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.

DIANNA is a free software developed to simulate atomic models of structures for an ensemble of nanoparticles and to calculate their whole X-ray powder diffraction patterns and the radial distribution function. The main objects of investigation are the particles whose coherent scattering domains do not exceed several nm. DIANNA is based on the ab initio method using the Debye scattering equation. This method makes it possible to obtain information on the atomic structure, shape and size of nanoparticles. It can be applied also to non-periodic materials or coherently ordered nanostructures. Basic program features, methods and some examples are demonstrated.

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.