convergent-beam electron diffraction

$: Convergent-beam electron diffraction$
PASI Santiago, Chile July 20061Eades / Convergent-Beam Diffraction: II

Convergent-beam electron diffraction

Applications


Bragg’s Law

sin2d


Applications - in common with spot patterns

• 1 Lattice spacings

• 2 Unit cell

• 3 Orientation


Applications - special to CBEDEstablished

• 1 Crystal symmetry

• 2 Local strain

• 3 Direct phase identification

• 4 Thickness


Applications - special to CBEDAdvanced

• 1 Crystal structure determination

• 2 Bonding measurement

• 3 Phase determination

• 4 Improved defect analysis


Advanced Techniques

• The Tanaka methods– The techniques

• LACBED

• Other variations (CBIM, SA-CBED)

– Applications• Spatial variation

• Defect analysis

• Other Techniques– Coherent CBED– Energy filtering


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.


FeS2 [110] K-C Hsieh


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.


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.


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.


Pyrite [001] K-C Hsieh


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.


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.


V3Si Doug Konitzer


InP [100] G. Rackham


M23C6 [110]


Ni3Al [110] S. Court


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.


Crystal Structure

• The phase problem

• Crystal structure determination

• Bonding measurement


Crystal Potential

)2exp()( rg g.gr iVV


• 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.


Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13


Tanaka, Terauchi, Tsuda and Saitoh CBED IV 2002


Tanaka, Terauchi and Tsuda CBED III 1994


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.


S p ec im e n S p ec im e n S p ec im e n


GaAs [100] K. Christenson


Ni3Mo


Ni3Mo BF Tanaka pattern


Al layer on GaAs Tanaka Group


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.


Fe,30Ni,19Cr [114] Cherns and Preston


Si Tanaka Group


• 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.

convergent-beam electron diffraction

Documents