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Springer Series in
CHEMICAL PHYSICS 80
Springer Series in
CHEMICAL PHYSICS
Series Editors: A. W. Castleman, Jr. J. P. Toennies W. Zinth
The purpose of this series is to provide comprehensive up-to-date monographs in both well established disciplines and emerging research areas within the broad fields of chemical physics and physical chemistry. The books deal with both fundamental science and applications, and may have either a theoretical or an experimental emphasis. They are aimed primarily at researchers and graduate students in chemical physics and related fields.
65 Fluorescence Correlation Spectroscopy Theory and Applications Editors: R. Rigler and E.S. Elson
66 Ultrafast Phenomena XII Editors: T. Elsaesser, S. Mukamel, M.M. Murnane, and N.E Scherer
6y Single Molecule Spectroscopy Nobel Conference Lectures Editors: R. Rigler, M. Orrit, T. Basche
68 Nonequilibrium Nondissipative Thermo dynamics With Application to Low-Pressure Diamond Synthesis ByJ.-T.Wang
69 Selective Spectroscopy of Single Molecules By I.S. Osad'ko
70 Chemistry of Nanomolecular Systems Towards the Realization of Molecular Devices Editors: T. Nakamura, T. Matsumoto, H. Tada, K.-I. Sugiura
71 Ultrafast Phenomena XIII Editors: D. Miller, M.M. Murnane, N.R. Scherer, and A.M. Weiner
72 Physical Chemistry of Polymer Rheology By J. Furukawa
73 Organometallic Conjugation Structures, Reactions and Functions of d-d and d-TT Conjugated Systems Editors: A. Nakamura, N. Ueyama, and K. Yamaguchi
74 Surface and Interface Analysis An Electrochmists Toolbox By R. Holze
75 Basic Principles in Applied Catalysis By M. Baerns
76 The Chemical Bond A Fundamental Quantum-Mechanical Picture By T. Shida
yy Heterogeneous Kinetics Theory of Ziegler-Natta-Kaminsky Polymerization By T. Keii
78 Nuclear Fusion Research Understanding Plasma-Surface Interactions Editors: R.E.H. Clark and D.H. Reiter
79 Ultrafast Phenomena XIV Editors: T. Kobayashi, T. Okada, T. Kobayashi, K.A. Nelson, S. De Silvestri
80 X-Ray Diffraction by Macromolecules By N. Kasai and M. Kakudo
N. Kasai M. Kakudo
X-Ray Diffraction by Macromolecules
With 351 Figures and 56 Tables
te\ Kodansha ^ Springer
Nobutami Kasai Masao Kakudo Professor Emeritus Professor Emeritus Osaka University Osaka University and and Kobe Women's University Former President
Himeji Institute of Technology
Series Editors: Professor A. W. Castleman, Jr. Department of Chemistry, The Pennsylvania State University 152 Davey Laboratory, University Park, PA 16802, USA
Professor J.P. Toennies Max-Planck-Institut fiir Stromungsforschung Bunsenstr. 10,37073 Gottingen, Germany
Professor W. Zinth Universitat Miinchen, Institut fiir Medizinische Optik Ottingerstr. 67, 80538 Munchen, Germany
ISSN 0172-6218
ISBN 4-06-207405-2 Kodansha Ltd., Tokyo
ISBN-io 3-540-25317-3 Springer Berlin Heidelberg New York ISBN-13 978-3-540-25317-4 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2005923756
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Preface
More than thirty years have past since the publication of X-Ray Diffraction by Polymers by the authors (original edition in Japanese published by Maruzen, Tokyo, 1968, and English edition by Kodansha-Elsevier, Tokyo-Amsterdam, 1972).
Since then, accelerated by the very rapid and the remarkable development of electronic computers, both hard- and software as well as new experimental techniques, marvelous developments have been achieved on X-ray sources. X-ray detectors. X-ray apparata in experimental technique and methods of identification of crystalline materials, methods of structure solution and structure analysis of small and macromolecular crystals X-ray diffraction data, presentation of the results obtained, i.e. crystal and molecular structures, and the crys-tallographic databases related to them.
Today, we can see the words, "'mail-in' crystallography" in scientific journals, referring to sending sample(s) with appropriate information to an institution by mail, making it possible to obtain the structure of a complex biological molecule by mail within days ('mail-in' service). However, the authors believe that there are many scientists who are not satisfied with the results obtained by conventional analysis and wish to try to find a way to obtain more detailed structural information on macromolecules or high polymers by themselves based on the fundamentals of X-ray diffraction.
