Transmission Electron Microscopy and Diffractometry of Materials

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1 Brent Fultz James Howe Transmission Electron Microscopy and Diffractometry of Materials Fourth Edition ~Springer

2 1 1 Diffraction and the X-Ray Powder Diffractometer Diffraction Introduction to Diffraction Bragg's Law Strain Effects Size Effects A Symmetry Consideration Momentum and Energy Experimental Methods The Creation ofx-rays Bremsstrahlung Characteristic Radiation Synchrotron Radiation The X-Ray Powder Diffractometer Practice of X-Ray Generation Goniometer for Powder Diffraction Monochromators, Filters, Mirrors X-Ray Detectors for XRD and TEM Detector Principles Solid State Detectors Position-Sensitive Detectors Charge Sensitive Preamplifier Other Electronics Experimental X-Ray Powder Diffraction Data * Intensities of Powder Diffraction Peaks Normals of Diffracting Planes Slit Width Lorentz Factor In section titles, the asterisk, "*," denotes a more specialized topic. The double dagger, "~," warns of a higher level of mathematics, physics, or crystallography.

3 xii Absorption Polarization Multiplicity and Density Measured Intensities Phase Fraction Measurement Peak Ratio Method Absorption Factors Example: Retained Austenite in Steels Lattice Parameter Measurement *Refinement Methods for Powder Diffraction Data Further Reading Problems The TEM and Its Optics Introduction to the Transmission Electron Microscope Working with Lenses and Ray Diagrams Single Lenses Multi-Lens Systems Modes of Operation of a TEM Dark-Field and Bright-Field Imaging Selected Area Diffraction Convergent-Beam Electron Diffraction Nanobeam Diffraction High-Resolution Imaging Practical TEM Optics Electron Guns Illumination Lens Systems Imaging Lens Systems Glass Lenses Interfaces Lenses and Rays Lenses and Phase Shifts Magnetic Lenses Focusing Image Rotation Pole Piece Gap Lens Aberrations and Other Defects Spherical Aberration Chromatic Aberration Diffraction Astigmati m Gun Brightne: Resolution Further Reading Problem

4 xiii Neutron Scattering Neutrons and Neutron Scattering Neutron Scattering Properties of Neutrons 3.2 Neutron Sources Fission and Spallation Moderation Neutron Powder Diffractometers Reactor-Based Powder Diffractometer Pulsed-Source-Based Powder Diffractometer 3.4 Waves of Phase Phase in Elastic Scattering * Phase in Inelastic Scattering Instruments for Measuring Larger Structures Small-Angle Scattering *Neutron Reflectivity * Inelastic Scattering * Triple-Axis Spectrometer *Fermi Chopper Spectrometer * Other Inelastic Instruments 3.7 * Quasielastic Scattering 3.8 *Magnetic Scattering. 3.9 Nuclear Scattering 3.10 Further Reading Problems... Scattering Waves and Scattering Wavefunctions Coherent and Incoherent Scattering Elastic and Inelastic Scattering Wave Amplitudes and Cross-Sections 4.2 X-Ray Scattering Electrodynamics of X-Ray Scattering * Inelastic Compton Scattering X-Ray Mass Attenuation Coefficients 4.3 Coherent Elastic Scattering :j: Born Approximation for Electrons Atomic Form Factors-Physical Picture :j: Scattering of Electrons by Model Potentials :j: *Atomic Form Factors-General Formulation 4.4 Further Reading Problems Inelastic Electron Scattering and Spectroscopy 5.1 Inelastic Electron Scattering Electron Energy-Loss Spectrometry (EELS)

5 xiv Instrumentation o General Features of EELS Spectra *Fine Structure Plasmon Excitations Plasmon Principles * Plasmons and Specimen Thickness Core Excitations o Scattering Angles and Energies-Qualitative :j: Inelastic Form Factor :j: *Double-Differential Cross-Section, d 2 uin/d de *Scattering Angles and Energies-Quantitative :j: * Differential Cross-Section, duin/de :j: Partial and Total Cross-Sections, O"in Quantification of EELS Core Edges Energy-Filtered TEM Imaging (EFTEM) Spectrum Imaging Energy Filters Chemical Mapping with Energy-Filtered Images Chemical Analysis with High Spatial Resolution Energy Dispersive X-Ray Spectrometry (EDS) Electron Trajectories Through Materials Fluorescence Yield EDS Instrumentation Considerations Artifacts in EDS Measurements Quantitative EDS Thin-Film Approximation o2 * ZAF Correction *Limits of Microanalysis Further Reading Problems Diffraction from Crystals Sums of Wavelets from Atoms Electron Diffraction from a Material Wave Diffraction from a Material The Reciprocal Lattice and the Laue Condition Diffraction from a Simple Lattice Reciprocal Lattice Laue Condition Equivalence of the Laue Condition and Bragg's Law Reciprocal Lattices of Cubic Crystals Diffraction from a Lattice with a Basis Structure Factor and Shape Factor Structure Factor Rules Symmetry Operations and Forbidden Diffractions 256

