Structure Determination by X-Ray Crystallography

1 Crystal Geometry. I.- 1.1 Introduction.- 1.2 The Crystalline State.- 1.3 Stereographic Projection.- 1.4 External Symmetry of Crystals.- Problems.- 2 Crystal Geometry. II.- 2.1 Introduction.- 2.2 Lattices.- 2.3 Families of Planes and Interplanar Spacings.- 2.4 Reciprocal Lattice.- 2.5 Rotational Symmetries of Lattices.- 2.6 Space Groups.- 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.- 3.4 Direction of Scattering of X-Rays by Crystals.- 3.5 X-Ray Techniques.- Problems.- 4 Intensity of Scattering of X-Rays by Crystals.- 4.1 Introduction.- 4.2 Path Difference.- 4.3 Combination of Two Waves.- 4.4 Argand Diagram.- 4.5 Combination of N Waves.- 4.6 Combined Scattering of X-Rays from the Contents of the Unit Cell.- 4.7 Structure Factor.- 4.8 Intensity Expressions.- 4.9 Phase Problem in Structure Analysis.- 4.10 Applications of the Structure Factor Equation.- 4.11 Preliminary Structure Analysis.- Problems.- 5 Methods in X-Ray Structure Analysis. I.- 5.1 Introduction.- 5.2 Analysis of the Unit-Cell Contents.- 5.3 Two Early Structure Analyses Revisited.- Problems.- 6 Methods in X-Ray Structure Analysis. II.- 6.1 Introduction.- 6.2 Fourier Series.- 6.3 Representation of Crystal Structures by Fourier Series.- 6.4 Methods of Solving the Phase Problem.- Problems.- 7 Some Further Topics.- 7.1 Introduction.- 7.2 Direct Methods of Phase Determination.- 7.3 Least-Squares Refinement.- 7.4 Molecular Geometry.- 7.5 Accuracy.- 7.6 Correctness of a Structure Analysis.- 7.7 Anomalous Scattering.- 7.8 Limitations of X-Ray Structure Analysis.- Problems.- 8 Examplesof Crystal Structure Analysis.- 8.1 Introduction.- 8.2 Crystal Structure of 2-Bromobenzo[b]indeno[3,2-e]pyran (BBIP).- 8.3 Crystal Structure of Potassium 2-Hydroxy-3,4-dioxocyclobut-1-ene-1-olate Monohydrate (KHSQ).- 8.4 Concluding Remarks.- Problems.- A.1 Stereoviews and Crystal Models.- A.1.1 Stereoviews.- A.1.2 Model of a Tetragonal Crystal.- A.2 Crystallographic Point-Group Study and Recognition Scheme.- A.3 Schoenflies’ Symmetry Notation.- A.3.1 Alternating Axis of Symmetry.- A.3.2 Notation.- A.4 Generation and Properties of X-Rays.- A.4.1 X-Rays and White Radiation.- A.4.2 Characteristic X-Rays.- A.4.3 Absorption of X-Rays.- A.4.4 Filtered Radiation.- A.5 Crystal Perfection and Intensity Measurement.- A.5.1 Crystal Perfection.- A.5.2 Intensity of Reflected Beam.- A.5.3 Intensity Measurements.- A.5.4 Intensity Corrections.- A.6 Transformations.- A.7 Comments on Some Orthorhombic and Monoclinic Space Groups.- A.7.1 Orthorhombic Space Groups.- A.7.2 Monoclinic Space Groups.- Solutions.