Hexagonal and trigonal sphere packings. IV. Trivariant lattice complexes of trigonal space groups

Sphere packings as a tool for the description of martensitic phase transformations

Martensitic transformations which play an important role in metallurgical processes are analysed using group-subgroup relations and sphere-packing considerations. This approach is applied to the transformations between body-centred cubic (b.c.c.) and face-centred cubic (f.c.c.) phases and yields the orientation relations according to the Nishiyama-Wassermann, the Kurdjumov-Sachs and the Pitsch mechanisms. The models proposed by Pitsch and Schrader and by Burgers for the transition between b.c.c. and hexagonally closest-packed (h.c.p.) type structures can be interpreted analogously. In addition, two mechanisms for the transition between cubic f.c.c. and h.c.p. structures are described.

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 Reticular Chemistry Structure Resource (RCSR) database of, and symbols for, crystal nets

During the past decade, interest has grown tremendously in the design and synthesis of crystalline materials constructed from molecular clusters linked by extended groups of atoms. Most notable are metal-organic frameworks (MOFs), in which polyatomic inorganic metal-containing clusters are joined by polytopic linkers. (Although these materials are sometimes referred to as coordination polymers, we prefer to differentiate them, because MOFs are based on strong linkages that yield robust frameworks.) The realization that MOFs could be designed and synthesized in a rational way from molecular building blocks led to the emergence of a discipline that we call reticular chemistry. MOFs can be represented as a special kind of graph called a periodic net. Such descriptions date back to the earliest crystallographic studies but have become much more common recently because thousands of new structures and hundreds of underlying nets have been reported. In the simplest cases (e.g., the structure of diamond), the atoms in the crystal become the vertices of the net, and bonds are the links (edges) that connect them. In the case of MOFs, polyatomic groups act as the vertices and edges of the net. Because of the explosive growth in this area, a need has arisen for a universal system of nomenclature, classification, identification, and retrieval of these topological structures. We have developed a system of symbols for the identification of three periodic nets of interest, and this system is now in wide use. In this Account, we explain the underlying methodology of assigning symbols and describe the Reticular Chemistry Structure Resource (RCSR), in which about 1600 such nets are collected and illustrated in a database that can be searched by symbol, name, keywords, and attributes. The resource also contains searchable data for polyhedra and layers. The database entries come from systematic enumerations or from known chemical compounds or both. In the latter case, references to occurrences are provided. We describe some crystallographic, topological, and other attributes of nets and explain how they are reported in the database. We also describe how the database can be used as a tool for the design and structural analysis of new materials. Associated with each net is a natural tiling, which is a natural partition of space into space-filling tiles. The database allows export of data that can be used to analyze and illustrate such tilings.