Transmission electron microscopy and diffractometry of materials: with numerous exercises
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| Language: | English |
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Berlin [u.a.]
Springer
2008
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| Edition: | 3. ed. |
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| Item Description: | Literaturangaben |
| Physical Description: | XIX, 758 S. zahlr. Ill. und graph. Darst. |
| ISBN: | 9783540738855 |
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| 245 | 1 | 0 | |a Transmission electron microscopy and diffractometry of materials |b with numerous exercises |c Brent Fultz ; James Howe |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XIX, 758 S. |b zahlr. Ill. und graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| adam_text | Titel: Transmission electron microscopy and diffractometry of materials
Autor: Fultz, Brent
Jahr: 2008
Contents
1. Diffraction and the X-Ray Powder Diffractometer........ 1
1.1 Diffraction............................................. 1
1.1.1 Introduction to Diffraction ........................ 1
1.1.2 Bragg s Law..................................... 3
1.1.3 Strain Effects.................................... 6
1.1.4 Size Effects...................................... 7
1.1.5 A Symmetry Consideration ....................... 9
1.1.6 Momentum and Energy........................... 10
1.1.7 Experimental Methods............................ 10
1.2 The Creation of X-Rays................................. 13
1.2.1 Bremsstrahlung.................................. 14
1.2.2 Characteristic Radiation .......................... 16
1.2.3 Synchrotron Radiation............................ 20
1.3 The X-Ray Powder Diffractometer........................ 23
1.3.1 Practice of X-Ray Generation...................... 23
1.3.2 Goniometer for Powder Diffraction ................. 25
1.3.3 Monochromators, Filters, Mirrors................... 28
1.4 X-Ray Detectors for XRD and TEM...................... 30
1.4.1 Detector Principles............................... 30
1.4.2 Position-Sensitive Detectors ....................... 34
1.4.3 Charge Sensitive Preamplifier...................... 36
1.4.4 Other Electronics................................. 37
1.5 Experimental X-Ray Powder Diffraction Data.............. 38
1.5.1 * Intensities of Powder Diffraction Peaks............ 38
1.5.2 Phase Fraction Measurement ...................... 45
1.5.3 Lattice Parameter Measurement.................... 49
1.5.4 * Refinement Methods for Powder Diffraction Data ... 52
Further Reading............................................ 54
Problems.................................................. 55
2. The TEM and its Optics.................................. 61
2.1 Introduction to the Transmission Electron Microscope....... 61
2.2 Working with Lenses and Ray Diagrams................... 66
2.2.1 Single Lenses.................................... 66
XII Contents
^ *. ... 69
2.2.2 Multi-Lens Systems..........................
2.3 Modes of Operation of a TEM...........................
2.3.1 Dark-Field and Bright-Field Imaging ............... *
2.3.2 Selected Area Diffraction.......................... ™
2.3.3 Convergent-Beam Electron Diffraction.............. 79
2.3.4 High-Resolution Imaging.......................... 8*
2.4 Practical TEM Optics................................... ™
2.4.1 Electron Guns................................... 85
2.4.2 Illumination Lens Systems......................... 87
2.4.3 Imaging Lens Systems ............................ 88
2.5 Glass Lenses...........................................
2.5.1 Interfaces ....................................... 91
2.5.2 Lenses and Rays................................. 2
2.5.3 Lenses and Phase Shifts........................... 95
2.6 Magnetic Lenses........................................ 97
2.6.1 Focusing........................................ 97
2.6.2 Image Rotation.................................. 99
2.6.3 Pole Piece Gap...................................100
2.7 Lens Aberrations and Other Defects......................102
2.7.1 Spherical Aberration..............................102
2.7.2 Chromatic Aberration............................103
2.7.3 Diffraction.......................................104
2.7.4 Astigmatism.....................................104
2.7.5 Gun Brightness..................................108
2.8 Resolution.............................................110
Further Reading............................................112
Problems..................................................113
3. Scattering................................................119
3.1 Waves and Scattering...................................119
3.1.1 Wavefunctions...................................119
3.1.2 Coherent and Incoherent Scattering.................122
3.1.3 Elastic and Inelastic Scattering.....................123
3.1.4 Wave Amplitudes and Cross-Sections...............124
3.2 X-Ray Scattering .....................................128
3.2.1 Electrodynamics of X-Ray Scattering...............128
3.2.2 * Inelastic Compton Scattering.....................132
3.2.3 X-Ray Mass Attenuation Coefficients...............134
3.3 Coherent Elastic Scattering................... 136
3.3.1 X Born Approximation for Electrons................136
3.3.2 Atomic Form Factors - Physical Picture.............141
3.3.3 X Scattering of Electrons by Model Potentials.......144
q , l tA , * * At°mic Form Factors ~ General Formulation......148
3.4 * Nuclear Scattering.............. 153
3.4.1 Properties of Neutrons............................153
Contents XIII
3.4.2 Time-Varying Potentials and Inelastic Neutron Scat-
tering ...........................................155
3.4.3 * Coherent Mössbauer Scattering...................158
Further Reading............................................160
Problems..................................................160
4. Inelastic Electron Scattering and Spectroscopy ...........163
4.1 Inelastic Electron Scattering.............................163
4.2 Electron Energy-Loss Spectrometry (EELS)................165
4.2.1 Instrumentation..................................165
4.2.2 General Features of EELS Spectra..................167
4.2.3 * Fine Structure .................................169
4.3 Plasmon Excitations....................................173
