Abstract
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.
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References
General References
Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics,W.B. Saunders Co., Philadelphia. Chapter 8 (27t/A, is used).
Howie, A. (1971) in Electron Microscopy in Materials Science (Ed. U. Valdrè), p. 275, Academic Press, New York.
Kittel, C.J. (1986) Solid-State Physics,6th edition, John Wiley and Sons, New York. Chapters 1, 10, and 11 are particularly relevant.
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).
Specific References
Bethe, H.A. (1928) Ann. Phys. Lpz. 87, 55. In German.
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.
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Williams, D.B., Carter, C.B. (1996). Bloch Waves. In: Transmission Electron Microscopy. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2519-3_14
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DOI: https://doi.org/10.1007/978-1-4757-2519-3_14
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