Cubic Closest Packing
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).
(crossed stereo pair)
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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