4.3.1 Plasmon Principles...............................173
4.3.2 * Plasmons and Specimen Thickness................175
4.4 Core Excitations .......................................177
4.4.1 Scattering Angles and Energies - Qualitative........177
4.4.2 X Inelastic Form Factor............................180
4.4.3 f * Double-Differential Cross-Section, d2ain/dcf dE ... 184
4.4.4 * Scattering Angles and Energies — Quantitative......186
4.4.5 X * Differential Cross-Section, do-in/d£..............187
4.4.6 X Partial and Total Cross-Sections, 7in..............189
4.4.7 Quantification of EELS Core Edges.................191
4.5 Energy-Filtered TEM Imaging (EFTEM)..................193
4.5.1 Spectrum Imaging................................193
4.5.2 Energy Filters ...................................193
4.5.3 Chemical Mapping with Energy-Filtered Images......196
4.5.4 Chemical Analysis with High Spatial Resolution......197
4.6 Energy Dispersive X-Ray Spectrometry (EDS) .............200
4.6.1 Electron Trajectories Through Materials ............200
4.6.2 Fluorescence Yield................................203
4.6.3 EDS Instrumentation Considerations................205
4.6.4 Thin-Film Approximation.........................208
4.6.5 * ZAF Correction................................211
4.6.6 Artifacts in EDS Measurements....................213
4.6.7 Limits of Microanalysis ...........................215
Further Reading............................................217
Problems..................................................217
5. Diffraction from Crystals.................................223
5.1 Sums of Wavelets from Atoms............................223
5.1.1 Electron Diffraction from a Material............-----224
5.1.2 Wave Diffraction from a Material...................226
5.2 The Reciprocal Lattice and the Laue Condition............230
5.2.1 Diffraction from a Simple Lattice...................230
XIV Contents
001
5.2.2 Reciprocal Lattice................................*
5.2.3 Laue Condition..........................^........23^
5.2.4 Equivalence of the Laue Condition and Bragg s Law .. 233
5.2.5 Reciprocal Lattices of Cubic Crystals...............234
5.3 Diffraction from a Lattice with a Basis....................235
5.3.1 Structure Factor and Shape Factor .................235
5.3.2 Structure Factor Rules............................237
5.3.3 Symmetry Operations and Forbidden Diffractions .... 242
5.3.4 Superlattice Diffractions...........................243
5.4 Crystal Shape Factor...................................247
5.4.1 Shape Factor of Rectangular Prism.................247
5.4.2 Other Shape Factors..............................252
5.4.3 Small Particles in a Large Matrix...................252
5.5 Deviation Vector (Deviation Parameter)...................256
5.6 Ewald Sphere..........................................257
5.6.1 Ewald Sphere Construction........................257
5.6.2 Ewald Sphere and Bragg s Law.....................259
5.6.3 Tilting Specimens and Tilting Electron Beams.......259
5.7 Laue Zones............................................262
5.8 * Effects of Curvature of the Ewald Sphere................262
Further Reading............................................266
Problems..................................................266
6. Electron Diffraction and Crystallography.................273
6.1 Indexing Diffraction Patterns............................273
6.1.1 Issues in Indexing................................274
6.1.2 Method 1 - Start with Zone Axis...................276
6.1.3 Method 2 - Start with Diffraction Spots.............279
6.2 Stereographic Projections and Their Manipulation..........282
6.2.1 Construction of a Stereographic Projection..........282
6.2.2 Relationship Between Stereographic Projections
and Electron Diffraction Patterns...................284
6.2.3 Manipulations of Stereographic Projections..........284
6.3 Kikuchi Lines and Specimen Orientation ..................290
6.3.1 Origin of Kikuchi Lines...........................290
6.3.2 Indexing Kikuchi Lines............................294
6.3.3 Specimen Orientation and Deviation Parameter.....296
6.3.4 The Sign of a...................................299
6.3.5 Kikuchi Maps................. ...... 299
6.4 Double Diffraction............... ...................3Q2
6.4.1 Occurrence of Forbidden Diffractions............ 302
6.4.2 Interactions Between Crystallites 303
6.5 * Convergent-Beam Electron Diffraction 304
6.5.1 Convergence Angle of Incident Electron Beam ....... 306
6.5.2 Determination of Sample Thickness . 307
Contents XV
6.5.3 Measurements of Unit Cell Parameters..............309
6.5.4 X Determination of Point Groups...................314
6.5.5 X Determination of Space Groups...................325
6.6 Further Reading........................................330
Problems..................................................330
7. Diffraction Contrast in TEM Images......................337
7.1 Contrast in TEM Images................................337
7.2 Diffraction from Crystals with Defects ....................339
7.2.1 Review of the Deviation Parameter, s...............339
7.2.2 Atom Displacements, Sr ..........................340
7.2.3 Shape Factor and t...............................341
7.2.4 Diffraction Contrast and {s, Sr, t} .................342
7.3 Extinction Distance.....................................342
7.4 The Phase-Amplitude Diagram...........................345
7.5 Fringes from Sample Thickness Variations.................347
7.5.1 Thickness and Phase-Amplitude Diagrams...........347
7.5.2 Thickness Fringes in TEM Images..................348
7.6 Bend Contours in TEM Images ..........................353
7.7 Diffraction Contrast from Strain Fields....................357
7.8 Dislocations and Burgers Vector Determination ............359
7.8.1 Diffraction Contrast from Dislocation Strain Fields ... 359
7.8.2 The gb Rule for Null Contrast ....................362
7.8.3 Image Position and Dislocation Pairs or Loops.......368
7.9 Semi-Quantitative Diffraction Contrast from Dislocations .... 369
7.10 Weak-Beam Dark-Field (WBDF) Imaging of Dislocations.... 378
7.10.1 Procedure to Make a WBDF Image.................378
7.10.2 Diffraction Condition for a WBDF Image............379
7.10.3 Analysis of WBDF Images.........................380
