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**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

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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

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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] S. Court

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FeS2 [110] 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 Pattern from small region of sample**

2 Pattern from well defined area 3 Better Kikuchi lines 4 More accurate orientation 5 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 convergent-beam 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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GaAs K. Christenson

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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 The other major group on convergent-beam diffraction is the group of Michiyoshi Tanaka at Sendai, Japan. They have produced a series of excellent books: Convergent-Beam Electron Diffraction M. Tanaka and M. Terauchi JEOL, Tokyo, 1985 Convergent-Beam Electron Diffraction II M. Tanaka, M. Terauchi and T. Kaneyama JEOL, Tokyo, 1988 Convergent-Beam Electron Diffraction III M. Tanaka, M. Terauchi and K. Tsuda JEOL, Tokyo, 1994 Convergent-Beam Electron Diffraction IV M. Tanaka, M. Terauchi, K. Tsuda and K. Saitoh JEOL, Tokyo, 2002 Review article on the basics: Convergent-Beam Diffraction J. A. Eades A chapter in "Electron Diffraction Techniques Volume 1", ed. J. M. Cowley, International Union of Crystallography and Oxford University Press(Oxford) 1992 pp This two-volume set make a very good place to start on all electron diffraction topics. References The books listed above contain many detailed references to research papers. I would draw attention to three tutorial papers of my own, which try to provide a clear introduction to some topics: Symmetry determination: 'Symmetry Determination by Convergent-beam Diffraction' EUREM 88; IOP Conf. Series 93 (1988) Vol. 1, 3-12 'Glide Planes and Screw Axes in Convergent-beam Diffraction: The Standard Procedure' Microbeam Analysis 1988 (D. E. Newbury Ed.) (1988) 75-80 The Tanaka method (though, of course, there is a lot on this topic in his books): 'Zone-Axis Patterns by the 'Tanaka' Method' J. Electron Microscopy Technique (1984) 1,

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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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