Transcript Convergent-beam electron diffraction

Convergent-beam electron
diffraction
Basics
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• In normal imaging mode, the illumination is
approximately parallel and the contrast in
the image comes from the fact that the
electrons are scattered..
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• Electrons which leave the specimen in the
same direction come to the same point in
the diffraction pattern.
• Conversely, electrons which travel in the
same direction at the diffraction pattern
come from the same place on the sample
and go to the same place in the image.
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Image formation
Specimen
Lens
Diffraction Pattern
(Back Focal Plane)
Image
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• A direction at the sample corresponds to a
position at the diffraction pattern.
• And vice versa.
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Two kinds of scattering from
crystalline specimens
• Inelastic scattering which can go in any
direction
• Elastic scattering which can go only in
specific directions.
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• Bragg’s Law
2d sin   
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• An electron after scattering is going in a
direction which is 2 away from the
direction it had before the scattering.
• 2 in a direction perpendicular to the planes
which diffract.
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• In convergent-beam diffraction, we do not
use parallel illumination.
• We focus the electrons so that they form a
focussed probe at the specimen.
• At the sample, the electrons are travelling in
a range of directions inside a cone.
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Convergent-beam with no sample
• The electrons in each different direction, in
the illumination cone, come to a different
place in the diffraction pattern.
• Since the directions in the cone of
illumination fill the cone, the electrons in
the diffraction pattern fill a circle.
• In the diffraction pattern there is a bright
disc.
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With a specimen
• The electrons are scattered though 2.
• Electrons are scattered from all the
directions in the convergent conical
illumination.
• Each point in the direct beam disc is one
direction of illumination so each point in
the disc can be scattered by the same 2.
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Specimen
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• Therefore the diffracted electrons also form
a disc.
• A convergent-beam pattern has an array of
discs - one for each Bragg reflection.
• For every spot in a diffraction pattern with
parallel illumination, there will be a disc in
the convergent-beam pattern
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Pyrite [001] K-C Hsieh
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Ni3Al [110]
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S. Court
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FeS2 [110]
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K-C Hsieh
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NbSe3
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Quartz
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InP [100] G. Rackham
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Si [111]
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Laves phase
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Ni3Mo
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Al/Ge
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Si [111]
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Si [111] Short camera length
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Inelastic scattering in a spot
pattern
• Inelastic scattering goes in all directions.
• It falls between the spots (and on top of the
spots).
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Inelastic scattering in CBED
• The inelastically scattered electrons go in
all directions.
• Between the discs - and into the discs.
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Advantages of CBED
1
2
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4
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Pattern from small region of sample
Pattern from well defined area
Better Kikuchi lines
More accurate orientation
Easy to track tilting
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Disadvantages
• 1 Weak reflections harder to see
• 2 Does not show diffuse scatter.
For example, from disordered materials
• 3 Not good for powder patterns – ring
patterns.
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Golden Rules
• Golden rule I:
Start with something easy
• Golden rule II: Take lots of pictures
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Practical details
• 1 Use a large spot size for tilting and set
up. Go to a small spot size only just before
taking the picture.
• 2 Choose a condenser aperture size to
give the convergence angle that you want.
• 3 In many cases, the ideal convergence is
that which makes the discs just touch.
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Conclusion
• There is every reason to use convergentbeam diffraction as the standard form of
diffraction.
• Only use selected-area diffraction for:
– checking for weak reflections
– looking for structure in the diffuse scatter
– for ring patterns
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Zone Axes
• A zone axis is a direction in a crystal that is
parallel to more than one set of planes
• At a zone-axis orientation, the electron
beam travels down rows of atoms
• At a zone-axis orientation, the diffraction
pattern consists of a regular net of spots or
discs
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Si [111]
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Si [111] Off axis
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Si [111] Short camera length
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Laue Zones
• At a zone-axis orientation, the reflections in
the diffraction pattern break up into zones
called Laue zones
• The central zone is called the zero-order
Laue zone
• The first ring is called the first-order Laue
zone - and so on
• The first-order, second-order, third order
(and so on) are known collectively as the
higher-order Laue zones
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HOLZ
• HOLZ is the acronym for higher-order Laue
zone
• The rings of reflections outside the central,
zero-order Laue zone are the HOLZ
• Because the narrow, dark, straight lines in
the bright field disc are associated with
diffraction into a HOLZ reflection, they are
known as HOLZ lines
• Do not confuse HOLZ with HOLZ lines
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Si [111]
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Si [111] Short camera length
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Si [111]
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Si [111] Short camera length
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The Tanaka Methods
• Traditional microscopy taught that the
microscope should be focussed on the
specimen or on the diffraction pattern in the
back focal plane.
• Tanaka liberated us and gave rise to a
family of new techniques by telling us to
look in other places.
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Specimen
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Specimen
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GaAs
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Ni3Mo
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Ni3Mo BF Tanaka pattern
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Ni3Mo DF Tanaka pattern
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References on convergent-beam diffraction
General book
There is good basic information in
Transmission Electron Microscopy
D. B. Williams and C. B. Carter
Plenum New York, 1996
Specific topics
More detailed information on specific topics is to be found in:
Electron Microdiffraction
J. C, H. Spence and J. M. Zuo
Plenum, New York, 1992
Large-Angle Convergent-Beam Electron Diffraction (LACBED)
J-P Morniroli
Societe Francaise des Microscopies, Paris, 2002
The atlas of convergent beam patterns from Bristol is:
Convergent Beam Electron Diffraction of Alloy Phases
The Bristol Group (Compiled by J. Mansfield)
Adam Hilger, Bristol, 1984
and the supplement (which includes an erratum list for the book) is
The Library of Convergent Beam Electron Diffraction Update: No 1.
J. F. Mansfield, Y. P. Lin and R. J. Graham
Norelco Reporter: Electron Optics 33 1986 54-66
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Acknowledgment
The convergent beam patterns used for this
talk have been stolen from many different
people especially the Bristol Group.
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