7.11 Fringes at Interfaces....................................384
7.11.1 Phase Shifts of Electron Wavelets Across Interfaces ... 384
7.11.2 Moire Fringes....................................387
7.12 Diffraction Contrast from Stacking Faults .................391
7.12.1 Kinematical Treatment............................391
7.12.2 Results from Dynamical Theory....................397
7.12.3 Determination of the Intrinsic or Extrinsic Nature
of Stacking Faults................................399
7.12.4 Partial Dislocations Bounding the Fault.............399
7.12.5 An Example of a Stacking Fault Analysis............400
7.12.6 Sets of Stacking Faults in TEM Images..............402
7.12.7 Related Fringe Contrast...........................403
7.13 Antiphase (ir) Boundaries and ö Boundaries ...............404
7.13.1 Antiphase Boundaries.............................404
7.13.2 S Boundaries ....................................405
7.14 Contrast from Precipitates and Other Defects..............407
XVI Contents
7.14.1 Vacancies .......................................40^
7.14.2 Coherent Precipitates.............................408
7.14.3 Semicoherent and Incoherent Particles..............413
Further Reading............................................41^
Problems..................................................414
8. Diffraction Lineshapes....................................423
8.1 Diffraction Line Broadening and Convolution..............423
8.1.1 Crystallite Size Broadening........................424
8.1.2 Strain Broadening................................426
8.1.3 Instrumental Broadening - Convolution.............430
8.2 Fourier Transform Deconvolutions........................433
8.2.1 Mathematical Features............................433
8.2.2 * Effects of Noise on Fourier Transform Deconvolutions 436
8.3 Simultaneous Strain and Size Broadening..................440
8.4 Diffraction Lineshapes from Columns of Crystals...........446
8.4.1 Wavelets from Pairs of Unit Cells in One Column .... 446
8.4.2 A Column Length Distribution.....................448
8.4.3 X Intensity from Column Length Distribution........450
8.5 Comments on Diffraction Lineshapes......................451
Further Reading............................................454
Problems..................................................455
9. Patterson Functions and Diffuse Scattering...............457
9.1 The Patterson Function.................................457
9.1.1 Overview........................................457
9.1.2 Atom Centers at Points in Space...................458
9.1.3 Definition of the Patterson Function................459
9.1.4 Properties of Patterson Functions ..................461
9.1.5 X Perfect Crystals................................463
9.1.6 Deviations from Periodicity and Diffuse Scattering.... 467
9.2 Diffuse Scattering from Atomic Displacements..............469
9.2.1 Uncorrelated Displacements - Homogeneous Disorder . 469
9.2.2 X Temperature..................... 472
9.2.3 * Correlated Displacements - Atomic Size Effects.....477
Diffuse Scattering from Chemical Disorder.................481
9.3.1 Uncorrelated Chemical Disorder - Random Alloys .... 481
9.3.2 X * SRO Parameters........................ 485
9.3.3 X * Patterson Function for Chemical SRO ...... 487
9.3.4 Short-Range Order Diffuse Intensity................488
9.3.5 X * Isotropic Materials......... 488
9.3.6 * Polycrystalline Average and Single Crystal SRO . . . . 490
* Amorphous Materials.............. 491
9-4.1 X One-Dimensional Model.........................491
9.4.2 X Radial Distribution Function.................. 495
9.3
9.4
Contents XVII
9.4.3 X Partial Pair Correlation Functions ................500
9.5 Small Angle Scattering..................................502
9.5.1 Concept of Small Angle Scattering..................502
9.5.2 * Guinier Approximation (small Ak)................504
9.5.3 * Porod Law (large ^life)...........................508
9.5.4 X * Density-Density Correlations (all Ak)............510
Further Reading............................................512
Problems..................................................513
10. High-Resolution TEM Imaging...........................517
10.1 Huygens Principle......................................518
10.1.1 Wavelets from Points in a Continuum...............518
10.1.2 Huygens Principle for a Spherical Wavefront -
Fresnel Zones....................................523
10.1.3 X Fresnel Diffraction Near an Edge..................527
10.2 Physical Optics of High-Resolution Imaging................532
10.2.1 X Wavefronts and Fresnel Propagator ............... 532
10.2.2 X Lenses......................................... 534
10.2.3 X Materials...................................... 536
10.3 Experimental High-Resolution Imaging.................... 538
10.3.1 Defocus and Spherical Aberration..................538
10.3.2 X Lenses and Specimens...........................543
10.3.3 Lens Characteristics..............................546
10.4 * Simulations of High-Resolution TEM Images.............555
10.4.1 Principles of Simulations..........................555
10.4.2 Practice of Simulations............................561
10.5 Issues and Examples in High-Resolution TEM Imaging......562
10.5.1 Images of Nanostructures..........................562
10.5.2 Examples of Interfaces............................565
10.5.3 * Specimen and Microscope Parameters.............568
10.5.4 * Some Practical Issues for HRTEM................576
Further Reading............................................580
Problems..................................................581
11. High-Resolution STEM Imaging..........................583
11.1 Characteristics of High-Angle Annular Dark-Field Imaging... 583
11.2 Electron Channeling Along Atomic Columns ..............586
11.2.1 Optical Fiber Analogy............................586
11.2.2 X Critical Angle..................................588
11.2.3 * Tunneling Between Columns.....................589
11.3 Scattering of Channeled Electrons........................591
11.3.1 Elastic Scattering of Channeled Electrons ...........591
11.3.2 * Inelastic Scattering of Channeled Electrons........593
11.4 * Comparison of HAADF and HRTEM Imaging............594
11.5 HAADF Imaging with Atomic Resolution .................595
XVIII Contents
595
11.5.1 * Effect of Defocus...............................
