Calculation Model for Activity of FeO in Quaternary Slag System SiO 2-CaO-Al 2 O 3-FeO

According to the coexistence theory of slag structure, a calculation model for the activity of FeO in the quaternary system SiO2-CaO-Al2O3-FeO of depleted copper slag was established. The model was used to calculate and analyze the effects of temperature (T), basicity (B), and Al2O3 content on the activity of FeO (NFeO). The results show that temperature has little impact on NFeO. With increased basicity, NFeO first increased slightly, then increased sharply, and finally decreased. It is easier for CaO to combine with SiO2 than FeO to form calcium silicate, which replaces FeO in 2FeO·SiO2 and increases NFeO. However, when basicity is higher than 2.0, CaO not only reacts with SiO2, but also combines with FeO to form calcium ferrate compounds to decrease NFeO. In addition, the activity of FeO decreases with increased Al2O3 content because of the reaction between CaO and Al2O3. The results can be used as a theoretical basis to guide the carbothermal reduction process of copper slag.


Introduction
In the last 50 years, copper consumption has tripled because of rapid industrial development [1].The production of refined copper was 23.33 Mt in 2016, and the quantity of copper increases year by year [1].According to a prediction by the International Copper Study Group (ICSG), the global supply of refined copper slightly increased by 0.9% in 2017, far below the average growth rate of 3% in the previous 10 years, due to the fact that the depletion of global mines is more and more serious, and the grade of newly discovered mines is low.Considering the huge consumption and lack of supply, it is extremely urgent to make full use of copper production and other Cu-containing wastes.
Copper slag is one of the byproducts of the copper production process.Typically, about 2.2-3 t of copper slag are generated per ton of matte produced [2,3], which indicates that the annual output of copper slag was at least 51.33 Mt in 2016.There are abundant metals in copper slag, in which the grades of copper and iron are close to or even higher than corresponding ores of copper and iron.There are several main processes of recycling copper and iron in copper slag, such as beneficiation, oxidation-magnetic separation, smelting reduction, and carbothermal reduction at high temperature.It is generally believed that smelting reduction and carbothermal reduction at high temperature are effective ways to reutilize copper slag, which can obtain carbon-saturated molten iron containing less than 0.4% copper [4][5][6][7].Zhang et al. [8] reported on copper slag and iron-bearing slag as flux to recover iron and separate phosphorus, where the recovery of iron could be as high as 90%.According to the results of Xing et al. [9], temperature has a great effect on the recovery of iron and zinc, but has little effect on the recovery of copper.The recovery of iron and copper can reach 91% and 99%, respectively.However, there is a high level of Cu in the recovered iron-bearing product, and it restricts these products from being used in the steelmaking process.Tang et al. [10] reported that the oxidizing ratio of copper in CuO-FeCl 2 can reach 62.5% with an argon flow of 50 mL/min at 973 K, based on the fact that it is easier for Cu to react with Cl than Fe and CuCl 2 can be volatilized easily.However, the high cost of the recycling process hinders the recycling of copper slag.Therefore, large amounts of copper slag are simply stockpiled or placed in landfills.The residual elements in copper slag, such as Zn, Pb, and As, are potentially leached with rainwater, resulting in excessive levels of heavy metals in groundwater and spread of small particles of copper slag in the air, causing health hazards for nearby people and animals [11,12].In order to make full use of copper slag and improve the ratio of recycling, the thermodynamics of the carbothermal reduction of copper slag should be further studied.
As the main iron-containing phase of copper slag is fayalite (2FeO•SiO 2 ), the activity of FeO has a significant effect on the reduction process.The activity of FeO in blast furnace slag has been investigated by O'Neill et al. [13], Taniguchi et al. [14], and Aroto et al. [15], and has been shown to have relatively low FeO content (<5 wt.%).Zhang [16] utilized the coexistence theory of slag structure to calculate the activity of FeO in the ternary slag system SiO 2 -CaO-FeO, and compared with other studies [17], the results are similar.However, the FeO content in copper slag is higher than that in steel slag.Wang et al. [18] employed the coexistence theory of slag structure for the ternary slag system SiO 2 -CaO-FeO to calculate the activity of FeO with different basicity in order to recovery iron in copper slag.However, Al 2 O 3 in the slag was ignored during the calculation, which led to errors in the results.
The coexistence theory of slag structure was initially proposed by Chuiko [19] and developed by Zhang [16].The coexistence theory is based on the relevant phase diagrams, thermodynamic relations, and the law of mass balance of ions and molecules coexisting in molten slag, and establishes some equations to calculate the concentrate of components, by which the activity of components is characterized.The theory has already been used in some slag systems, such as CaO-FeO-Fe 2 O 3 -SiO 2 -Cu 2 O and MnO-FeO-SiO 2 -Al 2 O 3 [20,21].
In this paper, a calculation model for the activity of FeO in the quaternary slag system SiO 2 -CaO-Al 2 O 3 -FeO is established according to the coexistence theory of slag structure, in order to analyze the variation of FeO activity with the effect of temperature (T), basicity (B), and Al 2 O 3 content and provide a theoretical basis to guide the carbothermal reduction process of copper slag.
Taking the composition of initial slag as x 1 = ∑FeO, x 2 = ∑CaO, x 3 = ∑SiO 2 , and x 4 = ∑Al 2 O 3 , ∑n is the sum of moles of ions and molecules in the slag system; N i (i represents each structural unit) is the mass action concentration of each structural unit after normalization; and N 1 , N 2 , N 3 , and N 4 are Fe 2+ + O 2− , Ca 2+ + O 2− , SiO 2 , and Al 2 O 3 , respectively.In these chemical equilibria between structural units (Table 2), k i is the equilibrium constant, which can be acquired from standard Gibbs free energy (∆G), T is temperature (K), and R is the gas constant, 8.314 J/(mol•K).Equations (1) to (5) are obtained by the law of mass balance, and Equations ( 6) to (9) can be deduced based on the mass balance equations and equilibrium constants in Table 2 and Equations (1) to (5).
Table 1.Structural units in the slag system.

