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Thermodynamics of boron removal in slag refining of Fe-Si alloy
Journal of Alloys and Compounds 768 (2018) 545e552
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Thermodynamics of boron removal in slag refining of Fe-Si alloy Ali Hosseinpour*, Leili Tafaghodi Khajavi University of British Columbia, Materials Engineering Department, Vancouver, British Columbia, V6T 1Z4, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2018 Received in revised form 19 July 2018 Accepted 21 July 2018 Available online 24 July 2018
Two metallurgical purification techniques, namely solvent refining and slag treatment, were combined to remove boron from silicon. Silicon was alloyed with iron and the alloy was subjected to slag treatment by a ternary of CaO-SiO2-Al2O3 at 1600 C (1873 K). Effects of oxygen potential and basicity of slag on boron removal were investigated through changing the SiO2/Al2O3 and CaO/SiO2 ratios, respectively. Results indicate that these two parameters have major effects on partition ratio of boron. A critical oxygen potential value, which yields the highest partition ratio of boron, was calculated as approximately 9 1018 atm. Partition ratio of boron was normalized with oxygen potential at each slag composition in order to isolate the effect of basicity. Borate capacity values were calculated for different slags and it was shown that this parameter is only a function of temperature and slag composition. The kinetics of boron removal was quantified and the total mass transfer coefficient of boron was calculated as 7.48 106 cm/s. © 2018 Elsevier B.V. All rights reserved.
Keywords: Metallurgical techniques Silicon purification Slag treatment Solvent refining Solar grade silicon Boron removal
1. Introduction The utilization of renewable energy sources is one of the main factors that must be considered in discussions of sustainable development. Among the current renewable energy sources, solar power is generally regarded as one of the most appropriate for satisfying the thriving demand. The huge gap between the potential supply of solar energy and the amount that is currently utilized is mostly due to the cost and energy issues associated with the production of solar cells [1,2]. Development of an energy-efficient and cost-effective technology for purification of Si, which is the key raw material in solar cells, can significantly help to narrow this gap [3]. The Siemens process is currently the most widespread industrial method for production of solar grade silicon (SoG-Si). This process involves the conversion of solid metallurgical grade silicon to gaseous compounds, which makes it an energy-intensive route. Also, toxic and corrosive reagents such as gaseous trichlorosilane are used as a precursor in this process. Thus, reducing the environmental impacts and improving the energy efficiency have been the main objectives behind the development of alternative processes for silicon purification [4e7]. Metallurgical purification techniques, that take place in the molten state, fit within the above
* Corresponding author. E-mail address: [email protected] (A. Hosseinpour). https://doi.org/10.1016/j.jallcom.2018.07.246 0925-8388/© 2018 Elsevier B.V. All rights reserved.
objective because of their lower energy consumption and lower cost [8]. The energy consumption of these processes is almost one sixth of Siemens and Siemens-like processes (~130 kW h/kg vs. ~20 kW h/kg) [9]. In addition, the energy payback time of a photovoltaic system using metallurgical route is about 1.1 years while this figure is about 1.3 years for a photovoltaic system using the Siemens process [10]. Metallurgical purification of silicon can lower the lifetime carbon emissions associated with photovoltaics to one-third (21 g C/kWh vs. 6.5 g C/kWh) [11]. Solvent refining is a metallurgical process in which silicon is alloyed with another metal. When the alloy melt is cooled to below the silicon-metal liquidus temperature, impurities with higher affinity for the solvent metal are rejected from the solid silicon and are trapped in the molten alloy phase. The ratio of the concentration of an impurity in liquid phase to that of solid phase is known as the segregation coefficient of the impurity. B is considered as one of the most problematic impurities in Si production because of its high segregation coefficient. A suitable metal for alloying with Si to remove B is one that has low solid solubility in Si and also high affinity for B [8]. Fe [12,13], Al [14e16], Cu [17,18], Mg [19], Sn [20,21], and Ni [22] are some of the alloying agents that have been used for solvent refining of silicon in previous studies. Slag refining is another purification technique which is used for removal of impurities from Si to produce SoG-Si [23e25]. In this method, impurities are removed from silicon through an oxidation reaction. The oxidized impurity is dissolved in the slag phase. Oxidation and dissolution reactions for the removal of B from
