Three-periodic semiregular nets are defined as those with just one kind of vertex and one kind of edge, but excluding the five regular and one quasiregular nets described earlier. Fourteen of these and their natural tilings are described and their importance in crystal chemistry is indicated.
Regular nets are de®ned as those with symmetry that requires the coordination ®gure to be a regular polygon or polyhedron. It is shown that this de®nition leads to ®ve regular 3-periodic nets. There is also one quasiregular net with a quasiregular coordination ®gure. The natural tiling of a net and its associated essential rings are also de®ned, and it is shown that the natural tilings of the regular nets have the property that there is just one kind of vertex, one kind of edge, one kind of ring and one kind of tile, i.e. transitivity 1111. The quasiregular net has two kinds of natural tile and transitivity 1112.
Our systematic enumeration of 4-connected crystalline networks (that is, networks in which each atom is connected to exactly four neighbours) used recent advances in tiling theory to evolve over 900 topologies. The results are relevant to the structures of zeolites and other silicates, aluminophosphates (AlPOs), oxides, nitrides, chalcogenides, halides, carbon networks, and even to polyhedral bubbles in foams. Given their importance as molecular sieves, ion exchangers, catalysts and catalyst supports, we have applied the results to microporous aluminosilicates and aluminophosphates (zeolites). Zeolite chemistry has to date produced 152 distinct types of structure. However, it was always clear that although many further structures can be synthesised, only a fraction of the mathematically generated networks would be chemically feasible (many are 'strained' frameworks requiring unrealistic bond lengths and bond angles), and that an effective 'filtering' process is needed to identify the most plausible frameworks. Here, we describe the use of computational chemistry methods to calculate optimized structural parameters, framework energies relative to alpha-quartz, volumes accessible to sorption, and X-ray diffraction patterns for systematically enumerated hypothetical 4-connected crystalline frameworks. Structures were treated as silica polymorphs with the empirical formula SiO(2), and their energies were minimized.
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