Complex Molecules
Table 2.Chemical equilibria of structural units.
The ternary phase diagram of SiO 2 -CaO-Al 2 O 3 is depicted in Figure 1 using FactSage software (Version 7.0, GTT-TECHNOLOGIES, Herzogenrath, Germany).According to the phase diagram, two kinds of slags are suitable to recover iron for less energy consumption, better liquidity, and less viscosity.The major chemical composition of the initial copper slag and the composition of the two kinds of slag are shown in Table 3. Considering high FeO content, the quaternary slag system of SiO 2 -CaO-Al 2 O 3 -FeO has been established.
The activity calculation program was developed based on Equations ( 6) to ( 9), the equilibrium constants in Table 2, and the components of slags in Table 3.The equilibrium constants k i (i = 1-15) were obtained first based on specific temperature and the standard Gibbs free energy.Then, the equilibrium constants and the composition of slags in Table 3 were substituted into Equations ( 6) to (9), and the contents of the composition in the SiO 2 -CaO-Al 2 O 3 -FeO slag system were calculated.According to the variation of temperature and compositions of slag, the effect of temperature, basicity, and Al 2 O 3 content were obtained. 19 x 4 = (N 4 + 3N 9 + N 10 + 7N 11 + 2N 12 + 6N 13 + N 14 + N 16 + N 17 + N 18 ) ∑ n (5) Metals 2018, 8, 714

Effect of Temperature on Activity of FeO
To consider the effect of temperature on the activity of FeO (NFeO), NFeO was calculated in the different slags shown in Table 3 and at a temperature range of 1573-1823 K.The results are shown in Figure 2. It was found that NFeO in the two slags increased slightly with increased temperature.Figure 3 shows the activity of some components in slag 2 at different temperatures.F, S, C, and A represent FeO, SiO2, CaO, and Al2O3, respectively.

