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Signals from a thin sample
Specimen
Inc
ide
nt b
ea
m
Auger electrons
Backscattered electronsBSE
secondary electronsSE Characteristic
X-rays
visible light
“absorbed” electrons electron-hole pairs
elastically scatteredelectrons
dire
ct
be
am
inelasticallyscattered electrons
BremsstrahlungX-rays
1-100 nm
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Interaction of high energetic electrons with matter
biological samples,polymers
crystalline structure,defect analysis,high-resolution TEM
chemical analysis,spectroscopy
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Interaction -> contrast
ED
S,
elem
ent
map
s
STEM-DF
Thin section of mouse brain: mass contrast of stained membrane structures(G.Knott)
Dark field image of differently ordered domains:Diffraction contrast
High-resolution image:Image contrast due to interference between transmitted and diffracted beam
Element distribution mapsOf Nb3Sn superconductor
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Two basic operation modesDiffraction <-> Image
Diffraction Mode Image Mode
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SEM
TEM
holey Carbon film(K,Nb)TaO3Nano-rods
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Shape, lattice parameters, defects, lattice planes
(K,Nb)O3Nano-rods
Bright field image
dark field image
Diffraction pattern
High-resolution image
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Diffraction theory
•Introduction to electron diffraction•Elastic scattering theory•Basic crystallography & symmetry•Electron diffraction theory•Intensity in the electron diffraction pattern
Thanks to Dr. Duncan Alexander for slides
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Diffraction: constructive and destructive interference of waves
• electrons interact very strongly with matter => strong diffraction intensity (can take patterns in seconds, unlike X-ray diffraction)
• diffraction from only selected set of planes in one pattern - e.g. only 2D information
• wavelength of fast moving electrons much smaller than spacing of atomic planes => diffraction from atomic planes (e.g. 200 kV e-, λ = 0.0025 nm)
• spatially-localized information(≳ 200 nm for selected-area diffraction;
2 nm possible with convergent-beam electron diffraction)
• orientation information
• close relationship to diffraction contrast in imaging
• immediate in the TEM!
• limited accuracy of measurement - e.g. 2-3%
• intensity of reflections difficult to interpret because of dynamical effects
Why use electron diffraction?
( diffraction from only selected set of planes in one pattern - e.g. only 2D information)
( limited accuracy of measurement - e.g. 2-3%)
( intensity of reflections difficult to interpret because of dynamical effects)
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BaTiO3 nanocrystals (Psaltis lab)
Image formation
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Insert selected area aperture to choose region of interest
BaTiO3 nanocrystals (Psaltis lab)
Area selection
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Press “D” for diffraction on microscope console - alter strength of intermediate lens and focus diffraction pattern on to screen
Find cubic BaTiO3 aligned on [0 0 1] zone axis
Take selected-area diffraction pattern
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Scatter range ofelectrons, neutrons and X-rays
(99% of intensity lost)
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electron, neutron X-ray scattering
wave Wavelength
Source Scattering at Differentiationof
Sample size
X-rays 0.07nm0.15nm
X-ray tubessynchrotrons
Electron cloud Lattice parametersUnit cell
0.1mm
Electrons 2pm @300keV
e guns(SEM/TEM)
Potential distribution(electrons & nucleus)
Lattice parameters,Orientations
0.1um
Neutrons (1)
~0.1nm Nuclear reactors
Nuclear scattering(nucleus)
LP, isotopes m
Neutrons (2)
“ “ Magnetic spin (outerelectrons)
Oxidation states
m
Scattering power: n : X-ray : e = 1 : 10 : 104
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Consider coherent elastic scattering of electrons from atom
Differential elastic scatteringcross section:
Atomic scattering factor for electrons
Scattering theory - Atomic scattering factor
The Mott-Bethe formula is used to calculate electron form factors from X-ray form factors (fx)
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Atoms closer together => scattering angles greater
=> Reciprocity!