The present volume is divided into three parts as in earlier editions: fundamental, experimental and analytical. In the fundamental part. X-ray small-angle scattering is more precisely described in Chapter 6. In the experimental part, recently developed devices and the latest version of X-ray instruments equipped with these detectors are described. On the other hand, for the basic understanding of X-ray diffraction, descriptions and usages of rather old X-ray instruments are also given. In the analytical section, in addition to the structure analysis of high polymers, a new introduction has been added on the crystallization and structure determination of biological macromolecules in Chapter 13.
In this way, it is hoped that whichever section the reader turns to, depending on the research field, knowledge and experience, a contribution will be made. That is to say, the volume is intended as an intermediate textbook bridging the gap between beginners and specialist workers. Explanatory daigrams have been planned as far as possible to provide an intuitive understanding, and in the description of the equipment and methods it is shown how these are adapted to suit the aims of the analysis. The procedure adopted in the analytical part is to advance from the simple to the complex, starting with analyses of crystalline diffraction spots, amorphous haloes, broadening of diffraction spots, and overall background scattering, then concentrating of X-ray diffraction pattern, and proceeding eventually to composite analytical methods constructed from these individual analyses. Also, many pages have been allotted to examples from original works in order to facilitate the practical application of the analysis for the less experienced. It is hoped that these examples will serve as a further step beyond the level of most primers, but without obscuring the forest for the trees.
VI Preface
Most of the revised manuscripts were finished at the end of 1994. However, the homes of both authors were severely damaged by the heavy earthquake which hit Kobe and nearby areas in Japan on 17 January, 1995, causing delay in the publication of the monograph. Last year minimum revisions were again made on the manuscripts and pictures of the latest instruments were included in the experimental part of the work.
The painstaking work of the staff of Kodansha Ltd. in preparing the text is gratefully acknowledged. One of the authors (N.K.) deeply thanks the late Mrs. Maria Hiroko KA-SAI for her assistance in the initial stages.
Kobe February 2005
Nobutami KASAI
Masao KAKUDO
Contents
Preface v
Part I Fundamental
1. Essential Properties of X-Rays 3
1.1 X-Rays as Electromagnetic Waves 3
1.2 Generation of X-Rays 3
1.2.1 X-ray tube 3
1.2.2 Synchrotron radiation 6
1.3 Properties and Effects of X-Rays 8
1.3.1 Absorption of X-rays 8
1.3.2 X-ray scattering 10
1.3.3 X-ray refraction 11
1.3.4 Effects used for the detection of X-rays 11
1.3.5 Other effects 12
References 13
2. X-Ray Scattering, Interference and Diffraction 15
2.1 Scattering by a Single Electron 16
2.2 Interference and Diffraction of Scattered X-Rays 18
2.2.1 The phenomena of interference and diffraction 18
2.2.2 Basis for calculating the amplitudes of, and phase differences
between, diffracted waves 21
2.2.3 The relationship between real and reciprocal space 23
2.3 Scattering of X-Rays by a Single Atom 25
2.3.1 Atomic scattering factor 25
2.3.2 Anomalous dispersion 27
2.3.3 Compton scattering intensity 27
2.4 Scattering of X-Rays by a Single Polyatomic Molecule 28
2.5 X-Ray Scattering from a Dense, Disordered Assemblage of Identical Atoms
(a Monatomic Liquid) 31
VIII Contents
2.6 A Dense, Disordered Assemblage of Dissimilar Atoms 33
2.7 A Dense, Disordered Assemblage of Polyatomic Molecules (a Molecular
Liquid) 34
2.8 Scattering of X-Rays by Amorphous Solids 35
2.9 Scattering of X-Rays by Crystals 37
2.9.1 Amplitude and intensity of the scattered rays 37
2.9.2 Form of the X-ray diffraction pattern 41
2.10 Summary 43
References 43
3. Crystal Structure 45
3.1 Crystal Systems and the Unit Cell 45
3.2 Crystal Planes and Their Indices 47
3.2.1 Crystal planes 47
