Phase equilibria were experimentally investigated in the MgO–MnOx and the ZrO2–MgO–MnOx systems for different oxygen partial pressures by powder X‐ray diffractometry, scanning electron microscopy, and differential thermal analysis. The formation of two compositionally and structurally different β‐spinel solid solutions was observed in the MgO–MnOx system in air in the temperature interval 1473–1713 K. Isothermal sections of the ZrO2–MgO–MnOx phase diagram were constructed for air conditions (bold-italicPboldObold2 = 0.21 bar) at 1913, 1813, 1713, 1613, and 1523 K. In addition, isothermal sections at 1913 and 1523 K were constructed for bold-italicPboldObold2 = 10−4 bar. The β‐spinel and halite phases of the MgO–MnOx system were found to dissolve up to 2 and 5 mol% ZrO2. A continuous c‐ZrO2 solid solution forms between the boundary ZrO2–MnOx and ZrO2–MgO systems. It stabilizes in the ZrO2–MgO–MnOx system down to at least 1613 K in air and down to 1506 K at bold-italicPboldObold2 = 10−4 bar.

where n S is the stoichiometric coefficient of the sublattice S, y S J is the site fraction of the constitutent J in the sublattice S, and R is the gas constant. 0 G end is the Gibbs energy of the end-members, which are the stoichiometric compounds formed by the constituents when each sublattice is occupied by only one species, e.g. (C 1 ) u (A 1 ) v . . .. Those 0 G end are to be determined in the optimization. The excess Gibbs energy E G m is expressed by:

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The system Cu-F-O was assessed with CALPHAD technique using computerized optimization procedure (PARROT). Two solid phases CuFe 2 O 4 and Fe 3 O 4 forming solid solution at high temperatures were modeled with compound energy formalism. Presence of Cu 1+ on tetrahedral sites in the samples with compositions close to CuFe 5 O 8 reported in the literature was taken into account. The second ternary compound, CuFeO 2 , was modeled as a stoichiometric phase. For the liquid phase, an ionic two-sublattice model was used. In total 17 adjustable parameters were optimized (9 for the spinel phase, 2 for the delafossite and 6 for the liquid phase) to describe the experimental data. The consistent dataset, which gives a description of the properties from 923 to 1273 K, was obtained.

The thermodynamic parameters of the Nd2O3–Y2O3 system were re-assessed for better reproduction of experimental data. The thermodynamic parameters were combined from binary descriptions to calculate phase diagrams for the ternary system ZrO2–Nd2O3–Y2O3. The calculated phase diagrams were used to select compositions for the experimental studies at 1 250, 1400 and 1 600°C. The samples were synthesised by co-precipitation and heat treated at 1 250–1 600 °C, investigated by X-ray diffraction and scanning electron microscopy combined with energy dispersive Xray spectroscopy. It was found that solubility of the Y2O3 in the pyrochlore phase exceeds 10 mol.%. The experimental data obtained for phase equilibra were used to derive thermodynamic parameters for fluorite, Y2O3 cubic phase C, monoclinic B and Nd2O3 hexagonal A phases by CALPHAD method. The isothermal sections and liquidus surface were calculated for the ZrO2–Nd2O3–Y2O3 system.

Phase relations in the MgO–TiO2 and Al2O3–MgO–TiO2 systems have been studied experimentally using X‐ray diffraction, scanning electron microscopy combined with dispersive X‐ray spectrometry, and differential thermal analysis. The heat capacity measurements of the Mg2TiO4, MgTiO3, and MgTi2O5 compounds have been carried out in the temperature range of 473‐1373 K using DSC. A new thermodynamic description of the MgO–TiO2 system has been derived based on obtained experimental results, data from literature, and taking into account the cation disordering of the intermediate compounds Mg2TiO4 and MgTi2O5. The liquid phase was described by the two‐sublattice partially ionic model (Mg+2,Ti+2,Ti+3)(O−2,Va,O,TiO2). For the Al2O3–MgO–TiO2 system: the solid‐state invariant reaction involving the intermediate phase of pseudobrookite solid solution have been found at the temperature of 1433 K. On the liquidus surface, the eutectic invariant reaction has been established at 1843 K and the transitional one—at 2006 K. Based on the obtained experimental results isothermal sections within the range 1269‐1697 K of the ternary system have been predicted. The MgTi2O5–Al2TiO5 section has been constructed.

Phase equilibria in the ZrO 2 -Nd 2 O 3 -Y 2 O 3 system at 1523-1873 K have been investigated by x-ray diffraction (XRD) and scanning electron microscopy combined with energy dispersive x-ray spectroscopy (SEM/EDX). Temperatures of phase transformations were determined by differential thermal analysis. Temperatures of invariant reactions in the ZrO 2 -Nd 2 O 3 system F = A + Pyr and H = F + A were determined as 1763 and 2118 K respectively and thermodynamic parameters of phases were re-assessed. Phase transformations in ternary systems were determined at 1732 K for composition ZrO 2 -48.46Nd 2 O 3 -5.38Y 2 O 3 (mol%) and at 1744 and 1881 K for composition ZrO 2 -79.09Nd 2 O 3 -2.75Y 2 O 3 (mol%). They were interpreted using XRD investigation before and after DTA as Pyr + B fi F, Pyr fi F and A fi B, respectively. The solubility of the Y 2 O 3 in pyrochlore phase was found to exceed 10 mol%. The thermodynamic parameters of the ZrO 2 -Nd 2 O 3 -Y 2 O 3 system were reassessed taking into account solubility of Y 2 O 3 in the Nd 2 Zr 2 O 7 pyrochlore phase (Pyr). It is assumed that Y 3+ substitutes Nd 3+ and Zr 4+ in their preferentially occupied sublattices. Ternary parameter was introduced into fluorite phase (F) for better reproducing of phase equilibria. Mixing parameters were reassessed for phase A (Nd 2 O 3 based solution), monoclinic phase B and cubic phase C (Y 2 O 3 based solution). The isothermal sections calculated for the ZrO 2 -Nd 2 O 3 -Y 2 O 3 system are in the reasonable agreement with experimental results.