Dynamical Theory of Grazing Diffuse Scattering of X-Rays by a Crystal with Subsurface Defect

O. Yu. Gaevskii, I. E. Golentus, V. B. Molodkin

G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03680 Kyiv-142, Ukraine

Received: 16.05.2013; final version - 24.03.2014. Download: PDF

Diffraction of X-rays in conditions of total external reflection (grazing-incidence diffraction–GID) is a powerful method for defects’ diagnostics in subsurface layers and thin films. In a given paper, the dynamical model of diffuse X-ray scattering in crystals, which contain subsurface dilatation-centre-type defects, is developed. Diffuse scattering near the specular reflected and specular diffracted coherent peaks provides the main information about subsurface lattice distortions. New approach developed for calculation of the diffuse scattering amplitude is based on the distorted wave Born approximation (DWBA). Fourier components of lattice distortions are expressed by exact formulas within the scope of the continuous approximation, which takes into account the image forces caused by surface boundary. The intensity maps calculated for diffuse grazing waves scattered by subsurface defects randomly distributed in a flat layer are presented. For different scanning schemes, the conditions of predominantly diffuse component registration in grazing diffraction are defined.

Key words: X-rays, grazing incidence diffraction, dynamical theory, coherent and diffuse scattering, distorted wave Born approximation, dilatation centers, image forces.

URL: http://mfint.imp.kiev.ua/en/abstract/v36/i03/0399.html

DOI: https://doi.org/10.15407/mfint.36.03.0399

PACS: 61.05.cc, 61.05.cp, 61.72.Dd, 61.72.J-, 68.49.Uv

Citation: O. Yu. Gaevskii, I. E. Golentus, and V. B. Molodkin, Dynamical Theory of Grazing Diffuse Scattering of X-Rays by a Crystal with Subsurface Defect, Metallofiz. Noveishie Tekhnol., 36, No. 3: 399—418 (2014) (in Russian)


REFERENCES
  1. M. A. Krivoglaz, Difraktsiya Rentgenovskih Luchej i Neytronov v Neideal'nykh Kristallakh (X-Ray and Neutron Diffraction in Nonideal Crystals) (Kiev: Naukova Dumka: 1983) (in Russian).
  2. P. H. Dederichs, Phys. Rev. B, 4: 1041 (1971). Crossref
  3. M. F. Thorpe, I. S. Chung, and Y. Cai, Phys. Rev. B, 43: 8282 (1991). Crossref
  4. A. Yu. Gaevskiy, M. A. Ivanov, and V. B. Molodkin, Metallofiz. Noveishie Tekhnol., 31, No. 5: 633 (2009) (in Russian).
  5. V. B. Molodkin, S. I. Olikhovskiy, and M. E. Osinovskiy, Metallofiz. Noveishie Tekhnol., 5, No. 5: 3 (1983) (in Russian).
  6. A. M. Afanas'ev and M. K. Melkonyan, Acta Crystallogr. A, 39: 207 (1983). Crossref
  7. A. M. Afanas'ev, P. A. Alexandrov, and R. M. Imamov, Rentgenodifraktsionnaya Diagnostika Submikronnykh Sloev (X-Ray Diffraction Diagnostics of Submicron Layers) (Moscow: Nauka: 1989) (in Russian).
  8. U. Pietsch, V. Holy, and T. Baumbach, High-Resolution X-Ray Scattering from Thin Films and Multilayers (New York: Springer-Verlag: 2004). Crossref
  9. U. Pietsch, Current Sci., 78: 25 (2000).
  10. E. A. Kondrashkina, S. A. Stepanov, M. Schmidbauer, R. Opitz, and R. Koehler, J. Appl. Phys., 81: 175 (1997). Crossref
  11. A. P. Ulyanenkov, S. A. Stepanov, U. Pietsch, and R. Kohler, J. Phys. D: Appl. Phys., 28: 2522 (1995). Crossref
  12. A. Yu. Gaevskiy, Metallofiz. Noveishie Tekhnol., 31, No. 10: 1317 (2009) (in Russian).
  13. R. D. Mindlin, Physics, 7: 195 (1936). Crossref
  14. J. Daillant, S. Mora, and A. Sentenacm, Diffuse Scattering Lect. Notes Phys., 770: 133 (2009).
  15. J. Daillant and O. Belorgey, J. Chem. Phys., 97: 5824 (1992). Crossref
  16. S. K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B, 38: 2297 (1988). Crossref
  17. S. Takagi, J. Phys. Soc. Jap., 13, No. 2: 278 (1958). Crossref
  18. S. M. Durbin and T. Gog, Acta Cryst. A, 45: 132 (1989). Crossref
  19. F. Oberhettinger, Tables of Bessel Transforms (New York: Springer-Verlag: 1972). Crossref