Effect of Temperature on Activity of FeO
To consider the effect of temperature on the activity of FeO (N FeO ), N FeO was calculated in the different slags shown in Table 3 and at a temperature range of 1573-1823 K.The results are shown in Figure 2. It was found that N FeO in the two slags increased slightly with increased temperature.Figure 3 shows the activity of some components in slag 2 at different temperatures.F, S, C, and A represent FeO, SiO 2 , CaO, and Al 2 O 3 , respectively.From Figure 3, it can be seen that temperature had little effect on NFeO in slag 2. With increased temperature, the activity of F2S (2FeO•SiO2) decreased and, on the contrary, the activity of CFS (CaO•FeO•SiO2) increased.From Table 2, it can be seen that the reaction between FeO and SiO2 is exothermic, and the reaction generating CaO•FeO•SiO2 is spontaneous.Namely, the consumption of FeO is reduced by limiting the reaction between FeO and SiO2, although the reaction generating CaO•FeO•SiO2 consumes FeO.These cause NFeO to increase slightly.

Effect of Basicity on Activity of FeO
To calculate the effect of basicity on NFeO, the contents of Al2O3 and FeO were kept constant at 7.61% and 43.36% in slag 1, respectively.In slag 2, the contents of Al2O3 and FeO were 11.90% and 33.68%, respectively.From Figure 2, it can be seen that temperature had little effect on NFeO, thus the study was carried out at 1723 K, and basicity was used with binary basicity R = w(CaO)%/w(SiO2)%.The results are shown in Figure 4, indicating that the tendency of NFeO was the same with different contents of Al2O3 and FeO.NFeO first increased slightly, then increased sharply, and finally decreased.In slag 1, the maximum activity was 0.64 at basicity of 1.7, while the maximum was 0.55 in slag 2 with basicity of 2.0.From Table 2, it can be seen that ∑n, the sum of moles of ions and molecules in the slag system, decreased because of the reactions between CaO and SiO2.According to the equation NFeO = 2xFeO/∑n, NFeO would increase as the reactions between CaO and SiO2 proceed.On the other hand, FeO would react with CaO, Al2O3, or SiO2, which would decrease the  From Figure 3, it can be seen that temperature had little effect on NFeO in slag 2. With increased temperature, the activity of F2S (2FeO•SiO2) decreased and, on the contrary, the activity of CFS (CaO•FeO•SiO2) increased.From Table 2, it can be seen that the reaction between FeO and SiO2 is exothermic, and the reaction generating CaO•FeO•SiO2 is spontaneous.Namely, the consumption of FeO is reduced by limiting the reaction between FeO and SiO2, although the reaction generating CaO•FeO•SiO2 consumes FeO.These cause NFeO to increase slightly.

Effect of Basicity on Activity of FeO
To calculate the effect of basicity on NFeO, the contents of Al2O3 and FeO were kept constant at 7.61% and 43.36% in slag 1, respectively.In slag 2, the contents of Al2O3 and FeO were 11.90% and 33.68%, respectively.From Figure 2, it can be seen that temperature had little effect on NFeO, thus the study was carried out at 1723 K, and basicity was used with binary basicity R = w(CaO)%/w(SiO2)%.The results are shown in Figure 4, indicating that the tendency of NFeO was the same with different contents of Al2O3 and FeO.NFeO first increased slightly, then increased sharply, and finally decreased.In slag 1, the maximum activity was 0.64 at basicity of 1.7, while the maximum was 0.55 in slag 2 with basicity of 2.0.From Table 2, it can be seen that ∑n, the sum of moles of ions and molecules in the slag system, decreased because of the reactions between CaO and SiO2.According to the equation NFeO = 2xFeO/∑n, NFeO would increase as the reactions between CaO and SiO2 proceed.On the other hand, FeO would react with CaO, Al2O3, or SiO2, which would decrease the From Figure 3, it can be seen that temperature had little effect on N FeO in slag 2. With increased temperature, the activity of F 2 S (2FeO•SiO 2 ) decreased and, on the contrary, the activity of CFS (CaO•FeO•SiO 2 ) increased.From Table 2, it can be seen that the reaction between FeO and SiO 2 is exothermic, and the reaction generating CaO•FeO•SiO 2 is spontaneous.Namely, the consumption of FeO is reduced by limiting the reaction between FeO and SiO 2 , although the reaction generating CaO•FeO•SiO 2 consumes FeO.These cause N FeO to increase slightly.

