Blake A.J.(ed.) Crystal Structure Analysis

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6 Introduction to crystallographic statistics

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7 Crystallographic instrumentation

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8 Direct phasing in crystallography

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9 The weak hydrogen bond

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10 Defect and microstructure analysis by diffraction

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11 Dynamical theory of X-ray diffraction

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20 Aperiodic crystals: from modulated phases to quasicrystals

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21 Incommensurate crystallography

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22 Structural crystallography of inorganic oxysalts

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23 The nature of the hydrogen bond: outline of a comprehensive hydrogen bond theory

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24 Macromolecular crystallization and crystal perfection

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11 Diffuse scattering and defect structure simulations: a cook book using the program DISCUS

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12 The basics of crystallography and diffraction, third edition

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13 Crystal structure analysis: principles and practice, second edition

W. Clegg, editor

Crystal Structure Analysis

Principles and Practice

Second Edition

Alexander J. Blake

School of Chemistry, University of Nottingham

William Clegg

Department of Chemistry, University of Newcastle upon Tyne

Jacqueline M. Cole

Cavendish Laboratory, University of Cambridge

John S.O. Evans

Department of Chemistry, University of Durham

Peter Main

Department of Physics, University of York

Simon Parsons

Department of Chemistry, University of Edinburgh

David J. Watkin

Chemical Crystallography Laboratory, University of Oxford

Edited by

William Clegg

Great Clarendon Street, Oxford ox26dp

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Crystal structure analysis : principles and practice / William Clegg ...[et al.]. — 2nd ed.

p. cm. — (International Union of Crystallography book series; 13)

ISBN 978–0–19–921946–9 (hardback) — ISBN 978–0–19–921947–6 (pbk.)

1. X-ray crystallography. 2. Crystals—Structure. I. Clegg, William, 1949–

QD945.C79 2009

548



.81—dc22 2009011644

Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India

Printed in Great Britain

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CPI Antony Rowe, Chippenham, Wilts

ISBN: 978–0–19–921946–9

ISBN: 978–0–19–921947–6

13579108642

Preface

The material in this book is derived from an intensive course in X-ray

structure analysis organized on behalf of the Chemical Crystallogra-

phy Group of the British Crystallographic Association and held every

two years since 1987. As with a crystal structure derived from X-ray

diffraction data, the course contents have been gradually reﬁned over

the years and they reached a stage in 1999 (the seventh course) where

we considered they could be published, and hence made available to a

far wider audience than can be accommodated on the course itself. The

result was the ﬁrst edition of this book, published in 2001. The authors

were the principal lecturers on the course in 1999 and they revised

and expanded the material, while converting the lecture notes into a

book format. Because of its origin, the book represented a snapshot of

the intensive course, which has continued to evolve, especially as the

subject of chemical crystallography has undergone signiﬁcant changes,

mainly due to the widespread availability of area detector technology,

the exponential increase in computing power and improvements in soft-

ware, and greater use of synchrotron radiation and powder diffraction.

Nevertheless, the underlying principles remain valid, and the particular

application of those principles can be adapted to new developments for

some time to come.

By the time of the eleventh course in 2007, its contents and the team

of principal lecturers had changed markedly, and we were asked to con-

sider a second edition of the book reﬂecting these developments. This

has been encouraged and assisted by the use of a consistent template for

the 2007 course notes, and these have been used as the basis for this new

edition. Nevertheless, any readers who participated in the 2007 course

will detect a number of changes, particularly in the inclusion of some

material not coveredin the lecture notes, some updating, anddifferences

of style made necessary by a non-interactive format.

Since this book, like its ﬁrst edition, owes its origins to the course, we

acknowledge here our large debt to those who have dedicated much

effort to the organization of the course since its inception; without them

thisbook would never have existed,evenas an idea. The ﬁrstﬁvecourses

were held at the University of Aston, where the local organizers Phil

Lowe and Carl Schwalbe set a gold standard of course administration

and smooth operation, establishing many ofthe enduring characteristics

valued by participants ever since. Following the move to the Univer-

sity of Durham, Vanessa Hoy and then Claire Wilson developed these

ﬁrm foundations to even further heights of excellence, presenting a

vi Preface

challenge to Andres Goeta, who took over for the 2009 Course. Through-

out the course’s history Judith Howard has provided overall guidance

and expertise, particularly in fund raising, and has spared the course

lecturers much concern with the practicalities of maintaining and pro-

moting the course. Several organizations, including the EPSRC, IUCr,

BCA and commercial sponsors, have been long-standing and generous

supporters of the course.