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silicon are shown in Eq. (1) and Eq. (2), respectively. Slag components, which are mostly oxides, should be chosen in a way that the melting point of the slag does not exceed the melting point of silicon. Also, the slag should not be miscible with Si and should chemically tend to react with impurities rather than silicon [26]. Elements, such as B, that show higher affinity for silicon than for oxygen cannot be easily oxidized and removed via slag refining. Thus, the slag components should be selected carefully to fulfill all the aforementioned requirements. The overall (oxidation and dissolution) B removal reaction through slag treatment is shown in Eq. (3). [B] þ 3/4 O2 / 1/2 B2O3
(1)
1=2B2 O3 þ 3=2O2 /BO3 3
(2)
2. Experimental 2.1. Materials Silicon powder (crystalline, 140 mesh) with purity of 98.5% and iron powder with purity of 99%, which are the main components of the alloy, were provided by Alfa Aesar CA and SigmaAldrich, respectively. Boron powder (1-mm average) with purity of 99.9% was provided by CERAC. The slag employed in this study consisted of SiO2, Al2O3, and CaO. The first two components were supplied by Alfa Aesar CA and the last one was provided by Fisher Scientific. Sodium hydroxide (NaOH, purity of min 97%, provided by Anachemia), Nitric acid (HNO3, purity of 70%, provided by Anachemia), Sulfuric acid (H2SO4, purity of 95%e98%, provided by Fisher Scientific), and Hydrofluoric acid (HF, purity of 48%, provided by Sigma Aldrich) were also used for digestion of the slag and alloy phases. 2.2. Methods
2
½B þ 3=2O
þ
3=4O2 /BO3 3
(3)
Eq. (3) indicates that the concentration of oxygen ions and partial pressure of oxygen (PO2) are crucial factors to enhance B removal. These two factors are represented by slag basicity and oxygen potential, respectively. Eqs. (4) and (5) show the reactions in which oxygen ions and oxygen molecules, required for B removal, are produced. Basic oxides such as CaO, have a great affinity for SiO2 in slag. Thus, increasing the CaO content of slag leads to lower activity of SiO2 which in turn results in a decline in PO2. In other words, slag basicity and oxygen potential are two counterbalancing factors and it is impossible to increase them simultaneously [27]. CaO (or any other basic oxide such as BaO, Na2O etc.) / Ca2þ þ O2
(4)
SiO2 / Si þ O2
(5)
Partition ratio of an impurity, which is shown by LI and is defined as the ratio of concentration of an impurity in slag to that of silicon, is a crucial factor for evaluating the efficiency of impurity removal via slag refining. Numerous studies have been conducted on increasing the partition ratio of B (LB) through changing the slag composition. Low partition ratios of B are attributed to an inevitable decrease in oxygen potential while increasing the slag basicity. Among all the binary, ternary and quaternary slags used, the highest partition ratio of B (5.5) was reported for a binary slag consisting of SiO2-48.3 mol% CaO at 1823 K (1550 C) [28]. Therefore, a combination of solvent and slag refining has been proposed as a route for improving the partition ratio of B [29e31]. It is worthwhile noting that simultaneous employment of two high temperature processes, i.e. solvent and slag refining is beneficial from the perspective of process energy efficiency. In the current work, Fe was employed as the alloying agent for Si purification. Iron is a favorable choice as the solid solubility of iron in silicon is significantly lower than most of the other solvent metals [32]. This will result in less residual iron in the purified silicon. Additionally iron is not expensive and has the advantage that the by-product of the process, ferrosilicon, can be used in other metallurgical processes. Various compositions within the CaOSiO2-Al2O3 ternary system were utilized as the slag phase. LB values were measured between slag and Si-Fe alloy at 1873 K (1600 C). The effect of basicity on partition ratio values was isolated through two parameters: normalized distribution and borate capacity. Finally, a kinetic analysis of the B removal process was carried out and the total mass transfer coefficient of B was calculated.
