Advanced Computing in Electron Microscopy (eBook)

Preface 
6 
Contents 
8 
1 Introduction 12
1.1 Computing in Electron Microscopy 12
1.2 Organization of this Book 14
2 The Transmission Electron Microscope 16
2.1 Introduction 16
2.2 Modeling the Electron Microscope 20
2.3 Relativistic Electrons 21
2.4 Reciprocity 24
2.5 Confocal Mode 26
2.6 Aberrations 26
2.7 Aberration Correction 30
2.8 More Aberrations 35
2.9 Further Reading 37
3 Linear Image Approximations 39
3.1 The Weak Phase Object in Bright Field 40
3.2 Partial Coherence in BF-CTEM 45
3.2.1 Aberration Correctors and Partial Coherence 51
3.3 Detector Influence (CTEM) 52
3.4 Incoherent Imaging of Thin Specimens (CTEM) 53
3.5 Annular Dark Field STEM 57
3.5.1 Minimum Probe Conditions 63
3.5.2 Source Size 64
3.5.3 Defocus Spread 66
3.6 Confocal Mode for Weak Phase Objects 66
3.7 Phase and Amplitude Contrast Revisited 69
4 Sampling and the Fast Fourier Transform 71
4.1 Sampling 72
4.2 Discrete Fourier Transform 76
4.3 The Fast Fourier Transform or FFT 76
4.4 Wrap Around Error and Rearrangement 79
4.5 Fourier Transforming Real Valued Data 80
4.6 Displaying Diffraction Patterns 81
4.7 An FFT Subroutine in C 82
4.8 Further Reading 86
5 Calculation of Images of Thin Specimens 87
5.1 The Weak Phase Object 88
5.2 Single Atom Properties 90
5.2.1 Radial Charge Distribution 91
5.2.2 Potential 91
5.2.3 Atomic Size 94
5.2.4 Scattering Factors 96
5.3 Total Specimen Potential 98
5.4 BF Phase Contrast Image Calculation 101
5.4.1 Single Atom Images 103
5.4.2 Thin Specimen Images 105
5.4.3 Partial Coherence and the Transmission Cross Coefficient 109
5.5 ADF STEM Images of Thin Specimens 114
5.5.1 Single Atom Images 116
5.5.2 Thin Specimen Images 118
5.6 Summary of Sampling Suggestions 122
6 Theory of Calculation of Images of Thick Specimens 124
6.1 Bloch Wave Eigenvalue Solution 127
6.1.1 Bloch Waves 127
6.1.2 Periodic Potential 129
6.1.3 Matrix Equation 130
6.1.4 Initial Conditions and the Exit Wave 133
6.1.5 Bloch Wave Eigenvalue Summary 135
6.2 The Wave Equation for Fast Electrons 136
6.3 A Bloch Wave Differential Equation Solution 139
6.4 The Multislice Solution 141
6.4.1 A Formal Operator Solution 141
6.4.2 A Finite Difference Solution 145
6.4.3 Free Space Propagation 146
6.5 Multislice Interpretation 146
6.6 The Multislice Method and FFT's 149
6.7 Slicing the Specimen 150
6.8 Aliasing and Bandwidth 154
6.9 Interfaces and Defects 157
6.10 Multislice Implementation 158
6.10.1 The Propagator Function and Specimen Tilt 160
6.10.2 Convergence Tests 161
6.10.3 Partial Coherence in BF-CTEM 162
6.10.4 Parallel Computing 163
6.11 More Accurate Slice Methods 165
6.11.1 Operator Solutions 165
6.11.2 Finite Difference Solutions 166
7 Multislice Applications and Examples 171
7.1 Gallium Arsenide 171
7.1.1 BF-CTEM Simulation 173
7.1.2 ADF-STEM Simulation 177
7.1.3 Channeling 179
7.2 Silicon Nitride 182
7.3 CBED Simulations 186
7.4 Thermal Vibrations of the Atoms in the Specimen 191
7.4.1 Silicon 111 CBED with TDS 193
7.4.2 Silicon 110 ADF-STEM with TDS 193
7.5 Specimen Edges or Interfaces 196
7.6 Biological Specimens 198
7.7 Quantitative Image Matching 202
7.8 Troubleshooting (What Can Go Wrong) 204
8 The Programs 206
8.1 Program Organization 206
8.2 Image Display 207
8.3 Programming Language 208
8.3.1 Disk File Format 209
8.4 BF-CTEM Sample Calculations for Periodic Specimens 211
8.4.1 Atomic Potentials 212
8.4.2 Multislice 215
8.4.3 Image Formation 217
8.4.4 Partial Coherence 218
8.5 ADF-STEM Sample Calculations for Periodic Specimens 221
8.6 NonPeriodic Specimens 224
8.6.1 Fixed Beam Calculation 227
8.6.2 Scanned Beam Calculation 231
8.6.2.1 Atomic Coordinates 232
8.6.2.2 Source Size 232
8.6.2.3 Sample Run 233
8.7 Program Display 236
8.8 Program Slicview 237
Appendix A: Plotting Transfer Functions 239
A.1 CTEM 240
A.2 STEM 242
Appendix B: The Fourier Projection Theorem 247
Appendix C: Atomic Potentials and Scattering Factors 249
C.1 Atomic Charge Distribution 250
C.2 X-ray Scattering Factors 252
C.3 Electron Scattering Factors 253
C.4 Parameterization 255
Appendix D: Bilinear Interpolation 267
Appendix E: 3D Perspective View 270
References 275
Index 291