Show that the packing efficiency of the face-centered cubic structure is actually 74%, as we have claimed.

Strategy This is essentially a geometry problem, and it requires us to understand the location of and spacing between the atoms in the fcc lattice. To find the packing efficiency, we’ll need to compare the volume of the atoms in the fcc unit cell and the volume of the cell itself. It should help if we start with a good diagram of the structure. We’ll start with the unit cell but will also use a simpler diagram of a single face of the cube because threedimensional crystal structures can be challenging to draw and interpret.