X-Ray Diffraction by Macromolecules

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1 N. Kasai M. Kakudo X-Ray Diffraction by Macromolecules With 351 Figures and 56 Tables Kodansha ~Springer

2 ... Contents Preface v Part I Fundamental 1. Essential Properties of X-Rays X-Rays as Electromagnetic Waves Generation ofx-rays X-ray tube Synchrotron radiation Properties and Effects of X-Rays Absorption of X-rays X -ray scattering X-ray refraction Effects used for the detection of X-rays Other effects References X-Ray Scattering, Interference and Diffraction Scattering by a Single Electron Interference and Diffraction of Scattered X-Rays The phenomena of interference and diffraction Basis for calculating the amplitudes of, and phase differences between, diffracted waves The relationship between real and reciprocal space Scattering of X-Rays by a Single Atom Atomic scattering factor Anomalous dispersion Compton scattering intensity Scattering of X-Rays by a Single Polyatomic Molecule X-Ray Scattering from a Dense, Disordered Assemblage of Identical Atoms (a Monatomic Liquid)... 31

3 VIII Contents 2.6 A Dense, Disordered Assemblage of Dissimilar Atoms A Dense, Disordered Assemblage ofpolyatomic Molecules (a Molecular Liquid) Scattering of X-Rays by Amorphous Solids Scattering of X-Rays by Crystals Amplitude and intensity of the scattered rays Form of the X-ray diffraction pattern Summary References Crystal Structure Crystal Systems and the Unit Cell Crystal Planes and Their Indices Crystal planes Lattice plane indices The spacing of lattice planes and the relationship between plane indices and Laue indices Coordinates of atoms, lattice points, and reciprocal lattice points and indices of crystal planes and zone axes Crystal Symmetry Point groups and their symmetries Space groups Relationship between the atoms present in the unit cell and the equivalent points of the space group References Detailed Interpretation of the Diffraction of X-Rays by Crystals The Bragg Diffraction Condition Lattice Structure Factors....' Reciprocal Space and Reciprocal Lattice Wider Applications of the Reciprocal Lattice Interpretation of rotating-crystal and oscillating-crystal photographs Interpretation ofweissenberg photographs Interpretation of diffraction from crystalline powders or polycrystalline specimens Fibrous polycrystalline specimens Reference

4 Contents IX 5. Diffraction of X-Rays by Imperfect Crystals and Paracrystals Ideal Crystals and Imperfect Crystals l.l Lattice distortions of the first kind Lattice distortions of the second kind Fourier Transform Theory of X-Ray Diffraction Fourier transform theorem Shape factor for the scattering body Scattering factor of atoms undergoing thermal vibrations in a crystal Optical experiments on Fourier transforms Diffraction of X-Rays by Paracrystals Statistical representation of paracrystalline lattice points and the derivation of their function Q(r) Lattice factor and diffraction intensity for a paracrystal Summary of the Relationship between Structure and X-Ray Diffraction Intensity References Scattering of X-Rays by Very Small Bodies Small-angle Diffuse Scattering Small-angle Scattering Theory X-ray scattering by a substance of any structure Small-angle scattering from systems of dilutely dispersed particles (or voids) Ill Correlation function and distance distribution function Polydispersed system of particles with uniform shape Small-angle scattering from systems of densely packed particles Small-angle scattering from a non-particulate system References Structure of High Polymeric Substances I Structure of High Polymer Chains in the Liquid State and in Solution Configuration and conformation Classification of chain molecules Molecular Aggregations in Solid High Polymers l Globular proteins Synthetic and some natural high polymers

5 X Contents 7.3 Structure of the Amorphous State and of Amorphous Regions in Solid High Polymers Random-coil model Folded-chain-fringed-micellar-grain model Fine Texture in Solid High Polymers References Part II Experimental 8. Experimental Methods Preliminary Considerations X-Ray Equipment X-ray generators X-ray detectors X-ray cameras X-ray diffractometers X-ray small-angle scattering cameras Selection of the X-Ray Parameters X-ray wavelength Production of monochromatic X-rays Elimination of unwanted scattered X-rays The Specimen Preparation of the specimen Determination of the specimen density Diffraction Studies for Identification Purposes Qualitative identification using polycrystal diffraction data (unoriented X-ray diagrams) Treatment of the results Diffraction Studies for Crystal Structure Analysis General remarks Weissenberg photographs Precession photographs Diffraction Studies for Analysis of Fine Textures Measurement of crystallinity Analysis of crystallite orientation Measurement of the size and shape of and/or lattice distortion in crystallites Measurement of diffuse halos due to amorphous solids and liquids Analysis of distorted crystalline diffraction

6 Contents XI Measurement of small-angle scattering (or diffraction) Special experimental methods References Part III Analytical 9. Identification of Crystals by X-Ray Diffraction Principles of Identification Identification by the Powder Method The JCPDS system Locating a JCPDS card Identification by the Single Crystal Method I Computer databases Others Identification of High Polymers Identification by unoriented X-ray patterns Identification by oriented X-ray patterns X-Ray Diffraction Patterns of Copolymers and Polymer Blends X-ray diffraction patterns of copolymers X-ray diffraction patterns of polymer blends Notes and References Analysis of Crystallite Orientation Crystallite Orientation and the X-Ray Diffraction Diagram General survey Types of orientation Interpretation of inclined X-ray diagrams Analysis of the Type of Crystallite Orientation Establishing the presence or absence of orientation Identification of the type of orientation I 0.3 Determination of the Degree of Orientation Criteria of the degree of orientation Determination of the mean of the crystallite orientation distribution (orientation coefficient) Analysis of the crystallite orientation distribution (orientation distribution functions) I 0.4 Preferred Orientation of Two-dimensional Lattices References

