Primitive Hexagonal
In a plane, spheres of equal size are
most densely packed (with the least amount of empty space) when each sphere
touches six other spheres arranged in the form of a regular hexagon.
(crossed stereo pair)
When two such hexagonally closest packed
planes are stacked directly on top of one another, a primitive hexagonal
array results.
(crossed stereo pair)
The primitive unit cell, outlined in black
in the crossed stereo pair above, has cell edges
a = b = 2r and c = 2r.
Thus, the ratio c:a = 1, and it can be shown that the packing efficiency
of this three dimensional lattice is only about 60% (compared to 74% for
closest packing), even though the atoms are closest packed in two
dimensions.
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