11.5.2 Experimental Examples...........................^
11.6 * Lens Aberrations and Their Corrections................. «»
11.6.1 Cs Correction with Magnetic Hexapoles.............599
11.6.2 % Higher-Order Aberrations and Instabilities.........602
11.7 Examples of Cs-Corrected Images ........................604
11.7.1 Three-Dimensional Imaging........................605
11.7.2 High Resolution EELS............................606
Further Reading............................................
Problems..................................................
12. Dynamical Theory........................................611
12.1 Chapter Overview......................................611
12.2 X* Mathematical Features of High-Energy Electrons
in a Periodic Potential..................................613
12.2.1 X * Ttle Schrödinger Equation......................613
12.2.2 X Kinematical and Dynamical Theory...............619
12.2.3 * The Crystal as a Phase Grating..................621
12.3 First Approach to Dynamical Theory - Beam Propagation... 623
12.4 X Second Approach to Dynamical Theory - Bloch Waves
and Dispersion Surfaces.................................627
12.4.1 Diffracted Beams, {$g}, are Beats
of Bloch Waves, {#« }............................627
12.4.2 Crystal Periodicity and Dispersion Surfaces..........633
12.4.3 Energies of Bloch Waves in a Periodic Potential......637
12.4.4 General Two-Beam Dynamical Theory..............640
12.5 Essential Difference Between Kinematical
and Dynamical Theories.................................646
12.6 X Diffraction Error, sg, in Two-Beam Dynamical Theory___651
12.6.1 Bloch Wave Amplitudes and Diffraction Error........651
12.6.2 Dispersion Surface Construction....................653
12.7 Dynamical Diffraction Contrast from Crystal Defects .......655
12.7.1 Dynamical Diffraction Contrast Without Absorption .. 655
12.7.2 X * Two-Beam Dynamical Theory
of Stacking Fault Contrast.........................660
12.7.3 Dynamical Diffraction Contrast with Absorption.....664
12.8 X * Multi-Beam Dynamical Theories of Electron Diffraction .. 669
Further Reading........................ 672
Problems............................. 672
Bibliography........................... 677
Further Reading..................... 677
References and Figures............... 682
Contents XIX
A. Appendix.................................................691
A.l Indexed Powder Diffraction Patterns......................691
A.2 Mass Attenuation Coefficients for Characteristic Kä X-Rays . 692
A.3 Atomic Form Factors for X-Rays.........................693
A.4 X-Ray Dispersion Corrections for Anomalous Scattering.....697
A.5 Atomic Form Factors for 200 keV Electrons
and Procedure for Conversion to Other Voltages............698
A.6 Indexed Single Crystal Diffraction Patterns: fee, bec, dc, hep . 703
A.7 Stereographic Projections................................713
A.8 Examples of Fourier Transforms..........................717
A.9 Debye-Waller Factor from Wave Amplitude...............720
A.10 Review of Dislocations .................................721
A.ll TEM Laboratory Exercises..............................728
A. 11.1 Preliminary - JEOL 2000FX Daily Operation........728
A. 11.2 Laboratory 1 - Microscope Procedures
and Calibration with Au and M0O3 ................732
A. 11.3 Laboratory 2 - Diffraction Analysis of 9 Precipitates . 735
A.11.4 Laboratory 3 - Chemical Analysis of 6 Precipitates .. 739
A.11.5 Laboratory 4 - Contrast Analysis of Defects.........740
A.12 Fundamental and Derived Constants.....................742
Index.........................................................745
In section titles, the asterisk, *, denotes a more specialized topic. The
double dagger, J, warns of a higher level of mathematics, physics, or crys-
tallography.
