Using Convergent-Beam Techniques

  • David B. Williams
  • C. Barry Carter


In the preceding chapter, we described how to obtain a variety of CBED patterns under various experimental conditions. In this chapter you will find out why these patterns are so useful: they contain a wealth of quantitative data, much of which you can’t obtain by any other technique and many of which augment standard X-ray crystallographic methods (but always at higher spatial resolution). The established techniques largely depend on simple observation of the patterns whereas newer techniques involve quantitative simulations of the patterns.


Point Group Mirror Plane Convergent Beam Electron Diffraction Thickness Determination Ewald Sphere 
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  1. By Tanaka, M et al, 1985-2002 Convergent Beam Electron Diffraction I-IV JEOL Tokyo. The details are in Chapter 20.Google Scholar


  1. Eades, JA 1989 (Ed.) Journal of Electron Microscopy Techniques 13 (I & II). Special issues on CBED with many useful papers covering much of the content of this chapter.Google Scholar
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  3. Mansfield, JF 1984 Convergent Beam Electron Diffraction of Alloy Phases Adam Hilger Ltd. Bristol UK. A great collection of CBED patterns and proof that steel can still be beautiful.Google Scholar
  4. Morniroli, J-P 2002 Large-Angle Convergent-Beam Electron Diffraction (LACBED) SFμ. (Société Française des Microcopies) Paris, France. The essential instructional text full of great diagrams and practical examples along with an excellent bibliographyGoogle Scholar
  5. Spence, JCH and Zuo, JM 1992 Convergent Beam Electron Diffraction Plenum Press New York. You will want a copy of this book if you use CBED extensively. You may find a reference to earlier CBED studies on your material here in the selective bibliography organized by material. Although now considered obsolete by some, the original code for plotting HOLZ lines is included in the appendices along with the Fortran code for one Bloch wave and one multislice program.Google Scholar

Thickness Determination

  1. Allen, SM 1981 Foil Thickness Measurements from Convergent-Beam Diffraction Patterns Phil. Mag. A43 325–335.Google Scholar
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  1. Eades, JA, Moore, S, Pfullman, T and Hangas, J 1993 Discrepancies in Kinematic Calculations of HOLZ Lines Microscopy Research and Technique 24 509–513. The importance of dynamical scattering for HOLZ line calculations.Google Scholar
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Indexing and Lattice Parameters

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  3. Morawiec, A 2007 A Program for Refinement of Lattice Parameters Based on Multiple Convergent-Beam Electron Diffraction Patterns J. Appl. Cryst. 40 618–622.Google Scholar
  4. Rozeveld, SJ and Howe, JM 1993 Determination of Multiple Lattice Parameters from Convergent-Beam Electron Diffraction Patterns Ultramicrosc. 50 41–56.Google Scholar


  1. Spackman, MA, Jiang, B, Groy, TL, He, H, Whitten, AE and Spence, JCH 2005 Phase Measurement for Accurate Mapping of Chemical Bonds in Acentric Space Groups Phys. Rev. Lett. 95 085502–05. Inversion symmetry.Google Scholar
  2. Zuo, JM, Kim, M, O’Keeffe, M and Spence, JCH 1999 Direct Observation of d-Orbital Holes and Cu-Cu Bonding in Cu2O Nature 401 49–52. ‘Imaging’ atomic orbitalsGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.The University of Alabama in HuntsvilleHuntsvilleUSA
  2. 2.University of ConnecticutStorrsUSA

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