EstImAtIng sulfIdE cApAcItIEs for tErnAry systEms wIth lImItEd solubIlIty

In view of successful application of mass triangle model in thermophysical properties, in the current work, the mass triangle model was extended to evaluate sulfide capacities of ternary systems with limited homogeneous region. Four ternary systems of Al2O3-FeO-SiO2, FeO-CaO-SiO2, CaO-CaCl2-CaF2 and CaO-CaF2-SiO2 were chosen to calculate iso-sulfide capacity based on the limited boundary data. The good agreement between reference data and calculated data indicated that this model is feasible and will play an indispensable role in the future. Compared with optical basicity model, the results obtained by mass triangle model are still competitive when containing Cland Fin the molten slag due to lacking the optical basicity values.


Introduction
The increasing demand for extremely clean steels has called for more efforts to decrease impurities to extra-low concentration.Sulfur is considered as a serious impurity which considerably deteriorates ductility and fatigue strength of steel materials [1][2][3].Therefore, desulphurization which aims at improving the production of clean steels plays a crucial role in ladle metallurgy.Commonly, the desulphurization was processed in ladle refining processes at very high temperatures.The fundamental slag systems are FeO-CaO-SiO 2 and Al 2 O 3 -FeO-SiO 2 .Moreover, with the development of hot metal pretreatment in recent years, more attention was focused on lowering Si, P, S contents before charging it to the basic oxygen furnace (BOF).The reagent used in this process is mainly composed of lime when desulfurization is required.For this reason, the evaluation of sulfide capacities of slags saturated with CaO, CaCl 2 , CaF 2 or SiO 2 at a lower temperature would be more meaningful.
In order to further understand the desulfurization and process control, it is of the utmost importance to acquire knowledge of sulfide capacities of slags.Up to now, numerous experimental studies have been carried out to explore the sulfide capacities of slag systems in metallurgical processes.M. M. Nzotta [4] studied the sulfide capacities of "FeO-SiO 2 \* MERGEFORMAT " melts with known sulfur and oxygen partial pressures in the temperature range of 1623 to 1723 K by the equilibrium measurement of gas-slag reaction.Meanwhile, Shiro Ban-ya [5] investigated the sulfide capacity of CaO-Al 2 O 3 -CaF 2 \* MERGEFORMAT \* slags at the temperature from 1823 to 1923 K. Kim Kärsrud [6] studied sulfide capacities of synthetic blast furnace slags at 1773 K. Recently, Simeonov et al [7] reported the sulfide capacity data for "FeO-MgO-SiO 2 " slag at 1473 K and 1523 K in MgO crucibles.The sulfide capacities in the "FeO-MnO-SiO 2 " system at 1823 K were determined by Hino and Fuwa [8].Wang et al [9] have measured the sulfide capacities of CaO-SiO 2 -CrO x pseudo-ternary slags between 1823 K and 1923 K.
Parallely, evaluation methods also have been developed in these years.The optical basicity model, first addressed by Duffy and Igram [10], was then further modified by R. W. Young et al [11].The Young model indicated below presented a satisfactory method for calculating sulfide capacities Cs as a function of optical basicity Λ, temperature T (K) and weight percent of some oxide components of the slag.
When Λ < 0.8, then: ( When Λ ≥ 0.8, then: ( However, limitations also have been placed on lacking the optical basicity values for chlorides and some transitional element oxides such as CaCl 2 , Cr 2 O 3 .
As an alternative to optical basicity model, geometrical model could be a better choice.With the development of the technology of computer calculation, various geometric models provide considerable valuable data which are too difficult to obtain through the experiments.These geometric models such as Toop, Hillert, Muggianu and Kohler models are used to predict not only thermodynamic properties but also thermophysical properties for ternary and multicomponent systems from binary ones including chlorides and transitional element oxides.One of the promising geometrical models is mass triangle model proposed by Chou et al [12]  . .
which applied limited data on the boundary of the homogeneous region to calculate the properties within it.Successful applications have been proved in evaluation of density [13], surface tension [14] as well as electrical conductivity in ternary system with limited solubility.In the present study, this model has been extended to evaluate one of the thermochemical properties, i.e. the sulfide capacities of several ternary systems with limited homogeneous phase region.

theoretical fundamentals
In order to orient readers, the brief introduction of mass triangle model was presented here.As shown in Figure 1, it represents a system with a boundary of the homogeneous field.Chou proposed a new model called mass triangle model using limited data on the boundary of the homogenous to calculate properties within it [15].If the sulfide capacities at points A, B, C are known, the sulfide capacities at any point within the homogenous solution region can be calculated.The detailed description of this new model can also be found in earlier papers [8,9].

Application to the Al 2 o 3 -feo-sio 2 system
In most steel-making practices, the knowledge of the sulfide capacities of FeO containing slags is valuable to master the desulfurization processes since FeO is an important component in these slags.However, due to experimental difficulties, especially at high temperatures, very few studies were carried out for the FeO containing slags.M. M. Nzotta et al [16] measured sulfide capacity for FeO-Al 2 O 3 -SiO 2 and FeO-CaO-SiO 2 system at 1873 K. Based on their experimental data, the sulfide capacity of FeO-Al 2 O 3 -SiO 2 was calculated . Schematic graph of ternary system with limited solubility region according to the mass triangle model, shown in Figure 2.
Four sulfide capacity contour lines were obtained.In this case, the lowering trends of the sulfide capacities by the addition of SiO 2 as well as the replacement of FeO by Al 2 O 3 are presented as expected.

