Phase equilibria of the Al2O3-SiO2-CrOx system at 1600 °C and pO2 of 10-10-10-11 atm

The equilibrium phase relations of the Al 2 O 3 -SiO 2 -CrO x system were experimentally studied at 1600 ◦ C and p O 2 of 10 -10 -10 -11 atm. The high-temperature isothermal equilibration experiments were conducted in a vertical tube furnace, followed by drop quenching and direct phase composition analysis using an Electron Probe X-ray Microanalyzer. The single liquid equilibria, liquid-solid phase equilibria including liquid-corundum, liquid-mullite, and liquid-cristobalite, as well as the three-phase equilibria of liquid-cristobalite-corundum and liquid-corundum-mullite, were observed. The 1600 ◦ C isothermal sections of the quasi-ternary Al 2 O 3 -SiO 2 -CrO x phase diagram at p O 2 of 10 -10 and 10 -11 atm were constructed. The present experimental results display significant discrepancies with the simulations by MTDATA, FactSage, and Thermo-Calc


Introduction
Chromium oxide is widely used in ceramics [1][2][3][4][5] and steel-making processes [6][7][8][9].For the ceramics employed in high-temperature environments, chromium oxide is usually blended with aluminum oxide (Al 2 O 3 ) [10][11][12], due to the properties of inherent hardness and good wear resistance [13,14].Among the Al 2 O 3 -Cr 2 O 3 -based ceramics, the Al 2 O 3 -SiO 2 -Cr 2 O 3 bricks are used as refractories in copper, nickel, and lead making and as filters, ion exchangers, and insulators [15][16][17][18][19][20][21].In high-temperature smelters, the life span of refractory materials is affected by various factors, such as temperature, oxygen partial pressure, and slag compositions.The refractories of furnaces are severely attacked by the molten oxide slag, and the reactions between refractories and molten oxide at smelting conditions with certain smelting temperatures and gas atmospheres can be generally estimated using the Al 2 O 3 -Cr 2 O 3 -based phase diagrams [22].Investigation of the phase equilibria of the Al 2 O 3 -SiO 2 -Cr-O system provides insight for designing the refractories and predicting the possible corrosion reactions of refractories by molten slag.
A critical review of the previous studies indicates that significant uncertainties exist for the equilibrium phase relations of the Al 2 O 3 -SiO 2 -CrO x system in reducing atmospheres.In this study, a laboratory experimental study of the phase equilibria in the Al 2 O 3 -SiO 2 -CrO x system was carried out at 1600 • C and pO 2 of 10 -10 -10 -11 atm using a hightemperature isothermal equilibration/quenching/EPMA (Electron probe X-ray Microanalyzer) technique.The new experimental data were compared with simulations by MTDATA, FactSage, and Thermo-Calc.

