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Crystal Structure AnalysisPrinciples and Practice$
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William Clegg, Alexander J Blake, Jacqueline M Cole, John S O Evans, Peter Main, Simon Parsons, and David J Watkin

Print publication date: 2009

Print ISBN-13: 9780199219469

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780199219469.001.0001

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Direct methods of crystal-structure determination

Direct methods of crystal-structure determination

(p.133) 10 Direct methods of crystal-structure determination
Crystal Structure Analysis

Peter Main

Oxford University Press

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

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