Transmission Electron Microscopy and Diffractometry of Materials

by Fultz, Brent; Howe, James M.

• ISBN13: 9783540437642
• ISBN10: 3540437649
• Edition: 2nd
• Format: Hardcover
• Copyright: 2002-11-01
• Publisher: Springer Verlag

Summary

This textbook develops the concepts of transmission electron microscopy (TEM) and x-ray diffractometry (XRD) that are important for the characterization of materials. It emphasizes themes common to both techniques, such as scattering from atoms, wave interference, and the formation and analysis of diffraction patterns. It explains the uniqueness of each technique, especially imaging and spectroscopy in the TEM. Simple citations of rules are avoided as much as possible, and both practical and theoretical issues are explained in detail. The book can be used as both an introductory and advanced-level graduate text since sections/chapters are sorted according to difficulty and grouped for use in quarter and semester courses on TEM and XRD. Numerous problems are provided at the end of each chapter to reinforce key concepts, and solutions are available to instructors. Appendices provide procedures for introductory laboratory exercises, and up-to-date tabulations of physical data useful for TEM and XRD.

Table of Contents

Diffraction and the X-ray Powder Diffractometer	1	(62)
Diffraction	1	(12)
Introduction to Diffraction	1	(2)
Bragg's Law	3	(3)
Strain Effects	6	(1)
Size Effects	7	(1)
A Symmetry Consideration	8	(1)
Experimental Methods	9	(4)
The Creation of X-Rays	13	(10)
Bremsstrahlung	13	(3)
Characteristic Radiation	16	(4)
Synchrotron Radiation	20	(3)
The X-Ray Powder Diffractometer	23	(6)
Practice of X-Ray Generation	23	(2)
Goniometer for Powder Diffraction	25	(3)
Monochromators and Filters	28	(1)
X-Ray Detectors for XRD and TEM	29	(8)
Detector Principles	29	(5)
Position-Sensitive Detectors	34	(1)
Charge Sensitive Preamplifier	35	(1)
Other Electronics	35	(2)
Experimental X-Ray Powder Diffraction Data	37	(26)
Intensities of Powder Diffraction Peaks	37	(8)
Phase Fraction Measurement	45	(5)
Lattice Parameter Measurement	50	(2)
Refinement Methods for Powder Diffraction Data	52	(3)
Pair Distribution Function Analysis	55	(1)
Further Reading	56	(1)
Problems	57	(6)
The TEM and its Optics	63	(60)
Introduction to the Transmission Electron Microscope	63	(4)
Working with Lenses and Ray Diagrams	67	(5)
Single Lenses	67	(3)
Multi-Lens Systems	70	(2)
Modes of Operation of a TEM	72	(17)
Conventional Modes	72	(11)
Convergent-Beam Electron Diffraction	83	(1)
High-Resolution Imaging	84	(5)
Real Lens Systems	89	(4)
Illumination Lens Systems	89	(4)
Imaging Lens Systems	93	(1)
Glass Lenses	93	(7)
Interfaces	93	(2)
Lenses and Rays	95	(3)
Lenses and Phase Shifts	98	(2)
Magnetic Lenses	100	(4)
Lens Aberrations and Other Defects	104	(9)
Spherical Aberration	105	(1)
Chromatic Aberration	106	(1)
Diffraction	107	(1)
Astigmatism	107	(4)
Gun Brightness	111	(2)
Resolution	113	(10)
Further Reading	115	(1)
Problems	116	(7)
Scattering	123	(44)
Coherence and Incoherence	123	(7)
Phase and Energy	123	(3)
Wave Amplitudes and Cross-Sections	126	(4)
X-Ray Scattering	130	(8)
Electrodynamics of X-Ray Scattering	130	(4)
Inelastic Compton Scattering	134	(2)
X-Ray Mass Attenuation Coefficients	136	(2)
Coherent Elastic Scattering	138	(17)
Born Approximation for Electrons	138	(5)
Atomic Form Factors--Physical Picture	143	(3)
Scattering of Electrons by Model Potentials	146	(4)
Atomic Form Factors--General Formulation	150	(5)
Nuclear Scattering	155	(12)
