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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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Diffraction by a three‐dimensional lattice

Diffraction by a three‐dimensional lattice

(p.254) 8 Diffraction by a three‐dimensional lattice
Crystals, X-rays and Proteins

Dennis Sherwood

Jon Cooper

Oxford University Press

This chapter describes the basis of X-ray diffraction by a three-dimensional crystal and introduces the Laue equations which describe the geometric conditions for constructive interference of X-rays diffracted by a crystal lattice. The discussion reinforces the importance of the reciprocal lattice and introduces the concepts of the reciprocal unit cell and the reciprocal lattice vector. Equations relating the real and reciprocal unit cell parameters, as well as the volumes of the real and reciprocal unit cells, are derived and the geometric relationship between the scattering vector and the corresponding reflecting plane in the crystal is established. These geometric considerations lead naturally to one of crystallography's most important rules, known as Bragg's law. Finally, the chapter introduces the concept of the Ewald sphere — an elegant geometric construction that encapsulates Bragg's law in a highly useful graphical form, which is used in many places in the subsequent text.

Keywords:   diffraction pattern, crystal, diffraction, three-dimensional lattice, Laue equations, reciprocal lattice, reciprocal unit cell, Bragg's law, Ewald construction

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