A brief review focuses on studies into the structural reasons for the nonlinear optical properties of crystals of the potassium titanyl phosphate family, performed at the Shubnikov Institute of Crystallography. Accurate X-ray diffraction data are discussed, providing evidence that the optical susceptibility of crystals is related not only to the alternation of long and short Ti–O bonds in the chains of TiO₆ octahedra, but to the geometry of tetrahedral anions and the alkaline cation arrangement in the structure channels, as well. The contribution of each of the three structural components depends on the crystal composition.

The literature data and the results obtained by the authors on the study of the structure and properties of a series of polycrystalline and single-crystal samples of pure and Mg-doped oxymolybdates Ln₂MoO₆ (Ln = La, Pr, Nd) are analyzed. Presumably, the high-temperature phase I4₁/acd of Nd₂MoO₆ single crystals is retained at room temperature. The reason for the loss of the center of symmetry in the structures of La₂MoO₆ and Pr₂MoO₆ and the transition to the space group I$\overline{4}$c2 is the displacement of oxygen atoms along the twofold diagonal axes. In all structures, Mg cations are localized near the positions of the Mo atoms, and the splitting of the positions of the atoms of rare-earth elements is found. Thermogravimetric studies, as well as infrared spectroscopy data for hydrated samples of Ln₂MoO₆ (Ln = La, Pr, Nd), pure and with an impurity of Mg, confirm their hygroscopic properties.

K _x Ln _{5− x} Mo ₃ O _{16− y} F _y (Ln = La, Pr, Nd) compositions were first synthesized. The conductive properties have been widely studied using a combination of theoretical and experimental approaches. The total conductivity reaches ∼10 ⁻² S cm ⁻¹ at 800 °C.

The fluorine-containing fluorite-like compounds of composition NaLn₄Mo₃O₁₅F (Ln = La, Pr, Nd) are produced using the method of solid-phase synthesis in air. Their thermomechanical and conducting properties, as well as hygroscopicity, are studied. It is confirmed that the synthesized specimens are isostructural to the cubic compounds Ln₅Mo₃O₁₆ with the fluorite-like structure. It is shown that in the temperature range of 20–600°C, the specimens of NaLn₄Mo₃O₁₅F (Ln = La, Pr, Nd) expand linearly, and their thermal expansion coefficients (13–14) × 10^–6 K^–1 are close to the coefficients of conventional SOFC electrolytes, for example, YSZ. Using the thermal gravimetric analysis, it is shown that the weight loss of the studied specimens in the range from 30 to 700°C is caused by their hygroscopicity. The electrophysical properties of the compounds are studied using the method of impedance spectroscopy in the humid atmosphere, and the proton component of conductivity is revealed.