The ﬁrst course in 1987 was the brainchild of David Watkin, who

worked extremely hard to launch it and establish it as the enduring

success that it has become. His role as course director was taken over in

the mid-1990s by Bob Gould, who passed on the baton to Sandy Blake

after 1999; from 2011 the director will be Simon Parsons. The template

for the lecture notes on which this book is based was developed by

Horst Puschmann, and Amber Thompson has looked after assembling

and producing the notes for the last few courses.

Many colleagues have made contributions to the course over the

years, in lectures and in the crucial grouptutorial sessions: a bookformat

can never reﬂect the intensive interaction and lively atmosphere. These

and the social aspects of the course are probably at least as important

in the memories of participants as the formal lecture presentations. One

aspect of the tutorial group sessions of the course has been retained in

modiﬁed form in the book. Most chapters include exercises, for which

answers are provided in an appendix. Readers are encouraged to tackle

the exercises at leisure and not consult the answers until they are satis-

ﬁed with their own efforts. In the spirit of the tutorials, these exercises

may also prove beneﬁcial as a basis for group discussion.

Over the twenty years of the course and its eleven occasions, we have

seen former students return as group tutors, and tutors move on into

lecturer roles. Course participants, from many countries, are established

practising crystallographers in academic and industrial posts around

the world. Courses elsewhere have been developed, modelled on our

experience. We dedicate this book to the hundreds of students who

have been the course’s primary beneﬁciaries and whose hard work and

commitment, intellectually and socially, have contributed much to its

success.

Bill Clegg,

Newcastle University

November 2008

Editor, on behalf of the authors

Acknowledgements

We are grateful to authors and publishers for their permission to

reproduce some of the Figures that appear in this book, as follows.

Figures 1.1, 1.8, 2.1, 2.2, 22.1, 22.2, and 22.4 from W. Clegg: Crystal

Structure Determination. Oxford University Press, Oxford, 1998.

Figures 1.2 and 4.1 from C. Giaccovazzo, H. L. Monaco, D. Viterbo,

F. Scordari, G. Gilli, G. Zanotti and M. Catti: Fundamentals of Crystal-

lography. Oxford University Press, Oxford, 1992.

Figures 1.3 and 1.5 from G. Harburn, C. A. Taylor and T. R. Welberry:

Atlas of Optical Transforms. G. Bell, London, 1975.

Figure 1.9 from J. P. Glusker and K. N. Trueblood: Crystal Structure

Analysis – A Primer, Second Edition. Oxford University Press, Oxford,

1985.

Figures 2.3 and 2.4 from Traidcraft plc, Gateshead, UK.

Figures 5.6 and 5.7 from Rigaku Corporation, Sevenoaks, Kent, UK.

Figure 6.1 from Stoe & Cie GmbH, Darmstadt, Germany.

American Chemical Society.

Figure 10.1, reprinted by permission from G. N. Ramachandran and

Ltd.

Figure 14.3 from R. B. Neder and T. Proffen: Diffuse Scattering and Defect

Structure Simulations: A Cook Book Using the Program DISCUS. Oxford

University Press, Oxford, 2008.

Figure 14.14 from International Tables for Crystallography, Volume A.

Kluwer Academic Press, Dordrecht, The Netherlands. Copyright

1983, International Union of Crystallography.

Figure 17.2 from Panalytical Ltd, Cambridge, UK.

Figure 17.4 from R. Haberkorn, personal communication to J. S. O.

Evans, 1999.

International Union of Crystallography, 2003.

Figure 22.3 from Diamond Light Source, Didcot, Oxfordshire, UK.

vii

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Contents

1 Introduction to diffraction 1

1.1 Introduction 1

1.2 X-ray scattering from electrons 1

1.3 X-ray scattering from atoms 1

1.4 X-ray scattering from a unit cell 2

1.5 The effects of the crystal lattice 2

1.6 X-ray scattering from the crystal 3

1.7 The structure-factor equation 4

1.8 The electron-density equation 5

1.9 A mathematical relationship 6

1.10 Bragg’s law 6

1.11 Resolution 7

1.12 The phase problem 8

2 Introduction to symmetry and diffraction 9

2.1 The relationship between a crystal structure

and its diffraction pattern 9

2.2 Translation symmetry in crystalline solids 10

2.3 Symmetry of individual molecules, with

relevance to crystalline solids 12

2.4 Symmetry in the solid state 16

2.5 Diffraction and symmetry 18

2.6 Further points 20

Exercises 24

3 Crystal growth and evaluation 27

3.1 Introduction 27

3.2 Protect your crystals 27

3.3 Crystal growth 28

3.4 Survey of methods 28

3.4.1 Solution methods 28

3.4.2 Sublimation 33

3.4.3 Fluid-phase growth 33

3.4.4 Solid-state synthesis 34

3.4.5 General comments 34