Tubular chains in the structures of natural and synthetic silicates

Tubular chains in the structures of natural and synthetic silicates have been described and systematized using the theory of graphs and by unfolding the tube topology onto a plane. Eight types of tubular chains have been considered: seven silicon-oxygen chains and one mixed titanosilicate chain; their topological and geometric characteristics are analyzed. It is shown that the presence of large cavities in tubes is generally related to their occupation by large low-valence cations (K⁺, Cs⁺, Ba²⁺, Sr²⁺, etc.) and water molecules. The overwhelming majority of minerals containing tubular silicate fragments were found in hydrothermal veins of alkaline massifs in Russia and abroad.