|
| adam_txt |
Titel: Transmission electron microscopy and diffractometry of materials
Autor: Fultz, Brent
Jahr: 2008
Contents
1. Diffraction and the X-Ray Powder Diffractometer. 1
1.1 Diffraction. 1
1.1.1 Introduction to Diffraction . 1
1.1.2 Bragg's Law. 3
1.1.3 Strain Effects. 6
1.1.4 Size Effects. 7
1.1.5 A Symmetry Consideration . 9
1.1.6 Momentum and Energy. 10
1.1.7 Experimental Methods. 10
1.2 The Creation of X-Rays. 13
1.2.1 Bremsstrahlung. 14
1.2.2 Characteristic Radiation . 16
1.2.3 Synchrotron Radiation. 20
1.3 The X-Ray Powder Diffractometer. 23
1.3.1 Practice of X-Ray Generation. 23
1.3.2 Goniometer for Powder Diffraction . 25
1.3.3 Monochromators, Filters, Mirrors. 28
1.4 X-Ray Detectors for XRD and TEM. 30
1.4.1 Detector Principles. 30
1.4.2 Position-Sensitive Detectors . 34
1.4.3 Charge Sensitive Preamplifier. 36
1.4.4 Other Electronics. 37
1.5 Experimental X-Ray Powder Diffraction Data. 38
1.5.1 * Intensities of Powder Diffraction Peaks. 38
1.5.2 Phase Fraction Measurement . 45
1.5.3 Lattice Parameter Measurement. 49
1.5.4 * Refinement Methods for Powder Diffraction Data . 52
Further Reading. 54
Problems. 55
2. The TEM and its Optics. 61
2.1 Introduction to the Transmission Electron Microscope. 61
2.2 Working with Lenses and Ray Diagrams. 66
2.2.1 Single Lenses. 66
XII Contents
^ *. . 69
2.2.2 Multi-Lens Systems.
2.3 Modes of Operation of a TEM.
2.3.1 Dark-Field and Bright-Field Imaging . '*
2.3.2 Selected Area Diffraction. ™
2.3.3 Convergent-Beam Electron Diffraction. 79
2.3.4 High-Resolution Imaging. 8*
2.4 Practical TEM Optics. ™
2.4.1 Electron Guns. 85
2.4.2 Illumination Lens Systems. 87
2.4.3 Imaging Lens Systems . 88
2.5 Glass Lenses.
2.5.1 Interfaces . 91
2.5.2 Lenses and Rays. "2
2.5.3 Lenses and Phase Shifts. 95
2.6 Magnetic Lenses. 97
2.6.1 Focusing. 97
2.6.2 Image Rotation. 99
2.6.3 Pole Piece Gap.100
2.7 Lens Aberrations and Other Defects.102
2.7.1 Spherical Aberration.102
2.7.2 Chromatic Aberration.103
2.7.3 Diffraction.104
2.7.4 Astigmatism.104
2.7.5 Gun Brightness.108
2.8 Resolution.110
Further Reading.112
Problems.113
3. Scattering.119
3.1 Waves and Scattering.119
3.1.1 Wavefunctions.119
3.1.2 Coherent and Incoherent Scattering.122
3.1.3 Elastic and Inelastic Scattering.123
3.1.4 Wave Amplitudes and Cross-Sections.124
3.2 X-Ray Scattering .128
3.2.1 Electrodynamics of X-Ray Scattering.128
3.2.2 * Inelastic Compton Scattering.132
3.2.3 X-Ray Mass Attenuation Coefficients.134
3.3 Coherent Elastic Scattering. 136
3.3.1 X Born Approximation for Electrons.136
3.3.2 Atomic Form Factors - Physical Picture.141
3.3.3 X Scattering of Electrons by Model Potentials.144
q , l'tA , * * At°mic Form Factors ~ General Formulation.148
3.4 * Nuclear Scattering. 153
3.4.1 Properties of Neutrons.153
Contents XIII
3.4.2 Time-Varying Potentials and Inelastic Neutron Scat-
tering .155
3.4.3 * Coherent Mössbauer Scattering.158
Further Reading.160
Problems.160
4. Inelastic Electron Scattering and Spectroscopy .163
4.1 Inelastic Electron Scattering.163
4.2 Electron Energy-Loss Spectrometry (EELS).165
4.2.1 Instrumentation.165
4.2.2 General Features of EELS Spectra.167
4.2.3 * Fine Structure .169
4.3 Plasmon Excitations.173
4.3.1 Plasmon Principles.173
4.3.2 * Plasmons and Specimen Thickness.175
4.4 Core Excitations .177
4.4.1 Scattering Angles and Energies - Qualitative.177
4.4.2 X Inelastic Form Factor.180
4.4.3 f * Double-Differential Cross-Section, d2ain/dcf dE . 184
4.4.4 * Scattering Angles and Energies — Quantitative.186
4.4.5 X * Differential Cross-Section, do-in/d£.187
4.4.6 X Partial and Total Cross-Sections, 7in.189
4.4.7 Quantification of EELS Core Edges.191
4.5 Energy-Filtered TEM Imaging (EFTEM).193
4.5.1 Spectrum Imaging.193
4.5.2 Energy Filters .193
4.5.3 Chemical Mapping with Energy-Filtered Images.196
4.5.4 Chemical Analysis with High Spatial Resolution.197
4.6 Energy Dispersive X-Ray Spectrometry (EDS) .200
4.6.1 Electron Trajectories Through Materials .200
4.6.2 Fluorescence Yield.203
4.6.3 EDS Instrumentation Considerations.205