Experimental
The slag mixtures were prepared using high-purity oxide powders of Al 2 O 3 (Sigma-Aldrich, 99.99 wt%), SiO 2 (Alfa Aesar, 99.995 wt%), and Cr 2 O 3 (Alfa Aesar, 99.97 wt%).The starting mixtures were prepared by mixing the accurately measured oxide powders in an agate mortar followed by pressing them into cylindrical pellets using a hydraulic press.Mo-substrate made by folding the molybdenum foil into a crucible shape was used for supporting the sample pellets.A long basket made of molybdenum wire was used to support the Mo crucible with samples.The gas atmospheres for target oxygen partial pressures of 10 -10 -10 -11 atm at 1600 • C was controlled by regulating the ratio of CO/CO 2 in the gas mixture of CO (99.97 vol%, AGA-Linde, Finland) and N 2 -CO 2 (95%N 2 -5%CO 2 , Woikoski Oy, Finland).The gas flow rates of CO and N 2 -CO 2 were calculated based on the equilibrium constant of Eq. ( 1): The high-temperature isothermal equilibration experiments were conducted in a vertical alumina tube furnace (Nabertherm, RHTV 120-150/1, Germany) equipped with silicon carbide heating elements, as shown in Fig. 1.The sample temperature was monitored using a calibrated S-type Pt/Pt-10% Rh thermocouple which was placed next to the sample.The gas flow rates for varying target oxygen partial pressures at the experimental temperature were regulated using DFC26 digital mass flow controllers (Aalborg, USA).The experiments started with pulling up the samples into the cold zone of the furnace followed by introducing the gas mixture into the furnace for stabilizing the atmosphere for 15 min.Then, the samples were lifted to the hot zone by a platinum wire for equilibration under reducing atmospheres at 1600 • C for at least 8 h.After equilibration, the lower end of the working tube was immersed in an ice-water mixture and the rubber plug was removed.The samples were quenched into the ice-water mixture by pulling up the platinum wire from the top of the working tube.Detailed information for the equilibration furnace and the experimental procedures is described in the literature [45][46][47].
The quenched samples were separated from the substrate and mounted in epoxy.The polished sections of samples were prepared by the wet metallographic method and carbon-coated using a carbon vacuum evaporator (JEOL IB-29510VET).A Tescan Mira 3 scanning electron microscope (SEM, Tescan, Brno, Czech Republic) equipped with UltraDry silicon drift energy dispersive X-ray spectrometer (EDS, Thermo Fisher Scientific, Waltham, MA, USA) was used to determine the microstructures of samples.The SEM-EDS analyses were conducted with the following analytical settings: accelerating voltage of 15 kV, beam current of 20 nA, and a working distance of 20 mm.The phase compositions were quantitatively acquired with a CAMECA (SX100) EPMA at the Geological Survey of Finland (GTK) using WDS (wavelength dispersive spectroscopy) technique.An accelerating voltage of 20 kV and a beam current of 40 nA were used for EPMA analyses.A focused, as well as a defocused beam diameter set to 5-20 µm, were used for solid and liquid phases, depending on the size of the phases.The external standard materials employed in EPMA analyses were obsidian (for O-Kα), quartz (for Si-Kα), almandine (for Al-Kα), and chromite (for Cr-Kα).The minimum number of EDS and EPMA analysis points selected from the well-quenched areas of each phase was six.The PAP online matrix correction program [48] was employed for raw EPMA data processing.1-2.EPMA results do not give any information about the valence state, therefore the concentration of chromium oxide in the present study was recalculated from the EPMA data as "CrO" to present the results obtained in the reducing atmospheres since the predominant valence state of chromium in silicate melt was Cr 2+ than Cr 3+ [36,41,49].The acquired phase equilibrium data of the system were plotted in the Al 2 O 3 -SiO 2 -CrO x triangular diagrams for the sake of simplicity.It should be noted that the solid phases in some samples were too small to be accurately analyzed by EPMA [50].Therefore, EDS results were employed for those phases.The two-phase equilibria of liquid-cristobalite, liquid-corundum, and liquid-mullite, as well as the three-phase equilibria of liquid-mullite-corundum, were observed at all oxygen partial pressures investigated in the present study.However, the liquid-corundum-cristobalite three-phase equilibria determined at 1600 • C and pO 2 of 10 -10 atm were not found at pO 2 of 10 -11 atm.

