Werner Massa. Crystal Structure Determination

Transcription

1 Werner Massa Crystal Structure Determination

2 Werner Massa CrystalStructure Determination Translated into English by Robert O. Gould With 102 Figures and 16 Tables, Springer

3 AUTHOR Professor Dr. Werner Massa University of Marburg Department of Chemistry Hans-Meerwein -Straße D Marburg Germany TRANSLATOR Dr. Robert O. Gould University of Edinburgh Department of Chemistry West Mains Road Edinburgh EH9 3JJ UK The book was originally published under the title "Massa, Kristallstrukturbestimmung, 2. überarb. Auflage" B.G. Teubner, Stuttgart Translation arranged with the approval of the publisher B. G. Teubner from the 2nd revised German edition into English. ISBN Library of Congress Cataloging-in-Publication Data Massa, Werner: [Kristallstrukturbestimmung. English] Crystal Structure Determination / Werner Massa; translated into English by Robert o. Gould. p. cm. Indudes bibliographical references and index. ISBN ISBN (ebook) DOI / X-ray crystallography. I. Title. QD94S.M This work is subject to copyright. All rights reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitations, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 2000 Originally published by Springer-Verlag Berlin Heidelberg New York in 2000 The use of general descriptive names, registerea names, traaemarks, eic. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Design & Production, Heidelberg Typesetting: Hilmar Schlegel, Berlin SPIN: / Printed on acid free paper

4 Preface to the First English Edition The English edition is largely based on the second German edition. In the meantime, area-detector systems for measurement of single crystal data have largely replaced the "classical" four-circle diffractometer, so the section on area detectors has been expanded and brought up to date. I am grateful to my colleague R. O. Gould not only for what is, so far as I can judge, an excellent translation, but also for many very useful improvements during what has been a friendly and fruitful collaboration. The initiation of the translation by Drs. M. Krieger and M. Müller, two former students who sang the praise of this book while studying in the U. K., is grateful acknowledged. Werner Massa Marburg, July 1999 Preface to the Second German Edition The necessity for a second edition has provided the opportunity to correct errors and unclarities in the first edition, as well as to make a few additions. Many thanks are offered to all the readers who kindly helped in this process. Werner Massa Marburg, March 1996 Preface to the First German Edition Crystal structure analysis using X-rays has undergone an expansion of avalanche proportions in the last twenty years, thanks to the development of rapid and automatic means of data collection and the enormous growth of the computer hardware and software for carrying out the necessary calculations. Because of its wide applicability and its precision, it has become one of the most important tools in both organic and inorganic chemical research. Despite the fact that crystallography plays a very minor role in most undergraduate study, many students have found that in the course of graduate or even undergraduate research, they need to undertake a crystal structure determination themselves, or at least to become competent to interpret crystallographic results. Thanks to ever improving program systems, the many complex steps of a structure analysis are certainly becoming less and less difficult for the beginner to master. Nonetheless, regarding the process simply as a "black box" is fraught with danger. This book is aimed at those students of chemistry and related subjects who wish to take a look into the black box before they step into its territory, or who simply wish to learn more of the fundamentals, the opportunities and the risks of the method. In view of the well-known fact that the likelihood a book will actually be read is inversely proportional to its number of pages, fundamentals of the method are treated here as briefly and as intuitively as possible. It seems more important that chemists should have a grasp of the basic principles and their application to a problem, than that they

5 VI be in a position to understand fully the complex mathematical formalisms employed by the computer programs. On the other hand, some aspects of the subject, which bear directly on the quality of a structure determination, are worth fuller treatment. These include discussion of a number of significant errors and the recognition and treatment of disorder and twinning. Most important crystallographic literature is available in English, but a few references in other languages, principally German, have been included. This book is based in part on lectures and on a seminar at the University of Marburg. Consciously or unconsciously, many colleagues have made their contributions. I am particularly grateful to Professor D. Babel for many helpful suggestions and a critical reading of the manuscript. I thank Dr. K. Harms for proofreading the manuscript and Mr. C. Frommen for considerable assistance with the production of camera-ready copy using the Ib.Tpc program. Finally, I acknowledge the help of my wife Hedwig and my children for all their assistance and patience during the preparation of this book. Werner Massa Marburg, April 1994

6 Contents 1 Introduction 1 2 Crystal Lattices The Lattice The Unit Cell Atom Parameters. 5 2.l.3 The Seven Crystal Systems The Fourteen Bravais Lattices The Hexagonal, Trigonal and Rhombohedral Systems The Reduced Cell The Geometry of X-Ray Diffraction X-Rays Interference by a One-Dimensional Lattice The Laue Equations Lattice Planes and hkl-indices The Bragg Equation Higher Orders of Diffraction The Quadratic Form of the Bragg Equation 23 4 The Reciprocal Lattice From the Direct to the Reciprocal Lattice The Ewald Construction Structure Factors Atom Formfactors Atom Displacement Factors Structure Factors Crystal Symmetry Simple Symmetry Elements Coupling of Symmetry Elements Combination of Symmetry Elements Symmetry Directions