3.2.2 Lattice plane indices 48
3.2.3 The spacing of lattice planes and the relationship between plane
indices and Laue indices 49
3.2.4 Coordinates of atoms, lattice points, and reciprocal lattice points and
indices of crystal planes and zone axes 51
3.3 Crystal Symmetry 52
3.3.1 Point groups and their symmetries 52
3.3.2 Space groups 55
3.3.3 Relationship between the atoms present in the unit cell and the
equivalent points of the space group 59
References 60
4. Detailed Interpretation of the Diffraction of X-Rays by Crystals 61
4.1 The Bragg Diffraction Condition 61
4.2 Lattice Structure Factors 63
4.3 Reciprocal Space and Reciprocal Lattice 63
4.4 Wider Applications of the Reciprocal Lattice 68
4.4.1 Interpretation of rotating-crystal and oscillating-crystal photographs .. 68
4.4.2 Interpretation of Weissenberg photographs 75
4.4.3 Interpretation of diffraction from crystalline powders or
polycrystalline specimens 78
4.4.4 Fibrous polycrystalline specimens 79
Reference 82
Contents IX
5. Diffraction of X-Rays by Imperfect Crystals and Paracrystals 83
5.1 Ideal Crystals and Imperfect Crystals 83
5.1.1 Lattice distortions of the first kind 85
5.1.2 Lattice distortions of the second kind 88
5.2 Fourier Transform Theory of X-Ray Diffraction 89
5.2.1 Fourier transform theorem 89
5.2.2 Shape factor for the scattering body 92
5.2.3 Scattering factor of atoms undergoing thermal vibrations in a crystal... 94
5.2.4 Optical experiments on Fourier transforms 95
5.3 Diffraction of X-Rays by Paracrystals 96
5.3.1 Statistical representation of paracrystalline lattice points and
the derivation of their function Q(r) 97
5.3.2 Lattice factor and diffraction intensity for a paracrystal 98
5.4 Summary of the Relationship between Structure and X-Ray Diffraction
Intensity 104
References 108
6. Scattering of X-Rays by Very Small Bodies 109
6.1 Small-angle Diffuse Scattering 109
6.2 Small-angle Scattering Theory 110
6.2.1 X-ray scattering by a substance of any structure 110
6.2.2 Small-angle scattering from systems of dilutely dispersed particles
(orvoids) I l l
6.2.3 Correlation function and distance distribution function 121
6.2.4 Poly dispersed system of particles with uniform shape 127
6.2.5 Small-angle scattering from systems of densely packed particles 128
6.2.6 Small-angle scattering from a non-particulate system 130
References 133
7. Structure of High Polymeric Substances 135
7.1 Structure of High Polymer Chains in the Liquid State and in Solution 136
7.1.1 Configuration and conformation 136
7.1.2 Classification of chain molecules 142
7.2 Molecular Aggregations in Solid High Polymers 146
7.2.1 Globular proteins 146
7.2.2 Synthetic and some natural high polymers 146
Contents
7.3 Structure of the Amorphous State and of Amorphous Regions in Sohd
High Polymers 150
7.3.1 Random-coil model 150
7.3.2 Folded-chain-fringed-micellar-grain model 151
7.4 Fine Texture in Solid High Polymers 151
References 155
Part II Experimental
Experimental Methods 159
8.1 Preliminary Considerations 159
8.2 X-Ray Equipment 159
8.2.1 X-ray generators 159
8.2.2 X-ray detectors 163
8.2.3 X-ray cameras 169
8.2.4 X-ray diffractometers 175
8.2.5 X-ray small-angle scattering cameras 183
8.3 Selection of the X-Ray Parameters 192
8.3.1 X-ray wavelength 192
8.3.2 Production of monochromatic X-rays 193
8.3.3 Elimination of unwanted scattered X-rays 196
8.4 The Specimen 197
8.4.1 Preparation of the specimen 197
8.4.2 Determination of the specimen density 200
8.5 Diffraction Studies for Identification Purposes 201
8.5.1 Qualitative identification using polycrystal diffraction data
(unoriented X-ray diagrams) 201
8.5.2 Treatment of the results 201
8.6 Diffraction Studies for Crystal Structure Analysis 202
8.6.1 General remarks 202
8.6.2 Weissenberg photographs 203
8.6.3 Precession photographs 214
8.7 Diffraction Studies for Analysis of Fine Textures 219
8.7.1 Measurement of crystallinity 219
8.7.2 Analysis of crystallite orientation 220
8.7.3 Measurement of the size and shape of and/or lattice distortion in
crystallites 220
8.7.4 Measurement of diffuse halos due to amorphous solids and liquids 222
8.7.5 Analysis of distorted crystalline diffraction 222
