Phase Equilibrium Studies of Nonferrous Smelting Slags: A Review

: Pyrometallurgy is the primary technique for the production of many nonferrous metals such as copper, lead, and zinc. The phase equilibrium information of smelting slags plays an important role in the e ﬃ cient extraction of metals and energy consumption. The experimental technologies used in phase equilibrium studies are compared. The presentation and applications of the pseudo-ternary and pseudo-binary phase diagrams are demonstrated in the Fe–Si–Ca–Zn–Mg–Al– Cu–S–O system. Experimental results are also compared with the predictions of FactSage to evaluate the accuracy of the current thermodynamic database. This review paper provides comprehensive information for the operation of nonferrous metals and optimization of the thermodynamic database.


Introduction
Most of the copper, lead, and zinc exist in the Earth's crust as sulfide minerals.Pyrometallurgy is the primary technique used to produce primary copper, lead, and zinc from the sulfide concentrates [1,2].Cathode copper can be obtained from copper concentrates through the smelting, converting, fire refining, and electrorefining of blister copper [3].Major smelting technologies include flash smelting and bath smelting, depending on the difference in the reaction medium and spatial distribution within the furnace [4,5].Flash smelting predominantly involves gas-solid reactions.By injecting dried and finely ground copper concentrates, along with oxygen and flux, into a flash furnace through a concentrate burner, rapid reactions occur to form molten matte and slag [6].Flash smelting has a high production capacity due to the rapid oxidation of the fine sulfide concentrate [7].The flash smelting technology is developing continuously through the optimization of burner operation and slag chemistry, resulting in reduced dust generation, increased oxygen concentration, and enhanced processing capacity [8][9][10].Bath smelting primarily involves liquid-gas reactions.Within the furnace, copper concentrates are vigorously mixed and stirred by high-pressure gas to achieve fast oxidation.Depending on the location of the tuyeres, bath smelting technologies include side-blowing, top-blowing, and bottom-blowing processes [11].Bottom-blowing smelting technology offers advantages such as feed adaptability, higher gas pressure, long lance life, autogenous smelting, and low-temperature smelting.Its technical superiority has become more prominent since Fangyuan Copper Co., Ltd.developed a two-step copper smelting process [11,12].Crude lead is obtained from lead concentrates through an oxidation process to remove sulfur and a reduction process to remove oxygen [13].Similar to the smelting technology used in copper production, flash smelting [14] and bath smelting [15] technologies are the main oxidation methods employed for lead concentrates.Bath technology has replaced the sinter plant-blast furnace process due to its high thermal efficiency, less feed preparation, and efficient SO2 utilization [16].Although oxygen pressure leaching has been developed for producing zinc in recent years, pyrometallurgy is still utilized to extract zinc from lead and zinc mixed concentrate [17].
Significant reactions in the production of copper, lead, and zinc occur related to the slags.The properties of slag, such as liquidus temperature, solid proportion, and composition, determine the operating temperature, flux addition, refractory, and efficient recovery during the metal production process.Phase equilibrium information of the slag is crucial for optimizing operations and developing new smelting processes.Accurate and reliable phase equilibrium data also serve as the foundation for the development of thermodynamic databases.The chemical compositions of the slags in copper, lead, and zinc production can be represented by the Fe-Cu-Si-Ca-Zn-Mg-Al-S-O system.
In this paper, experimental technologies used in phase equilibrium studies under different oxygen partial pressures, and related phase diagrams and thermodynamic optimization are critically reviewed.Applications of the pseudo-ternary and pseudo-binary phase diagrams of the Fe-Cu-Si-Ca-Zn-Mg-Al-S-O system are discussed.

