Part I Background
1 The Electron Microscope as a Crystallographic Instrument
1.1 The Thin Lens ........................................... 3
1.2 Fourier Transform Pairs ................................. 4
1.3 The Electron Microscope ................................ 17
1.3.1 Illumination System ............................. 18
1.3.2 Functions ....................................... 19
1.3.2.1 Imaging ................................ 19
1.3.2.2 Diffraction ............................ 22
1.4 Geometrical Aspects of Electron Diffraction ............ 26
2 Crystal Symmetry
2.1 The Unit Cell .......................................... 31
2.2 Symmetry Groups ........................................ 36
2.2.1 Point Groups .................................... 37
2.2.2 Plane Groups .................................... 43
2.2.3 Space Groups .................................... 49
2.2.4 "Two-Sided Plane Groups" ........................ 54
2.3 Unit Cell and Space-Group Identification ............... 55
2.4 Preferred Crystal Packing Motifs for Organic
Molecules .............................................. 63
3 Crystallization and Data Collection
3.1. Crystallization of Organic Compounds ................... 67
3.1.1 Growth from Dilute Solution ..................... 67
3.1.2 Crystallization by "Self-Seeding" ............... 68
3.1.3 Crystallization by Sublimation .................. 68
3.1.4 Langmuir-Blodgett Layers ........................ 69
3.1.5 Epitaxial Orientation ........................... 69
3.1.5.1 Growth from the Vapor Phase ............ 70
3.1.5.2 Growth from a Co-Melt .................. 70
3.1.6 Sonication ...................................... 76
3.2 Crystallization of Globular Macromolecules ............. 76
3.2.1 Crystallization from Solution ................... 76
3.2.2 In Situ Crystals ................................ 76
3.2.3 Reconstitution of Transmembrane Proteins ........ 77
3.2.4 Surface Orientation of Proteins ................. 77
3.3 Crystallization of Inorganic Structures ................ 77
3.4 Preservation of Samples in the Electron Microscope
Vacuum ................................................. 78
3.4.1 Environmental Chambers .......................... 78
3.4.2 Cryostages ...................................... 80
3.4.3 Solvent Replacement ............................. 80
3.5 Data Collection and Processing ......................... 81
3.5.1 Goniometry ...................................... 81
3.5.2 Data Collection ................................. 83
3.5.2.1 Electron Diffraction ................... 83
3.5.2.2 Electron Microscopy .................... 86
4 Crystal Structure Analysis
4.1 Solution of the Phase Problem .......................... 95
4.1.1 Crystallographic Phases via Image Analysis ...... 95
4.1.2 Trial-and-Error Methods ......................... 99
4.1.3 Patterson Function ............................. 103
4.1.4 Direct Phasing Methods ......................... 105
4.1.4.1 Sayre Equation ........................ 107
4.1.4.2 Phase Invariant Sums (Symbolic
Addition) ............................. 109
4.1.4.3 Tangent Formula ....................... 119
4.1.4.4 Patterson Search Techniques ........... 122
4.1.4.5 The Minimal Principle ................. 123
4.1.4.6 Density Modification .................. 124
4.1.4.7 Maximum Entropy ....................... 124
4.2 Structure Refinement .................................. 126
4.2.1 Identification of a Structure .................. 126
4.2.2 Fourier Refinement ............................. 127
4.2.3 Least-Squares Refinement ....................... 130
4.2.4 Continuous Density Maps ........................ 131
4.3 Derived Quantities .................................... 133
5 Data Perturbations
5.1 Dynamical Scattering .................................. 135
5.2 Secondary Scattering .................................. 149
5.3 Diffraction Incoherence due to Crystal Bending ........ 153
5.4 Radiation Damage ...................................... 159
5.5 Conclusions ........................................... 166
Part II Applications
6 Molecular Organic Structures
6.1 Background ............................................ 169
6.2 Early Data Sets from Moscow ........................... 169
6.2.1 Diketopiperazine ............................... 169
6.2.2 Urea ........................................... 176
6.2.3 Thiourea, Paraelectric Form .................... 179
6.2.4 Thiourea, Ferroelectric Form ................... 184
6.3 Recent Analyses Based upon Selected Area Diffraction
Data .................................................. 188
6.3.1 Copper Perchlorophthalocyanine ................. 188
6.3.2 Copper Perbromophthalocyanine .................. 198
6.3.3 Ceo Buckminsterfullerene ....................... 202
6.3.4 Graphite ....................................... 206
6.4 Conclusions ........................................... 207
7 Inorganic Structures
7.1 Background ............................................ 209
7.2 Structures Solved from Electron Diffraction Data ...... 211
7.2.1 Boric Acid ..................................... 211
7.2.2 Celadonite ..................................... 215
