Hexagonal Closest Packing

Instead of stacking hexagonal closest packed planes directly above one another, they can be stacked such that atoms in successive planes nestle in the triangular "grooves" of the adjacent plane. (note that there are six of these "grooves" surrounding each atom in the hexagonal plane, but only three of them can be covered by atoms in the adjacent plane).

(crossed stereo pair)

Let the first plane (at the bottom) be labeled "A" and the next plane above it be labeled "B". If a third hexagonal closest packed plane is stacked above B but in the "A" orientation, and succeeding planes are stacked in the repeating pattern ABABA... = (AB), a hexagonal unit cell can be chosen (using the nine atoms labeled "h"), with Z = 2.

(crossed stereo pair)

For the stack of hexagonally closest packed spheres of equal radius (r) described above, the interplanar spacing between adjacent planes is proportional to r. The proportionality constant is an irrational number called the Closest Packed Interlayer Spacing, CPIS, and its value is about 1.6. Thus, the interlayer spacing is about 1.6^.r (compared to 2^.r for simple hexagonal stacking).

Thus, the "c" unit cell edge (in the stacking direction) has a length c = 2^.CPIS^.r, the ratio c:a = CPIS, and it can be shown that this lattice has a packing efficiency which is identical to the FCC lattice. Thus, the name Hexagonal Closest Packing (HCP) for this array is justified.

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