Effect of Basicity on Activity of FeO
To calculate the effect of basicity on N FeO , the contents of Al 2 O 3 and FeO were kept constant at 7.61% and 43.36% in slag 1, respectively.In slag 2, the contents of Al 2 O 3 and FeO were 11.90% and 33.68%, respectively.From Figure 2, it can be seen that temperature had little effect on N FeO , thus the study was carried out at 1723 K, and basicity was used with binary basicity R = w(CaO)%/w(SiO 2 )%.The results are shown in Figure 4, indicating that the tendency of N FeO was the same with different contents of Al 2 O 3 and FeO.N FeO first increased slightly, then increased sharply, and finally decreased.In slag 1, the maximum activity was 0.64 at basicity of 1.7, while the maximum was 0.55 in slag 2 with basicity of 2.0.From Table 2, it can be seen that ∑n, the sum of moles of ions and molecules in the slag system, decreased because of the reactions between CaO and SiO 2 .According to the equation N FeO = 2x FeO /∑n, N FeO would increase as the reactions between CaO and SiO 2 proceed.On the other hand, FeO would react with CaO, Al 2 O 3 , or SiO 2 , which would decrease the content of FeO.Since these two are opposite factors, the activity of FeO would appear at the maximum value.From Figure 6, it can be seen that the tendency of the activity of 2CaO•SiO2 is same as that of FeO when basicity is higher than 0.
When basicity reaches near 2.0, maximum NFeO as the affinity of CaO for SiO2 reaches the maximum value at the ratio of NCaO/N SiO 2 = 2 [14].When the value of Si/O is smaller, the structure of silicate is more stable and simpler.With basicity higher than 2.0, the CaO content still increases.By this, all the silicate exists as SiO 4-4 , which is the most stable structure (Si/O = 1/4) [23], and O 2- cannot continue to be consumed to form silicate.Residual O 2-reacts with Fe 2+ to form FeO -2 , decreasing the FeO content; in the meantime, residual CaO reacts with FeO to form calcium ferrate compounds.With these two results, the activity of FeO decreases [24].

Effect of Al2O3 on Activity of FeO
NFeO was calculated in different contents of Al2O3 for slag 1 and slag 2 with basicity of 1.7 and 2.0, respectively, at 1723 K, as shown in Figure 7.It can be seen that the value of NFeO slightly decreased with increased Al2O3 content, but the variation was very small.To study the variation further, the activity of some components in the slag system were calculated and are shown in Figure 8.
From Figure 8, it can be seen that the value of the activity of FA (FeO•Al2O3) is very small, just like the value of the activity of S (SiO2).Although the activity of FeO•Al2O3 increased with increased Al2O3 content, the value of activity of FeO•Al2O3 was so small to be ignored, which means it is hard for Al2O3 to react with FeO in this slag system.On the other hand, the activity of CaO•Al2O3 increased, indicating that the Al2O3 reacted with CaO and decreased its activity.With such a decrease, it is difficult for CaO to replace FeO from 2FeO•SiO2, which decreases the NFeO [24].CaO can only react with 2FeO•SiO2 to form CaO•FeO•SiO2, as in Equation (10).Therefore, the activity of 2CaO•SiO2 decreases and the activity of CaO•FeO•SiO2 increases when the content of Al2O3 increases.From Figure 6, it can be seen that the tendency of the activity of 2CaO•SiO 2 is same as that of FeO when basicity is higher than 0.
When basicity reaches near 2.0, maximum N FeO as the affinity of CaO for SiO 2 reaches the maximum value at the ratio of N CaO /N SiO 2 = 2 [14].When the value of Si/O is smaller, the structure of silicate is more stable and simpler.With basicity higher than 2.0, the CaO content still increases.By this, all the silicate exists as SiO 4− 4 , which is the most stable structure (Si/O = 1/4) [23], and O 2− cannot continue to be consumed to form silicate.Residual O 2− reacts with Fe 2+ to form FeO − 2 , decreasing the FeO content; in the meantime, residual CaO reacts with FeO to form calcium ferrate compounds.With these two results, the activity of FeO decreases [24].

