Hydrothermal crystallization of Na2Ti6O13, Na2Ti3O7, and Na16Ti10O28 in the NaOH-TiO2-H2O system at a temperature of 500°C and a pressure of 0.1 GPa: The structural mechanism of self-assembly of titanates from suprapolyhedral clusters

An increase in the NaOH concentration in the NaOH-TiO₂ (rutile)-H₂O system at a temperature of 500°C and a pressure of 0.1 GPa leads to the crystallization R-TiO₂ + Na₂Ti₆O₁₃ → Na₂Ti₃O₇ → Na₁₆Ti₁₀O₂₈. Crystals of the Na₂Ti₆O₁₃ titanate (space group C2/m) have the three-dimensional framework structure Ti₆O₁₃. The structure of the Na₂Ti₃O₇ titanate (space group P2 ₁/m) contains the two-dimensional layers Ti₃O₇. The structure of the Na₁₆Ti₁₀O₂₈ titanate (space group P-1) is composed of the isolated ten-polyhedron cluster precursors Ti₁₀O₂₈. In all the structures, the titanium atoms have an octahedral coordination (MTiO₆). The matrix self-assembly of the Na₂Ti₆O₁₃ and Na₂Ti₃O₇ (Na₄Ti₆O₁₄) crystal structures from Na₄ M ₁₂ invariant precursors is modeled. These precursors are clusters consisting of twelve M polyhedra linked through the edges. It is demonstrated that the structurally rigid precursors Na₄ M ₁₂ control all processes of the subsequent evolution of the crystal-forming titanate clusters. The specific features of the self-assembly of the Na₂Ti₃O₇ structure that result from the additional incorporation of twice the number of sodium atoms into the composition of the high-level clusters are considered.