Periodic array of scattering centres (atoms)
Plane electron wave generates secondary wavelets
Secondary wavelets interfere => strong direct beam and multiple orders of diffracted beams from constructive interference
Scattering theory - Huygen’s principle
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Repetition of translated structure to infinity
Basic crystallographyCrystals: translational periodicity & symmetry
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Unit cell is the smallest repeating unit of the crystal latticeHas a lattice point on each corner (and perhaps more elsewhere)
Defined by lattice parameters a, b, c along axes x, y, zand angles between crystallographic axes: α = b^c; β = a^c; γ = a^b
Crystallography: the unit cell
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7 possible unit cell shapes with different symmetries that can be repeated by translation in 3 dimensions
=> 7 crystal systems each defined by symmetry
Triclinic Monoclinic Orthorhombic Tetragonal Rhombohedral
Hexagonal Cubic
Diagrams from www.Wikipedia.org
The seven crystal systems
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Combinations of crystal systems and lattice point centring that describe all possible crystals- Equivalent system/centring combinations eliminated => 14 (not 7 x 4 = 28) possibilities
Diagrams from www.Wikipedia.org
14 Bravais lattices
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Path difference between reflection from planes distance dhkl apart = 2dhklsinθ
Electron diffraction: λ ~ 0.001 nmtherefore: λ << dhkl
=> small angle approximation: nλ ≈ 2dhklθReciprocity: scattering angle θ ~ dhkl
-1
2dhklsinθ = λ/2 - destructive interference2dhklsinθ = λ - constructive interference=> Bragg law:nλ = 2dhklsinθ
Diffraction theory - Bragg law
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Bragg’s law
2 sin dhkl = n
Distance between lattice planes d
Difference in path
dhkl = n sin
kk’
g = k-k’
Elastic diffraction
|k| = |k’|
Periodic arrangement of lattice planes:g : reciprocal lattice vector
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For scattering from plane (h k l) the diffraction vector:ghkl = ha* + kb* + lc*
rn = n1a + n2b + n3cReal lattice
vector:
In diffraction we are working in “reciprocal space”; useful to transform the crystal lattice in toa “reciprocal lattice” that represents the crystal in reciprocal space:
r* = m1a* + m2b* + m3c*Reciprocal lattice
vector:
a*.b = a*.c = b*.c = b*.a = c*.a = c*.b = 0
a*.a = b*.b = c*.c = 1
a* = (b ^ c)/VC
where:
i.e. VC: volume of unit cell
Plane spacing:
The reciprocal lattice
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kI: incident beam wave vector
Ewald sphere
Reciprocal space: sphere radius 1/λ represents possible scattering wave vectors intersecting reciprocal space
Electron diffraction: radius of sphere very large compared to reciprocal lattice=> sphere circumference almost flat
kI
A vector in reciprocal space:ghkl = h a* + k b* + l c*
diffraction if : kI – kD = g and |kI| =|kD|Bragg and elastic scattering
real space
reciprocal space
a* b*
Bragg: dhkl = /2 sin = 1/ |g|
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kI: incident beam wave vector
kD: diffracted wave vector
Ewald sphere
Reciprocal space: sphere radius 1/λ represents possible scattering wave vectors intersecting reciprocal space
Electron diffraction: radius of sphere very large compared to reciprocal lattice=> sphere circumference almost flat
kI
kD
A vector in reciprocal space:ghkl = h a* + k b* + l c*
diffraction if : kI – kD = g and |kI| =|kD|Bragg and elastic scattering
real space
reciprocal space
a* b*
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Laue Zones
O H
E
k k'
g
Zonesde Laued'ordre
32
10
Ewald
p
lan
s ré
flec
teu
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• Laue zones
J.-P. MorniroliMSE-621 2013 122
Ewald Sphere : Laue Zones (ZOLZ+FOLZ)
=2.0mrads=0.2
ZOLZ6-fold
FOLZ3-fold
Source: P.A. Buffat
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Ewald Sphere: Laue Zones (ZOLZ+FOLZ) tilted sample
=2.0mrads=0.2
ZOLZ6-fold
FOLZ3-fold
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Symmetry informationZone axis SADPs have symmetry closely related to symmetry of crystal lattice
Example: FCC aluminium[0 0 1]
[1 1 0]
[1 1 1]
4-fold rotation axis
2-fold rotation axis
6-fold rotation axis - but [1 1 1] actually 3-fold axisNeed third dimension for true symmetry!
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Twinning in diffractionExample: Co-Ni-Al shape memory FCC twins observed on [1 1 0] zone axis
Images provided by Barbora Bartová, CIME
(1 1 1) close-packed twin planes overlap in SADP
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Epitaxy and orientation relationshipsSADP excellent tool for studying
orientation relationships across interfaces
Example: Mn-doped ZnO on sapphire
Sapphire substrate Sapphire + film
Zone axes:[1 -1 0]ZnO // [0 -1 0]sapphire
Planes:c-planeZnO // c-planesapphire
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Ring diffraction patternsIf selected area aperture selects numerous, randomly-oriented nanocrystals,
SADP consists of rings sampling all possible diffracting planes- like powder X-ray diffraction
Example: “needles” of contaminant cubic MnZnO3 - which XRD failed to observe!
