The packing efficiency of spheres in a crystal is the percentage of the space occupied by the spheres. Calculate the packing efficiencies of the simple cubic, body-centered cubic, and face-centered cubic cells. Hint: The volume of a sphere is 4 πr^3 / 3. Use the number of spheres contained in each unit cell and determine the lengths of the sides of the unit cells from the spheres that are in contact with each other (edge of cube, body diagonal of body-centered, face diagonal of face-centered). |
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