Solubility of CrO x in mullite and corundum
Mullite and corundum solid solutions have general compositions of Al 4+2x Si 2-2x O 10−x [51] and (Al 1−x Cr x ) 2 O 3 (0 ≤ x ≤ 1) [31], respectively.The mullite structure is able to incorporate transition metals such as Ti, V, Cr, Mn, and Fe [43] due to the substitution of Al 3+ by other metal cations.Tables 1-2 indicate that the solubility of chromium oxide in mullite and corundum has high relevance to the oxygen partial pressure and the equilibrium liquid oxide composition.Fig. 4 shows the concentrations of CrO x in mullite and corundum solid solutions as a function of CrO x in liquid.The dissolution of CrO x in corundum calculated by MTDATA and FactSage was also plotted for comparison.However, the solubility data for CrO x in mullite were not included in the MTDATA Mtox database and the FactSage FToxid database.
The solubility of CrO x in corundum determined at 1600 • C and pO 2  show that SiO 2 was not observed to dissolve substantially in corundum which agrees well with the observations in literature [22,42].The dissolution of CrO x in mullite determined in this study had a linear increasing trend with increasing CrO x in liquid at 1600 • C and pO 2 of 10 -10 to 10 -11 atm.The present experimentally determined highest solubility of CrO x in mullite at pO 2 of 10 -10 and 10 -11 atm was around 11 mol% and 8 mol%, respectively.The increase of oxygen partial pressure from 10 -11 to 10 -10 atm at 1600 • C led to an increase of CrO x concentration in mullite at the same CrO x concentration in liquid oxide, like the predictions by Thermo-Calc.The solubility of CrO x in mullite determined in the present study was higher than the simulation by Thermo-Calc.
Contrary to the present experimental results determined at 1600 • C and pO 2 of 10 -10 atm, the dissolution of CrO x in corundum at pO 2 of 10 -10 atm computed by MTDATA (Mtox database [52,53]) and FactSage exhibited nonlinearly increasing trends with increasing CrO x in liquid.The dissolution of CrO x in mullite at 1600 • C and pO 2 of 10 -10 atm predicted by Thermo-Calc displayed a similar decreasing trend as the present experimental results with increasing CrO x in liquid, although the predicted value was slightly higher than the present results.The results calculated by MTDATA at pO 2 of 10 -10 atm for the liquid phase in equilibrium with corundum covered a wider CrO x range compared to the results by FactSage.The present experimental results for the dissolution of CrO x in corundum at 1600 • C and pO 2 of 10 -11 atm were closer to the calculation by MTDATA than by FactSage and Thermo-Calc, although the lowest CrO x concentration in corundum in this study was higher than the predictions by MTDATA.The predicted dissolution of CrO x in corundum by FactSage was lower than the present experimental observations, and the discrepancies between FactSage predictions and the present results decreased with increasing CrO x in liquid phase.The solubility of CrO x in corundum at 1600 • C and pO 2 of 10 -11 atm by Thermo-Calc was lower than the present results when the CrO x in liquid was higher than approximately 30 mol%.

Discussion
The isothermal phase diagram is key for estimating the evolution of the phase assemblages in ceramics and metallurgical slags as temperature, oxygen partial pressure, and compositions change.Therefore, the stability and the phase relations of a ceramic material or slag at high temperatures in well-defined atmospheres can be obtained from the phase diagram.

