Structure Determination by X-Ray Crystallography

ISBN-13: 9781461579410 / Angielski / Miękka / 2012 / 502 str.

R. a. Palmer; M. F. C. Ladd

Opis

X-ray crystallography provides us with the most accurate picture we can get of atomic and molecular structures in crystals. It provides a hard bedrock of structural results in chemistry and in mineralogy. In biology, where the structures are not fully crystalline, it can still provide valuable results and, indeed, the impact here has been revolutionary. It is still an immense field for young workers, and no doubt will provide yet more striking develop- ments of a major character. It does, however, require a wide range of intellectual application, and a considerable ability in many fields. This book will provide much help. It is a very straightforward and thorough guide to every aspect of the subject. The authors are experienced both as research workers themselves and as teachers of standing, and this is shown in their clarity of exposition. There are plenty of iliustrations and worked examples to aid the student to obtain a real grasp of the subject.

Spis treści

1 Crystal Geometry. I.- 1.1 Introduction.- 1.2 The Crystalline State.- 1.2.1 Reference Axes.- 1.2.2 Equation of a Plane.- 1.2.3 Miller Indices.- 1.2.4 Axial Ratios.- 1.2.5 Zones.- 1.3 Stereographic Projection.- 1.4 External Symmetry of Crystals.- 1.4.1 Two-Dimensional Point Groups.- 1.4.2 Three-Dimensional Point Groups.- Problems.- 2 Crystal Geometry.II.- 2.1 Introduction.- 2.2 Lattices.- 2.2.1 Two-Dimensional Lattices.- 2.2.2 Choice of Unit Cell.- 2.2.3 Three-Dimensional Lattices.- 2.3 Families of Planes and Interplanar Spacings.- 2.4 Reciprocal Lattice.- 2.5 Rotational Symmetries of Lattices.- 2.6 Space Groups.- 2.6.1 Two-Dimensional Space Groups.- 2.6.2 Limiting Conditions Governing X-Ray Reflection.- 2.6.3 Three-Dimensional Space Groups.- 2.6.4 Screw Axes.- 2.6.5 Glide Planes.- 2.6.6 Analysis of the Space-Group Symbol.- Problems.- 3 Preliminary Examination of Crystals by Optical and X-Ray Methods.- 3.1 Introduction.- 3.2 Polarized Light.- 3.3 Optical Classification of Crystals.- 3.3.1 Uniaxial Crystals.- 3.3.2 Birefringence.- 3.3.3 Biaxial Crystals.- 3.3.4 Interference Figures.- 3.4 Direction of Scattering of X-Rays by Crystals.- 3.4.1 Laue Equations for X-Ray Scattering.- 3.4.2 Bragg’s Treatment of X-Ray Diffraction.- 3.4.3 Equivalence of Laue and Bragg Treatments of X-Ray Diffraction.- 3.5 X-Ray Techniques.- 3.5.1 Laue Method.- 3.5.2 Oscillation Method.- 3.5.3 Ewald’s Construction.- 3.5.4 Weissenberg Method.- 3.5.5 Precession Method.- 3.6 Recognition of Crystal System.- Problems.- 4 Intensity of Scattering of X-Rays by Crystals.- 4.1 Introduction.- 4.2 Path Difference.- 4.3 Mathematical Representation of a Wave: Amplitude and Phase.- 4.4 Combination of Two Waves.- 4.5 Argand Diagram.- 4.6 Combination of N Waves.- 4.7 Combined Scattering of X-Rays from the Contents of the Unit Cell.- 4.7.1 Phase Difference.- 4.7.2 Scattering by Atoms.- 4.8 Structure Factor.- 4.9 Intensity Expressions.- 4.10 Phase Problem in Structure Analysis.- 4.11 Applications of the Structure Factor Equation.- 4.11.1 Friedel’s Law.- 4.11.2 Structure Factor for a Centrosymmetric Crystal.- 4.11.3 Limiting Conditions and Systematic Absences.- 4.11.4 Determination of Unit-Cell Type.- 4.11.5 Structure Factors and Symmetry Elements.- 4.11.6 Limiting Conditions from Screw-Axis Symmetry.- 4.11.7 Centrosymmetric Zones.- 4.11.8 Limiting Conditions from Glide-Plane Symmetry.- 4.12 Preliminary Structure Analysis.- 4.12.1 Practical Determination of Space Groups.- Problems.- 5 Methods in X-Ray Structure Analysis. I.- 5.1 Introduction.- 5.2 Analysis of the Unit-Cell Contents.- 5.2.1 Papaverine Hydrochloride,C20H21NO4 HCl.- 5.2.2 Naphthalene, C10H8.- 5.2.3 Molecular Symmetry.- 5.2.4 Special Positions.- 5.2.5 Nickel Tungstate, NiWO4.- 5.3 Two Early Structure Analyses Revisited.- 5.3.1 Sodium Chloride, NaCl.- 5.3.2 Pyrite, FeS2.- Problems.- 6 Methods in X-Ray Structure Analysis. II.- 6.1 Introduction.- 6.2 Fourier Series.- 6.2.1 Computation of ?(x) for a Square Wave.- 6.2.2 Exponential Form of Fourier Expressions.- 6.3 Representation of Crystal Structures by Fourier Series.- 6.3.1 Electron Density and Structure Factors.- 6.3.2 Electron Density Equations.