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Suppose the first two layers of hexagonal closest
packed planes are stacked in "AB" fashion but the third layer is
positioned so that its atoms lie over the three grooves in the A layer
which were not covered by the atoms in the B layer. Then the third
layer is in a different orientation from either A or B and is labeled "C".
If a fourth layer then repeats the A layer orientation, and succeeding
layers repeat the pattern ABCABCA... = (ABC), the resulting unit cell is
hexagonal with three host atoms (Z = 3), unit cell edge c =
3.CPIS.r and c:a =
1.5.CPIS. Note that for identical atoms in all
layers, (ACB) is identical to (ABC).
 It can be shown that this
is a closest packed structure because the three host atoms occupy
74% of the total hexagonal unit cell volume. Furthermore, the standard
reduced cell in this array is as follows: choose the two central atoms in
the top and bottom "A" layers, and connect them to the six atoms shown in
the "B" and "C" layers . This unit cell is identical to the standard
reduced cell chosen for the face centered cubic lattice. Thus, the
(ABC) repeat structure is identical to the face centered cubic lattice
(CCP = FCC), with the stacking direction along the body diagonal of
the cubic unit cell.
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