| Also by the Editors | 8 |
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| Preface | 10 |
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| Contents | 12 |
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| Part I: Direct Methods | 15 |
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| X-Ray Crystallography: The Past and Present of the Phase Problem | 16 |
| Introduction | 16 |
| Part I: Crystals and Bragg Spots | 17 |
| Fourier Refinement (Early 1930s) | 17 |
| The Patterson Map (1934), Heavy Atoms (Mid- and Later 1930s) | 17 |
| Three Brief Digressions | 18 |
| The State of Affairs at the Start of the Postwar Period (1946) | 18 |
| A Bit of Personal History | 18 |
| The Beginnings of Digital Computation (Late 1940s, Early 1950s) | 19 |
| Direct Methods (Late 1940s–Present) | 19 |
| Macromolecules: DNA (1953), Isomorphous Replacement (1953–Present) | 20 |
| Macromolecules: Anomalous Dispersion (1949–Present) | 21 |
| Macromolecules: Additional Methods | 21 |
| One More Method: Three-Beam Diffraction (1977–Present) | 22 |
| The Sparse or “Dream” Crystal | 22 |
| Part II: Finer Sampling (1980–Present) | 23 |
| Overview and Brief History | 23 |
| The Two Probable Experimental Regimes | 24 |
| The Free-Electron Laser-Flash Technique for Molecules | 24 |
| A Synchrotron/Cryoprotection Technique for Supramolecular Specimens | 24 |
| Phasing the Pattern | 26 |
| Summary | 28 |
| References | 30 |
| History of X-Ray Crystallographya | 32 |
| References | 35 |
| Gas Electron Diffraction and Its Influence on the Solution of the Phase Problem in Crystal Structure Determinationa | 36 |
| Introduction to Gas Electron Diffraction | 36 |
| Getting Started at NRL | 37 |
| Problems to Be Overcome | 38 |
| Early Studies | 39 |
| Implications | 39 |
| Non-negativity | 40 |
| The Period Between the 1940s and 1963 | 40 |
| Introduction | 40 |
| Historical Background | 41 |
| Titles of Additional Topics | 42 |
| The Remaining Problem | 43 |
| Some Later Structure Analyses | 45 |
| References | 46 |
| Part II: Beyond the Classical System | 48 |
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| Generalized Crystallography | 49 |
| Introduction | 49 |
| The Reality of Spatial Structure | 50 |
| Generalised Microscopy | 50 |
| Generalized Geometric Algebra (Clifford Algebra) | 51 |
| The Description of Structure | 51 |
| Crystal Chemistry and Informatics | 52 |
| Recognition of Higher Level Structure | 52 |
| Hierarchic Structures | 52 |
| Synthesis on Growth and Form | 52 |
| References | 53 |
| Mackay, Anti-Mackay, Double-Mackay, Pseudo-Mackay, and Related Icosahedral Shell Clustersa,b | 55 |
| Introduction | 55 |
| Icosahedron and Related Polyhedra | 56 |
| Icosahedral Shell Structures | 57 |
| Hierarchic Icosahedral Structures | 59 |
| I13(I) Cluster | 60 |
| I13(V) Cluster | 61 |
| I13(P) Cluster | 61 |
| References | 63 |
| Crystallography Without a Latticea,b | 65 |
| Prologue | 65 |
| Introduction | 66 |
| Experimental | 67 |
| Theory | 68 |
| Results | 68 |
| Partial Radial Distribution Functions | 68 |
| Spatial Distribution Functions | 72 |
| Orientational Distribution Functions | 74 |
| Structural Basis of the Hydrophobic Interaction | 77 |
| Conclusions | 79 |
| References | 80 |
| Polygrammal Symmetries in Biomacromolecules: Heptagonal Poly d (As4T) · poly d (As4T) and Heptameric ?-Hemolysina,b | 81 |
| Introduction | 81 |
| Crystallography of Star Heptagons | 83 |
| ?-Hemolysin | 87 |
| Poly d(As4T) · poly d(As4T) | 88 |
| References | 91 |
| Helical Structures: The Geometry of Protein Helices and Nanotubesa,b | 92 |
| Introduction | 92 |
| Nomenclature | 92 |
| Metrical Parameters of a CHL | 93 |
| Metrical Parameters of a THP | 93 |
| The Boerdijk–Coxeter Structure | 95 |
| Sphere Packings | 95 |
| Extension of the Helical Sphere Packing | 96 |
| Nanotubes | 97 |
| Collagen and the Polytope {3, 3, 5} | 97 |
| Defects in THPS and Nanotubes | 98 |
| Miscellany | 99 |
| Conclusions | 101 |
| References | 101 |
| From Waxes to Polymers—Crystallography of Polydisperse Chain Assembliesa,b | 102 |
| Introduction | 102 |
| Why Electron Diffraction? | 102 |
| n-Paraffin Binary Solid Solutions | 103 |
| Fractionation of n-Paraffin Binaries—Miscibility Gap | 105 |
| Fractionation of n-Paraffin Binaries—Eutectic Interactions | 106 |
| “Typical” Lamellar Paraffin Wax Structures | 106 |
| From Wax to Polymer Crystal—Interlayer Bridges | 107 |
| What Is Wax and What Is Polyethylene? | 109 |
| References | 109 |
| Structure, Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onionsa,b | 111 |
| Introduction | 111 |
| Euler’s Law in Graphitic Structures | 112 |
| Stability of Giant Icosahedral Fullerenes and Geometrical Rules | 113 |
| Polyhedral Particles and Graphitic Onion Formation | 116 |
| Sphericity of Graphitic Onions | 117 |
| Conclusions | 120 |
| References | 121 |
| A Generalized Model for the Shell Structure of Icosahedral Virusesa | 123 |
| Introduction | 123 |
| Capsids of Non-Quasi-Equivalent Viruses | 124 |
| Concluding Remarks | 125 |
| References | 126 |
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