Fundamentals of Powder Diffraction and Structural Characterization of Materials pp 239-262 | Cite as
Solving the Crystal Structure
As we established in Chaps. 7–9, the diffraction pattern of either a single crystal or a polycrystalline material is a transformation of an ordered atomic structure into reciprocal space, rather than a direct image of the former, and the three-dimensional distribution of atoms in a lattice can be restored only after the diffraction pattern has been transformed back into direct space. In powder diffraction, the situation is complicated by the fact that the diffraction pattern is a one-dimensional projection of a three-dimensional reciprocal space. We have no intention of covering the comprehensive derivation of relevant mathematical tools since it is mainly of interest to experts, and can be found in many excellent books and reviews.1 Therefore, in this chapter we only briefly describe a general approach to the problem of solving the crystal structure.
Keywords
Phase Angle Bragg Peak Reciprocal Space Pair Distribution Function Powder Diffraction DataPreview
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10.4 Additional Reading
- 1.International Tables for Crystallography, vol. A, Fifth Revised Edition, Theo Hahn, Ed. (2002); vol. B, Third Edition, U. Shmueli, Ed. (2008); vol. C, Third Edition, E. Prince, Ed. (2004). All volumes are published jointly with the International Union of Crystallography (IUCr) by Springer. Complete set of the International Tables for Crystallography, Vol. A-G, H. Fuess, T. Hahn, H. Wondratschek, U. Müller, U. Shmueli, E. Prince, A. Authier, V. Kopský, D.B. Litvin, M.G. Rossmann, E. Arnold, S. Hall, and B. McMahon, Eds., is available online as eReference at http://www.springeronline.com.
- 2.P. Coppens, X-ray charge densities and chemical bonding. IUCr Texts on Crystallography 4, Oxford University Press, Oxford (1997).Google Scholar
- 3.V.G. Tsirelson and R.P. Ozerov, Electron density and bonding in crystals: principles, theory and X-ray diffraction experiments in solid state physics and chemistry, Institute of Physics, Bristol, UK (1996).Google Scholar
- 4.C. Giacovazzo, Direct phasing in crystallography: fundamentals and applications. IUCr monographs on crystallography 8, Oxford University Press, Oxford (1998).Google Scholar
- 5.T. Egami and S.J.L. Billinge, Underneath the Bragg peaks. Structural analysis of complex materials. Pergamon Materials Series. Pergamon, Amsterdam (2003).CrossRefGoogle Scholar
- 6.R.B. Neder and T. Proffen, Fitting of nano particle structures to powder diffraction pattern using DISCUS, p. 49 in: CPD Newsletter “2D Powder Diffraction,” Issue 32 (2005), available at http://www.iucr-cpd.org/pdfs/CPD32.pdf.