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:
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.
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