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A review of Debye Function Analysis

Published online by Cambridge University Press:  14 November 2013

Kenneth R. Beyerlein
Kenneth R. Beyerlein*
Affiliation:
Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract

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The employment of the Debye function to model line profiles in the powder diffraction pattern from small crystallites is briefly reviewed. It is also demonstrated that for the case of very small spherical particles, it is necessary to average patterns from multiple constructions of the particle to have complete agreement with reciprocal space models. In doing so it is demonstrated that the technique of Debye function analysis is best suited for systems with only a few possible atomic arrangements.

Keywords

nanocrystalline materialsline profile analysisDebye function

Information

Type
Technical Articles
Information
Powder Diffraction , Volume 28 , Supplement S2 , September 2013 , pp. S2 - S10
Copyright
Copyright © International Centre for Diffraction Data 2013 

References

Bardhan, J., Park, S. and Makowski, L. (2009). “SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules,” J. Appl. Crystallogr. 42, 932–943.CrossRefGoogle ScholarPubMed
Berry, C. R. (1952). “Electron diffraction from Small Crystals,” Phys. Rev. 88, 596–599.CrossRefGoogle Scholar
Beyerlein, K. R., Snyder, R. L. and Scardi, P. (2011). “Powder diffraction line profiles from size and shape of nanocrystallites,” J. Appl. Crystallogr. 44, 945–953.CrossRefGoogle Scholar
Buljan, M., Desnica, U. V., Radic, N., Drazic, G., Matej, Z., Vales, V. and Holy, V. (2009). “Crystal structure of defect-containing semiconductor nanocrystals – an X-ray diffraction study,” J. Appl. Crystallogr. 42, 660–672.CrossRefGoogle Scholar
Cervellino, A., Giannini, C. and Guagliardi, A. (2006). “On the efficient evaluation of Fourier patterns for nanoparticles and clusters,” J. Comput. Chem. 27, 995–1008.CrossRefGoogle ScholarPubMed
Debye, P. (1915). “Zerstreuung von Röntgenstrahlen,” Ann. Phys. (Berlin, Ger.) 351, 809–823.CrossRefGoogle Scholar
Derlet, P. M., Van Petegem, S. and Van Swygenhoven, H. (2005). “Calculation of x-ray spectra for nanocrystalline materials,” Phys. Rev. B: Condens. Matter Mater. Phys. 71, 024114.CrossRefGoogle Scholar
Fargas, J., de Feraudy, M. F., Raolt, B. and Torchet, G. (1983). “Noncrystalline structure of argon clusters. I. Polyicosahedral structure of Ar clusters, 20<N<50,” J. Chem. Phys. 78, 5067–5080.Google Scholar
Gelisio, L., Azanza Ricardo, C. L., Leoni, M. and Scardi, P. (2010). “Real-space calculation of powder diffraction patterns on graphics processing units,” J. Appl. Crystallogr., 43, 647–653.CrossRefGoogle Scholar
Germer, L. H. and White, A. H. (1941). “Electron diffraction studies of thin films. II. Anomalous powder patterns produced by small crystals,” Phys. Rev. 60, 447–454.CrossRefGoogle Scholar
Gnutzman, V. and Vogel, W. (1990). “Structural Sensitivity of the standard Pt/SiO2 Catalyst EuroPt-1 to H2 and O2 Exposure by in situ X-ray diffraction,” J. Phys. Chem. 94, 4991–4997.Google Scholar
Hall, B. D., Flueli, M., Monot, R. and Borel, J. P. (1991). “Multiply twinned structures in unsupported ultrafine silver particles observed by electron diffraction,” Phys. Rev. B: Condens. Matter Mater. Phys. 43, 3906–3917.CrossRefGoogle ScholarPubMed
Hall, B. D. and Monet, R. (1991). “Calculating the Debye–Scherrer diffraction pattern for large lusters,” Comput. Phys, 5, 414–417.Google Scholar
Ino, T. and Minami, N. (1979). “X-ray diffraction by small crystals,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 35, 163–170.CrossRefGoogle Scholar
Minami, N. and Ino, T. (1979). “Diffraction profiles from small crystallites,” Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 35, 171–176.Google Scholar
Morozumi, C. and Ritter, H. L. (1953). “Calculated powder patterns from very small crystals: body-centered cubic cubes,” Acta Crystallogr. 6, 588–590.CrossRefGoogle Scholar
Niederdraenk, F., Seufert, K., Luczak, P., Kulkarni, S. K., Chory, C., Neder, R. B. and Kumpf, C. (2007). “Structure of small II-VI semiconductor nanoparticles: A new approach based on powder diffraction,” Phys. Status Solidi C 4, 3234–3243.Google Scholar
Oddershede, J., Christiansen, T. L. and Stahl, K. (2008). “Modelling the X-ray powder diffraction of nitrogen expanded austenite using the Debye formula,” J. Appl. Crystaollogr. 41, 537–543.Google Scholar
Patterson, A. L. (1939). “Diffraction of X-rays by Small Crystalline Particles,” Phys. Rev. 56, 972–977.CrossRefGoogle Scholar
Scardi, P., Leoni, M. and Beyerlein, K. R. (2011). “On the modeling of the powder pattern from a nanocrystalline material,” Z. Kristallogr. 226, 924–933.CrossRefGoogle Scholar
Thomas, N. W. (2011). “A Fourier transform method for powder diffraction based on the Debye scattering equation,” Acta Crystallogr., Sect. A: Found. Crystallogr. 67, 491–506.Google Scholar
Torchet, G., Bouchier, H., Fargas, J., de Feraudy, M., and Raoult, B. (1984). “Size effects in the structure and dynamics of CO2 clusters,” J. Chem. Phys. 81, 2137–2143.Google Scholar
Zernike, F. and Prins, J. A. (1927). “Die beugung von Rontgenstrahlen in flussigkeiten als effekt der molekuhlanordnung,” Z. Phys. 41, 184–194.Google Scholar