Hexagonal and trigonal sphere packings. II. Bivariant lattice complexes

Homo Citans and Carbon Allotropes: For an Ethics of Citation

Cite we must, cite we do. We cite because we are links in a chain, using properties and methods validated by others. We also cite to negotiate the anxiety of influence. And to be fair. After outlining the reasons for citation, we use two case studies of citation amnesia in the field of hypothetical carbon allotropes to present a computer-age search tool (SACADA) in that subsubfield. Finally, we advise on good search practice, including what to do if you miss a citation.

Monoclinic sphere packings. I. Invariant, univariant and bivariant lattice complexes

All homogeneous sphere packings were derived that refer to the two invariant, the four univariant and the three bivariant lattice complexes belonging to the monoclinic crystal system. In total, sphere packings of 29 types have been found. Only for five types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for nine types, tetragonal for five types, hexagonal for six types and cubic for four types.

The cubic limiting complexes of lattice complexes with trigonal characteristic symmetry

Point configurations with cubic inherent symmetry may be generated within certain trigonal space groups. The corresponding limiting-complex relationships were studied. They are caused by a specialization of the axial ratio c/a and require also special coordinate parameters in most cases.

The limiting complexes were derived with the aid of group-subgroup relationships. The material was checked making use of the occurrence of cubic sphere packings within trigonal space groups. The results are presented in a table referring to all lattice complexes with rhombohedral characteristic space groups (two invariant, five univariant, four bivariant, four trivariant) and to one univariant, one bivariant and one trivariant lattice complex with trigonal characteristic space groups.

On sphere packings of arbitrarily low density

The search for a least dense packing of spheres (circles) makes sense only under suitable restrictions because otherwise sphere packings of arbitrarily low density may be constructed. An effective restriction is that all spheres have to be symmetrically equivalent. It has been tried to weaken this condition such that the spheres (circles) have only to be equal in size as well as in their number of contacts. It turned out, however, that even then series of packings may be derived within which the density approaches zero. Examples for such series are presented.