7 VIII CONTENTS 6.3 Symmetry Elements Involving Translation Combination of Translation with Other Symmetry Elements Coupling of Translation with Other Symmetry Elements The 230 Space Groups l Space-group Notation in International Tables for Crystallography Centrosymmetric Crystal Structures The Asymmetric Unit Space Group Types Group-Subgroup Relationships Visible Effects of Symmetry Microscopic Structure Macroscopic Properties and Crystal Classes Symmetry of the Lattice Symmetry of the Diffraction Pattern - The Laue Groups Determination of the Space Group Determination of the Laue Group Systematic Absences Transformations 65 7 Experimental Methods 7.1 Growth, Choice and Mounting of a Single Crystal 7.2 Film Methods Rotation and Weissenberg Methods The Precession Method Other Film Methods The Single-Crystal Diffractometer Types of Instruments Determination of the Orientation Matrix Refiection Profile and Scan Type Selection of Data to be Measured 7.4 Area Detectors Data Reduction Lp Correction Standard Uncertainty Absorption Correction 7.6 Other Diffraction Methods Synchrotron Radiation Neutron Scattering Electron Scattering

8 IX 8 Structure Solution 8.1 Fourier Transforms Patterson Methods Symmetry in Patterson Space Structure Solution Using Harker Peaks Image-Seeking Methods Direct Methods Harker-Kasper Inequalities Normalized Structure Factors The Sayre Equation The Triplet Relationship Origin Fixation Strategies of Phase Determination 9 Structure Refinement 9.1 The Method of Least Squares Refinement Based on Fo or F; Data 9.2 Weights Crystallographic R-Values Refinement Techniques Location and Treatment of Hydrogen Atoms Restricted Refinement Damping Symmetry Restrictions Residual Electron Density 9.5 Rietveld Refinement Additional Topics 10.1 Anomalous Dispersion and "Absolute Structure" Chiral and Polar Space Groups Extinction The Renninger Effect The A/2-Effect Thermal Diffuse Scattering (TDS) 11 Errors and Pitfalls 11.1 Wrong Atom-Types Disorder Site Occupancy Disorder Positional and Orientational Disorder One- and Two-Dimensional Disorder Modulated Structures Quasicrystals Twinning Classification by the Twin-Element l1s

9 X CONTENTS Classification According to Macroscopic Appearance Classification According to Origin Diffraction Patterns of Twinned Crystals and their Interpretation Twinning or Disorder? 11.4 False Unit Cells Space Group Errors Misplaced Origins Poor Atom Displacement Parameters Interpretation and Presentation of Results 12.1 Bond Lengths and Bond Angles Best Planes and Torsion Angles Structural Geometry and Symmetry 12.4 Structural Diagrams 12.5 Electron Density Crystallographic Databases 13.1 The Inorganic Crystal Structure Database (ICSD) 13.2 The Cambridge Structural Database (CSD) The Metals Crystallographic Data File (CRYST-MET) 13.4 Other Collections of Crystal Structure Data 13.5 Deposition of Structural Data in Data Bases 13.6 Crystaliography on the Internet Outline of a Crystal Structure Determination 15 Worked Example of a Structure Determination Bibliography Index

10 XI Commonly used Symbols a,b,c a*, b*, c* A B d d* E f Fe F o FOM hkl I L M r n P R SH TDS U w wr wr2 x,y,z Z a,ß,y L1,6, J',,6, J" E: fj A /L Q lattice constants or symbols for axial glide planes reciprocallattice constants Angström unit (= m) Debye-Waller Factor (= 8n 2 U) lattice-plane spacing or symbol for diamond glide plane scattering vector in reciprocal space normalized structure factor atomic scattering factor (formfactor) calculated structure factor observed structure factor figure of merit Miller indices refiection intensity Lorentz factor mass of a mole order of diffraction or symbol for diagonal glide plane polarization factor conventional residual, calculated from Fo-data sign of a structure factor thermal diffuse scattering atomic dis placement factor (= B/8n 2 ) or unitary structure factor weight of a structure factor weighted residual, calculated from Fo-data weighted residual, calculated from F;-data atomic coordinates number of formula units per unit cell unit cell angles path difference for interference or other differences components of anomalous scattering extinction coefficient scattering angle X-ray wavelength absorption coefficient or various angles desity standard error phase angle of a structure factor