The hexagonal close-packed
(hcp) structure is one of the most common and
important crystal structures adopted by metals
and other atomic solids. Despite its
prominence in nature, the hcp structure has
not been treated at the same level of geometric
rigor as the common cubic structures. The
illustrations of the hcp unit cell that are
used in textbooks at all levels and also in
crystallography and solid state reference works
are incomplete, in that they fail to include
fractions of middle layer atomic spheres with
centers lying outside of the unit cell. These
fractions are necessary to properly determine
the number of atoms enclosed in the unit cell. Though
it seems unlikely that the middle layer fractions
of atomic spheres have not been previously
determined, we have found no evidence of this
in our survey of textbooks and reference works. We
have shown how these fractions may be determined
using the solids of revolution method and have
prepared animated 3D ‘cutaway’ computer
models and templates for paper and glue models
to more accurately illustrate the hcp unit
cell.
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Filling in the
Hexagonal Close-Packed Unit Cell