- 6.3.3 Interpretation of Electron Density Distributions.- 6.4 Methods of Solving the Phase Problem.- 6.4.1 Number of Reflections in the Data Set.- 6.4.2 The Patterson Function.- 6.4.3 Examples of the Use of the Patterson Function in Solving the Phase Problem.- 6.4.4 Absolute Scale of |Fo| and Overall Temperature Factor.- 6.4.5 Heavy-Atom Method and Partial Fourier Synthesis.- 6.4.6 Difference-Fourier Synthesis.- 6.4.7 Limitations of the Heavy-Atom Method.- 6.4.8 Isomorphous Replacement.- 6.4.9 Further Details of the Isomorphous Replacement Phasing Procedure.- 6.4.10 Anomalous Scattering.- Problems.- 7 Direct Methods and Refinement.- 7.1 Introduction.- 7.2 Direct Methods of Phase Determination.- 7.2.1 Normalized Structure Factors.- 7.2.2 Structure Invariants and Origin-Fixing Reflections.- 7.2.3 Sign Determination—Centrosymmetric Crystals.- 7.2.4 Amplitude Symmetry and Phase Symmetry.- 7.2.5 ?2 Listing.- 7.2.6 Symbolic-Addition Procedure.- 7.2.7 Calculation of E Maps.- 7.2.8 Phase Determination—Noncentrosymmetric Crystals.- 7.2.9 Phase Determination in Space Group P21.- 7.2.10 Advantages and Disadvantages of Symbolic Addition.- 7.2.11 Multisolution Philosophy and Brief Description of the Program multan.- 7.2.12 Figures of Merit.- 7.2.13 Example of the Use of multan.- 7.2.14 Some Experiences.- 7.3 Patterson Search Methods.- 7.3.1 Orientation Search.- 7.3.2 Translation Search.- 7.3.3 Example of a Structure Solution by Vector Verification.- 7.4 Least-Squares Refinement.- 7.4.1 Unit-Cell Dimensions.- 7.4.2 Atomic Parameters.- 7.5 Molecular Geometry.- 7.5.1 Bond Lengths and Angles.- 7.5.2 Torsion Angles.- 7.5.3 Conformational Analysis.- 7.5.4 Mean Planes.- 7.6 Precision.- 7.7 Correctness of a Structure Analysis.- 7.8 Limitations of X-Ray Structure Analysis.- 7.9 Disorder in Single Crystals.- Problems.- 8 Examples of Crystal Structure Analysis.- 8.1 Introduction.- 8.2 Crystal Structure of 2-Bromobenzo[b]indeno[1,2-e]pyran (BBIP).- 8.2.1 Preliminary Physical and X-Ray Measurements.- 8.2.2 Intensity Measurement and Correction.- 8.2.3 Structure Analysis in the (010) Projection.- 8.2.4 Three-Dimensional Structure Determination.- 8.2.5 Refinement.- 8.2.6 Molecular Geometry.- 8.3 Crystal Structure of Potassium 2-Hydroxy-3,4-dioxocyclobut-1-ene-1-olate Monohydrate (KHSQ).- 8.3.1 Preliminary X-Ray and Physical Measurements.- 8.3.2 Intensity Measurement and Correction.- 8.3.3 ?2 Listing.- 8.3.4 Specifying the Origin.- 8.3.5 Sign Determination.- 8.3.6 The E Map.- 8.3.7 Completion and Refinement of the Structure.- 8.4 Concluding Remarks.- Problems.- A.1 Stereoviews and Crystal Models.- A1.1 Stereoviews.- A1.2 Model of a Tetragonal Crystal.- A1.3 Stereoscopic Space-Group Drawings.- A.2 Crystallographic Point-Group Study and Recognition Scheme.- A.3 Schoenflies’ Symmetry Notation.- A3.1 Alternating Axis of Symmetry.- A3.2 Notation.- A.4 Generation and Properties of X-Rays.- A4.1 X-Rays and White Radiation.- A4.2 Characteristic X-Rays.- A4.3 Absorption of X-Rays.- A4.4 Filtered Radiation.- A.5 Crystal Perfection and Intensity Measurement.- A5.1 Crystal Perfection.- A5.2 Intensity of Reflected Beam.- A5.3 Intensity Measurements.- A5.3.1 Film Measurements.- A5.3.2 Diffractometer Geometry and Data Collection.- A5.4 Data Processing.- A5.4.1 Introduction.- A5.4.2 Standard Deviation of Intensity.- A5.4.3 Absorption Corrections.- A5.4.4 Scaling.- A5.4.5 Merging Equivalent Reflections.- A5.5 Synchrotron Radiation.- A.6 Transformations.- A.7 Comments on Some Orthorhombic and Monoclinic Space Groups.- A7.1 Orthorhombic Space Groups.- A7.2 Monoclinic Space Groups.- A.8 Vector Algebraic Relationships in Reciprocal Space.- A8.1 Introduction.- A8.2 Reciprocal Lattice.- A8.2.1 Interplanar Spacings.- A8.2.2 Reciprocity of Unit Cell Volumes.- A8.2.3 Angle between Bravais Lattice Planes.- A8.3 X-Ray Diffraction and the Reciprocal Lattice.- A8.3.1 Bragg’s Equation.- A8.4 Laue Photographs.- A8.5 Crystal Setting.- A8.5.1 Setting Technique.- A.9 Intensity Statistics.- A9.1 Weighted Reciprocal Lattice.- A9.1.1 Laue Symmetry.- A9.1.2 Systematic Absences.- A9.1.3 Accidental Absences.- A9.1.4 Enhanced Averages.- A9.1.5 Special Distributions.- A.10 Enantiomorph Selection.- Solutions.

O autorze

Mark F. C. Ladd is a professor at the University of Surrey.