4.6.4 Thin-Film Approximation.208
4.6.5 * ZAF Correction.211
4.6.6 Artifacts in EDS Measurements.213
4.6.7 Limits of Microanalysis .215
Further Reading.217
Problems.217
5. Diffraction from Crystals.223
5.1 Sums of Wavelets from Atoms.223
5.1.1 Electron Diffraction from a Material.-----224
5.1.2 Wave Diffraction from a Material.226
5.2 The Reciprocal Lattice and the Laue Condition.230
5.2.1 Diffraction from a Simple Lattice.230
XIV Contents
001
5.2.2 Reciprocal Lattice.*"
5.2.3 Laue Condition.^.23^
5.2.4 Equivalence of the Laue Condition and Bragg's Law . 233
5.2.5 Reciprocal Lattices of Cubic Crystals.234
5.3 Diffraction from a Lattice with a Basis.235
5.3.1 Structure Factor and Shape Factor .235
5.3.2 Structure Factor Rules.237
5.3.3 Symmetry Operations and Forbidden Diffractions . 242
5.3.4 Superlattice Diffractions.243
5.4 Crystal Shape Factor.247
5.4.1 Shape Factor of Rectangular Prism.247
5.4.2 Other Shape Factors.252
5.4.3 Small Particles in a Large Matrix.252
5.5 Deviation Vector (Deviation Parameter).256
5.6 Ewald Sphere.257
5.6.1 Ewald Sphere Construction.257
5.6.2 Ewald Sphere and Bragg's Law.259
5.6.3 Tilting Specimens and Tilting Electron Beams.259
5.7 Laue Zones.262
5.8 * Effects of Curvature of the Ewald Sphere.262
Further Reading.266
Problems.266
6. Electron Diffraction and Crystallography.273
6.1 Indexing Diffraction Patterns.273
6.1.1 Issues in Indexing.274
6.1.2 Method 1 - Start with Zone Axis.276
6.1.3 Method 2 - Start with Diffraction Spots.279
6.2 Stereographic Projections and Their Manipulation.282
6.2.1 Construction of a Stereographic Projection.282
6.2.2 Relationship Between Stereographic Projections
and Electron Diffraction Patterns.284
6.2.3 Manipulations of Stereographic Projections.284
6.3 Kikuchi Lines and Specimen Orientation .290
6.3.1 Origin of Kikuchi Lines.290
6.3.2 Indexing Kikuchi Lines.294
6.3.3 Specimen Orientation and Deviation Parameter.296
6.3.4 The Sign of a.299
6.3.5 Kikuchi Maps. . 299
6.4 Double Diffraction. .3Q2
6.4.1 Occurrence of Forbidden Diffractions. 302
6.4.2 Interactions Between Crystallites 303
6.5 * Convergent-Beam Electron Diffraction "" 304
6.5.1 Convergence Angle of Incident Electron Beam . 306
6.5.2 Determination of Sample Thickness . 307
Contents XV
6.5.3 Measurements of Unit Cell Parameters.309
6.5.4 X Determination of Point Groups.314
6.5.5 X Determination of Space Groups.325
6.6 Further Reading.330
Problems.330
7. Diffraction Contrast in TEM Images.337
7.1 Contrast in TEM Images.337
7.2 Diffraction from Crystals with Defects .339
7.2.1 Review of the Deviation Parameter, s.339
7.2.2 Atom Displacements, Sr .340
7.2.3 Shape Factor and t.341
7.2.4 Diffraction Contrast and {s, Sr, t} .342
7.3 Extinction Distance.342
7.4 The Phase-Amplitude Diagram.345
7.5 Fringes from Sample Thickness Variations.347
7.5.1 Thickness and Phase-Amplitude Diagrams.347
7.5.2 Thickness Fringes in TEM Images.348
7.6 Bend Contours in TEM Images .353
7.7 Diffraction Contrast from Strain Fields.357
7.8 Dislocations and Burgers Vector Determination .359
7.8.1 Diffraction Contrast from Dislocation Strain Fields . 359
7.8.2 The gb Rule for Null Contrast .362
7.8.3 Image Position and Dislocation Pairs or Loops.368
7.9 Semi-Quantitative Diffraction Contrast from Dislocations . 369
7.10 Weak-Beam Dark-Field (WBDF) Imaging of Dislocations. 378
7.10.1 Procedure to Make a WBDF Image.378
7.10.2 Diffraction Condition for a WBDF Image.379
7.10.3 Analysis of WBDF Images.380
7.11 Fringes at Interfaces.384
7.11.1 Phase Shifts of Electron Wavelets Across Interfaces . 384
7.11.2 Moire Fringes.387
7.12 Diffraction Contrast from Stacking Faults .391
7.12.1 Kinematical Treatment.391
7.12.2 Results from Dynamical Theory.397
7.12.3 Determination of the Intrinsic or Extrinsic Nature
of Stacking Faults.399
7.12.4 Partial Dislocations Bounding the Fault.399
7.12.5 An Example of a Stacking Fault Analysis.400
7.12.6 Sets of Stacking Faults in TEM Images.402
7.12.7 Related Fringe Contrast.403
7.13 Antiphase (ir) Boundaries and ö Boundaries .404