Contents XI
8.7.6 Measurement of small-angle scattering (or diffraction) 222
8.7.7 Special experimental methods 223
References 223
Part III Analytical
9. Identification of Crystals by X-Ray Diffraction 229
9.1 Principles of Identification 229
9.2 Identification by the Powder Method 229
9.2.1 The JCPDS system 229
9.2.2 Locating a JCPDS card 230
9.3 Identification by the Single Crystal Method 231
9.3.1 Computer databases 231
9.3.2 Others 231
9.4 Identification of High Polymers 231
9.4.1 Identification by unoriented X-ray patterns 232
9.4.2 Identification by oriented X-ray patterns 232
9.5 X-Ray Diffraction Patterns of Copolymers and Polymer Blends 232
9.5.1 X-ray diffraction patterns of copolymers 232
9.5.2 X-ray diffraction patterns of polymer blends 235
Notes and References 236
10. Analysis of Crystallite Orientation 239
10.1 Crystallite Orientation and the X-Ray Diffraction Diagram 239
10.1.1 General survey 241
10.1.2 Types of orientation 244
10.1.3 Interpretation of inclined X-ray diagrams 248
10.2 Analysis of the Type of Crystallite Orientation 250
10.2.1 Establishing the presence or absence of orientation 250
10.2.2 Identification of the type of orientation 251
10.3 Determination of the Degree of Orientation 258
10.3.1 Criteria of the degree of orientation 258
10.3.2 Determination of the mean of the crystallite orientation
distribution (orientation coefficient) 259
10.3.3 Analysis of the crystallite orientation distribution (orientation
distribution functions) 263
10.4 Preferred Orientation of Two-dimensional Lattices 270
References 271
XII Contents
11. Crystal Structure Analysis of High Polymers 273
11.1 Use of Unoriented Diffraction Patterns 273
11.1.1 Rietveld method 273
11.1.2 Pattern decomposition method 276
11.1.3 Extension to fibrous materials 277
11.2 Structure Analyses Using Uniaxially Oriented Diffraction Patterns 277
11.2.1 Determination of fiber period 277
11.2.2 Indexing diffractions and determining unit cell parameters 280
11.2.3 Determination of the space group 281
11.2.4 Structure analysis 285
11.2.5 Fourier transforms and syntheses and Patterson functions 289
11.2.6 Determination of phases in Fourier syntheses 293
11.2.7 Refinement of the structure 294
11.2.8 Crystal structure analysis of polyetylene 295
11.3 Analyses Using Biaxially or Doubly Oriented Diffraction Patterns 302
11.4 Analyses Using Diffraction Patterns from Helical Structures 304
11.4.1 Diffraction of X-rays by a continuous helix 304
11.4.2 Diffraction of X-rays by a discontinuous helix 305
11.4.3 Interpretation of the diffraction pattern and structure analysis of
helical polymers 307
11.4.4 Determination of helical structures 311
References 318
12. Crystal Structure Determination of Macromolecules 321
12.1 Characteristics of Protein Crystals 322
12.1.1 Solvent of crystallization 322
12.1.2 Special features of X-ray diffraction by a protein crystal 322
12.2 Crystallization 323
12.2.1 Solubility of protein 323
12.2.2 Techniques for crystallization 324
12.2.3 Preparation of isomorphous heavy atom derivative crystals 327
12.2.4 Crystal mounting 328
12.3 Data Collection 329
12.3.1 Determination of preliminary crystallographic data 329
12.3.2 Collection of intensity data 330
12.4 Phase Determination 331
12.4.1 Isomorphous replacement 331
12.4.2 Anomalous scattering 334
Contents XIII
12.4.3 Determination of the position of heavy atoms 337
12.5 Molecular Replacement Method 341
12.5.1 Structure solution of bacterial cytochrome C2 from
Rhodopseudomonas viridis (Rps. viridis) 341
12.6 Interpretation of Electron Density Maps: Model Building 343
12.7 Refinement of the Structure 345
12.7.1 Restrained least-squares refinement 345
12.7.2 Crystallographic refinement by simulated annealing 346
12.7.3 Further refinement 348
12.7.4 Expression of the result 348
12.8 Structure Analysis of Macromolecules by Image Reconstruction from
Electron Micrographs (Electron Crystallography) 350
12.8.1 Principle 350
12.8.2 Procedures for the image reconstruction 352
12.9 Structural Study of Macromolecules in Solution—NMR Investigations —.. 354
References 355
13. Analysis of the Breadth and Shape of Diffraction Patterns 359
