Low-temperature $\gamma$-, $\eta$-, and $\chi \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ polymorphs were studied by high resolution transmission electron microscopy and x-ray powder diffraction along with computer simulation of the diffraction patterns. Planar defects lying on the {111}, {110}, and {100} planes, which are the origin of the broadening of x-ray diffraction peaks in different forms of aluminium oxide, were revealed. In addition to providing strong experimental support for the imperfect character of the specimen structures, these results demonstrate the possibility of using nanosized crystalline domains with a spinel-type arrangement, which are regularly shaped and have a specified, developed face and bounding surfaces, for the description of the nanostructure of a whole variety of low-temperature ${\mathrm{Al}}_2{\mathrm{O}}_3$ derivatives. It was found that different ways of domain packing in the oxide particles with a subsequent formation of planar defects contribute to specific kinds of line-shape broadening observed in the x-ray diffraction patterns of these materials. The mechanism of the vacancy generation upon propagation of the shear-type defect in the {110} plane of the spinel structure, which changes the ${\mathrm{Al}}_3{\mathrm{O}}_4$ stoichiometry to ${\mathrm{Al}}_2{\mathrm{O}}_3$, is also discussed.

Despite the fact that metastable aluminum oxides are actively used in industry, there is a discrepancy in the literature regarding their crystal structure. All this leads to difficulties in data interpretation and, as a consequence, classification problems. This work is aimed at solving these tasks. The main features of powder X-ray diffraction of typical samples of three Al₂O₃ polymorphs (γ-, χ-, η-) are analyzed. Specifics and fundamental differences in X-ray scattering and their relationship with the structural organization at the nanostructure level are clearly shown. The work demonstrates the possibilities of analyzing experimental powder X-ray diffraction data using a modern approach based on the Debye Scattering Equation for studying the organization of such complex systems.

Problems of X-ray diffraction analysis of ultradisperse systems with the particle size up to 5 nm are discussed in the review. A method for calculating X-ray diffraction patterns using the Debye formula within the kinematic theory of X-ray scattering (Debye Function Analysis-DFA) is presented. The DFA method makes it possible to obtain information on the atomic structure, shape and size of nanoparticles, and verify hypotheses on the presence of deformations, stacking faults and other structural features of ultradisperse and nanostructured systems. The method is applicable for modeling the diffraction patterns of objects with an arbitrary (not necessarily crystal) structure. Applications of the method for examining the structure of various objects are discussed.

An X-ray approach to analyzing ultradisperse systems is suggested. The approach is based on the simulation of diffraction patterns from an ensemble of nanoparticles with a given structure, size, and shape, including intensity calculations at each profile point. A program for calculations was developed. Its possibilities were demonstrated for the example of studies of samples prepared by solid-state oxidative thermolysis of iron oxalate dihydrate. The size of sample crystallites (coherent scattering regions) did not exceed 1–2 nm.

The Mn-Ce oxide catalysts active in the oxidation of CO were studied by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), temperature-programmed reduction (TPR), transition electron microscopy (TEM), energy dispersive X-Ray (EDX), and a differential dissolution technique. The Mn-Ce catalysts were prepared by thermal decomposition of oxalates by varying the Mn:Ce ratio. The nanocrystalline oxides with a fluorite structure and particle sizes of 4–6 nm were formed. The introduction of manganese led to a reduction of the oxide particle size, a decrease in the surface area, and the formation of a Mn_yCe_1−yO_2−δ solid solution. An increase in the manganese content resulted in the formation of manganese oxides such as Mn₂O₃, Mn₃O₄, and Mn₅O₈. The catalytic activity as a function of the manganese content had a volcano-like shape. The best catalytic performance was exhibited by the catalyst containing ca. 50 at.% Mn due to the high specific surface area, the formation of the solid solution, and the maximum content of the solid solution.

Methane oxidative coupling (OCM) is considered a potential direct route to produce C₂ hydrocarbons. Layered perovskite-like Sr₂TiO₄ is a promising OCM catalyst. Mechanochemical activation (MA) is known to be an environmentally friendly method for perovskite synthesis. Sr₂TiO₄ were synthesized using MA of the mixtures containing SrCO₃ or SrO and TiO₂ or TiO(OH)₂ and annealing at 900 and 1100 °C. XRD and FT-IRS showed that MA leads to the starting component disordering and formation of SrTiO₃ only for SrO being pronounced when using TiO(OH)₂. After annealing at 900 °C, Sr₂TiO₄ was mainly produced from the mixtures of SrCO₃ or SrO and TiO(OH)₂. The single-phase Sr₂TiO₄ was only obtained from MA products containing SrCO₃ after calcination at 1100 °C. The surface enrichment with Sr was observed by XPS for all samples annealed at 1100 °C depending on the MA product composition. The OCM activity of the samples correlated with the surface Sr concentration and the ratio of the surface oxygen amount in SrO and perovskite (O_o/O_p). The maximal CH₄ conversion and C₂ yield (25.6 and 15.5% at 900 °C, respectively), and the high long-term stability were observed for the sample obtained from (SrCO₃ + TiO₂), showing the specific surface morphology and optimal values of the surface Sr concentration and O_o/O_p ratio.