Bloch Waves

  • David B. Williams
  • C. Barry Carter


This topic is rather mathematical, with sequences of differential equations. The discussion of Bloch waves given here follows the treatment of Hirsch et al (1977) which, in turn, was based on the original analysis of electron diffraction by Bethe (1928). The notation we will use closely follows that used by Bethe. Remember that g can be any reciprocal lattice vector, although we will also use it to represent a specific vector.


Periodic Potential SchrOdinger Equation Schr6dinger Equation Bloch Wave Reciprocal Lattice Vector 
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General References

  1. Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics,W.B. Saunders Co., Philadelphia. Chapter 8 (27t/A, is used).Google Scholar
  2. Howie, A. (1971) in Electron Microscopy in Materials Science (Ed. U. Valdrè), p. 275, Academic Press, New York.Google Scholar
  3. Kittel, C.J. (1986) Solid-State Physics,6th edition, John Wiley and Sons, New York. Chapters 1, 10, and 11 are particularly relevant.Google Scholar
  4. Metherell, A.J.F. (1975) in Electron Microscopy in Materials Science, II (Eds. U. Valdrè and E. Ruedl), p. 397, CEC, Brussels. This is perhaps the clearest and most comprehensive article available on this subject (over 150 pages long).Google Scholar

Specific References

  1. Bethe, H.A. (1928) Ann. Phys. Lpz. 87, 55. In German.Google Scholar
  2. 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. Chapter 9.Google 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

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