Advertisement

Glass Physics and Chemistry

, Volume 33, Issue 3, pp 276–282 | Cite as

Determination of the particle sizes, microstrains, and degree of inhomogeneity in nanostructured materials from X-ray diffraction data

  • A. S. Kurlov
  • A. I. Gusev
Proceedings of the Topical Meeting of the European Ceramic Society “Structural Chemistry of Partially Ordered Systems, Nanoparticles, and Nanocomposites” (St. Petersburg, Russia, June 27–29, 2006)

Abstract

The mean particle size, the microstrains, and the degree of inhomogeneity in compacted and dispersed nanostructured materials are determined from the broadening of diffraction reflections. A method is described for separating the contributions from the small size of particles, the microstrains, and the inhomogeneity of materials to the broadening. The application of the proposed method is illustrated using a nanocrystalline powder of tungsten carbide WC.

Keywords

Glass Physic Lorentz Function Substitutional Solid Solution Nanocrystalline Powder Nonstoichiometric Compound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Krivoglaz, M.A., Teoriya rasseyaniya rentgenovskikh luchei i teplovykh neitronov real’nymi kristallami (Theory of X-Ray and Thermal Neutron Scattering by Real Crystals), Moscow: Nauka, 1967 [in Russian].Google Scholar
  2. 2.
    Rempel’, A.A., Rempel’, S.V., and Gusev, A.I., Quantitative Assessment of Homogeneity of Nonstoichiometric Compounds, Dokl. Akad. Nauk, 1999, vol. 369, no. 4, pp. 486–490 [Dokl. Phys. Chem. (Engl. transl.), 1999, vol. 369, no. 4–6, pp. 321–325].Google Scholar
  3. 3.
    Rempel, A.A. and Gusev, A.I., Preparation of Disordered and Ordered Highly Nonstoichiometric Carbides and Evaluation of Their Homogeneity, Fiz. Tverd. Tela (St. Petersburg), 2000, vol. 42, no. 7, pp. 1243–1249 [Phys. Solid State (Engl. transl.), 2000, vol. 42, no. 7, pp. 1280–1286].Google Scholar
  4. 4.
    Gusev, A.I. and Rempel, A.A., Nestekhiometriya, besporyadok i poryadok v tverdom tele (Nonstoichiometry: Disorder and Order in Solids), Yekaterinburg: Ural Division of the Russian Academy of Sciences, 2001 [in Russian].Google Scholar
  5. 5.
    Gusev, A.I., Rempel, A.A., and Magerl, A.J., Disorder and Order in Strongly Nonstoichiometric Compounds: Transition Metal Carbides, Nitrides, and Oxides, Berlin: Springer, 2001.Google Scholar
  6. 6.
    Gusev, A.I., Nanomaterialy, nanostruktury, nanotekhnologii (Nanomaterials, Nanostructures, and Nanotechnologies), Moscow: Fizmatlit, 2005 [in Russian].Google Scholar
  7. 7.
    Dasgupta, P., On Use of Pseudo-Voigt Profiles in Diffraction Line Broadening Analyses, Fizika A (Croatia), 2000, vol. 9, no. 2, pp. 61–66.Google Scholar
  8. 8.
    Puerta, J. and Martin, P., Three and Four Generalized Lorentzian Approximations for the Voigt Line Shape, Appl. Opt., 1981, vol. 20, no. 22, pp. 3923–3928.Google Scholar
  9. 9.
    Cagliotti, G., Paoletti, A., and Ricci, F.P., Choice of Collimators for a Crystal Spectrometer for Neutron Diffraction, Nucl. Instrum. Methods, 1958, vol. 3, no. 3, pp. 223–228.Google Scholar
  10. 10.
    Rietveld, H.M., A Profile Refinement Method for Nuclear and Magnetic Structures, J. Appl. Crystallogr., 1969, vol. 2, no. 2, pp. 65–71.CrossRefGoogle Scholar
  11. 11.
    Scherrer, P., Bestimmung der Grösse und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 1918, vol. 2, pp. 98–100.Google Scholar
  12. 12.
    Warren, B.E., Averbach, B.L., and Roberts, B.W., Atomic Size Effect in the X-Ray Scattering by Alloys, Appl. Phys., 1951, vol. 22, no. 1, pp. 1493–1496.CrossRefGoogle Scholar
  13. 13.
    Williamson, G.K. and Hall, W.H., X-Ray Line Broadening from Filed Aluminium and Wolfram, Acta Metall., 1953, vol. 1, no. 1, pp. 22–31.CrossRefGoogle Scholar
  14. 14.
    Gusev, A.I. and Rempel’, S.V., X-Ray Diffraction Study of the Nanostructure Resulting from Decomposition of (ZrC)1−x(NbC)x Solid Solutions, Neorg. Mater., 2003, vol. 39, no. 1, pp. 49–53 [Inorg. Chem. (Engl. transl.), 2003, vol. 39, no. 1, pp. 43–46].CrossRefGoogle Scholar
  15. 15.
    Rempel’, S.V., Gusev, A.I., and Rempel’, A.A., A Method for Determining the Particle Size in Compacted and Dispersed Nanomaterials, in Fizikokhimiya ul’tradispersnykh (nano-) sistem (Physical Chemistry of Ultradisperse (Nano-)Systems), Moscow: Moscow Institute of Engineering Physics, 2003, pp. 378–384 [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • A. S. Kurlov
    • 1
  • A. I. Gusev
    • 1
  1. 1.Institute of Solid-State Chemistry, Ural DivisionRussian Academy of SciencesYekaterinburgRussia

Personalised recommendations