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PASI Santiago, Chile July 20061Eades / Convergent-Beam Diffraction: II
Convergent-beam electron diffraction
Applications
PASI Santiago, Chile July 20062Eades / Convergent-Beam Diffraction: II
Bragg’s Law
sin2d
PASI Santiago, Chile July 20063Eades / Convergent-Beam Diffraction: II
Applications - in common with spot patterns
• 1 Lattice spacings
• 2 Unit cell
• 3 Orientation
PASI Santiago, Chile July 20064Eades / Convergent-Beam Diffraction: II
Applications - special to CBEDEstablished
• 1 Crystal symmetry
• 2 Local strain
• 3 Direct phase identification
• 4 Thickness
PASI Santiago, Chile July 20065Eades / Convergent-Beam Diffraction: II
Applications - special to CBEDAdvanced
• 1 Crystal structure determination
• 2 Bonding measurement
• 3 Phase determination
• 4 Improved defect analysis
PASI Santiago, Chile July 20066Eades / Convergent-Beam Diffraction: II
Advanced Techniques
• The Tanaka methods– The techniques
• LACBED
• Other variations (CBIM, SA-CBED)
– Applications• Spatial variation
• Defect analysis
• Other Techniques– Coherent CBED– Energy filtering
PASI Santiago, Chile July 20067Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 20068Eades / Convergent-Beam Diffraction: II
FeS2 [110] K-C Hsieh
PASI Santiago, Chile July 20069Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200610Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200611Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200612Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200613Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200614Eades / Convergent-Beam Diffraction: II
Pyrite [001] K-C Hsieh
PASI Santiago, Chile July 200615Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200616Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200617Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200618Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200619Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200620Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200621Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200622Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200623Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200624Eades / Convergent-Beam Diffraction: II
V3Si Doug Konitzer
PASI Santiago, Chile July 200625Eades / Convergent-Beam Diffraction: II
InP [100] G. Rackham
PASI Santiago, Chile July 200626Eades / Convergent-Beam Diffraction: II
M23C6 [110]
PASI Santiago, Chile July 200627Eades / Convergent-Beam Diffraction: II
Ni3Al [110] S. Court
PASI Santiago, Chile July 200628Eades / Convergent-Beam Diffraction: II
Ni3Al [110] S. Court
PASI Santiago, Chile July 200629Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200630Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200631Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200632Eades / Convergent-Beam Diffraction: II
PASI Santiago, Chile July 200633Eades / Convergent-Beam Diffraction: II
Crystal Structure
• The phase problem
• Crystal structure determination
• Bonding measurement
PASI Santiago, Chile July 200634Eades / Convergent-Beam Diffraction: II
Crystal Potential
)2exp()( rg g.gr iVV
PASI Santiago, Chile July 200635Eades / Convergent-Beam Diffraction: II
• 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.
PASI Santiago, Chile July 200636Eades / Convergent-Beam Diffraction: II
Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13
PASI Santiago, Chile July 200637Eades / Convergent-Beam Diffraction: II
Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13
PASI Santiago, Chile July 200638Eades / Convergent-Beam Diffraction: II
Tanaka, Terauchi, Tsuda and Saitoh CBED IV 2002
PASI Santiago, Chile July 200639Eades / Convergent-Beam Diffraction: II
Tanaka, Terauchi and Tsuda CBED III 1994
PASI Santiago, Chile July 200640Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200641Eades / Convergent-Beam Diffraction: II
S p ec im e n S p ec im e n S p ec im e n
PASI Santiago, Chile July 200642Eades / Convergent-Beam Diffraction: II
GaAs [100] K. Christenson
PASI Santiago, Chile July 200643Eades / Convergent-Beam Diffraction: II
Ni3Mo
PASI Santiago, Chile July 200644Eades / Convergent-Beam Diffraction: II
Ni3Mo BF Tanaka pattern
PASI Santiago, Chile July 200645Eades / Convergent-Beam Diffraction: II
Al layer on GaAs Tanaka Group
PASI Santiago, Chile July 200646Eades / Convergent-Beam Diffraction: II
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.
PASI Santiago, Chile July 200647Eades / Convergent-Beam Diffraction: II
Fe,30Ni,19Cr [114] Cherns and Preston
PASI Santiago, Chile July 200648Eades / Convergent-Beam Diffraction: II
Fe,30Ni,19Cr [114] Cherns and Preston
PASI Santiago, Chile July 200649Eades / Convergent-Beam Diffraction: II
Fe,30Ni,19Cr [114] Cherns and Preston
PASI Santiago, Chile July 200650Eades / Convergent-Beam Diffraction: II
Si Tanaka Group
PASI Santiago, Chile July 200651Eades / Convergent-Beam Diffraction: II
• 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.