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Crystals, X-rays and ProteinsComprehensive Protein Crystallography$
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Dennis Sherwood and Jon Cooper

Print publication date: 2010

Print ISBN-13: 9780199559046

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199559046.001.0001

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The contents of the unit cell

The contents of the unit cell

(p.297) 9 The contents of the unit cell
Crystals, X-rays and Proteins

Dennis Sherwood

Jon Cooper

Oxford University Press

This chapter discusses the underlying principles X-ray scattering by a distribution of electrons. The theory is then extended to the diffraction of X-rays by an infinite lattice of molecular motifs and the concept of the structure factor, which describes the diffraction pattern, is introduced. The theory of calculating the electron density distribution within the unit cell by Fourier inversion of the structure factors is then covered. The fact that only the amplitudes and not the phases of the structure factors can be measured experimentally represents the major practical problem of diffraction analysis that is known as the phase problem. The process of calculating structure factors from a known structure can be simplified by treating each atom as a scattering centre that is assigned a scattering factor related to its atomic number. In the second half of the chapter, the rules relating the symmetry of the diffraction pattern to that of the crystal are derived, and the basis for the inherent inversion symmetry of the diffraction pattern, known as Friedel's law, is described. Situations where this important law breaks down are touched upon due to their importance in solving the phase problem. The phenomenon of systematic absences, essentially missing diffraction spots, and how they can yield key information on the symmetry of the crystal is explained.

Keywords:   scattering, electrons, electron density function, Fourier synthesis, calculation of structure factors, atomic scattering factors, anomalous scattering, diffraction pattern symmetry, Friedel's law, systematic absences

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