Аннотация:Investigation of phase equilibria in nanosystems has become one of the new trends in chemical thermodynamics. For binary alloys with limited mutual solubilities, a reduction of the system’s volume can be accompanied by significant changes of solubilities and the appearance of unusual metastable phases. To comprehend the structural characteristics and the thermodynamical stability of nanoalloys and to improve their performance, a knowledge of their phase equilibria, that considers their size and shape dependence, is critically needed. Due to the fact that experimental investigations are extremely challenging to perform at the nanoscale, useful predictions can be provided by nanothermodynamical simulations. In this paper, size- and shape-dependent phase equilibria in core-shell nanoparticles of the Pb5(VO4)3Cl–Pb5(PO4)3Cl stratifying solid solution are calculated. Those compounds are subjects of biochemistry and geochemistry, known as natural minerals vanadinite and pyromorphite. In a core-shell structure, two heterogeneous states are possible. At the nanoscale, one of them is metastable and the size- and shapedependent properties of co-existing phases are different in each state. The shape of each phase is modeled by its shape coefficient which is equal to the ratio between surface areas of the phase and the sphere of the same volume. The thermodynamical stability of heterogeneous states depends on shape coefficients of both phases. The geometrical properties of core-shell-nanoparticles are also determined by using the methods of fractal geometry