Construction of the 1600 • C phase diagram at pO 2 of 10 -10 atm
The 1600 • C isothermal phase diagram section for the Al 2 O 3 -SiO 2 -CrO x system at pO 2 of 10 -10 atm was constructed based on the present experimentally determined liquid and solid compositions, as shown in Fig. 5(a).Fig. 5(b)-(d) represent comparisons between the present results and the simulations by MTDATA using its Mtox database [52,53], FactSage using the FactPS and FToxid databases [54,55], and Thermo-Calc [56] with the TCOX12 database [57], respectively.The FactSage database on the Al 2 O 3 -SiO 2 -CrO x system was based on the assessment by Degterov and Pelton [36].The calculations by MTDATA in this study was based on the assessment of the Al 2 O 3 -CaO-Cr-O-MgO-SiO 2 system in the Mtox database [58].However, no assessment by Thermo-Calc regarding the Al 2 O 3 -SiO 2 -CrO x system has been published.
The liquid oxide domain and the primary phase fields of cristobalite, corundum, and mullite with tie-lines were experimentally determined at 1600 • C and pO 2 of 10 -10 atm in this study.The phase domains for the two-phase equilibria, including mullite-corundum and cristobalitecorundum, were also constructed based on the phase rule, although no experimental data were obtained from those domains.Fig. 5(b) shows that the liquid domain determined in the present study deviated significantly from the simulation by MTDATA.Compared with the predictions by MTDATA, the experimentally determined isotherms for the primary phase fields of cristobalite and mullite exhibited higher SiO 2 but lower Al 2 O 3 concentrations.Furthermore, the experimentally determined isotherm for the corundum primary phase field displayed lower chromium oxide concentration than the MTDATA simulation.The liquid-liquid-mullite and liquid-liquid-cristobalite three-phase equilibria predicted by MTDATA were not observed in the present study.* EDS results adopted due to the too small crystal size for EPMA analyses.
especially the contours for the primary phase fields of corundum and cristobalite.The isotherm for the mullite primary phase field determined in this study shifted slightly toward the area with lower Al 2 O 3 concentration but displayed a similar trend when compared with the predictions by FactSage.The present liquid points for the three-phase equilibria of liquid-mullite-corundum and liquid-corundum-cristobalite displayed compositions with higher SiO 2 but lower chromium oxide concentrations than the FactSage simulation.
The prediction by Thermo-Calc for the Al 2 O 3 -SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -10 atm, as shown in Fig. 5(d), was more similar to the present experimental results compared with the simulations by MTDATA and FactSage.However, the liquid domain modeled by Thermo-Calc shifted slightly more to the SiO 2 -rich corner of the Gibbs triangle than the present results.atm.The primary phase fields of cristobalite, mullite, and corundum were also determined at 1600 • C and pO 2 of 10 -11 atm.However, the phase domain for the three-phase equilibria of liquid-cristobalitecorundum determined at 1600 • C and pO 2 of 10 -10 atm was not observed at pO 2 of 10 -11 atm.This can be understood by the presence of the liquid-cristobalite and liquid-corundum two-phase equilibria in the SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -11 atm [59].In the study by Pretorius et al. [39], the liquid was observed to be in equilibrium with cristobalite/eskolaite (i.e., corundum in this study) and metallic chromium in the SiO 2 -CrO x system at 1500 • C and pO 2 of 10 -12.5 atm.
Compared with the results obtained in air [22,42,44], it was found that the liquid domain expanded toward the area with higher CrO x but at lower SiO 2 concentrations with decreasing oxygen partial pressure.Compared with the primary phase fields of cristobalite and corundum, the decrease of oxygen partial pressure had a lower impact on the  primary phase domain of mullite, although the SiO 2 concentration of the liquid phase composition for the liquid-mullite-corundum three-phase equilibria determined at 1600 • C and pO 2 of 10 -11 atm was approximately 6 mol% lower than that obtained at pO 2 of 10 -10 atm.
Fig. 6(b) shows a comparison of the present experimental results with simulations by MTDATA.The liquid domain determined in this study displayed significant discrepancies from the predictions by MTDATA, especially in the primary phase fields of cristobalite and mullite.The present phase domain for mullite is wider and expanded towards the area with a higher SiO 2 but lower Al 2 O 3 concentration.The primary phase field of cristobalite by MTDATA displayed higher Al 2 O 3 but lower SiO 2 concentrations than the present experimental results.The liquid-liquid-cristobalite and liquid-liquid-mullite three-phase equilibria simulated by MTDATA were not observed in this study.
Fig. 6(c) represents the comparison of the present experimental results obtained at 1600 • C and pO 2 of 10 -11 atm with predictions by FactSage.It can be seen that the isotherms for the primary phase fields of corundum and mullite determined in the present study were close to the predictions by FactSage.The composition of the liquid point for the liquid-corundum-mullite equilibria predicted by FactSage had lower SiO 2 but higher CrO x concentrations than the present experimental results.The simulated phase domain of cristobalite by FactSage is wider than the present results.
Fig. 6(d) illustrates the comparison of the present results with computations by Thermo-Calc.The primary phase field of cristobalite determined in this study was not predicted by Thermo-Calc.The isotherm in the mullite primary phase field determined in this study displayed higher Al 2 O 3 concentration than simulations by Thermo-Calc.The isotherm in the corundum primary phase domain constructed in the present study exhibited lower SiO 2 concentration than predictions by Thermo-Calc when CrO x in liquid was lower than approximately 40 mol %, after which the present experimental results showed higher SiO 2 concentration than Thermo-Calc simulations.