6 contents 6.4 Chemically-Ordered Structures Superlattice Diffractions Order Parameters Crystal Shape Factor Shape Factor of Rectangular Prism Other Shape Factors Small Particles in a Large Matrix. 6.6 Deviation Vector (Deviation Parameter) 6.7 Ewald Sphere Ewald Sphere Construction Ewald Sphere and Bragg's Law Tilting Specimens and Tilting Electron Beams. 6.8 Laue Zones * Effects of Curvature of the Ewald Sphere 6.10 Further Reading Problems Electron Diffraction and Crystallography 7.1 Indexing Diffraction Patterns Issues in Indexing Method 1-Start with Zone Axis Method 2-Start with Diffraction Spots 7.2 Stereo graphic Projections and Their Manipulation Construction of a Stereographic Projection Relationship Between Stereographic Projections and Electron Diffraction Patterns Manipulations of Stereographic Projections 7.3 Kikuchi Lines and Specimen Orientation Origin of Kikuchi Lines Indexing Kikuchi Lines Specimen Orientation and Deviation Parameter The Sign of s Kikuchi Maps Double Diffraction Occurrence of Forbidden Diffractions Interactions Between Crystallites *Convergent-Beam Electron Diffraction Convergence Angle of Incident Electron Beam Determination of Sample Thickness Measurements of Unit Cell Parameters * Determination of Point Groups Determination of Space Groups 7.6 Further Reading. 7.7 Problems XV

7 xvi 8 Diffraction Contrast in TEM Images Contrast in TEM Images Diffraction from Crystals with Defects Review of the Deviation Parameter, s Atom Displacements, or Shape Factor and t Diffraction Contrast and {s, or, t} 8.3 Extinction Distance The Phase-Amplitude Diagram Fringes from Sample Thickness Variations Thickness and Phase-Amplitude Diagrams Thickness Fringes in TEM Images Bend Contours in TEM Images Diffraction Contrast from Strain Fields Dislocations and Burgers Vector Determination Diffraction Contrast from Dislocation Strain Fields The g b Rule for Null Contrast Image Position and Dislocation Pairs or Loops Semi-Quantitative Diffraction Contrast from Dislocations Weak-Beam Dark-Field (WBDF) Imaging of Dislocations Procedure to Make a WBDF Image Diffraction Condition for a WBDF Image Analysis ofwbdf Images Fringes at Interfaces Phase Shifts of Electron Wavelets Across Interfaces Moire Fringes Diffraction Contrast from Stacking Faults Kinematical Treatment Results from Dynamical Theory Determination of the Intrinsic or Extrinsic Nature of Stacking Faults Partial Dislocations Bounding the Fault An Example of a Stacking Fault Analysis Sets of Stacking Faults in TEM Images Related frjnge Contra t Antiphase (n) Boundaries and 8 Boundaries Antiphase Boundaries Boundaries Contrast from Precipitates and Other Defects Vacancies Coherent Precipitates Semicoherent and Incoherent Particles Further Reading Problems

8 contents xvii 9 Diffraction Lineshapes Diffraction Line Broadening and Convolution Crystallite Size Broadening Strain Broadening Instrumental Broadening-Convolution 9.2 Fourier Transform Deconvolutions Mathematical Features *Effects of Noise on Fourier Transform Deconvolutions 9.3 Simultaneous Strain and Size Broadening Diffraction Lineshapes from Columns of Crystals Wavelets from Pairs of Unit Cells in One Column A Column Length Distribution :j: Intensity from Column Length Distribution 9.5 Comments on Diffraction Lineshapes 9.6 Further Reading Problems Patterson Functions and Diffuse Scattering The Patterson Function Overview Atom Centers at Points in Space Definition of the Patterson Function Properties of Patterson Functions :j: Perfect Crystals Deviations from Periodicity and Diffuse Scattering Diffuse Scattering from Atomic Displacements Uncorrelated Displacements-Homogeneous Disorder :j: Temperature * Correlated Displacements-Atomic Size Effects Diffuse Scattering from Chemical Disorder Uncorrelated Chemical Disorder-Random Alloys :j: * SRO Parameters :j: *Patterson Function for Chemical SRO SRO Diffuse Intensity :j: *Isotropic Materials * Polycrystalline Average and Single Crystal SRO *Amorphous Materials :j: One-Dimensional Model :j: Radial Distribution Function :j: Partial Pair Correlation Functions Small Angle Scattering Concept of Small Angle Scattering * Guinier Approximation (Small L1k) * Porod Law (Large i1k) :j: *Density-Density Correlations (All i1k). 514