Application to the feo-cao-sio 2 system
In the case of FeO-CaO-SiO 2 system at 1773 K, boundary data were still using the experimental values provided by M. M. Nzotta [16], the sulfide capacity of this system was evaluated.Seven sulfide capacity contour lines were shown in Figure 3.
As seen in this figure, the increase in the SiO 2 content or the decrease of FeO content resulted in the sharp decrease of sulfide capacities while the influence of CaO can be ignored.
In order to compare the effectivity of this new model, one reference data (a circle in Figure 3) located within the middle miscible area was used for comparison as shown in Table 1.The deviation of calculation results with experimental data was measured by the error rate, defined as eq.( 5).The error rate was referred to as the percentage of incorrect recognitions for each data, as showed in the equation below: (5) It was demonstrated that this new model worked very well in predicting sulfide capacity for the FeO-CaO-SiO 2 system, while the deviation of optical basicity method went up to -10.7%.

Application to the cao-caf 2 -sio 2 system
CaF 2 was applied in desulfurization slag in order to decrease the melting point of corresponding slags.The typical ternary system is CaO-CaF 2 -SiO .Katsujiro et al [17] measured sulfide capacities of CaO-CaF 2 -SiO 2 in the temperature range of 1473 K-1623 K.According to their work, the sulfide capacities contours were evaluated based on the new model, as shown in Figure 4.
The sulfide capacities showed a drastic increase with the increase of CaO/SiO 2 ratio.Meanwhile, the increasing CaF 2 in slags also increases sulfide capacities, which suggests the important role of CaF 2 in the desulfurization.
In this case, several reference data (circles in Figure 4) located within the middle miscible were used for comparison as shown in Table 2.
It was demonstrated that mass triangle model works better in view of the deviations of both mass triangle model and optical basicity model, in spite of the three relatively large deviations in the case of mass triangle model.The possible reason of the larger deviation occurred in the case of optical basicity method was due to this model was developed for slags in higher temperature range.Moreover, the optical basicity model used in this system had seven relatively large deviations.The optical basicity values used for CaO, CaF 2 and SiO 2 were 1.0, 0.43, 0.46 respectively and the sulfide capacities for this system were calculated using eq.( 1) and eq.( 2) as shown in the introduction.

Application to the cao-cacl 2 -caf 2 system
In order to select proper reagents in hot metal pretreatment, it is vital to obtain the thermodynamic data of the melts at lower temperatures.However, the data for sulfide capacity of molten slag is still scarce, especially containing with Cl -and F -whose abilities of holding elements like S have been found by few reports [18][19][20][21][22]. Simeon et al [23] have measured sulfide capacity of CaO-CaCl 2 -CaF 2 at 1373 K. Based on the boundary data provided by Simeon, the sulfide capacities based on mass triangle model were calculated as shown in Figure 5.
It shows that the sulfide capacities increased with the replacing chloride by fluoride at constant content of CaO.At the same time, the sulfide capacities increased slightly with increasing CaO content at the constant ratio of CaF 2 /CaCl 2 since the lime content mainly defined the basicity of slag.
Similarly, two reference data (circles in Figure 5) located within the middle miscible area have been selected for comparison as shown in Table 3.
The maximum error rate is 1.04% and the minimum error rate is 0.798%.It was demonstrated that mass triangle model works

conclusion
In view of the great importance of sulfide capacities in industry practice, it was essential to obtain reliable values from both experimental and theoretical.In theoretical aspect, optical basicity model is widely used in this field.However, with the development of hot-metal treatment, optical basicity model faced great challenges due to lacking the theoretical optical basicity of fluorides and chlorides.As a promising alternative, mass triangle model has been demonstrated its flexibility and reliability not only in high temperature cases, CaO-SiO 2 -FeO, FeO-Al 2 O 3 -SiO 2 etc. but also in lower temperature cases with containing F -and Cl - : CaO-CaF 2 -SiO 2 , CaO-CaF 2 -CaCl 2 .Thus, based on the present study, mass triangle model is a powerful tool in evaluating sulfide capacities of ternary systems with miscible gap.
Figure 1, the sulfide capacities at point O, C o is expressed as the weight summation of the sulphide capacities of the other three points A, B and C. (3) Three lines OD, OE and OC are drawn from the point O parallel to three sides and intersect the boundary of the homogenous phase region at A, B, C. The boundary in where C A , C B and C C represent sulfide capacity at points A, B, C, respectively; W A , W B , and W C are the weight factors corresponding to these three points.The weight factors are determined by triangle area ratios.(4)

Table 1
Comparison between the calculated sulfide capacities using new model and optical basicity method and the reference values in the FeO-CaO-SiO 2 system at 1773 K

Table 2
Comparison between the calculated sulfide capacity using new model and optical basicity method and the reference values in the CaO-CaF 2 -SiO 2 system

Table 3
Comparison between the calculated sulfide capacities using new model the reference values in the CaO-CaCl 2 -CaF 2 system at 1373 K