Abstract
This topic is rather mathematical, with long sequences of differential equations. The discussion of Bloch waves given here follows the treatment of Hirsch et al. 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
This chapter follows the treatment given by Hirsch et al. in Chapter 9 of their classic text; the details are provided by Metherell.
Bloch Waves
Ashcroft, NW and Mermin, ND 1976 Solid State Physics W.B. Saunders Co. Philadelphia PA. Chapter 8 (2π/λ is used).
Bethe, HA 1928 Theorie der Beugung von Elektronen an Kristallen Ann. Phys. Lpz. 87 55–129. Another classic reference (in German).
Howie, A 1971 in Electron Microscopy in Materials Science 275–305 Ed. U Valdré Academic Press New York.
Kittel, CJ 2004 Solid-State Physics 8th Ed. John Wiley & Sons New York. For the physicists.
Metherell, AJF 1975 in Electron Microscopy in Materials Science II 397–552 Eds. U Valdré and E Ruedl CEC, Brussels. This is perhaps the clearest and most comprehensive article available on this subject (over 150 pages long). It is strongly recommended reading if you’ve made it through this chapter and want to begin programming.
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Williams, D.B., Carter, C.B. (2009). Bloch Waves. In: Transmission Electron Microscopy. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76501-3_14
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DOI: https://doi.org/10.1007/978-0-387-76501-3_14
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