SeventyFour-Facet Model of a Diamond Cubic Crystal

The earlier fifty-facet model used facets tangent to an inscribed sphere, whose diameter was adjusted to 0.921429 times the vertex sphere so that the ratio between long and short sides of the {001} faces was three i.e. approximately that seen in the experimental images. This page shows the beginnings of an upgrade to better match observations.

In this model, which faces are missing? How do the facets compare to those found in nature? For example, how do shapes of the {110} and {111} faces compare? Do experimental face sizes, in comparison to this model, reflect the surface energies and/or growth kinetics expected for their respective surface lattice structures? Also, this model has been created to take into account the experimentally-observed biplanarity of the {110} and the "leftover" ~{227} facets. Will those "leftover" facets become more "crystallographic" in the process, e.g. might the "leftover facet" bend detail in the closeup image be showing us that {112} faces are more stable than {114}?

Note: We began this 74-facet model by giving each face its own inscribed radius, decoupling the {110} and {111} faces from the {100} set, and forcing 6-fold symmetry (experimentally observed) for the {111} faces. The {100} facet is shrunk while keeping it's edge ratio the same, and keeping the space between it and the {111} facets rectangular by shrinking the {111} facets as well. What indices will the new facets try to assume? What kinds of reconstruction might one expect on those facets?

Technical details: All vertices in the model are on a single circumscribed sphere. Each type of vertex however has its own inscribed sphere radius. Size of the hexagons was fixed by setting r111 to 0.9393 of the circumscribed radius r. Making the hexagons regular then fixed r110 to 0.938484 r. Octagons were given a 3:1 edge ratio, and then fixed in size by setting r100 to 0.911752 r. Add symmetry, and all vertices of all 74 polygons are determined thereby.

Discussion of transitional facets, and facial "tattoos": Their irregular surface textures, and their varying orientations, suggest that both facet types that adjoin the square {100} faces are derivative i.e. less the result of preferred growth on those planes than a result of transition between other facets. In particular, the rectangular facets which transition from square {100} to hexagonal {111} in this model have indices {2.91,1,1}~{311} and r311~0.964 r. The almost triangular plates which effectively make up "the wings" of each {011} facet have indices {2.97,2,0}~{320} and r320~0.954 r. In the {311} case, the mid-point bend in these rectangular plates (see experimental closeup) suggests perhaps a preference for {211} growth with a grudging transition to {100}. In the {320} case, the "curve into the wings" suggests their reluctance to deviate from {110} growth. We still have no idea what to make of the more detailed textures e.g. the round and polygonal grooves on {110} and {100}, respectively, or the bright spots near each {110} wing transition. Might the latter have something to do with the contact point of the void's {320} normal?