Introduction to Conventional Transmission Electron Microscopy

by Marc De Graef

• ISBN13: 9780521620062
• ISBN10: 0521620066
• Edition: 1st
• Format: Hardcover
• Copyright: 2003-04-21
• Publisher: Cambridge University Press

Summary

This book covers the fundamentals of conventional transmission electron microscopy (CTEM) as applied to crystalline solids. In addition to including a large selection of worked examples and homework problems, the volume is accompanied by a supplementary website (http://ctem.web.cmu.edu/) containing interactive modules and over 30,000 lines of free Fortran 90 source code. The work is based on a lecture course given by Marc De Graef in the Department of Materials Science and Engineering at Carnegie Mellon University.

Table of Contents

Preface	xiv
Acknowledgements	xix
Figure reproductions	xxi
Basic crystallography	1	(78)
Introduction	1	(1)
Direct space and lattice geometry	2	(7)
Basis vectors and unit cells	2	(3)
The dot product and the direct metric tensor	5	(4)
Definition of reciprocal space	9	(14)
Planes and Miller indices	9	(1)
The reciprocal basis vectors	10	(4)
Lattice geometry in reciprocal space	14	(2)
Relations between direct space and reciprocal space	16	(2)
The non-Cartesian vector cross product	18	(5)
The hexagonal system	23	(6)
Directions in the hexagonal system	24	(2)
The reciprocal hexagonal lattice	26	(3)
The stereographic projection	29	(5)
Drawing a point	32	(1)
Constructing a great circle through two poles	32	(1)
Constructing a small circle around a pole	33	(1)
Finding the pole of a great circle	34	(1)
Measuring the angle between two poles	34	(1)
Measuring the angle between two great circles	34	(1)
Crystal symmetry	34	(13)
Symmetry operators	35	(4)
Mathematical representation of symmetry operators	39	(3)
Point groups	42	(2)
Families of planes and directions	44	(2)
Space groups	46	(1)
Coordinate transformations	47	(8)
Transformation rules	48	(2)
Examples of coordinate transformations	50	(3)
Rhombohedral and hexagonal settings of the trigonal system	53	(2)
Converting vector components into Cartesian coordinates	55	(4)
Crystallographic calculations on the computer	59	(18)
Preliminary remarks	59	(3)
Implementing the metric tensor formalism	62	(2)
Using space groups on the computer	64	(4)
Graphical representation of direct and reciprocal space	68	(2)
Stereographic projections on the computer	70	(7)
Recommended additional reading	77	(2)
Exercises	77	(2)
Basic quantum mechanics, Bragg's Law and other tools	79	(57)
Introduction	79	(1)
Basic quantum mechanics	80	(9)
Scalar product between functions	81	(1)
Operators and physical observables	82	(2)
The Schrodinger equation	84	(1)
The de Broglie relation	85	(1)
The electron wavelength (non-relativistic)	86	(1)
Wave interference phenomena	87	(2)
Elements of the special theory of relativity	89	(7)
Introduction	89	(2)
The electron wavelength (relativistic)	91	(3)
Relativistic correction to the governing equation	94	(2)
The Bragg equation in direct and reciprocal space	96	(7)
The Bragg equation in direct space	96	(2)
The Bragg equation in reciprocal space	98	(2)
The geometry of electron diffraction	100	(3)
Fourier transforms and convolutions	103	(8)
Definition	103	(2)
The Dirac delta-function	105	(1)
The convolution product	106	(2)
Numerical computation of Fourier transforms and convolutions	108	(3)
The electrostatic lattice potential	111	(22)
Elastic scattering of electrons by an individual atom	111	(5)
Elastic scattering by an infinite crystal	116	(3)
Finite crystal size effects	119	(2)
The excitation error or deviation parameter sg	121	(1)
Phenomenological treatment of absorption	122	(4)
Atomic vibrations and the electrostatic lattice potential	126	(2)
