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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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