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Engineering LibreTexts

20.6: Summary

  • Page ID
    8302
  • Following completion of this TLP you should understand what a reciprocal lattice is, and how it is constructed. You should understand that the Ewald sphere is a geometric tool to find reflections and angles that satisfy the Bragg equation. Thus it is used to set up diffraction experiments and interpret the data. The package has also shown how reciprocal vectors are important in understanding periodic structures and diffraction, which have a reciprocal nature.

    Going further

    Books

    Reciprocal space is described in most Crystallography books. For example:

    • C. Hammond, The Basics of Crystallography and Diffraction, 2nd edition, OUP, 2001
    • B. D. Cullity and S. R. Stock, Elements of X-ray Diffraction, 3rd edition, Prentice Hall, 2001
    • Eds F H Chung and D K Smith Industrial Applications of X-ray Diffraction 2000 has a chapter on history of Rolls Royce on-line Laue system

    Websites

    • Matter has an interactive tutorial on the reciprocal lattice and Ewald sphere.
    • A tutorial on reciprocal space by the Universities of Munich and Würzburg.
    • Indexing Electron Diffraction Patterns TLP uses reciprocal space to relate the diffraction pattern to real space.
    • Brillouin Zones, an important tool in solid state physics, are also worked in reciprocal space.
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