Diffracted Beams

  • David B. Williams
  • C. Barry Carter


In Chapter 11 we discussed why diffraction occurs; in this chapter we give a more detailed mathematical treatment. It may be more detail than you need at this stage. Diffraction is one of those phenomena which lends itself directly to a detailed mathematical modeling, but there is a danger: don’t become so engrossed in the math that you miss the principles involved; conversely, don’t ignore the subject because it is mathematically daunting!The topic of this chapter is one which causes major problems for many microscopists. The treatment we will follow is known as the “dynamical theory.” Later we will make some gross simplifications, partly because this is instructive, and partly because these simplifications do apply to some important special cases; the kinematical approximation is one such simplification. Many other texts begin with the so-called “kinematical” treatment and then advance to the dynamical case. We will not do this but we will introduce the words and assumptions elsewhere.


Direct Beam Diffract Beam Fresnel Zone Bloch Wave Diffraction Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


General References

  1. Hirsch, P.B., Howie, A., Nicholson, R.B., Pashley, D.W., and Whelan, M.J. (1977) Electron Microscopy of Thin Crystals, 2nd edition, Krieger, Huntington, New York.Google Scholar

Specific References

  1. Darwin, C.G. (1914) Phil. Mag. 27, 315 and 675.Google Scholar
  2. Hecht, E. (1987) Optics, 2nd edition, Addison-Wesley, Reading, Massachusetts.Google Scholar
  3. Howie, A. and Whelan, M.J. (1961) Proc. Roy. Soc. A263, 217.CrossRefGoogle Scholar
  4. Howie, A. and Basinski, Z.S. (1968) Phil. Mag. 17, 1039.CrossRefGoogle Scholar
  5. Spence, J.C.H. (1988) Experimental High-Resolution Electron Microscopy, p. 155, Oxford University Press, New York.Google Scholar
  6. Takagi, S. (1962) Acta Cryst. 15, 1311.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • David B. Williams
    • 1
  • C. Barry Carter
    • 2
  1. 1.Lehigh UniversityBethlehemUSA
  2. 2.University of MinnesotaMinneapolisUSA

Personalised recommendations