Effect of Al 2 O 3 on Activity of FeO
N FeO was calculated in different contents of Al 2 O 3 for slag 1 and slag 2 with basicity of 1.7 and 2.0, respectively, at 1723 K, as shown in Figure 7.It can be seen that the value of N FeO slightly decreased with increased Al 2 O 3 content, but the variation was very small.To study the variation further, the activity of some components in the slag system were calculated and are shown in Figure 8.
From Figure 8, it can be seen that the value of the activity of FA (FeO•Al 2 O 3 ) is very small, just like the value of the activity of S (SiO 2 ).Although the activity of FeO•Al 2 O 3 increased with increased Al 2 O 3 content, the value of activity of FeO•Al 2 O 3 was so small to be ignored, which means it is hard for Al 2 O 3 to react with FeO in this slag system.On the other hand, the activity of CaO•Al 2 O 3 increased, indicating that the Al 2 O 3 reacted with CaO and decreased its activity.With such a decrease, it is difficult for CaO to replace FeO from 2FeO•SiO 2 , which decreases the N FeO [24].CaO can only react with 2FeO•SiO 2 to form CaO•FeO•SiO 2 , as in Equation (10).Therefore, the activity of 2CaO•SiO 2 decreases and the activity of CaO•FeO•SiO 2 increases when the content of Al 2 O 3 increases.(Si/O = 1/4).When basicity is higher than 2.0, CaO not only reacts with SiO2, but also combines with FeO to form calcium ferrate compounds to decrease NFeO.3. The value of NFeO slightly decreases with increased Al2O3 content, as CaO reacts with Al2O3, which limits the free FeO generated from 2FeO•SiO2.

Figure 2 .
Figure 2. Effect of temperature on activity of FeO.

Figure 2 . 10 Figure 2 .
Figure 2. Effect of temperature on activity of FeO.

Figure 3 .
Figure 3. Activity of some components in slag 2 at different temperatures, F 2 S and CFS represent 2FeO•SiO 2 and CaO•FeO•SiO 2 , respectively.

Metals 2018, 8 ,
x FOR PEER REVIEW 6 of 10 content of FeO.Since these two are opposite factors, the activity of FeO would appear at the maximum value.

Figure 5 .
Figure 5.Comparison of present work and reference works.

Figure 6
Figure 6 shows the activity of some components in slag 2 at 1723 K.When basicity was below 0.8, the activity of Al2O3 and SiO2 declined and the activity of CFS (CaO•FeO•SiO2) increased.As basicity increased to 0.8, there was little activity of 2CaO•SiO2 and 2FeO•SiO2 disappeared gradually, which means that CaO reacts with 2FeO•SiO2 first to form CaO•FeO•SiO2, instead of forming 2CaO•SiO2.It proves that while the content of CaO is low, it is hard to replace the FeO from 2FeO•SiO2.During the process, ∑n decreased and NFeO increased.Therefore, although the content of FeO decreased, NFeO increased slowly.

Figure 4 .
Figure 4. Effect of basicity on N FeO .In Figure 5, the measured γ FeO results are plotted for slag systems of SiO 2 -CaO-Al 2 O 3 -FeO and SiO 2 -CaO-FeO by Taniguchi et al. [14], Arato et al. [15], and Wang et al. [18].It is found that the present work is in good agreement with the results of Taniguchi et al. and Arato et al., while it is within the wide variation range reported by Wang et al.This is possibly because Al 2 O 3 was not considered by Wang et al.Comparing the results of Taniguchi et al., Arato et al., and the present work, the results here are very small, which probably means that the effect of Al 2 O 3 on γ FeO is inert in the system.