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Ring diffraction patternsLarger crystals => more “spotty” patterns
Example: ZnO nanocrystals ~20 nm in diameter
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XRD
• X-ray diffraction
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Laue Method
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Debeye-Scherrer
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X-ray tube
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Diffractometer
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“Transmission Electron Microscopy”, Williams & Carter, Plenum Press
http://www.doitpoms.ac.uk
“Transmission Electron Microscopy: Physics of Image Formation and Microanalysis (Springer Series in Optical Sciences)”, Reimer, Springer
Publishing
“Large-Angle Convergent-Beam Electron Diffraction Applications to Crystal Defects”, Morniroli, Taylor & Francis Publishing
References
http://crystals.ethz.ch/icsd - access to crystal structure file databaseCan download CIF file and import to JEMS
Web-based Electron Microscopy APplication Software (WebEMAPS)http://emaps.mrl.uiuc.edu/
JEMS Electron Microscopy Software Java versionhttp://cimewww.epfl.ch/people/stadelmann/jemsWebSite/jems.html
“Electron diffraction in the electron microscope”, J. W. Edington, Macmillan Publishers Ltd
http://escher.epfl.ch/eCrystallography
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Electron Microscopy
MSE-621 2013
1. Introduction, types of microscopes, some examples
2. Electron guns, Electron optics, Detectors
3. SEM, interaction volume, contrasts
4. Electron diffraction, X-ray diffraction
5. TEM, contrast, image formation
140
Shape, lattice parameters, defects, lattice planes
(K,Nb)O3Nano-rods
Bright field image
dark field image
Diffraction pattern
High-resolution image
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BaTiO3 nanocrystals (Psaltis lab)
Image formation
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Bright Field ImagingDiffraction Contrast
Au (nano-) particles on C film
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Bright Field / Dark Field
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Bend Contours /Bragg Contours
Bragg conditions change across the bent sample
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Twin lamellae in PbTiO3
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Ni based Superalloy
BF image DF image
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For interpretation of intensities in diffraction pattern, single scattering would be ideal
- i.e. “kinematical” scattering
However, in electron diffraction there is often multiple elastic scattering:
i.e. “dynamical” behaviour
This dynamical scattering has a high probability because a Bragg-scattered beam
is at the perfect angle to be Bragg-scattered again (and again...)
As a result, scattering of different beams is not independent from each other
Dynamical scattering
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Thickness Fringesextinction contours
Wedge shaped crystal GaAs/AlxGa1-xAs
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TEM dark field image g=(200)dyn
HRTEM zone axis [001] HRTEM zone axis [001]
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the TEM in “high-resolution” mode
A high-resolution image is an interference image of the transmitted and the diffracted beams!
Diffracted electrons: coherent elastic scattering(the electrons have seen the crystal lattice )
The quality of the image depends on the optical system that makes the beams interfere
Bright Field High-Resolution
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High resolution
• The image should resemble the atomic structure of the sample !
• Atoms…?Thin samples: atom columns: sample orientation (beam // atom columns)
• Contrast varies with sample thickness and defocus…!
• Comparison with simulation necessary !
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High-resolution TEM
Pb
Ti O
Pb
Ti
• K. Ishizuka (1980) “Contrast Transfer of Crystal Images in TEM”, Ultramicroscopy 5,pages 55-65.
• L. Reimer (1993) “Transmission Electron Microscopy”, Springer Verlag, Berlin.• J.C.H. Spence (1988), “Experimental High Resolution Electron Microscopy”, Oxford
University Press, New York.
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Scherzer-defocus: “black-atom” contrast
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Cu
O2
Hg Hg
“White-atom” contrast
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the TEM in “high-resolution” mode
A high-resolution image is an interference image of the transmitted and the diffracted beams!
Diffracted electrons: coherent elastic scattering(the electrons have seen the crystal lattice )
The quality of the image depends on the optical system that makes the beams interfere
Bright Field High-Resolution
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High resolution
• The image should resemble the atomic structure of the sample !
• Atoms…?Thin samples: atom columns: sample orientation (beam // atom columns)
• Contrast varies with sample thickness and defocus…!
• Comparison with simulation necessary !
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