Conclusions
The phase relations of the Al 2 O 3 -SiO 2 -CrO x system under pO 2 of 10 - 10 -10 -11 atm at 1600 • C were experimentally determined using an isothermal equilibration and quenching method.The phase compositions were analyzed from the polished cross-sections with EPMA.Three primary phases (cristobalite, corundum, and mullite) and two threephase equilibria (liquid-cristobalite-corundum and liquid-corundummullite) were observed.The relationship between CrO x concentration in liquid and the dissolution of CrO x in solid solutions of mullite and corundum were characterized experimentally for the first time at 1600 • C and pO 2 of 10 -10 and 10 -11 atm.The 1600 • C isothermal sections of the Al 2 O 3 -SiO 2 -CrO x phase diagram were constructed at pO 2 of 10 -10 and 10 -11 atm based on the present experimental results.The constructed isotherms were compared with predictions calculated by MTDATA Mtox database, FactSage FactPS and FToxid databases, and Thermo-Calc TCOX12 database.Significant differences were observed between the present experimental results and the simulations.The different databases and models used in the simulations with different thermodynamic software contributed to the discrepancies.The novel experimental results of this study are useful for updating the CrO xcontaining databases.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figs. 2 -
Figs. 2-3 show the backscattered electron (BSE) images of typical samples obtained at 1600 • C and pO 2 of 10 -10 -10 -11 atm.The equilibrium average phase compositions with standard deviations (±1σ) of all samples determined by EPMA are listed in Tables1-2.EPMA results do not give any information about the valence state, therefore the concentration of chromium oxide in the present study was recalculated from the EPMA data as "CrO" to present the results obtained in the reducing atmospheres since the predominant valence state of chromium in silicate melt was Cr 2+ than Cr 3+[36,41,49].The acquired phase equilibrium data of the system were plotted in the Al 2 O 3 -SiO 2 -CrO x triangular diagrams for the sake of simplicity.It should be noted that the solid phases in some samples were too small to be accurately analyzed by EPMA[50].Therefore, EDS results were employed for those phases.The two-phase equilibria of liquid-cristobalite, liquid-corundum, and liquid-mullite, as well as the three-phase equilibria of liquid-mullite-corundum, were observed at all oxygen partial pressures investigated in the present study.However, the liquid-corundum-cristobalite three-phase equilibria determined at 1600 • C and pO 2 of 10 -10 atm were not found at pO 2 of 10 -11 atm.

Fig. 5 (
c) indicates that the liquid domain simulated by FactSage had significant discrepancies with the present experimental results,

4. 2 .
Fig. 6(a) shows the present experimentally constructed 1600 • C isothermal section of the Al 2 O 3 -SiO 2 -CrO x phase diagram at pO 2 of 10 -11atm.The primary phase fields of cristobalite, mullite, and corundum were also determined at 1600 • C and pO 2 of 10 -11 atm.However, the phase domain for the three-phase equilibria of liquid-cristobalitecorundum determined at 1600 • C and pO 2 of 10 -10 atm was not observed at pO 2 of 10 -11 atm.This can be understood by the presence of the liquid-cristobalite and liquid-corundum two-phase equilibria in the SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -11 atm[59].In the study by Pretorius et al.[39], the liquid was observed to be in equilibrium with cristobalite/eskolaite (i.e., corundum in this study) and metallic chromium in the SiO 2 -CrO x system at 1500 • C and pO 2 of 10 -12.5 atm.Compared with the results obtained in air[22,42,44], it was found that the liquid domain expanded toward the area with higher CrO x but at lower SiO 2 concentrations with decreasing oxygen partial pressure.Compared with the primary phase fields of cristobalite and corundum, the decrease of oxygen partial pressure had a lower impact on the

Fig. 4 .
Fig. 4. Solubility of CrO x in mullite and corundum as a function of CrO x in liquid oxide.

Fig. 5 .
Fig. 5. Isothermal section of the Al 2 O 3 -SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -10 atm: (a) present EPMA results; (b) a comparison with predictions by MTDATA; (c) a comparison with predictions by FactSage; (d) a comparison with predictions by Thermo-Calc.

Fig. 6 .
Fig. 6.Isothermal section of the Al 2 O 3 -SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -11 atm: (a) present EPMA results; (b) a comparison with simulations by MTDATA; (c) a comparison with simulations by FactSage; (d) a comparison with simulations by Thermo-Calc.

Table 1
Equilibrium average phase compositions for the Al 2 O 3 -SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -10 atm measured by EPMA.
* EDS results adopted due to the too small crystal size for EPMA analyses.

Table 2
Equilibrium phase compositions for the Al 2 O 3 -SiO 2 -CrO x system at 1600 • C and pO 2 of 10 -11 atm determined using EPMA.