Direct methods of crystal-structure determination

Peter Main

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

Direct methods of crystal-structure determination

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Reflection phases are essential for crystal structure solution but are not available experimentally. They can be estimated from probability and other relationships derived from known or assumed constraints on the electron density, such as its positivity and atomicity. Direct methods of estimating phases use normalized structure factors, appropriate for point atoms at rest, which are calculated from the observed amplitudes and some assumptions. Various direct methods are based on inequalities, determinants, and probability relationships for relationships among phases of reflections with related indices. This chapter introduces concepts such as triplet and quartet relationships, the tangent formula, structure invariants, and maximum entropy approaches. The main steps involved in a direct methods structure solution are outlined, including the assignment of starting phases, the use of figures of merit for recognising possible solutions, and the interpretation of electron density maps (E-maps).

Keywords: direct methods; phases; normalized structure factors; E-values; inequalities; tangent formula; triplets; quartets; structure invariants; figures of merit

Chapter.  6816 words.  Illustrated.

Subjects: Crystallography

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