Important physical properties of nanoparticles are determined mainly by their atomic structure, especially by their phase composition and the presence of structure defects. X-ray diffraction is a good tool for studying the structure of the nanoparticles, its application for very small particles is however limited by very small intensity of the scattered wave. For this reason special experimental setups, like e.g. diffraction with small incidence angle, are used and many experiments have to be done at synchrotrons. Standard methods of the measured data analysis based on the description of the diffraction using instrumental functions and functions of physical broadening of the lines fail in the case of very small particles. An ab-initio calculation method (based on the Debye formula) has to be used instead. In this work the Debye formula is used for the description of the diffraction of iron oxide samples measured at ANKA synchrotron in Karlsruhe. Using this approach we determine basic parameters of the particles such as lattice parameters and the size of the particles, as well as the presence of different phases. During annealing, subsequent phase transitions from γ-Fe₂O₃ to ε-Fe₂O₃ and to α-Fe₂O₃ take place. New phases nucleate at the surface of the nanoparticles and the phase transformation proceeds towards the particle center, so that the structure of the nanoparticles can be described by a core-shell model; this model was used in the Debye-formula based simulation. From the analysis of the experimental data we determined the kinetic parameters of the phase transitions and their dependence on the nanoparticle sizes. The results of the structure studies are compared with the SQUID measurements of the magnetic properties of the iron-oxide phases.

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