7.2.3 Muscovite ...................................... 219
7.2.4 Phlogopite-Biotite ............................. 220
7.2.5 λ-Alumina ...................................... 224
7.2.6 Basic Copper Chloride .......................... 225
7.2.7 High Tc Superconductor ......................... 231
7.2.8 Potassium Niobium Oxide ........................ 231
7.2.9 Aluminum-Germanium Alloys ...................... 231
7.3 Structures from High-Resolution Electron
Micrographs ........................................... 232
7.3.1 Potassium Niobium Tungsten Oxide ............... 232
7.3.2 Staurolite ..................................... 234
7.3.3 Sodium Niobium Fluoroxide ...................... 234
7.3.4 Zeolites ....................................... 237
7.4 Conclusions ........................................... 238
8. The Alkanes
8.1 Background ............................................ 239
8.2 Contemporary Structure Analyses ....................... 240
8.2.1 Even-Chain Paraffins ........................... 240
8.2.2 Odd-Chain Paraffins ............................ 258
8.2.3 Thermotropic Phase Transitions of Linear
Paraffins ...................................... 261
8.2.4 Binary (and Multicomponent) Phase Behavior
in Paraffins ................................... 268
8.2.4.1 Solid Solutions ....................... 268
8.2.4.2 Binodal Phase Boundary ................ 278
8.2.4.3 Eutectics ............................. 281
8.2.5 Cycloalkanes ................................... 283
8.2.6 Perfluoroalkanes ............................... 287
8.3. Conclusions ........................................... 292
9 Alkane Derivatives
9.1 Background ............................................ 293
9.2 Contemporary Structure Analyses ....................... 294
9.2.1 Fatty Alcohols ................................. 294
9.2.2 Fatty Acids .................................... 297
9.2.3 Ketoalkanes .................................... 298
9.2.4 Wax Esters ..................................... 298
9.2.5 Alkyl Halides .................................. 307
9.2.6 Detergents ..................................... 308
9.3 Conclusions ........................................... 310
10 The Lipids
10.1 The Methylene Subcell: Its Significance for Electron
Diffraction from Lipids ............................... 311
10.2 Structure Analyses of Glycerolipids ................... 316
10.2.1 1,3-Diglycerides ............................... 316
10.2.2 1,2-Diglycerides ............................... 317
10.2.3 Triglycerides .................................. 321
10.2.4 Phospholipids and Glycolipids .................. 323
10.2.4.1 Phosphatidylethanolamines ............. 327
10.2.4.2 N-Methylphosphatidylethanolamines ..... 333
10.2.4.3 N,N-
Dimethylphosphatidylethanolamines ..... 337
10.2.4.4 Phosphatidylcholines .................. 340
10.2.4.5 Phosphatide Acids ..................... 343
10.2.4.6 Monogalactosyl Diglyceride ............ 343
10.3 Cholesteryl Esters .................................... 344
10.4 Conclusions ........................................... 360
11 Linear Polymers
11.1 Background ............................................ 361
11.2 Crystal Structure Analyses ............................ 361
11.2.1 Two-Dimensional Data Sets ...................... 361
11.2.1.1 Polyethylene Sulfide) ................. 362
11.2.1.2 Poly(3,3-bis(chloromethyl)
oxacyclobutane (BCMO) ................. 363
11.2.1.3 γ-Poly(pivalolactone) ................. 365
11.2.1.4 Poly(p-xylylene) ...................... 366
11.2.1.5 MannanI ............................... 368
11.2.1.6 Cellulose Triacetate II ............... 370
11.2.1.7 Chitosan .............................. 371
11.2.1.8 Anhydrous Nigeran ..................... 372
11.2.1.9 Poly(hexamethylene Terephthalate) ..... 373
11.2.1.10 β-Form of Poly-γ-methyl-L-
glutamate ............................ 374
11.2.2 Three-Dimensional Data Sets .................... 376
11.2.2.1 Poly( 1,4-trans-cyclohexanediyl
Dimethylene Succinate)(Poly-t-CDS) .... 377
11.2.2.2 Mannan I .............................. 379
11.2.2.3 Polyethylene .......................... 383
11.2.2.4 Poly(ε-caprolactone) .................. 390
11.2.2.5 Poly(l-butene), Form III .............. 396
11.3 Conclusions ........................................... 403
12 Globular Macromolecules
12.1 Background ............................................ 405
12.2 Structure Analyses of Membrane Proteins at High
Resolution ............................................ 409
12.2.1 Bacteriorhodopsin .............................. 409
12.2.2 Outer Membrane Porins from Gram-Negative
Bacteria ....................................... 410
12.2.3 Light-Harvesting Chlorophyll α/b-Protein
Complex ........................................ 420
12.3 Prospects for the Use of Direct Methods in Protein
Electron Crystallography .............................. 420
12.4 Conclusions ........................................... 426
References .................................................... 429
Index ......................................................... 447
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