Natural Tilings for Zeolite-Type Frameworks

The concept of natural tiling is applied to find primitive cages in all 194 types of the zeolite frameworks currently collected in the Zeolite Framework Database. Natural tile is considered as a new type of the zeolite building unit (natural building unit, NBU) that has a number of advantages over other polyhedral building units. (i) The choice of the NBU is unambiguous and can easily be done for the framework of any complexity by computer methods. (ii) NBUs fill the crystal space; the framework is completely composed by the NBUs. (iii) NBUs enumerate all minimal cavities in the framework; all larger cages can be obtained by gluing NBUs. (iv) The NBU faces enumerate all windows in the framework. It is shown that the natural tiling approach provides a universal classification scheme that can be used for all zeolite-type structures to find resemblances in their organization. The natural tiles and tilings as well as their topological properties are catalogued, and a number of resemblance schemes are proposed between NBUs and other types of zeolite building units. Two kinds of close similarity between zeolite frameworks are revealed, signature-equal zeolites that have the same tiling signature and tile-equal zeolites built of the same types of NBUs.