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8.5: Zone Folding

  • Page ID
    7832
  • An important property of the Brillouin Zones is that, because the reciprocal lattice is periodic, there exists for any point outside the first zone a unique reciprocal lattice vector that will translate that point back inside the first zone. Each point in reciprocal space is only unique up to a reciprocal lattice vector. Each Zone contains every single physically distinguishable point, and so they all have the same area (in 2-D) or volume (in 3-D).

    This is easiest to see by example. The illustrations below will show how the first six zones for the 2-D square and hexagonal lattices can be translated or 'folded' back on top of the first zone.

    Example \(\PageIndex{1}\)

    2-D square Zone folding

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    Example \(\PageIndex{1}\)

    2-D hexagonal Zone folding

    clipboard_e542cbfdaf5057e4524dc04be3a554577.png

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