Phase Equilibrium Studies at Iron Saturation
The quenching technique is commonly employed to investigate phase equilibria of silicate-based slags, which are readily converted into glass upon rapid cooling.The compositions of the glasses can be easily measured at room temperature.The "FeO"-SiO2-CaO system serves as the fundamental slag in non-ferrous smelting processes.Bowen et al. [18,19] and Allen et al. [20] utilized the quenching technique to investigate the "FeO"-SiO2-CaO system at metallic iron saturation.In earlier studies [18,19], a master slag was prepared by mixing and melting SiO2, FeC2O4 (or Fe2O3), and CaCO3 powders in air.Small samples of the master slag were equilibrated in Fe crucibles under a stream of N2 and then quenched.A petrographic microscope was used to identify the phases present in the quenched samples.The liquidus temperature was determined between the temperature at which the mixture was all liquid and some lower temperatures at which crystals were present in the sample.
The Ca2SiO4-Fe2SiO4 phase diagram, describing the extensive solid solutions of the olivine slags, was reported by Bowen et al. [18,19] and is shown in Figure 1.As illustrated in the figure, the liquidus temperatures of an olivine slag (Fe2SiO4) decrease first and then increase with increasing CaO addition.The minimum liquidus temperature in the olivine primary phase field was found to be 1117 °C.This means that a fully liquid slag can be obtained at temperatures above 1117 °C with optimum flux additions.Mukhopadhyay et al. [21] studied the phase relations in CaFeSiO4-Fe2SiO4 and found a miscibility gap below approximately 1041 °C.Slag Atlas [22] summarized the existing data and constructed a ternary phase diagram for the "FeO"-SiO2-CaO system, as shown in Figure 2. The primary phase fields within the investigated composition range were identified, which mainly included tridymite, wollastonite, pseudo-wollastonite, olivine, and wüstite.Impurities such as MgO and Al2O3 are also introduced into the slag in the smelting process from gangue and refractory.Many researchers [23][24][25] have studied phase equilibria in the "FeO"-SiO2-CaO--Al2O3 and "FeO"-SiO2-CaO-MgO systems in equilibrium at iron saturation.The liquidus line in the "FeO"-SiO2-Anorthite, "FeO"-Al2O3-Anorthite, "FeO"-CaSiO3-Anorthite, "FeO"-Gehlenite-Anorthite, and "FeO"-CaSiO3-Gehlenite systems at iron saturation has been studied by Schairer et al. [23,24], which reported three univariant lines in the "FeO"-SiO2-CaO-MgO system at iron saturation, i.e., liquid + merwinite + olivine + magnesiowüstite, liquid + merwinite + olivine + melilite, and liquid + pseudowollastonite + olivine + melilite.Kalmanovitch et al. [25] reported liquidus lines in the CaO-SiO2-Al2O3 system at 5~30 wt% "FeO" planes and iron saturation.
An improved methodology to accurately measure the compositions of the phases present in the quenched sample was developed with the wide application of electron probe microanalysis (EPMA) [26].In these studies, the initial mixture was prepared with high-purity chemicals including excess Fe powder to ensure that the slag was equilibrated with iron at 1031~1280 °C.A small amount of mixture (0.1-0.3 g) was pelletized and equilibrated in Fe envelopes under a stream of N2 at the target temperature.A thermocouple was placed adjacent to the sample to accurately measure the temperature.After equilibration, the sample was dropped into water to achieve fast cooling.It is easy for the small sample used in the experiments to attain equilibrium and rapid cooling.The microstructure and compositions of the phases presented in the quenched sample can be determined by EPMA.
To understand the effects of minor elements on the liquidus temperature of copper smelting slags, Zhao et al. [26] investigated the phase equilibria of the "FeO"-SiO2-CaO-MgO-Al2O3 system in equilibrium with metallic iron.This study focused on the olivine primary phase field related to copper smelting slags.Figure 3 shows that MgO increases and Al2O3 decreases the liquidus temperatures of the slag in the olivine primary phase field.The difference in the effects of MgO and Al2O3 on the liquidus temperature can be explained by the contrasting distribution behavior of these elements between the slag and olivine.Up to 21 wt% of MgO can be dissolved in the olivine, resulting in a significant increase in liquidus temperature.An amount of 6 wt% of MgO in the slag can increase the liquidus temperature by approximately 140 °C.In contrast, Al2O3 was not detected in the olivine.An amount of 6 wt% of Al2O3 in the slag decreases the liquidus temperature by approximately 20 °C. Figure 3  ZnO is commonly present in nonferrous slags.However, phase equilibrium studies for ZnO-containing slag are difficult due to the vaporization of zinc under reducing conditions.Accurate phase equilibria studies for the slag systems containing zinc depend on the appropriate experimental procedure [27][28][29][30][31][32][33].ZnO-containing master slags were prepared at high temperature in air.The quenched master slag was ground and mixed with metallic iron powders to obtain the final mixtures.The pellet was placed in a sealed envelope made of Fe foil or Pt foil.The mixtures were equilibrated at the target temperature under an N2 gas atmosphere and then water-quenched to prepare the sample for EPMA analysis.The reaction between ZnO and Fe provided "FeO" for the slag.Pre-"fixed" ZnO in the matte and slag, sealed envelope, and controlled equilibration time enabled sufficient ZnO to remain in the final slag.
