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Atoms - Packing fraction

  1. Nov 23, 2008 #1
    In a simple cubic arrangement the atoms sit at the corners of imaginary cubes with their curved surfaces just touching. Show that the ratio of filled space to empty space between the atoms is pi/6 or about 0.5. This "packing fraction" is related to the density of the material. The volume of a sphere of radius r is 4/3 pi r³.

    If the atoms in the simple cubic arrangement in part A have diameter d, show that largest impurity atom that can just fit in between the host atoms has a diameter of 0.4d.

    Please Help! I don't understand how to approach this Question!!
  2. jcsd
  3. Nov 24, 2008 #2


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    This is really just about calculating volumes. If there are 8 spheres at the corner of a cube what fraction of the volume of each sphere is in the cube. Compare that to the volume of the cube.
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