Convergent-beam electron diffraction
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Transcript Convergent-beam electron diffraction
Convergent-beam electron
diffraction
Applications
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Bragg’s Law
2d sin
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Applications - in common with
spot patterns
• 1 Lattice spacings
• 2 Unit cell
• 3 Orientation
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Applications - special to CBED
Established
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Crystal symmetry
Local strain
Direct phase identification
Thickness
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Applications - special to CBED
Advanced
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1 Crystal structure determination
2 Bonding measurement
3 Phase determination
4 Improved defect analysis
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Advanced Techniques
• The Tanaka methods
– The techniques
• LACBED
• Other variations (CBIM, SA-CBED)
– Applications
• Spatial variation
• Defect analysis
• Other Techniques
– Coherent CBED
– Energy filtering
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Lattice Spacings
The lattice spacing is determined from the
distance between the diffracted beams.
In spot patterns it is the distance between
spots. In convergent-beam patterns it is the
distance between discs.
These are generally equally accurate.
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FeS2 [110]
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K-C Hsieh
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Unit Cell Determination
If a very short camera length is used, the unit
cell can be determined, in principle, from a
single diffraction pattern.
In practice this may be tricky.
The centering of the Bravais lattice can be
easily obtained at a suitable zone axis.
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Orientation
If the diffraction pattern is indexed, the
orientation of the sample is determined.
A selected area pattern can determine the
orientation to within a few degrees.
In convergent-beam diffraction additional
information, from details in the discs or
from Kikuchi lines, gives the result to a
fraction of a degree.
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Symmetry
The determination of the symmetry of a
crystalline specimen is one of the most
powerful applications of convergent-beam
diffraction. It is valuable both to identify
known phases and to determine the
symmetry of new phases.
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Pyrite [001] K-C Hsieh
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Strain from HOLZ lines
• Limitations
– The strain must be uniform through the
thickness of the specimen.
– The result is for the strain in the thin foil - not
the strain in the original sample.
– Results are relative not absolute without
dynamical calculation.
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Phase Identification
• All convergent-beam zone axis patterns are
unique and serve to identify phases.
• You must educate your eye.
• Limitations
– The patterns do change with thickness
– The uniqueness is not absolute.
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V3Si Doug Konitzer
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InP [100] G. Rackham
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M23C6 [110]
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Ni3Al [110]
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S. Court
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Ni3Al [110]
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S. Court
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Thickness
• The method uses two-beam conditions.
• Some care must be taken in the analysis.
• The thickness is for the crystalline part of
the sample only.
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Crystal Structure
• The phase problem
• Crystal structure determination
• Bonding measurement
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Crystal Potential
V (r) Vg exp(2ig.r)
g
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• Because of the complex interference
between diffracted beams in dynamical
electron diffraction, electron diffraction
intensities are very sensitive to small
changes in Vg.
• Electron diffraction can thus determine
bonding electron densities - but the
calculations are complicated.
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Midgley, Saunders, Vincent and Steeds
Ultramicroscopy 59 (1995) 1-13
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Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13
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Tanaka, Terauchi, Tsuda and Saitoh
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CBED IV 2002
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Tanaka, Terauchi and Tsuda
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CBED III
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1994
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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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Specimen
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GaAs [100] K. Christenson
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Ni3Mo
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Ni3Mo BF Tanaka pattern
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Al layer on GaAs Tanaka Group
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Defect Analysis
• Large-Angle Convergent-Beam patterns
provide an improved method of
determining the Burgers vectors of
dislocations. (And characterizing other
defects.)
• The dislocations have to be well separated.
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Fe,30Ni,19Cr [114] Cherns and Preston
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Fe,30Ni,19Cr [114] Cherns and Preston
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Fe,30Ni,19Cr [114] Cherns and Preston
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Si Tanaka Group
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• My apologies to those whose pictures are
not acknowledged because I do not
remember where they came from.
• All the Ni3Mo pictures are Mike Kaufman’s
work.
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