Al2O3 is commonly present in nonferrous smelting slags and comes from ores, coal ash, and refractory.Zhao et al. [28][29][30] systematically investigated the phase equilibria in the "FeO"-SiO2-CaO-Al2O3-ZnO system at iron saturation.The effects of CaO/SiO2 and (CaO + SiO2)/Al2O3 ratios on primary phase fields and liquidus temperatures were discussed.It was found that the presence of Al2O3 in the slag results in the formation of a spinel phase, which was consistent with the observations of industrial slags.Figure 4a shows that at a fixed CaO/SiO2 of 0.71 and "FeO"/(Al2O3 + CaO + SiO2) of 0.52, the liquidus temperatures in the spinel primary phase field increase with increasing ZnO concentration and decreasing (CaO + SiO2)/Al2O3 ratio.Therefore, a low liquidus temperature for the slag can be obtained by reducing the ZnO and Al2O3 concentrations.Similarly, it can be seen from Figure 4b that at a fixed (CaO + SiO2)/Al2O3 of 7.0 and "FeO"/(Al2O3 + CaO + SiO2) of 1.0, the liquidus temperatures in the wüstite primary phase field increase with increasing ZnO concentration and CaO/SiO2 ratio.A low CaO/SiO2 ratio is beneficial to control the liquidus temperature.However, the reduction of PbO and ZnO is also influenced by the CaO/SiO2 ratio which must be considered.The compositions of the solid solutions were also accurately measured by EPMA in these studies.ZnO in the spinel was found to be much higher than that in the corresponding liquid.In the zinc-fuming process, formation of the spinel phase must be avoided to increase the recovery of zinc from the dust.Effects of minor elements such as Na2O, K2O, MgO, and sulfur on liquidus temperatures of the "FeO"-SiO2-CaO-Al2O3-ZnO slag at iron saturation were reported by Zhao et al. [31][32][33].The presence of up to 1 wt% of Na2O and K2O did not introduce new primary phases in the composition range investigated.The size of the wüstite primary phase field was extended and the size of the spinel primary phase field was reduced with the addition of Na2O or K2O.Liquidus temperatures are slightly increased in the wüstite primary phase field and decreased in the spinel primary phase field by the addition of 1.0 wt% of Na2O or K2O [31].In contrast, the presence of MgO in the slag can increase the liquidus temperatures significantly in both wüstite and spinel primary phase fields.For example, at a fixed CaO/SiO2 of 0.71, (CaO + SiO2)/Al2O3 = 5 and 6 wt% of MgO in the slag can increase the liquidus temperatures by 140 °C in the wüstite primary phase field and 70 °C in the spinel primary phase field [32].Figure 5a shows the effect of sulfur on the phase boundary between wüstite and spinel, as well as 1523 K isotherms at a fixed CaO/SiO2 of 0.71 and (CaO + SiO2)/Al2O3 of 5.0.Fact53 and FToxid databases were selected for the calculations.It can be seen from Figure 5a that with 2 wt% of S in the slag, the wüstite/spinel phase boundary moved toward the "FeO" apex, resulting in a smaller wüstite primary phase field and a greater spinel primary phase field.Figure 5b shows that 2 wt% of S can significantly decrease the liquidus temperature in the wüstite primary phase field.FactSage 6.2 predicted a more accurate liquidus temperature for the sulfur-free slag than the sulfur-containing slag.

