 1988); https://doi.org/10.1007/978-1-4899-0148-4.

A. Authier, Dynamical еheory of X-ray diﬀraction (New York, Oxford Press, 2001).

Z.G. Pinsker, Dynamical Scattering of X-Rays in Crystals (Springer Berlin, Heidelberg, 1978).

W. H. Zachariasen, Theory of X-ray diffraction in crystals (Dover Publications, Inc., 1967).

O. I. Liubchenko, V. P. Kladko, O. Yo. Gudymenko, Modeling of X-ray rocking curves for layers after two-stage ion-implantation, Semiconductor Physics, Quantum Electronics & Optoelectronics, 20(3), 355 (2017); https://doi.org/10.15407/spqeo20.03.355.

A. Lomov, K. Shcherbachev, Y. Chesnokov et al., The microstructure of Si surface layers after plasma-immersion He+ ion implantation and subsequent thermal annealing, J. Appl. Cryst, 50, 539 (2017); https://doi.org/10.1107/S1600576717003259.

A. Boullea, A. Debelleb, Strain-profile determination in ion-implanted single crystals using generalized simulated annealing. J. Appl. Cryst, 43, 1046–1052 (2010); https://doi.org/10.1107/S0021889810030281.

M. A. Krivoglaz X-Ray and Neutron Diffraction in Nonideal Crystals, Springer Berlin, Heidelberg (1996); https://doi.org/10.1007/978-3-642-74291-0.

G. Balestrino, S. Lagomarsino, E. Milani et al., Reconstruction mechanism in ion implanted yttrium iron garnet films. J. Appl. Phys, 63(8), 2751 (1988); https://doi.org/10.1063/1.340972.

S. Takagi, Dynamical theory of diffraction applicable to crystals with any kind of small distortion, Acta Crystall, 15, 1311 (1962); https://doi.org/10.1107/S0365110X62003473.

I A Vartanyants, M V Kovalchuk, Theory and applications of x-ray standing waves in real crystals. Reports on Progress in Physics, 64(9), 1009 (2001); https://doi.org/10.1088/0034-4885/64/9/201.

N. Kato, Statistical Theory of Dynamical Diffraction in Crystals. In: A. Authier, S. Lagomarsino, B.K. Tanner, (eds) X-Ray and Neutron Dynamical Diffraction. NATO ASI Series, vol 357 (Springer, Boston, MA); https://doi.org/10.1007/978-1-4615-5879-8_7.

V.A. Bushuev, Statistical dynamic theory of X-ray diffraction in imperfect crystals taking into account the angular distribution of intensities, Crystallography 34(2), 279 (1989).

V.I. Punegov, Correlation length in the statistical theory of X-ray diffraction on one-dimensionally distorted crystals with defects. Model of discrete layered structure, Crystallography 41(1), 23 (1996);

P. H. Dederics, Effect of defect clustering on anomalous x-ray transmission, Physical review B, 1(4), 1306 (1970); https://doi.org/10.1103/PhysRevB.1.1306.

V. B. Molodkin, S. I. Olikhovskii, E. N. Kislovskii et al., Bragg diffraction of X-rays by single crystals with large microdefects. I. Generalized dynamical theory, Phys. Stat. Sol B, 227(2), 429 (2001); https://doi.org/10.1002/1521-3951(200110)227:2<429::AID-PSSB429>3.0.CO;2-C.

S. I. Olikhovskii, V. B. Molodkin, E. N. Kislovskii et al., Bragg diffraction of X-rays by single crystals with large microdefects. II. Dynamical diffuse scattering amplitude and intensity, Phys. Stat. Sol B, 231(1), 199 (2002); https://doi.org/10.1002/1521-3951(200205)231:1<199::AID-PSSB199>3.0.CO;2-Y.

S. I. Olikhovskii, V. B. Molodkin, O. S. Skakunova, et al., Dynamical X-ray diffraction theory: characterization of defects and strains in as-grown and ion-implanted garnet structures. Physica Status Solidi B, 254(7), 1600689 (2017); https://doi.org/10.1002/pssb.201600689.

V. B. Molodkin, S. I. Olikhovskii, E. N. Kislovskii et al., Dynamical theory of X-ray diffraction by multilayered structures with microdefects. Phys. Status Solidi A, 204(8), 2606 (2007); https://doi.org/10.1002/pssa.200675686.

V. B. Molodkin, S. I. Olikhovskii, E. G. Len et al., Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals, Metallofiz. Noveishie Tekhnol., 38(1), 99-139 (2016); https://doi.org/10.15407/mfint.38.01.0099.

I.P. Yaremiy, S.I. Yaremiy, M.M. Povkh, et al., X-ray diagnostics of the structure of near¬surface layers of ion¬implanted monocrystalline materials. Eastern-European Journal of Enterprise Technologies, 6(96), (12), 50 (2018); http://dx.doi.org/10.15587/1729-4061.2018.151806.

I. M. Fodchuk, V. V. Dovganiuk, I. I. Gutsuliak et. al., X-Ray diffractometry of lanthanum-doped iron-Yttrium garnet structures after ion implantation, Metallofizika i Noveishie Tekhnologii, 35(9), 1209 (2013);

I. M. Fodchuk, I. I. Gutsuliak, R. A. Zaplitnyy, I.P. Yaremiy, The influence of high-dose irradiation by N+ ions on the Y2.95La0.05Fe5O12 crystal structure, Metallofizika i Noveishie Tekhnologii, 35(7), 993 (2013).

B. K. Ostafiychuk, I. P. Yaremiy, S. I. Yaremiy, et. al., Modification of the crystal structure of gadolinium gallium garnet by helium ion irradiation, Crystallography Reports, 58(7), 1077 (2013); https://doi.org/10.1134/s1063774513070122.

I. P. Yaremiy, B. K. Ostafiychuk, U. O. Tomyn, et al., Effects of Anisotropy in Prismatic Dislocation Loops and Disc-Shape Clusters Orientation in the Statistical Dynamical Theory of X-Ray Scattering, Metallofiz. Noveishie Tekhnol., 41(6), 699-715 (2019) (in Ukrainian); https://doi.org/10.15407/mfint.41.06.0699.

V.P. Kladko, O.M. Efanov, V.F. Machulin, V.Y. Molodkin, Dynamic diffraction of X-rays in multilayer structures (Kyiv, Naukova dumka, 2009).

I.P. Yaremiy, S.I. Yaremiy, V.D. Fedoriv, et al., Developing and programming the algorithm of refinement of the crystal structure of materials with possible isomorphous substitution. Eastern-European Journal of Enterprise Technologies, 5(5), (95), 61 (2018); http://dx.doi.org/10.15587/1729-4061.2018.142752.