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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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SOLVED:Close packing of spheres in two dimensions can be achieved by arranging them in sheets as shown by the spheres labeled A in the first diagram shown. Close packing in three dimensions can be achieved by stacking these sheets so that each atom "rests" in the "hollows" formed by three atoms in the sheet below. Frequently encountered close packed arrangements are hexagonal close packed (ABAB sequence) and cubic close packed (ABCABC sequence), where A, B, and C indicate the different registrie
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