Phase Equilibrium Studies under Controlled Po2
It is relatively easy to conduct high-temperature experiments at iron saturation.Iron can be used as a container and to control the oxygen partial pressure.However, Po2 at iron saturation is around 10 −10 atm, which is much lower than that in the process of nonferrous smelting.The mixture of CO and CO2 was commonly used to control the Po2 of the slag system through gas-liquid reactions [34][35][36][37][38][39][40].The CO/CO2 ratio at a given temperature and Po2 was calculated by FactSage.The gas flow rate was accurately controlled by the flow meters and confirmed by a DS-type oxygen probe.As gas is involved in the reactions, it takes longer for the slag samples to attain equilibrium at high temperature.Inert material such as Pt was usually used as the container for the experiments.Nikolic et al. [38][39][40] studied the phase equilibrium of the "FeO"-SiO2-CaO system at 1150~1350 °C under Po2 from 10 −5 to 10 −9 atm.The primary phase fields determined in the composition range investigated included tridymite, wollastonite, pseudo-wollastonite, olivine, and wüstite.Wüstite will convert to spinel at high Po2. Figure 6 compares the positions of the 1200 °C isotherms as a function of Po2 [38][39][40].In the composition range investigated, primary phase fields of spinel, tridymite, and wollastonite were determined.The isotherms in the spinel primary phase field significantly move towards the higher-SiO2 and -CaO regions with increasing Po2.The isotherms in the tridymite and wollastonite primary phase fields do not move significantly with Po2.As a result, the fully liquid area of the slag decreases significantly with increasing Po2.At a higher increasing Po2, more SiO2 and CaO are required to keep the slag fully liquid at 1200 °C.The effect of oxygen partial pressure on the 1300 °C isotherms of the "FeO"-SiO2-CaO-MgO and "FeO"-SiO2-CaO-Al2O3 slags was investigated by Zhao et al. [41] at Po2 = 10 −5 ~10 −9 atm.Wüstite, spinel, and tridymite were found to be the primary phase fields in the composition range investigated.Henao et al. [42] reported the phase equilibria of the "FeO"-SiO2-CaO-MgO-Al2O3 system at Po2 = 10 −8 atm and 1250 to 1350 °C.This study focused on the tridymite primary phase field at a fixed amount of 3.3 wt% of Al2O3 or 3.3 + 3.3 wt% of MgO + Al2O3.Xie et al. [43] studied 1200 °C isotherms of the "FeO"-SiO2-CaO-MgO-Al2O3 system at a fixed Po2 of 10 −8 atm.Effects of up to 6 wt% of MgO and/or Al2O3 on the isotherm positions were discussed.The experimental results were also compared with the FactSage 8.2 predictions.Figure 7 shows the effect of Po2 on 1300 ºC isotherms in the "FeO"-SiO2-CaO-4 wt% MgO system (Figure 7a) and "FeO"-SiO2-CaO-4 wt% Al2O3 system (Figure 7b) [41].It can be seen that the wüstite phase is only stable at low Po2.Spinel is the primary phase in the high-"FeO" region at high Po2.The isotherms in the tridymite primary phase field are not sensitive to oxygen partial pressure.The isotherms in the spinel primary phase field move towards the high-SiO2 region with increasing Po2, resulting in a smaller fully liquid area.Effect of oxygen partial pressures on 1300 °C isotherms in (a) "FeO"-SiO2-CaO-4 wt% MgO system, (b) "FeO"-SiO2-CaO-4 wt% Al2O3 system.Reprinted from Ref. [41].