7.13.1 Antiphase Boundaries.404
7.13.2 S Boundaries .405
7.14 Contrast from Precipitates and Other Defects.407
XVI Contents
7.14.1 Vacancies .40^
7.14.2 Coherent Precipitates.408
7.14.3 Semicoherent and Incoherent Particles.413
Further Reading.41^
Problems.414
8. Diffraction Lineshapes.423
8.1 Diffraction Line Broadening and Convolution.423
8.1.1 Crystallite Size Broadening.424
8.1.2 Strain Broadening.426
8.1.3 Instrumental Broadening - Convolution.430
8.2 Fourier Transform Deconvolutions.433
8.2.1 Mathematical Features.433
8.2.2 * Effects of Noise on Fourier Transform Deconvolutions 436
8.3 Simultaneous Strain and Size Broadening.440
8.4 Diffraction Lineshapes from Columns of Crystals.446
8.4.1 Wavelets from Pairs of Unit Cells in One Column . 446
8.4.2 A Column Length Distribution.448
8.4.3 X Intensity from Column Length Distribution.450
8.5 Comments on Diffraction Lineshapes.451
Further Reading.454
Problems.455
9. Patterson Functions and Diffuse Scattering.457
9.1 The Patterson Function.457
9.1.1 Overview.457
9.1.2 Atom Centers at Points in Space.458
9.1.3 Definition of the Patterson Function.459
9.1.4 Properties of Patterson Functions .461
9.1.5 X Perfect Crystals.463
9.1.6 Deviations from Periodicity and Diffuse Scattering. 467
9.2 Diffuse Scattering from Atomic Displacements.469
9.2.1 Uncorrelated Displacements - Homogeneous Disorder . 469
9.2.2 X Temperature. 472
9.2.3 * Correlated Displacements - Atomic Size Effects.477
Diffuse Scattering from Chemical Disorder.481
9.3.1 Uncorrelated Chemical Disorder - Random Alloys . 481
9.3.2 X * SRO Parameters. 485
9.3.3 X * Patterson Function for Chemical SRO . 487
9.3.4 Short-Range Order Diffuse Intensity.488
9.3.5 X * Isotropic Materials. 488
9.3.6 * Polycrystalline Average and Single Crystal SRO '.'.'.'. 490
* Amorphous Materials. 491
9-4.1 X One-Dimensional Model.491
9.4.2 X Radial Distribution Function.' 495
9.3
9.4
Contents XVII
9.4.3 X Partial Pair Correlation Functions .500
9.5 Small Angle Scattering.502
9.5.1 Concept of Small Angle Scattering.502
9.5.2 * Guinier Approximation (small Ak).504
9.5.3 * Porod Law (large ^life).508
9.5.4 X * Density-Density Correlations (all Ak).510
Further Reading.512
Problems.513
10. High-Resolution TEM Imaging.517
10.1 Huygens Principle.518
10.1.1 Wavelets from Points in a Continuum.518
10.1.2 Huygens Principle for a Spherical Wavefront -
Fresnel Zones.523
10.1.3 X Fresnel Diffraction Near an Edge.527
10.2 Physical Optics of High-Resolution Imaging.532
10.2.1 X Wavefronts and Fresnel Propagator . 532
10.2.2 X Lenses. 534
10.2.3 X Materials. 536
10.3 Experimental High-Resolution Imaging. 538
10.3.1 Defocus and Spherical Aberration.538
10.3.2 X Lenses and Specimens.543
10.3.3 Lens Characteristics.546
10.4 * Simulations of High-Resolution TEM Images.555
10.4.1 Principles of Simulations.555
10.4.2 Practice of Simulations.561
10.5 Issues and Examples in High-Resolution TEM Imaging.562
10.5.1 Images of Nanostructures.562
10.5.2 Examples of Interfaces.565
10.5.3 * Specimen and Microscope Parameters.568
10.5.4 * Some Practical Issues for HRTEM.576
Further Reading.580
Problems.581
11. High-Resolution STEM Imaging.583
11.1 Characteristics of High-Angle Annular Dark-Field Imaging. 583
11.2 Electron Channeling Along Atomic Columns .586
11.2.1 Optical Fiber Analogy.586
11.2.2 X Critical Angle.588
11.2.3 * Tunneling Between Columns.589
11.3 Scattering of Channeled Electrons.591
11.3.1 Elastic Scattering of Channeled Electrons .591
11.3.2 * Inelastic Scattering of Channeled Electrons.593
11.4 * Comparison of HAADF and HRTEM Imaging.594
11.5 HAADF Imaging with Atomic Resolution .595
XVIII Contents
595
11.5.1 * Effect of Defocus.
11.5.2 Experimental Examples.^
11.6 * Lens Aberrations and Their Corrections. «»
11.6.1 Cs Correction with Magnetic Hexapoles.599
11.6.2 % Higher-Order Aberrations and Instabilities.602
11.7 Examples of Cs-Corrected Images .604
11.7.1 Three-Dimensional Imaging.605
11.7.2 High Resolution EELS.606
Further Reading.
Problems.
