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Calculating Packing Efficiency
It is not possible to pack spheres together without leaving some void spaces between the spheres. Packing efficiency is the fraction of space in a crystal that is actually occupied by atoms. Determine the packing efficiency of a face-centered cubic metal.
Consider the two-dimensional square lattice of Figure 12.4. The “packing efficiency” for a two-dimensional structure would be the area of the atoms divided by the area of the unit cell, times 100%. What is the packing efficiency for a square lattice for atoms of radius a/2 that are centered at the lattice points? (a) 3.14% (b) 15.7% (c) 31.8% (d) 74.0% (e) 78.5%
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