Phase equilibrium studies of the ZnO-contained slag systems under controlled Po2 have been conducted by Liu et al. [44].The Po2 was fixed at 10 −8 atm, which is related to the copper smelting slags.The systems investigated included "FeO"-SiO2-ZnO, ZnO-"FeO"-SiO2-Al2O3, ZnO-"FeO"-SiO2-CaO, and ZnO-"FeO"-SiO2-MgO [44]. Figure 8 shows examples of the pseudo-ternary and pseudo-binary phase diagrams for these systems.The databases of FToxid and FactPS were selected for the solution species and pure compounds, respectively.It can be seen from Figure 8a that the spinel primary phase field dominates the composition range investigated.In addition, the primary phase fields of tridymite, willemite, wüstite, and zincite are also present.The liquidus temperatures in the spinel and tridymite primary phase fields are mainly dependent on the "FeO"/SiO2 ratio.In the industrial operations of copper smelting, the Fe/SiO2 ratio is usually used to represent the composition of the slag.Liquidus temperatures as a function of Fe/SiO2 ratio are presented in Figure 8b with a fixed amount of 5 wt% of ZnO in the slag [44].It can be seen that spinel and tridymite are the primary phases in the composition range of the copper smelting slag.The liquidus temperatures decrease in the spinel primary phase field and increase in the SiO2 primary phase field with decreasing Fe/SiO2 ratio at a fixed CaO concentration.The primary phase fields of spinel and tridymite move towards the low-Fe/SiO2 direction with increasing CaO concentration from 0 to 6 wt%.The liquidus temperatures increase in the spinel primary phase field and decrease in the SiO2 primary phase field with increasing CaO concentration at a fixed Fe/SiO2 ratio.Figure 8b  The effect of MgO on liquidus temperature of the "FeO"-SiO2-ZnO slag was studied by Liu et al. [44] at a fixed Po2 of 10 −8 atm.The pseudo-binary phase diagrams are presented in various directions to meet the needs of the engineers and researchers.It can be seen from Figure 9a that, at low MgO and low ZnO, tridymite is the primary phase.The liquidus temperatures in the tridymite primary phase field decrease with increasing MgO and ZnO concentrations in the slag.In the spinel primary phase field, the liquidus temperatures increase with increasing MgO and ZnO concentrations in the slag.FactSage predicted olivine and willemite primary phase fields rather than spinel.The liquidus temperatures predicted by FactSage are much lower than the experimental results.Figure 9b shows that the fully liquid area moves towards low-Fe/SiO2 ratios with increasing MgO concentration in the slag.Therefore, more SiO2 flux is required to keep the slag liquid if MgO is high in the slag.FactSage predicted a willemite primary phase field between spinel and tridymite primary phase fields, which was not observed in the experiments.Again, FactSage underestimated the liquidus temperatures, which could mislead industrial operations.

Phase Equilibrium Studies under Controlled Po2 and Pso2
In the sulfide smelting process, sulfur is in equilibrium between the slag and gas phases.It is more accurate to investigate the phase equilibria by involving sulfur.In the case of the copper smelting process, liquid matte is also in equilibrium with slag and gas.The experimental data close to the operating conditions can be obtained by equilibrium experiments under controlled matte grades and Po2 and Pso2.The experimental procedure was also more complicated [45][46][47].The oxide mixture was prepared by mixing the required SiO2, CaO, MgO, Al2O3, and pre-conditioned Fe3O4, which was prepared from Fe foil at the same Po2 and temperature as the equilibrium experiments.The required matte was prepared by mixing and melting the Cu2S and FeS mixture under Ar atmosphere.The open substrate was made from the primary phase of silica or spinel.FactSage was used to calculate the SO2/CO/CO2 ratios to obtain the target Po2 and Pso2 at the required temperature.The oxide pellet and matte were placed on the substrate to react at the required temperature for at least 16 h under the flow of SO2/CO/CO2.After quenching, the compositions of all phases present in the samples including liquid slag, oxide crystals, and matte were measured by EPMA.