Numerical computation of the Fourier coefficients of the lattice potential	128	(5)
Recommended additional reading	133	(3)
Exercises	134	(2)
The transmission electron microscope	136	(99)
Introduction	136	(1)
A brief historical overview	137	(1)
Overview of the instrument	138	(4)
Basic electron optics: round magnetic lenses	142	(24)
Cross-section of a round magnetic lens	142	(2)
Magnetic field components for a round lens	144	(2)
The equation of motion for a charged particle in a magnetic field	146	(2)
The paraxial approximation	148	(2)
Numerical trajectory computation	150	(6)
General properties of round magnetic lenses	156	(5)
Lenses and Fourier transforms	161	(5)
Basic electron optics: lens aberrations	166	(8)
Introduction	166	(1)
Aberration coefficients for a round magnetic lens	166	(8)
Basic electron optics: magnetic multipole lenses	174	(5)
Beam deflection	176	(2)
Quadrupole elements	178	(1)
Basic electron optics: electron guns	179	(16)
Introduction	179	(1)
Electron emission	179	(8)
Electron guns	187	(3)
Beam energy spread and chromatic aberration	190	(3)
Beam coherence	193	(2)
How many electrons are there in the microscope column?	195	(1)
The illumination stage: prespecimen lenses	195	(4)
The specimen stage	199	(17)
Types of objective lenses	199	(2)
Side-entry, top-entry and special purpose stages	201	(3)
The objective lens and electron diffraction geometry	204	(4)
Numerical computation of electron diffraction patterns	208	(3)
Higher-order Laue zones	211	(5)
The magnification stage: post-specimen lenses	216	(5)
Electron detectors	221	(14)
General detector characteristics	221	(6)
Viewing screen	227	(1)
Photographic emulsions	228	(2)
Digital detectors	230	(3)
Exercises	233	(2)
Getting started	235	(68)
Introduction	235	(2)
The xtalinfo.f90 program	237	(1)
The study materials	238	(14)
Material I: Cu-15 at% Al	238	(3)
Material II: Ti	241	(2)
Material III: GaAs	243	(7)
Material IV: BaTiO3	250	(2)
A typical microscope session	252	(20)
Startup and alignment	252	(5)
Basic observation modes	257	(15)
Microscope calibration	272	(5)
Magnification and camera length calibration	273	(3)
Image rotation	276	(1)
Basic CTEM observations	277	(14)
Bend contours	279	(3)
Tilting towards a zone axis pattern	282	(2)
Sample orientation determination	284	(4)
Convergent beam electron diffraction patterns	288	(3)
Lorentz microscopy: observations on magnetic thin foils	291	(9)
Basic Lorentz microscopy (classical approach)	291	(2)
Experimental methods	293	(7)
Recommended additional reading	300	(3)
Exercises	301	(2)
Dynamical electron scattering in perfect crystals	303	(42)
Introduction	303	(1)
The Schrodinger equation for dynamical electron scattering	304	(2)
General derivation of the Darwin--Howie--Whelan equations	306	(5)
Formal solution of the DHW multibeam equations	311	(2)
Slice methods	313	(2)
The direct space multi-beam equations	315	(5)
The phase grating equation	316	(1)
The propagator equation	317	(2)
Solving the full direct-space equation	319	(1)
Bloch wave description	320	(8)
General solution method	322	(4)
Determination of the Bloch wave excitation coefficients	326	(1)
Absorption in the Bloch wave formalism	327	(1)
Important diffraction geometries and diffraction symmetry	328	(12)
Diffraction geometries	328	(2)
Thin-foil symmetry	330	(1)
The reciprocity theorem	331	(9)
Concluding remarks and recommended reading	340	(5)
Exercises	343	(2)
Two-beam theory in defect-free crystals	345	(50)
Introduction	345	(1)
The column approximation	346	(2)
The two-beam case: DHW formalism	348	(13)
The basic two-beam equations	348	(1)
The two-beam kinematical theory	348	(4)
The two-beam dynamical theory	352	(9)
The two-beam case: Bloch wave formalism	361	(10)
