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Crystal packing

  1. Aug 23, 2007 #1


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    1. The problem statement, all variables and given/known data

    Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the Hexagonal structure

    Relevant eq: Volume of spheres is number of lattice points multiplied with the maximum volume of one sphere.

    3. The attempt at a solution

    I know maxium is obtained when c = a i.e when height of the cell is as high as one of the sides in the hexagon. Hence, maximum sphere radius is a/2 (I have shown geometrically that the spheres can touch eachother).

    Now I am to determine the number of lattice points in this structure, I know that one primitive cell contains totally one lattice point, and a unit cell of a hexagonal structure can be made up by exactly three primitve cells, so the number of lattice points is 3. Is that the correct way to do this?

    The rest I can figure out by my self, just are unsure how to determine the number of lattice points.
  2. jcsd
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