Phase equilibria of copper smelting and converting slags have been extensively studied involving slag, matte, and gas [45][46][47].The correlations of matte grade with Po2, Pso2, and temperature were reported by Chen et al. [45].The experiments were carried out using a spinel substrate.The experimental results together with the FactSage 7.2 predictions (dash lines) are shown in Figure 10.The databases selected in FactSage 7.2 were "FactPS", "FToxide", and "FTmisc".The matte grade increases significantly with increasing Po2 at a fixed temperature.The increment in the matte grade is more sensitive at high temperature.However, at a fixed Po2, the matte grade decreases with increasing temperature and Pso2.When the matte grade and Pso2 are stable, the liquidus temperatures in the spinel primary phase field increase with increasing Po2.For example, at a matte grade of 70% and Pso2 = 0.3 atm, the increase in Po2 from 10 −8.35 atm to 10 −7.8 atm results in an increase in the liquidus temperature by 50 °C.On the other hand, high oxygen enrichment in the copper smelting process results in a higher Pso2 in the gas.A comparison between Figure 10a,b shows that, at a fixed matte grade and Po2, the liquidus temperatures in the spinel primary phase field increase with increasing Pso2.Therefore, any change in the operating conditions, such as matte grade or oxygen enrichment, can cause a significant change in the slag properties.Changes in other parameters, including operating temperature and fluxing conditions, must be followed accordingly to maintain a smooth operation.Figure 10 also shows that FactSage 7.2 underestimated the liquidus temperatures for the spinel slags.At the same matte grade, Po2 and Pso2, the liquidus temperatures predicted by FactSage 7.2 are lower than the experimental results.In these studies involving matte [46,47], "Cu2O" was reported in the liquid slag.The "Cu2O" concentration in the slag as a function of temperature, slag composition, and gas composition are also discussed.The effect of CaO on gas/slag/matte/solid phase equilibria in the Fe-Cu-Si-O-S system was investigated at a fixed Pso2 in the spinel primary phase by Sun et al. [48], and in the tridymite primary phase field by Fallah-Mehrjardi et al. [49] and Sineva et al. [50].It can be seen from Figure 11a that less than 1 wt% of "Cu2O" and S were present in the liquid slag in equilibrium with spinel.Po2 is constant for a given matte grade, temperature, and Pso2.The increase in temperature from 1180 to 1250 °C caused the Po2 in the system to increase from 10 −8.38 to 10 −7.77 atm.The pseudo-binary phase diagram shown in Figure 11b indicates that the liquidus temperatures in the spinel primary phase field increase with increasing CaO concentration in the slag at a fixed Fe/SiO2 ratio and decrease with decreasing Fe/SiO2 ratio at a fixed CaO concentration.Figure 12 shows that, at a fixed CaO concentration and Fe/SiO2 ratio, the increase in Pso2 caused a higher liquidus temperature in the spinel primary phase field.The liquidus temperatures decrease with decreasing Fe/SiO2 ratio at a fixed CaO concentration and Pso2.FactSage 7.2 predicted the same trends as the experimental results.However, the liquidus temperatures predicted by FactSage 7.2 are much lower than the experimental results.When 2 wt% of MgO is present in the slag, it can be seen from Figure 13a that the liquidus temperatures in the spinel primary phase field decrease with decreasing Fe/SiO2 ratio and Pso2 [51].Similarly, the liquidus temperatures predicted by FactSage 7.2 are much lower than the experimental results.Figure 13b shows that both CaO and MgO can increase the liquidus temperatures of the spinel slag to the same extent.FactSage predicted much lower liquidus temperatures than the experimental results in the same conditions.According to the FactSage predictions, CaO has a stronger effect than MgO on increasing the liquidus temperatures, which was not observed in the experimental results.The effect of Al2O3 on the matte/slag/spinel/gas equilibria in the Fe-Cu-Si-Al-S-O system in the spinel primary phase field has been investigated by Chen et al. [52] at 1250 °C and Pso2 = 0.25 atm, and by Sineva et al. [53] at 1200 °C and Pso2 = 0.25 atm.The presence of Al2O3 in the slag decreased the iron, sulfur, and copper concentrations in the slag.The effect of Al2O3 showed the same trends as that of MgO and CaO [53].The combined effects of CaO, MgO, and Al2O3 on gas/slag/matte/solid equilibria were studied in the Cu-Fe-O-S-Si-Al-Ca-Mg system at a fixed Pso2 of 0.25 atm and 