Abstract
The diffraction of X rays incident on a crystal surface under grazing angles under conditions of total external reflection has been investigated. An approach is proposed in which exact solutions to the dynamic problem of grazing-incidence diffraction in an ideal crystal are used as initial functions to calculate the diffuse component of diffraction in a crystal with defects. The diffuse component of diffraction is calculated for a crystal with surface defects of a dilatation-center type. Exact formulas of the continuum theory which take into account the mirror-image forces are used for defect-induced atomic displacements. Scattering intensity maps near Bragg peaks are constructed for different scan modes, and the conditions for detecting primarily the diffuse component are determined. The results of dynamic calculations of grazing-incidence diffraction in defect-containing crystals are compared with calculations in the kinematic approximation.
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References
A. M. Afanas’ev, P. A. Aleksandrov, and R. M. Imamov, X-ray Diffraction Diagnostics of Submicron Layers (Nauka, Moscow, 1989) [in Russian].
U. Pietsch, V. Holy, and T. Baumbach, High-Resolution X-Ray Scattering from Thin Films and Multilayers (Springer, New York, 1999).
M. Schmidbauer, D. Grigoriev, M. Hanke, et al., Phys. Rev. B 71, 115324 (2005).
T. H. Metzger, I. Kegel, R. Paniago, et al., Thin Solid Films 336, 1 (1998).
A. Yu. Gaevskii, I. E. Golentus, and V. B. Molodkin, Metallofiz. Noveishie Tekhnol. 36(2), 141 (2014).
A. M. Afanas’ev and M. K. Melkonyan, Acta Crystallogr. A 39, 207 (1983).
S. M. Durbin and T. Gog, Acta Crystallogr. A 45, 132 (1989).
J. Daillant and O. Belorgey, J. Chem. Phys. 97, 5824 (1992).
S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 2297 (1988).
A. Yu. Gaevskii, Metallofiz. Noveishie Tekhnol. 31(10), 1317 (2009).
R. D. Mindlin, Physics 7, 195 (1936).
S. Grotehans, G. Wallner, E. Burkel, et al., Phys. Rev. B 39, 8450 (1989).
D. Bahr and W. Press, Phys. Rev. B 51, 12223 (1995).
A. Yu. Gaevskii, I. E. Golentus, and V. B. Molodkin, Metallofiz. Noveishie Tekhnol. 36(3), 401 (2014).
S. Takagi, J. Phys. Soc. Jpn. 13(2), 278 (1958).
M. A. Krivoglaz, Diffraction of X rays and Neutrons in Nonideal Crystals (Naukova Dumka, Kiev, 1983) [in Russian].
A. Yu. Gaevskii, I. E. Golentus, and V. B. Molodkin, Crystallogr. Rep. 57(5), 708 (2012).
U. Pietsch, Current Sci. 78, 25 (2000).
F. Oberhettinger, Tables of Bessel Transforms (Springer, New York, 1972).
V. B. Molodkin, S. I. Olikhovskii, and M. E. Osinovskii, Metallofizika 5(1), 3 (1983).
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Original Russian Text © A.Yu. Gaevskii, I.E. Golentus, 2015, published in Kristallografiya, 2015, Vol. 60, No. 2, pp. 212–220.
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Gaevskii, A.Y., Golentus, I.E. Grazing-incidence X-ray diffraction from a crystal with subsurface defects. Crystallogr. Rep. 60, 189–197 (2015). https://doi.org/10.1134/S1063774515010095
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DOI: https://doi.org/10.1134/S1063774515010095