1. Convergent-beam electron diffraction
Basics

4. In normal imaging mode, the illumination is approximately parallel and the contrast in the image comes from the fact that the electrons are scattered..

5. 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.

6. Image formation

7. A direction at the sample corresponds to a position at the diffraction pattern.
And vice versa.

8. Two kinds of scattering from crystalline specimens
Inelastic scattering which can go in any direction
Elastic scattering which can go only in specific directions.

9. Bragg’s Law

10. 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.

11. 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.

12. 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.

13. 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.

14. Specimen

15. 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

16. Pyrite [001] K-C Hsieh

17. Ni3Al [110] S. Court

18. FeS2 [110] K-C Hsieh

19. NbSe3

20. Quartz

21. InP [100] G. Rackham

22. Si [111]

23. Laves phase

24. Ni3Mo

25. Al/Ge

26. Si [111]

27. Si [111] Short camera length

28. Inelastic scattering in a spot pattern
Inelastic scattering goes in all directions.
It falls between the spots (and on top of the spots).

29. Inelastic scattering in CBED
The inelastically scattered electrons go in all directions.
Between the discs - and into the discs.

30. 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

32. 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.

33. Golden Rules Golden rule I: Start with something easy
Golden rule II: Take lots of pictures

34. 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.

35. 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

36. 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

37. Si [111]

38. Si [111] Off axis

39. Si [111] Short camera length

40. 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

42. 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

43. Si [111]

44. Si [111] Short camera length

45. Si [111]

46. Si [111] Short camera length

47. 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.

49. GaAs K. Christenson

50. Ni3Mo

51. Ni3Mo BF Tanaka pattern

52. Ni3Mo DF Tanaka pattern

53. 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,

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