Properties of Neutrons	156	(2)
Inelastic Neutron Scattering	158	(4)
Mossbauer Scattering	162	(2)
Further Reading	164	(1)
Problems	164	(3)
Inelastic Electron Scattering and Spectroscopy	167	(58)
Inelastic Electron Scattering	167	(2)
Electron Energy-Loss Spectrometry (EELS)	169	(8)
Instrumentation	169	(1)
General Features of EELS Spectra	170	(2)
Fine Structure	172	(5)
Plasmon Excitations	177	(4)
Plasmon Principles	177	(2)
Plasmons and Specimen Thickness	179	(2)
Core Excitations	181	(17)
Scattering Angles and Energies--Qualitative	182	(2)
Inelastic Form Factor	184	(4)
Double-Differential Cross-Section, d2σin/dφdE	188	(2)
Scattering Angles and Energies--Quantitative	190	(2)
Differential Cross-Section, dσin/dE	192	(1)
Partial and Total Cross-Sections σin	193	(3)
Quantification of EELS Core Edges	196	(2)
Energy-Filtered TEM Imaging (EFTEM)	198	(5)
Energy Filters	199	(1)
Chemical Mapping with Energy-Filtered Images	200	(2)
Chemical Analysis with High Spatial Resolution	202	(1)
Energy Dispersive X-Ray Spectrometry (EDS)	203	(22)
Electron Trajectories Through Materials	203	(4)
Fluorescence Yield	207	(3)
EDS Instrumentation Considerations	210	(3)
Thin-Film Approximation	213	(3)
ZAF Correction	216	(2)
Limits of Microanalysis	218	(2)
Further Reading	220	(1)
Problems	221	(4)
Diffraction from Crystals	225	(50)
Sums of Wavelets from Atoms	225	(7)
Electron Diffraction from a Material	226	(2)
Wave Diffraction from a Material	228	(4)
The Reciprocal Lattice and the Laue Condition	232	(5)
Diffraction from a Simple Lattice	232	(1)
Reciprocal Lattice	233	(2)
Laue Condition	235	(1)
Equivalence of the Laue Condition and Bragg's Law	235	(1)
Reciprocal Lattices of Cubic Crystals	236	(1)
Diffraction from a Lattice with a Basis	237	(12)
Structure Factor and Shape Factor	237	(2)
Structure Factor Rules	239	(5)
Symmetry Operations and Forbidden Diffractions	244	(1)
Superlattice Diffractions	245	(4)
Crystal Shape Factor	249	(9)
Shape Factor of Rectangular Prism	249	(4)
Other Shape Factors	253	(1)
Small Particles in a Large Matrix	254	(4)
Deviation Vector (Deviation Parameter)	258	(1)
Ewald Sphere	259	(4)
Ewald Sphere Construction	259	(2)
Ewald Sphere and Bragg's Law	261	(1)
Tilting Specimens and Tilting Electron Beams	261	(2)
Laue Zones	263	(3)
Effects of Curvature of the Ewald Sphere	266	(9)
Further Reading	267	(1)
Problems	268	(7)
Electron Diffraction and Crystallography	275	(64)
Indexing Diffraction Patterns	275	(9)
Issues in Indexing	276	(2)
Method 1--Start with Zone Axis	278	(4)
Method 2--Start with Diffraction Spots	282	(2)
Stereographic Projections and Their Manipulation	284	(9)
Construction of a Stereographic Projection	284	(1)
Relationship Between Stereographic Projections and Electron Diffraction Patterns	285	(1)
Manipulations of Stereographic Projections	286	(7)
Kikuchi Lines and Specimen Orientation	293	(11)
Origin of Kikuchi Lines	293	(4)
Indexing Kikuchi Lines	297	(1)
Specimen Orientation and Deviation Parameter	298	(3)
The Sign of s	301	(1)
Kikuchi Maps	301	(3)
Double Diffraction	304	(2)
Occurrence of Forbidden Diffractions	304	(1)
Interactions Between Crystallites	305	(1)
Convergent-Beam Electron Diffraction	306	(26)
Convergence Angle of Incident Electron Beam	308	(1)
Determination of Sample Thickness	309	(2)
Measurements of Unit Cell Parameters	311	(5)
Determination of Point Groups	316	(11)
Determination of Space Groups	327	(5)
Further Reading	332	(7)
Problems	332	(7)
Diffraction Contrast in TEM Images	339	(84)
Contrast in TEM Images	339	(2)
