File:Brillouin-zone construction by 300keV electrons.jpg

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Summary

Description
English: Selected area electron diffraction (SAED) pattern of a thick Si specimen with many diffusely-scattered 100keV electrons, and a beam direction nearly parallel to the Si<111> zone.

The λ ≈ 0.0370 Å electron-wavelength makes the radius 1/λ Ewald-sphere nearly planar on the scale of the inner-star radius g220 ≡ 1/d220 ≈ 1/1.92Å, and the beam half-angle facilitates weak excitation of many Bragg-reflections even though no reflections are at the Bragg-condition (where a Kikuchi-band in the star-pattern e.g. of width θscatt = 2θBragg = 2asin[λ/(2d220)] ≈ 19.2 mrad would have been shifted to intersect both the incident beam's central dot and a diffraction spot).

These electrons either had enough leptonic-imagination by themselves to construct the 2D Wigner-Seitz cell[1] (lattice-point bisectors) for this reciprocal-lattice slice, or else Brillouin-zone surfaces in a crystal are so real that they can be directly imaged. What do you think?
Date
Source Own work
Author P. Fraundorf

Footnotes

  1. J. M. Ziman (1972 2nd ed) Principles of the theory of solids (Cambridge U. Press, Cambridge UK).

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30 January 1974

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