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Convergent-beam electron diffraction

Basics

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PASI Santiago, Chile July 20063Eades / Convergent-Beam Diffraction: I

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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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S p ec im en

L en s

D iffrac tio n P a tte rn(B ac k F o c a l P lan e )

Im ag e

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

sin2d

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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

PASI Santiago, Chile July 200617Eades / Convergent-Beam Diffraction: I

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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PASI Santiago, Chile July 200632Eades / Convergent-Beam Diffraction: I

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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PASI Santiago, Chile July 200642Eades / Convergent-Beam Diffraction: I

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

PASI Santiago, Chile July 200645Eades / Convergent-Beam Diffraction: I

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

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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 33 1986 54-66

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 313-359

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'

J. A. Eades

EUREM 88; IOP Conf. Series 93 (1988) Vol. 1, 3-12

'Glide Planes and Screw Axes in Convergent-beam Diffraction: The Standard Procedure'

J. A. Eades

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. A. Eades

J. Electron Microscopy Technique (1984) 1, 279-284.

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Acknowledgment

The convergent beam patterns used for this talk have been stolen from many different people especially the Bristol Group.