12. Dynamical Theory.611
12.1 Chapter Overview.611
12.2 X* Mathematical Features of High-Energy Electrons
in a Periodic Potential.613
12.2.1 X * Ttle Schrödinger Equation.613
12.2.2 X Kinematical and Dynamical Theory.619
12.2.3 * The Crystal as a Phase Grating.621
12.3 First Approach to Dynamical Theory - Beam Propagation. 623
12.4 X Second Approach to Dynamical Theory - Bloch Waves
and Dispersion Surfaces.627
12.4.1 Diffracted Beams, {$g}, are Beats
of Bloch Waves, {#« }.627
12.4.2 Crystal Periodicity and Dispersion Surfaces.633
12.4.3 Energies of Bloch Waves in a Periodic Potential.637
12.4.4 General Two-Beam Dynamical Theory.640
12.5 Essential Difference Between Kinematical
and Dynamical Theories.646
12.6 X Diffraction Error, sg, in Two-Beam Dynamical Theory_651
12.6.1 Bloch Wave Amplitudes and Diffraction Error.651
12.6.2 Dispersion Surface Construction.653
12.7 Dynamical Diffraction Contrast from Crystal Defects .655
12.7.1 Dynamical Diffraction Contrast Without Absorption . 655
12.7.2 X * Two-Beam Dynamical Theory
of Stacking Fault Contrast.660
12.7.3 Dynamical Diffraction Contrast with Absorption.664
12.8 X * Multi-Beam Dynamical Theories of Electron Diffraction . 669
Further Reading. 672
Problems. 672
Bibliography. 677
Further Reading. 677
References and Figures. 682
Contents XIX
A. Appendix.691
A.l Indexed Powder Diffraction Patterns.691
A.2 Mass Attenuation Coefficients for Characteristic Kä X-Rays . 692
A.3 Atomic Form Factors for X-Rays.693
A.4 X-Ray Dispersion Corrections for Anomalous Scattering.697
A.5 Atomic Form Factors for 200 keV Electrons
and Procedure for Conversion to Other Voltages.698
A.6 Indexed Single Crystal Diffraction Patterns: fee, bec, dc, hep . 703
A.7 Stereographic Projections.713
A.8 Examples of Fourier Transforms.717
A.9 Debye-Waller Factor from Wave Amplitude.720
A.10 Review of Dislocations .721
A.ll TEM Laboratory Exercises.728
A. 11.1 Preliminary - JEOL 2000FX Daily Operation.728
A. 11.2 Laboratory 1 - Microscope Procedures
and Calibration with Au and M0O3 .732
A. 11.3 Laboratory 2 - Diffraction Analysis of 9' Precipitates . 735
A.11.4 Laboratory 3 - Chemical Analysis of 6' Precipitates . 739
A.11.5 Laboratory 4 - Contrast Analysis of Defects.740
A.12 Fundamental and Derived Constants.742
Index.745
In section titles, the asterisk, "*," denotes a more specialized topic. The
double dagger, "J," warns of a higher level of mathematics, physics, or crys-
tallography. |
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| any_adam_object_boolean | 1 |
| author | Fultz, Brent 1955- Howe, James M. 1955- |
| author_GND | (DE-588)122354796 (DE-588)122354818 |
| author_facet | Fultz, Brent 1955- Howe, James M. 1955- |
| author_role | aut aut |
| author_sort | Fultz, Brent 1955- |
| author_variant | b f bf j m h jm jmh |
| building | Verbundindex |
| bvnumber | BV023054887 |
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| classification_tum | WER 770f PHY 605f WER 780f PHY 608f PHY 606f |
| ctrlnum | (OCoLC)315750804 (DE-599)BVBBV023054887 |
| dewey-full | 620.11299 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.11299 |
| dewey-search | 620.11299 |
| dewey-sort | 3620.11299 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Werkstoffwissenschaften Werkstoffwissenschaften / Fertigungstechnik |
| discipline_str_mv | Physik Werkstoffwissenschaften Werkstoffwissenschaften / Fertigungstechnik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV023054887 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:26:13Z |
| indexdate | 2024-07-09T21:09:56Z |
| institution | BVB |
| isbn | 9783540738855 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016258192 |
| oclc_num | 315750804 |
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| physical | XIX, 758 S. zahlr. Ill. und graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| spelling | Fultz, Brent 1955- Verfasser (DE-588)122354796 aut Transmission electron microscopy and diffractometry of materials with numerous exercises Brent Fultz ; James Howe 3. ed. Berlin [u.a.] Springer 2008 XIX, 758 S. zahlr. Ill. und graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Röntgendiffraktometrie (DE-588)4336833-5 gnd rswk-swf Durchstrahlungselektronenmikroskopie (DE-588)4215608-7 gnd rswk-swf Durchstrahlungselektronenmikroskopie (DE-588)4215608-7 s Röntgendiffraktometrie (DE-588)4336833-5 s 1\p DE-604 DE-604 Howe, James M. 1955- Verfasser (DE-588)122354818 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fultz, Brent 1955- Howe, James M. 1955- Transmission electron microscopy and diffractometry of materials with numerous exercises Röntgendiffraktometrie (DE-588)4336833-5 gnd Durchstrahlungselektronenmikroskopie (DE-588)4215608-7 gnd |
| subject_GND | (DE-588)4336833-5 (DE-588)4215608-7 |
| title | Transmission electron microscopy and diffractometry of materials with numerous exercises |
| title_auth | Transmission electron microscopy and diffractometry of materials with numerous exercises |
| title_exact_search | Transmission electron microscopy and diffractometry of materials with numerous exercises |
| title_exact_search_txtP | Transmission electron microscopy and diffractometry of materials with numerous exercises |
| title_full | Transmission electron microscopy and diffractometry of materials with numerous exercises Brent Fultz ; James Howe |
| title_fullStr | Transmission electron microscopy and diffractometry of materials with numerous exercises Brent Fultz ; James Howe |
| title_full_unstemmed | Transmission electron microscopy and diffractometry of materials with numerous exercises Brent Fultz ; James Howe |
| title_short | Transmission electron microscopy and diffractometry of materials |
| title_sort | transmission electron microscopy and diffractometry of materials with numerous exercises |
| title_sub | with numerous exercises |
| topic | Röntgendiffraktometrie (DE-588)4336833-5 gnd Durchstrahlungselektronenmikroskopie (DE-588)4215608-7 gnd |
| topic_facet | Röntgendiffraktometrie Durchstrahlungselektronenmikroskopie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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