Symbols and abbreviations .................................... xvii
1 Preliminaries ................................................ 1
1.1 Elementary principles of phase-contrast ТЕМ imaging ..... 2
1.2 Instrumental requirements for high resolution ........... 8
1.3 First experiments ...................................... 10
References .................................................. 11
2 Electron optics ............................................. 13
2.1 The electron wavelength and relativity ................. 13
2.2 Simple lens properties ................................. 16
2.3 The paraxial ray equation .............................. 22
2.4 The constant-field approximation ....................... 24
2.5 Projector lenses ....................................... 25
2.6 The objective lens ..................................... 28
2.7 Practical lens design .................................. 29
2.8 Aberrations ............................................ 31
2.9 The pre-field .......................................... 37
2.10 Aberration correction .................................. 38
References .................................................. 43
Bibliography ................................................ 45
3 Wave optics ................................................. 46
3.1 Propagation and Fresnel diffraction .................... 47
3.2 Lens action and the diffraction limit .................. 50
3.3 Wave and ray aberrations (to fifth order) .............. 55
3.4 Strong-phase and weak-phase objects .................... 61
3.5 Diffractograms for aberration analysis ................. 63
References .................................................. 65
Bibliography ................................................ 66
4 Coherence and Fourier optics ................................ 67
4.1 Independent electrons and computed images .............. 69
4.2 Coherent and incoherent images and the damping
envelopes .............................................. 70
4.3 The characterization of coherence ...................... 76
4.4 Spatial coherence using hollow-cone illumination ....... 79
4.5 The effect of source size on coherence ................. 81
4.6 Coherence requirements in practice ..................... 83
References .................................................. 86
Bibliography ................................................ 87
5 ТЕМ imaging of thin crystals and their defects .............. 88
5.1 The effect of lens aberrations on simple lattice
fringes ................................................ 89
5.2 The effect of beam divergence on depth of field ........ 93
5.3 Approximations for the diffracted amplitudes ........... 96
5.4 Images of crystals with variable spacing-spinodal
decomposition and modulated structures ................ 102
5.5 Are the atom images black or white? A simple
symmetry argument ..................................... 104
5.6 The multislice method and the polynomial solution ..... 106
5.7 Bloch wave methods, bound states, and 'symmetry
reduction' of the dispersion matrix ................... 107
5.8 Partial coherence effects in dynamical computations—
beyond the product representation. Fourier images ..... 113
5.9 Absorption effects .................................... 115
5.10 Dynamical forbidden reflections ....................... 117
5.11 Relationship between algorithms. Supercells,
patching .............................................. 122
5.12 Sign conventions ...................................... 125
5.13 Image simulation, quantification, and the Stobbs
factor ................................................ 126
5.14 Image interpretation in germanium—a case study ........ 129
5.15 Images of defects and nanostructures .................. 134
5.16 Tomography at atomic resolution-imaging in three
dimensions ............................................ 143
5.17 Imaging bonds between atoms ........................... 145
References ................................................. 146
6 Imaging molecules: radiation damage ........................ 154
6.1 Phase and amplitude contrast .......................... 154
6.2 Single atoms in bright field .......................... 157
6.3 The use of a higher accelerating voltage .............. 165
6.4 Contrast and atomic number ............................ 169
6.5 Dark-field methods .................................... 171
6.6 Inelastic scattering .................................. 174
6.7 Noise, information, and the Rose equation ............. 177
6.8 Single-particle cryo-electron microscopy:
tomography ............................................ 180
6.9 Electron crystallography of two-dimensional
crystals .............................................. 188
6.10 Organic crystals ...................................... 190
6.11 Radiation damage: organics and low-voltage EM ......... 192
6.12 Radiation damage: inorganics .......................... 195
References ................................................. 197
7 Image processing, super-resolution, and difiractive
imaging .................................................... 204
7.1 Through-focus series, coherent detection,
optimization, and error metrics ....................... 204
7.2 Tilt series, aperture synthesis ....................... 210
7.3 Off-axis electron holography .......................... 211
7.4 Imaging with aberration correction: STEM and ТЕМ ...... 212
7.5 Combining diffraction and image data for crystals ..... 215
7.6 Ptychography, Ronchigrams, shadow images, in-line
holography, and diffractive imaging ................... 219
7.7 Direct inversion from dynamical diffraction
patterns .............................................. 226
References ................................................. 226
8 Scanning transmission electron microscopy and Z-contrast ... 233
8.1 Imaging modes, reciprocity, and Bragg scattering ...... 233
8.2 Coherence functions in STEM ........................... 240
8.3 Dark-field STEM: incoherent imaging, and resolution
limits ................................................ 243
8.4 Multiple elastic scattering in STEM: channelling ...... 249
8.5 Z-contrast in STEM: thermal diffuse scattering ........ 251
8.6 Three-dimensional STEM tomography ..................... 257
References ................................................. 260
9 Electron sources and detectors ............................. 264
9.1 The illumination system ............................... 265
9.2 Brightness measurement ................................ 268
9.3 Biasing and high-voltage stability for thermal
sources ............................................... 270
9.4 Hair-pin tungsten filaments ........................... 274
9.5 Lanthanum hexaboride sources .......................... 274
9.6 Field-emission sources ................................ 275
9.7 The charged-coupled device detector ................... 276
9.8 Image plates .......................................... 281
9.9 Film .................................................. 282
9.10 Direct detection cameras .............................. 283
References ................................................. 286
10 Measurement of electron-optical parameters ................. 289
10.1 Objective-lens focus increments ....................... 289
10.2 Spherical aberration constant ......................... 291
10.3 Magnification calibration ............................. 293
10.4 Chromatic aberration constant ......................... 295
10.5 Astigmatic difference: three-fold astigmatism ......... 295
10.6 Diffractogram measurements ............................ 296
10.7 Lateral coherence width ............................... 299
10.8 Electron wavelength and camera length ................. 302
10.9 Resolution ............................................ 303
10.10 Ronchigram analysis for aberration correction ........ 306
References ................................................. 312
11 Instabilities and the microscope environment ............... 315
11.1 Magnetic fields ....................................... 315
11.2 High-voltage instability .............................. 318
11.3 Vibration ............................................. 319
11.4 Specimen movement ..................................... 319
11.5 Contamination and the vacuum system ................... 321
11.6 Pressure, temperature, and draughts ................... 323
References ................................................. 323
12 Experimental methods ....................................... 324
12.1 Astigmatism correction ................................ 325
12.2 Taking the picture .................................... 326
12.3 Recording atomic-resolution images—an example ......... 328
12.4 Adjusting the crystal orientation using
non-eucentric specimen holders ........................ 335
12.5 Focusing techniques and auto-tuning ................... 337
12.6 Substrates, sample supports, and graphene ............. 340
12.7 Film analysis and handling for cryo-EM ................ 343
12.8 Ancillary instrumentation for HREM .................... 344
12.9 A checklist for high-resolution work .................. 345
References ................................................. 346
13 Associated techniques ...................................... 348
13.1 X-ray microanalysis and ALCHEMI ....................... 348
13.2 Electron energy loss spectroscopy in STEM ............. 357
13.3 Microdiffraction, CBED, and precession methods ........ 363
13.4 Cathodoluminescence in STEM ........................... 372
13.5 Environmental HREM, imaging surfaces, holography of
fields, and magnetic imaging with twisty beams ........ 376
References ................................................. 380
Appendices .................................................... 388
Index ......................................................... 403
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