1200 °C [54] and 1300 °C [55].Figure 14a shows the predictions by FactSage 7.3 together with the experimental results.The predicted Po2 in the system increases with increasing matte grade and the increment in Po2 is much sharper at a matte grade greater than 70% Cu.The Po2 in the spinel slag is higher than that in the tridymite slag at the same matte grade.The presence of CaO, MgO, and Al2O3 slightly decreases the Po2 in the spinel primary phase field but does not have a significant effect on the tridymite primary phase field.The experimental results show similar trends but much lower Po2 than the predictions.No clear trends can be seen from the experimental points shown in Figure 14b, because the small concentrations of Cu in the slag could not be accurately measured.FactSage predictions show that Cu in the slag initially decreases and then increases with increasing matte grade.The increment in the Cu in the slag is more significant when the matte grade is greater than 75% Cu.The presence of CaO, MgO, and Al2O3 decreases the Cu in the slag at a matte grade below 70% Cu.Both MgO and Al2O3 are present in the spinel phase to form extensive solid solutions, which are important for development of the thermodynamic database.Figure 15 shows the distributions of Al2O3 and MgO between liquid slag and spinel as a function of matte grade, at 1200 °C and Pso2 = 0.25 atm [54].It can be seen from Figure 15a that the experimental results did not give a clear trend.FactSage predictions show an increase in logL(Al2O3)slag/spinel with increasing matte grade.Figure 15b shows a clearer trend from both predictions and experiments that logL(MgO)slag/spinel increases with increasing matte grade.The experimental results are lower than that predicted by FactSage 7.3.

Conclusions
Phase equilibrium studies for nonferrous smelting slags have been critically reviewed and summarized.The experimental techniques used to determine high-temperature phase equilibria have been compared.Advanced research techniques are required to obtain more accurate data for industrial applications and development of a thermodynamic database.Master slag preparation, high-temperature equilibration under controlled Po2 and Pso2, followed by quenching and EPMA were found to be more efficient and accurate to determine the phase diagrams for complex slag systems.The presentation and application of pseudo-ternary and pseudo-binary phase diagrams for different slags have been demonstrated.The isotherms in the spinel primary phase field significantly move towards higher SiO2 and CaO directions with increasing Po2.The presence of MgO, Al2O3, CaO, and ZnO in the slag considerably changed the primary phase and liquidus temperatures of the slag.The liquidus temperatures in the spinel primary phase field increase with increasing Pso2.More detailed information can be obtained from the comprehensive references included in the present paper.Comparison of the experimental results and FactSage calculations shows that FactSage is a powerful thermodynamic tool to predict phase equilibrium information.General trends predicted by FactSage agree with the experimental results.However, significant discrepancies between the experimental data and predictions indicate that further optimization is required for the thermodynamic database, which relies on accurate experimental data.

Figure 11 .
Figure11.Equilibria of gas/slag/matte/spinel in the Ca-Fe-Cu-Si-O-S system at a fixed Pso2 of 0.3 atm and matte grade of 72 wt% Cu.(a) Isotherms in the spinel primary phase field of "FeO"-SiO2-CaO system, (b) liquidus temperature as a function of slag, square is experimental measurements.Reprinted with permission from Ref.[48].2020, Chen, M.

Figure 13 .
Figure 13.Comparison of experimentally determined liquidus temperatures versus FactSage predictions at fixed matte grade of 72 wt% Cu.Reprinted with permission from Ref. [51].2020, Chen, M. (a) Comparison of the liquidus temperatures with a fixed amount of 2 wt% MgO; (b) comparison of the liquidus temperatures at a fixed Pso2 of 0.3 atm, solid and dashed lines are experimental results and FactSage predictions respectively, square, circle and triangle are experimental measurements.

Figure 14 .
Figure 14.The combined effects of CaO, MgO, and Al2O3 on the phase equilibria of the Fe-Cu-Si-Ca-Mg-Al-S-O system at a constant 1200 °C and Pso2 of 0.25 atm.Reprinted from Ref. [54], the lines are FactSage predictions, symbols denote experimental data.(a) Correlation between matte grade and Po2, (b) correlation between matte grade and Cu in slag.