7 XII Contents 11. Crystal Structure Analysis of High Polymers Use of Unoriented Diffraction Patterns Rietveld method Pattern decomposition method Extension to fibrous materials Structure Analyses Using Uniaxially Oriented Diffraction Patterns Determination of fiber period Indexing diffractions and determining unit cell parameters Determination of the space group Structure analysis Fourier transforms and syntheses and Patterson functions Determination of phases in Fourier syntheses Refinement of the structure Crystal structure analysis of polyetylene Analyses Using Biaxially or Doubly Oriented Diffraction Patterns Analyses Using Diffraction Patterns from Helical Structures Diffraction of X-rays by a continuous helix Diffraction of X-rays by a discontinuous helix Interpretation of the diffraction pattern and structure analysis of helical polymers Determination of helical structures References Crystal Structure Determination of Macromolecules Characteristics of Protein Crystals Solvent of crystallization Special features of X-ray diffraction by a protein crystal Crystallization Solubility of protein Techniques for crystallization Preparation of isomorphous heavy atom derivative crystals Crystal mounting Data Collection Determination of preliminary crystallographic data Collection of intensity data Phase Detennination Isomorphous replacement Anomalous scattering

8 Contents XIII Determination of the position of heavy atoms Molecular Replacement Method Structure solution of bacterial cytochrome Cz from Rhodopseudomonas viridis (Rps. viridis) Interpretation of Electron Density Maps: Model Building Refinement of the Structure Restrained least-squares refinement Crystallographic refinement by simulated annealing Further refinement Expression of the result Structure Analysis of Macromolecules by Image Reconstruction from Electron Micrographs (Electron Crystallography) Principle Procedures for the image reconstruction Structural Study of Macromolecules in Solution-NMR Investigations References Analysis of the Breadth and Shape of Diffraction Patterns Instrumental Broadening Systematic errors in measured diffraction breadths Methods of correcting the line profile Relationship between the Size and Shape of an Ideal Crystal and the Broadening of Its Diffraction Pattern Broadening due to the Laue function Variation in the shape of diffractions with IF 1 2 G Calculation of Crystallite Size from the Broadening of the Diffraction Pattern The Scherrer formula Effect of crystallite size distribution Effect of crystallite shape Application to very small crystallites Estimation of Lattice Distortion from Line Broadening Separation of Line Broadenings Due to Crystallite Size and Lattice Distortion Method of integral breadths Method of profile fitting Method of Fourier transforms Analyses Including Background Scattering Due to Imperfect Crystals

9 XIV Contents Broadening of diffraction patterns from paracrystalline structures Analysis of the broadening of diffractions from paracrystal structures Shape of the diffraction pattern of a three-dimensional paracrystal and calculation of the degree of distortion References Analyses Using the Total Diffraction Intensity Distribution Curves of High Polymers Correction for Coherent Background Scattering Correction of the measured intensity for the effect of polarization Normalization of the scattering intensity Determination of Crystallinity Principles of the measurement of crystallinity Differentiation between crystalline and amorphous scattering in coherent scattering Measurement of crystallinity Analysis of the Radial Distribution Function P(r)... ; Calculation of the radial distribution function The radial distribution function of Nylon 6, Special cases where the shape of the molecular chains can be deduced without determining the radial distribution function Recognition of Oriented Diffraction Mixed with Unoriented Amorphous Scattering Resolution of oriented diffraction masked by unoriented amorphous scattering Analysis of the Orientation of Molecular Chains in Amorphous Regions Orientation of molecular chains in amorphous regions Degree of orientation of the molecular chains; practical measure of parallelism of amorphous chains Estimation of the degree of orientation of molecular chains in amorphous regions by methods other than X-ray methods Cylindrical Patterson Functions of Uniaxially Oriented Fiber Diffraction Patterns The cylindrical distribution function Representation of Q(r) in polar coordinates Where there is periodicity along the cylinder axis References

10 Contents XV 15. Analysis of X-ray Small-angle Scattering Preparative Procedure Detection and recording of the small-angle scattering Corrections to the scattering intensity distribution Analysis of Particle Size and Shape The Guinier plot Comparison of the measured scattering intensity curve with the theoretical curve (Curve fitting metl"lod) The distance distribution function Other analytical methods Analysis of Small-angle Scattering for Solutions of Chain Macromolecules Persistence of polymer chain Scattering intensity from stiff chain molecules Analysis of the "Long-period Pattern" Long-period small-angle scattering patterns Anisotropy in the small-angle scattering pattern and in orientation and particle distribution Analysis of Crystallinity from Small-angle Scattering Analysis using the long-period pattern Analysis using the central diffuse scattering Analysis of Well-oriented Small- and Wide-angle Diffractions X-ray diffraction patterns from contracting muscle References Appendix Index

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