New developments in crystal chemistry have been considered for 34 titanium disilicate minerals that contain the TS (Titanium-Silicate) block, a central trioctahedral (O) sheet, and two adjacent heteropolyhedral (H) sheets of [5–7]-coordinated polyhedra and Si2O7 groups. The general formula of the TS block is AP2BP2MH2MO4(Si2O7)2X4+n, where MH2 and MO4 = cations of the H and O sheets; MH = Ti, Nb, Zr, Mn, Ca + REE, Ca; MO = Ti, Zr, Nb, Fe2+, Mg, Mn, Ca, Na; AP and BP = cations at the peripheral (P) sites = Na, Ca + REE, Ca, Ba, Sr, K; X = anions, O, OH, F, and H2O groups; X4+n = XO4 + XPn, n = 0, 1, 1.5, 2, 4. There are three topologically distinct TS blocks based on three types of linkage of H and O sheets. In the crystal structures of TS-block minerals, TS blocks either link directly or alternate with intermediate (I) blocks. The I block consists of alkali and alkaline-earth cations, oxyanions (PO4), (SO4) and (CO3), and H2O groups. There are four groups of TS-block structures, based on the topology and stereochemistry of the TS block: Groups I, II, III, and IV, where Ti (+ Nb + Zr + Mg + Mn) = 1, 2, 3, and 4 apfu, respectively. In a TS-block structure, four types of self-linkage between adjacent TS blocks occur.
The concept of basic and derivative structures has been introduced for TS-block minerals. A basic structure has the following four characteristics: (1) there is only one type of TS block; (2) the two H sheets of the TS block are identical; (3) there is only one type of I block, or it is absent; and (4) there is only one type of self-linkage of TS blocks. Basic structures obey the general structural principles of Sokolova (2006). A derivative structure has one or more of the three following characteristics: (1) there is more than one type of TS block; (2) there is more than one type of I block; (3) there is more than one type of self-linkage of TS blocks. A derivative structure is related to two or more basic structures of the same Group: it can be derived by adding these structures via sharing the central O sheet of the TS blocks of adjacent structural fragments which represent basic structures. There are 30 basic TS-block structures and four derivative TS-block structures. Based on established relations between basic and derivative structures, possible atomic arrangements and chemical formulae have been predicted for 12 derivative structures and two basic structures.