Figure 5 .
Figure 5.Comparison of present work and reference works.

Figure 6
Figure 6 shows the activity of some components in slag 2 at 1723 K.When basicity was below 0.8, the activity of Al2O3 and SiO2 declined and the activity of CFS (CaO•FeO•SiO2) increased.As basicity increased to 0.8, there was little activity of 2CaO•SiO2 and 2FeO•SiO2 disappeared gradually, which means that CaO reacts with 2FeO•SiO2 first to form CaO•FeO•SiO2, instead of forming 2CaO•SiO2.It proves that while the content of CaO is low, it is hard to replace the FeO from 2FeO•SiO2.During the process, ∑n decreased and NFeO increased.Therefore, although the content of FeO decreased, NFeO increased slowly.

Figure 5 .
Figure 5.Comparison of present work and reference works.

Figure 6
Figure 6 shows the activity of some components in slag 2 at 1723 K.When basicity was below 0.8, the activity of Al 2 O 3 and SiO 2 declined and the activity of CFS (CaO•FeO•SiO 2 ) increased.As basicity increased to 0.8, there was little activity of 2CaO•SiO 2 and 2FeO•SiO 2 disappeared gradually, which means that CaO reacts with 2FeO•SiO 2 first to form CaO•FeO•SiO 2 , instead of forming 2CaO•SiO 2 .It proves that while the content of CaO is low, it is hard to replace the FeO from
8, and the activity of CaO increases while the activity of CaO•FeO•SiO2 declines.This indicates that CaO reacted with CaO•FeO•SiO2 to form FeO and 2CaO•SiO2 with increased basicity, making the activity of FeO and 2CaO•SiO2 increase.The formation of 2CaO•SiO2 in copper slag has two steps, shown in Equations (10) and (11): first CaO reacts with 2FeO•SiO2 to form CaO•FeO•SiO2 and FeO, and then CaO reacts with CaO•FeO•SiO2 to form 2CaO•SiO2 and FeO.CaO is alkaline oxide and can dissociate O 2-and Ca 2+ easily.Meanwhile, CaO has higher alkalinity than FeO.On the contrary, SiO2 is acidic oxide, which reacts more easily with CaO.FeO bound with SiO2 in the form of 2FeO•SiO2 would be free to increase the NFeO.
8, and the activity of CaO increases while the activity of CaO•FeO•SiO 2 declines.This indicates that CaO reacted with CaO•FeO•SiO 2 to form FeO and 2CaO•SiO 2 with increased basicity, making the activity of FeO and 2CaO•SiO 2 increase.The formation of 2CaO•SiO 2 in copper slag has two steps, shown in Equations (10) and (11): first CaO reacts with 2FeO•SiO 2 to form CaO•FeO•SiO 2 and FeO, and then CaO reacts with CaO•FeO•SiO 2 to form 2CaO•SiO 2 and FeO.CaO is alkaline oxide and can dissociate O 2− and Ca 2+ easily.Meanwhile, CaO has higher alkalinity than FeO.On the contrary, SiO 2 is acidic oxide, which reacts more easily with CaO.FeO bound with SiO 2 in the form of 2FeO•SiO 2 would be free to increase the N FeO .(Ca 2+ + O 2− ) + 2FeO•SiO 2 = CaO•FeO•SiO 2 + FeO (10)
calculation model can predict the activity of components generated in the quaternary slag system SiO2-CaO-Al2O3-FeO with different temperatures, basicity, and Al2O3 content.Temperature influences the activity of NFeO slightly at 1573-1773 K. 2. Basicity is the major factor affecting the activity of FeO.With basicity ranging from 0.4 to 0.8, NFeO increased slightly due to the formation of CaO•FeO•SiO2.When basicity reaches near 2.0, there is maximum NFeO, as CaO can react with SiO2 to form the most stable and simplest structure, SiO 4-4