Zeolites and zeolite-like became important because of their ion exchange capacities and their outstanding catalytic properties. Millions of tons of zeolites have been produced in the past years for the oil refining industry alone and, in even greater quantities, as ion-exchanging softening agents for detergents. Numerous other applications, e.g. in environmental protection, farming, gas separation, medicine, and pharmacy, are known, making zeolites almost a necessity of daily life. Consequently, there are many, research activities dealing with zeolites properties and characterization. However, a strictly systematic description of zeolite-type crystal structures was not available but is now presented in this series of volumes. It is designed as a reference work for zeolite chemists and materials scientists, but it also serves as a tool to interpret structural similarities and to derive new structures from known topologies.
Introduction.- Mathematical description, classification and invention of nets.- Chemical background.- Mathematical characterization of a crystal structure.- Concise history of relevant mathematics.- Mathematical reference books.- Various mathematical concepts and tools.- Polyhedra & related concepts.- Circle and sphere packing.- One-dimensional units.- Two-dimensional units.- Three-dimensional nets: topology.- Three-dimensional nets: geometry & chemical stability of related materials.- Three-dimensional nets: relation to minimal surfaces.- Challenges.- Compilation of units.- References.- Acknowledgements.