13.1 Instrumental Broadening 360
13.1.1 Systematic errors in measured diffraction breadths 360
13.1.2 Methods of correcting the line profile 361
13.2 Relationship between the Size and Shape of an Ideal Crystal and the
Broadening of Its Diffraction Pattern 363
13.2.1 Broadening due to the Laue function 363
13.2.2 Variation in the shape of diffractions with | F p • G 364
13.3 Calculation of Crystallite Size from the Broadening of the Diffraction
Pattern 364
13.3.1 The Scherrer formula 364
13.3.2 Effect of crystallite size distribution 366
13.3.3 Effect of crystallite shape 366
13.3.4 Application to very small crystallites 367
13.4 Estimation of Lattice Distortion from Line Broadening 372
13.5 Separation of Line Broadenings Due to Crystallite Size and Lattice
Distortion 373
13.5.1 Method of integral breadths 373
13.5.2 Method of profile fitting 374
13.5.3 Method of Fourier transforms 375
13.6 Analyses Including Background Scattering Due to Imperfect Crystals 376
XIV Contents
13.6.1 Broadening of diffraction patterns from paracrystalline structures... 376
13.6.2 Analysis of the broadening of diffractions from paracrystal
structures 379
13.6.3 Shape of the diffraction pattern of a three-dimensional paracrystal
and calculation of the degree of distortion 388
References 391
14. Analyses Using the Total Diffraction Intensity Distribution Curves
of High Polymers 393
14.1 Correction for Coherent Background Scattering 393
14.1.1 Correction of the measured intensity for the effect of polarization .. 393
14.1.2 Normalization of the scattering intensity 393
14.2 Determination of Crystallinity 394
14.2.1 Principles of the measurement of crystallinity 395
14.2.2 Differentiation between crystalline and amorphous scattering in
coherent scattering 396
14.2.3 Measurement of crystallinity 398
14.3 Analysis of the Radial Distribution Function P(r) 402
14.3.1 Calculation of the radial distribution function 402
14.3.2 The radial distribution function of Nylon 6,6 403
14.3.3 Special cases where the shape of the molecular chains can be
deduced without determining the radial distribution function 404
14.4 Recognition of Oriented Diffraction Mixed with Unoriented Amorphous
Scattering 405
14.4.1 Resolution of oriented diffraction masked by unoriented
amorphous scattering 407
14.5 Analysis of the Orientation of Molecular Chains in Amorphous Regions 407
14.5.1 Orientation of molecular chains in amorphous regions 407
14.5.2 Degree of orientation of the molecular chains; practical measure
of parallelism of amorphous chains 408
14.5.3 Estimation of the degree of orientation of molecular chains in
amorphous regions by methods other than X-ray methods 409
14.6 Cylindrical Patterson Functions of Uniaxially Oriented Fiber Diffraction
Patterns 410
14.6.1 The cylindrical distribution function 411
14.6.2 Representation of g(r) in polar coordinates 412
14.6.3 Where there is periodicity along the cylinder axis 416
References 417
Contents XV
15. Analysis of X-ray Small-angle Scattering 419
15.1 Preparative Procedure 419
15.1.1 Detection and recording of the small-angle scattering 419
15.1.2 Corrections to the scattering intensity distribution 420
15.2 Analysis of Particle Size and Shape 422
15.2.1 The Guinier plot 422
15.2.2 Comparison of the measured scattering intensity curve with
the theoretical curve (Curve fitting method) 427
15.2.3 The distance distribution function 431
15.2.4 Other analytical methods 440
15.3 Analysis of Small-angle Scattering for Solutions of Chain
Macromolecules 441
15.3.1 Persistence of polymer chain 441
15.3.2 Scattering intensity from stiff chain molecules 445
15.4 Analysis of the "Long-period Pattern" 450
15.4.1 Long-period small-angle scattering patterns 450
15.4.2 Anisotropy in the small-angle scattering pattern and
in orientation and particle distribution 467
15.5 Analysis of Crystallinity from Small-angle Scattering 469
15.5.1 Analysis using the long-period pattern 469
15.5.2 Analysis using the central diffuse scattering 469
15.6 Analysis of Well-oriented Small- and Wide-angle Diffractions 469
15.6.1 X-ray diffraction patterns from contracting muscle 470
References 478
Appendix 481
Index 497