PASI Santiago, Chile July 2006 1 Eades / Convergent-Beam Diffraction: II Convergent-beam electron diffraction Applications.

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References on convergent-beam diffraction. Contents: General book Specific topics I Specific topics II Eades articles.

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

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Bragg’s Law

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Applications - in common with spot patterns 1Lattice spacings 2Unit cell 3Orientation

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Applications - special to CBED Established 1Crystal symmetry 2Local strain 3Direct phase identification 4Thickness

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Applications - special to CBED Advanced 1 Crystal structure determination 2Bonding measurement 3Phase determination 4Improved defect analysis

PASI Santiago, Chile July Eades / 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 Eades / 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 Eades / Convergent-Beam Diffraction: II FeS2 [110] K-C Hsieh

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / 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 Eades / 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 Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Pyrite [001] K-C Hsieh

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II V 3 Si Doug Konitzer

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II InP [100] G. Rackham

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II M 23 C 6 [110]

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Ni 3 Al [110] S. Court

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Ni 3 Al [110] S. Court

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Crystal Structure The phase problem Crystal structure determination Bonding measurement

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Crystal Potential

PASI Santiago, Chile July Eades / 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 V g. Electron diffraction can thus determine bonding electron densities - but the calculations are complicated.

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Midgley, Saunders, Vincent and Steeds Ultramicroscopy 59 (1995) 1-13

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Tanaka, Terauchi, Tsuda and Saitoh CBED IV 2002

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Tanaka, Terauchi and Tsuda CBED III 1994

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II GaAs [100] K. Christenson

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Ni 3 Mo

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Ni3Mo BF Tanaka pattern

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Al layer on GaAs Tanaka Group

PASI Santiago, Chile July Eades / 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 Eades / Convergent-Beam Diffraction: II Fe,30Ni,19Cr [114] Cherns and Preston

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Fe,30Ni,19Cr [114] Cherns and Preston

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Fe,30Ni,19Cr [114] Cherns and Preston

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II Si Tanaka Group

PASI Santiago, Chile July Eades / Convergent-Beam Diffraction: II My apologies to those whose pictures are not acknowledged because I do not remember where they came from. All the Ni 3 Mo pictures are Mike Kaufman’s work.