Introduction to symmetry and diffraction

William Clegg

in Crystal Structure Analysis

Second edition

Published in print June 2009 | ISBN: 9780199219469
Published online September 2009 | e-ISBN: 9780191722516 | DOI:

Series: International Union of Crystallography Texts on Crystallography

Introduction to symmetry and diffraction

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This chapter explores how a crystal structure and its diffraction pattern are related, with reference to aspects of symmetry. Pure translation symmetry is characteristic of crystal structures, leading to concepts of lattices, unit cells, and crystal systems. Molecules, crystals, and other individual objects have point-group symmetry, while crystal structures, with their combination of translation with other forms of symmetry, are characterized by space groups. Symmetry elements found in crystal structures but impossible in finite molecules are glide planes and screw axes. The symmetry of a diffraction pattern is related to the symmetry of the crystal structure and is revealed in its point-group symmetry (the Laue class) and in systematic absences, classes of related X-ray reflections with exactly zero intensity as a consequence of translational symmetry. Other important concepts introduced are: the asymmetric unit of a structure, and general and special positions. The main symmetry properties of crystallographic point groups are summarized.

Keywords: symmetry; point group; space group; Laue class; crystal system; lattice; unit cell; asymmetric unit

Chapter.  7378 words.  Illustrated.

Subjects: Crystallography

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