A Review of Structure and Shape Factors	341	(2)
Extinction Distance	343	(3)
The Phase-Amplitude Diagram	346	(2)
Fringes from Sample Thickness Variations	348	(5)
Thickness and Phase-Amplitude Diagrams	348	(1)
Thickness Contours in TEM Images	349	(4)
Bend Contours in TEM Images	353	(4)
Diffraction Contrast from Strain Fields	357	(4)
Dislocations and Burgers Vector Determination	361	(9)
Diffraction Contrast from Dislocation Strain Fields	361	(2)
The g.b Rule for Null Contrast	363	(4)
Image Position and Dislocation Pairs or Loops	367	(3)
Semi-Quantitative Diffraction Contrast from Dislocations	370	(8)
Weak-Beam Dark-Field (WBDF) Imaging of Dislocations	378	(7)
Procedure to Make a WBDF Image	379	(1)
Diffraction Condition for a WBDF Image	380	(2)
Analysis of WBDF Images	382	(3)
Fringes at Interfaces	385	(7)
Phase Shifts of Electron Wavelets Across Interfaces	385	(4)
Moire Fringes	389	(3)
Diffraction Contrast from Stacking Faults	392	(13)
Kinematical Treatment	393	(4)
Results from Dynamical Theory	397	(3)
Determination of the Intrinsic or Extrinsic Nature of Stacking Faults	400	(1)
Partial Dislocations Bounding the Fault	400	(1)
An Example of a Stacking Fault Analysis	401	(2)
Sets of Stacking Faults in TEM Images	403	(1)
Related Fringe Contrast	404	(1)
Antiphase (π) Boundaries and δ Boundaries	405	(3)
Antiphase Boundaries	405	(1)
δBoundaries	406	(2)
Contrast from Precipitates and Other Defects	408	(15)
Vacancies	408	(1)
Coherent Precipitates	409	(5)
Semicoherent and Incoherent Particles	414	(1)
Further Reading	414	(1)
Problems	415	(8)
Diffraction Lineshapes	423	(42)
Diffraction Line Broadening and Convolution	423	(11)
Crystallite Size Broadening	424	(3)
Strain Broadening	427	(3)
Instrumental Broadening--Convolution	430	(4)
Fourier Transform Deconvolutions	434	(7)
Mathematical Features	434	(3)
Effects of Noise on Fourier Transform Deconvolutions	437	(4)
Simultaneous Strain and Size Broadening	441	(6)
Fourier Methods with Multiple Orders	447	(12)
Formulation	447	(5)
Strain Heterogeneity and Peak Asymmetry	452	(3)
Column Lengths	455	(1)
Size Coefficients	456	(2)
Practical Issues in Warren-Averbach Analysis	458	(1)
Comments on Diffraction Lineshapes	459	(6)
Further Reading	462	(1)
Problems	462	(3)
Patterson Functions and Diffuse Scattering	465	(56)
The Patterson Function	465	(9)
Overview	465	(1)
Atom Centers at Points in Space	466	(1)
Definition of the Patterson Function	467	(2)
Properties of Patterson Functions	469	(2)
Perfect Crystals	471	(3)
Patterson Functions for Homogeneous Disorder and Atomic Displacement Diffuse Scattering	474	(11)
Deviations from Periodicity	474	(1)
Uncorrelated Displacements	475	(3)
Correlated Displacements: Atomic Size Effects	478	(2)
Temperature	480	(5)
Diffuse Scattering from Chemical Disorder	485	(10)
Randomness--Uncorrelated Chemical Disorder	485	(4)
SRO Parameters	489	(2)
Patterson Function for Chemical SRO	491	(1)
Short-Range Order Diffuse Intensity	492	(1)
Isotropic Materials	493	(1)
Polycrystalline Average and Single Crystal SRO	494	(1)
Amorphous Materials	495	(11)
One-Dimensional Model	495	(5)
Radial Distribution Function	500	(4)
Partial Pair Correlation Functions	504	(2)
Small Angle Scattering	506	(15)
Concept of Small Angle Scattering	506	(3)
Guinier Approximation (small Δκ)	509	(2)
Porod Law (large Δκ)	511	(3)
Density-Density Correlations (all Δκ)	514	(2)
Further Reading	516	(1)
Problems	517	(4)
High-Resolution TEM Imaging	521	(76)
Huygens Principle	522	(14)
Wavelets from Points in a Continuum	522	(5)