Mathematical solution	362	(5)
Graphical solution	367	(4)
Numerical two-beam image simulations	371	(24)
Numerical computation of extinction distances and absorption lengths	371	(6)
The two-beam scattering matrix	377	(5)
Numerical (two-beam) Bloch wave calculations	382	(2)
Example two-beam image simulations	384	(4)
Two-beam convergent beam electron diffraction	388	(6)
Exercises	394	(1)
Systematic row and zone axis orientations	395	(65)
Introduction	395	(1)
The systematic row case	396	(23)
The geometry of a bend contour	396	(2)
Theory and simulations for the systematic row orientation	398	(14)
Thickness integrated intensities	412	(7)
The zone axis case	419	(20)
The geometry of the zone axis orientation	420	(2)
Example simulations for the zone axis case	422	(13)
Bethe potentials	435	(2)
Application of symmetry in multi-beam simulations	437	(2)
Computation of the exit plane wave function	439	(11)
The multi-slice and real-space approaches	439	(7)
The Bloch wave approach	446	(1)
Example exit wave simulations	446	(4)
Electron exit wave for a magnetic thin foil	450	(8)
The Aharonov--Bohm phase shift	450	(3)
Direct observation of quantum mechanical effects	453	(1)
Numerical computation of the magnetic phase shift	454	(4)
Recommended reading	458	(2)
Exercises	458	(2)
Defects in crystals	460	(58)
Introduction	460	(1)
Crystal defects and displacement fields	460	(5)
Numerical simulation of defect contrast images	465	(13)
Geometry of a thin foil containing a defect	466	(4)
Example of the use of the various reference frames	470	(4)
Dynamical multi-beam computations for a column containing a displacement field	474	(4)
Image contrast for selected defects	478	(37)
Coherent precipitates and voids	479	(2)
Line defects	481	(11)
Planar defects	492	(19)
Planar defects and the systematic row	511	(3)
Other displacement fields	514	(1)
Concluding remarks and recommended reading	515	(3)
Exercises	516	(2)
Electron diffraction patterns	518	(67)
Introduction	518	(1)
Spot patterns	518	(17)
Indexing of simple spot patterns	518	(5)
Zone axis patterns and orientation relations	523	(2)
Double diffraction	525	(5)
Overlapping crystals and Moire patterns	530	(5)
Ring patterns	535	(2)
Linear features in electron diffraction patterns	537	(13)
Streaks	537	(3)
HOLZ lines	540	(4)
Kikuchi lines	544	(6)
Convergent beam electron diffraction	550	(6)
Point group determination	551	(3)
Space group determination	554	(2)
Diffraction effects in modulated crystals	556	(15)
Modulation types	556	(2)
Commensurate modulations	558	(11)
Incommensurate modulations and quasicrystals	569	(2)
Diffuse intensity due to short range ordering	571	(4)
Diffraction effects from polyhedral particles	575	(10)
Exercises	584	(1)
Phase contrast microscopy	585	(76)
Introduction	585	(2)
A simple experimental example	586	(1)
The microscope as an information channel	587	(51)
The microscope point spread and transfer functions	589	(17)
The influence of beam coherence	606	(15)
Plug in the numbers	621	(5)
Image formation for an amorphous thin foil	626	(3)
Alignment and measurement of various imaging parameters	629	(9)
High-resolution image simulations	638	(3)
Lorentz image simulations	641	(8)
Example Lorentz image simulations for periodic magnetization patterns	642	(6)
Fresnel fringes for non-magnetic objects	648	(1)
Exit wave reconstruction	649	(10)
What are we looking for?	649	(3)
Exit wave reconstruction for Lorentz microscopy	652	(6)
Exercises	658	(1)
Final remarks	659	(2)
Appendix A1 Explicit crystallographic equations	661	(4)
Appendix A2 Physical constants	665	(1)
Appendix A3 Space group encoding and other software	666	(1)
Appendix A4 Point groups and space groups	667	(10)
List of symbols	677	(8)
Bibliography	685	(20)
Index	705