9 xviii 10.6 Further Reading Problems High-Resolution TEM Imaging Huygens Principle Wavelets from Points in a Continuum Huygens Principle for a Spherical Wavefront-Fresnel Zones :j: Fresnel Diffraction Near an Edge Physical Optics of High-Resolution Imaging :j: Wavefronts and Fresnel Propagator :j: Lenses :j: Materials Experimental High-Resolution Imaging Defocus and Spherical Aberration :j: Lenses and Specimens Lens Characteristics * Simulations of High-Resolution TEM Images Principles of Simulations Practice of Simulations Issues and Examples in High-Resolution TEM Imaging Images ofnanostructures Examples oflnterfaces * Specimen and Microscope Parameters *Some Practical Issues for HRTEM *Geometric Phase Analysis Further Reading Problems High-Resolution STEM and Related Imaging Techniques Characteristics of High-Angle Annular Dark-Field Imaging Electron Channeling Along Atomic Columns Optical Fiber Analogy :j: Critical Angle * Tunneling Between Columns Scattering of Channeled Electrons Elastic Scattering of Channeled Electrons * Inelastic Scattering of Channeled Electrons * Comparison of HAADF and HRTEM Imaging HAADF Imaging with Atomic Resolution *Effect of Defocus Experimental Examples * Lens Aberrations and Their Corrections Cs Correction with Magnetic Hexapoles :j: Higher-Order Aberrations and Instabilities Examples of Cs-Corrected Images

10 xix Three-Dimensional Imaging High Resolution EELS 12.8 Electron Tomography 12.9 Further Reading Problems... Dynamical Theory Chapter Overview :j: * Mathematical Features of High-Energy Electrons in a Periodic Potential :j: *The Schrodinger Equation :j: Kinematical and Dynamical Theory *The Crystal as a Phase Grating First Approach to Dynamical Theory-Beam Propagation 13.4 :j: Second Approach to Dynamical Theory-Bloch Waves and Dispersion Surfaces Diffracted Beams, { c:p g}, are Beats of Bloch Waves, {ljr ())} Crystal Periodicity and Dispersion Surfaces Energies of Bloch Waves in a Periodic Potential General Two-Beam Dynamical Theory Essential Difference Between Kinematical and Dynamical Theories :j: Diffraction Error, sg, in Two-Beam Dynamical Theory Bloch Wave Amplitudes and Diffraction Error Dispersion Surface Construction Dynamical Diffraction Contrast from Crystal Defects Dynamical Diffraction Contrast Without Absorption :j: * Two-Beam Dynamical Theory of Stacking Fault Contrast Dynamical Diffraction Contrast with Absorption :j: *Multi-Beam Dynamical Theories of Electron Diffraction 13.9 Further Reading Problems Appendix A.1 Indexed Powder Diffraction Patterns A.2 Mass Attenuation Coefficients for Characteristic Kii X-Rays A.3 Atomic Form Factors for X-Rays.... A.4 X-Ray Dispersion Corrections for Anomalous Scattering.. A.5 Atomic Form Factors for 200 ke V Electrons and Procedure A.6 A.7 A.8 A.9 A.lO for Conversion to Other Voltages Indexed Single Crystal Diffraction Patterns: fcc, bee, de, hcp Stereographic Projections Examples of Fourier Transforms Debye-Waller Factor from Wave Amplitude.... Time-Varying Potentials and Inelastic Neutron Scattering

11 XX Aoll Review of Dislocations Ao12 TEM Laboratory Exercises Ao12ol Laboratory!-Microscope Procedures and Calibration with Au and Mo Aol2o2 Laboratory 2-Diffraction Analysis of(}' Precipitates 725 A.l2o3 Laboratory 3-Chemical Analysis of e' Precipitates A.12.4 Laboratory 4-Contrast Analysis of Defects A.13 Fundamental and Derived Constants 730 Bibliography 0 Further Reading 0 References and Figures Index

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