Huygens Principle for a Spherical Wavefront-Fresnel Zones	527	(4)
Fresnel Diffraction Near an Edge	531	(5)
Physical Optics of High-Resolution Imaging	536	(6)
Wavefronts and Fresnel Propagator	536	(2)
Lenses	538	(2)
Materials	540	(2)
Experimental High-Resolution Imaging	542	(17)
Defocus and Spherical Aberration	542	(5)
Lenses and Specimens	547	(3)
Lens Characteristics	550	(9)
Simulations of High-Resolution TEM Images	559	(7)
Principles of Simulations	559	(6)
Practice of Simulations	565	(1)
Issues and Examples in High-Resolution TEM Imaging	566	(20)
Images of Nanostructures	566	(3)
Examples of Interfaces	569	(3)
Effects of Solute Misfit and Scattering Factor Differences on Spot Intensities	572	(4)
Specimen and Microscope Parameters	576	(7)
Hints and Tricks for HRTEM	583	(3)
Z-Contrast Imaging	586	(11)
Characteristics of Z-Contrast Imaging	586	(4)
Comparison of Z-Contrast Imaging with HRTEM Imaging	590	(2)
Z-Contrast Imaging with Atomic Resolution	592	(2)
Developments in Atomic-Resolution Imaging	594	(1)
Further Reading	594	(1)
Problems	595	(2)
Dynamical Theory	597	(66)
Chapter Overview	597	(2)
Mathematical Features of High-Energy Electrons in a Periodic Potential	599	(10)
The Schrodinger Equation	599	(6)
Kinematical and Dynamical Theory	605	(2)
The Crystal as a Phase Grating	607	(2)
First Approach to Dynamical Theory--Beam Propagation	609	(4)
Second Approach to Dynamical Theory--Bloch Waves and Dispersion Surfaces	613	(19)
Diffracted Beams, {φg}, are Beats of Bloch Waves, {ψ(j)}	613	(6)
Crystal Periodicity and Dispersion Surfaces	619	(4)
Energies of Bloch Waves in a Periodic Potential	623	(3)
General Two-Beam Dynamical Theory	626	(6)
Essential Difference Between Kinematical and Dynamical Theories	632	(5)
Diffraction Error, sg, in Two-Beam Dynamical Theory	637	(4)
Bloch Wave Amplitudes and Diffraction Error	637	(2)
Dispersion Surface Construction	639	(2)
Dynamical Diffraction Contrast from Crystal Defects	641	(14)
Dynamical Diffraction Contrast Without Absorption	641	(5)
Two-Beam Dynamical Theory of Stacking Fault Contrast	646	(4)
Dynamical Diffraction Contrast with Absorption	650	(5)
Multi-Beam Dynamical Theories of Electron Diffraction	655	(8)
Further Reading	658	(1)
Problems	658	(5)
Bibliography	663	(14)
Further Reading	663	(4)
References and Figures	667	(10)
A. Appendix	677	(58)
A.1 Indexed Powder Diffraction Patterns	677	(1)
A.2 Mass Attenuation Coefficients for Characteristic α X-Rays	678	(1)
A.3 Atomic Form Factors for X-Rays	679	(4)
A.4 X-Ray Dispersion Corrections for Anomalous Scattering	683	(1)
A.5 Atomic Form Factors for 200 keV Electrons and Procedure for Conversion to Other Voltages	684	(5)
A.6 Indexed Single Crystal Diffraction Patterns: fcc, bcc, dc, hcp	689	(10)
A.7 Stereographic Projections	699	(4)
A.8 Examples of Fourier Transforms	703	(3)
A.9 α1, α2 Splitting and the Rachinger Correction	706	(1)
A.10 Numerical Approximation for the Voigt Function	707	(1)
A.11 Debye--Waller Factor from Wave Amplitude	708	(1)
A.12 Review of Dislocations	709	(7)
A.13 TEM Laboratory Exercises	716	(16)
A.13.1 Preliminary--JEOL 2000FX Daily Operation	716	(4)
A.13.2 Preliminary--Philips 400T Daily Operation	720	(2)
A.13.3 Laboratory 1 -- Microscope Procedures and Calibration with Au and MoO3	722	(4)
A.13.4 Laboratory 2 -- Diffraction Analysis of θ' Precipitates	726	(3)
A.13.5 Laboratory 3 -- Chemical Analysis of θ' Precipitates	729	(1)
A.13.6 Laboratory 4 -- Contrast Analysis of Defects	730	(2)
A.14 Fundamental and Derived Constants	732	(3)
Index	735