Directly solidified ceramic eutectics and transformation toughened sintered ceramics based on stabilized zirconia and hafnia are considered advanced structural and functional ceramic materials. Binary and ternary ceramic alloys, containing hafnia, zirconia, yttria and lanthanides are crystallized forming the ultrafine structures, the grain size of which is determined by both the cooling rate and phase composition. Present work is about phase equilibria and nanostructures development resulting from the quenching of the melts and from the moderate temperature sintering.

Phase equilibria in the systems HfO₂(ZrO₂)-Y₂O₃-Ln₂O₃ (where Ln= La, Ce, Sm, Eu, Gd, Er) were studied in the wide range of temperatures (1100-2800 °C) and concentrations by experimental methods: X-ray diffraction, thermal analysis in air using a solar furnace at temperatures to 3000 °C, differential thermal analysis in He at temperatures to 2500 °C, microstructural and petrographic analyses, electron microscopy using melted and annealed samples and theoretical means: development of a mathematical models for the liquidus surfaces by a reduced polynomial method.

Isothermal sections of these phase diagrams at 1900, 1600, 1500, 1250, 1100 °C is created. No new phases were found. The crystallization of the alloys in the ZrO₂ (HfO₂)-Y₂O₃-Ln₂O₃ (where Ln= La, Eu, Er) systems was investigated using the data on the structure of the liquidus and solidus surfaces. The crystallization paths for the alloys and the schematic of the reactions are constructed. The equilibrium phase diagrams have been deduced. The temperature and composition of invariant phase - equilibria as well as interconnection between grain size, Ln₂O₃ content and the type polymorphous transformation were determined. The systems ZrO₂ (HfO₂)-Y₂O₃-Er₂O₃ are characterized by the formation of extended solid solutions based on F-ZrO₂(HfO₂), C- and H-Y₂O₃, Er₂O₃.

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