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Nearest Neighbors in solid state, but with basis

  1. Jan 27, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the area of the primitive cell for the lattice shown below? The nearest neighbor separation is "a."

    2. Relevant equations
    Here's the lattice we were given on our handout, and I have added the lines to indicate the square lattice (in red), the basis (in purple), and lattice points (circled in blue). Another potential basis is in green.

    3. The attempt at a solution
    Is the "nearest neighbor" any atom in the crystal, or is it only referring to lattice point-related neighbors?

    If any atom (not necessarily lattice points) counts as a nearest neighbor, then the primitive cell has area 8a2.

    If it's only between lattice points, then the area would be a2.

    Any text I refer to (I've looked at 4) only talk about nearest neighbors in terms of lattices without a basis. (For example, the SC lattice has 6 nearest neighbors, etc). But they never seem to indicate what the case might be when you have a basis...
  2. jcsd
  3. Jan 27, 2016 #2


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    2017 Award

    Staff: Mentor

    Lattice-point-related neighbors only. For the overall crystal structure, the inner details of a cell do not matter.
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