Polymorf - Knowhwere- FCC packing

Face centered cubic packing (FCC)

In contrast, adding a third triangulated layer of spheres to the existing two layers

so that none of the spheres of the three layers eclipse each other results in the face

centered cubic (FCC) packing arrangement. Due to the vertical staggering of the



			( 24 T, 12 pinges)
overhead view
			click image to enlarge

Figure 39 - Face centered cubic (FCC) sphere packing

spheres in all three layers the arrangement is referred to as ABC. Like the HCP

packing, each sphere in the FCC packing is twelve coordinated. However due to

the staggered arrangement of the thirteen sphere array the sphere centers lie on

the vertices of a regular cuboctahedron.

Notice in particular that the triangulated layers of close packed spheres in the

HCP "twist" cuboctahedron are aligned parallel to each other. In contrast, the FCC

cuboctahedron cluster is demonstrated to possess four intersecting layers of closest

packed spheres that correspond to the four (111) planes of cubic symmetry. As a

result the FCC cuboctahedron cluster of spheres possess full cubic symmetry with

nine mirror planes and seven axes of rotational symmetry. In contrast, the "twist"

cuboctahedron cluster has only four mirror planes and seven axes of rotational

symmetry. Therefore the FCC sphere packing and lattice is demonstrated to be

inherently more symmetrical than the HCP packing.

Since the spheres of both the HCP and FCC arrangement are closest packed they

both can be modeled as a CCP lattice, that is, a space filling of tetrahedra and

octahedra in the ratio of 2:1 respectively.

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