Si-20 wt% Fe alloy was made at 1600 C. The sample was held at this temperature for 10 h to provide enough time for preparing a homogeneous alloy. B was also added to the alloy as the impurity in the starting material. The prepared alloy was then crushed and ground for subsequent high temperature experiments. Five grams of pre-melted Si-Fe alloy was charged in an alumina crucible together with 5 g of the desired composition of CaO-SiO2-Al2O3 slag. The crucible was suspended form the upper cap of a vertical tube furnace and heated to 1600 C. Through some preliminary experiments, the holding time required for reaching equilibrium between the slag and the alloy was determined as 8 h. To avoid the oxidation of the samples, argon was purged into the furnace with the flow rate of ~4 lit/h. Fig. 1 shows the schematic of suspension of the sample from the upper cap of the furnace. After equilibrium, the lower cap was opened and the sample was quickly released from the top cap and quenched in a water bath that was placed under the furnace. Fig. 2 shows the temperature profile of the samples in slag/ alloy equilibrium experiments. For each quenched sample, the slag was separated from the alloy and each phase was ground and digested for chemical analysis. 0.1 g of the alloy phase was charged in a Teflon beaker containing 2 ml of H2SO4 and 5 ml of HNO3. HF was also added drop by drop to the beaker until the alloy was completely digested. The beaker was kept in a water/ice bath during the whole digestion process to avoid a sudden increase of the solution temperature. Finally, the solution was diluted with distilled water to prepare it for analysis. 0.3 g of the ground slag was mixed with 4.5 g of NaOH. The mixture was charged in a zirconium crucible (highly resistant to corrosion) and placed in the furnace. It was maintained at 450 C for 2 h followed by slow cooling to room temperature. 0.1 g of the ground fused slag was digested in 5 ml of diluted HNO3. B content of the alloy and the slag were measured by inductively coupled plasma optical emission spectrometry (ICP-OES). 3. Results and discussion 3.1. Determining the equilibrium time Mass transfer occurs slower in slags with higher viscosity because diffusivity is inversely proportional to viscosity [33]. In other words, the slag with the highest viscosity takes the longest time to reach equilibrium. Table 1 shows different slag compositions that were used in the current study. Since decreasing the CaO content of slag results in higher viscosity [34], slag 8 with the lowest CaO content was chosen for determining the equilibrium
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547
Fig. 1. Schematic of the furnace setup used for high temperature experiments.
Table 1 Composition of the slags equilibrated with Si-Fe alloy.
Fig. 2. Temperature profile for alloy/slag equilibrium experiments.
Samples
CaO (wt%)
Al2O3 (wt%)
SiO2 (wt%)
LB
1 2 3 4 5 6 7 8 9 10 11 12
40 40 40 40 40 40 40 20 25 30 35 45
5 7 10 15 20 30 35 15 15 15 15 15
55 53 50 45 40 30 25 65 60 55 50 40
0.9 1.0 3.2 5.3 4.6 1.7 1.5 1.1 0.8 1.4 1.5 11.4
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time between the alloy and the slag. Equilibrium experiments were performed with holding times of 2, 4, 6 and 8 h. Results for these experiments are shown in Table 2 and Fig. 3. Partition ratio of B increases with increasing the holding time. However, it levels off after a specific time which indicates that the slag/alloy equilibrium has been reached. Considering the results presented in Fig. 3, holding time of 8 h was chosen for equilibrium experiments. 3.2. Effect of oxygen potential In order to investigate the effect of oxygen potential on B removal from Si-Fe alloy, CaO content of slag was kept constant at 40 wt% while SiO2/Al2O3 ratio was changed. For this purpose, slag compositions 1 to 7 in Table 1 were chosen. Results of these experiments are presented in Table 1 and Fig. 4. B removal reaction (Eq. (3)) shows that PO2 is one of the factors that can enhance B removal. Thus, it is expected to observe an increase in LB values by increasing the SiO2 content of slag. Fig. 4 shows that the expected trend is achieved at SiO2/Al2O3 ratios smaller than 3. However further increase in SiO2/Al2O3 ratio leads to a decline in LB values. Since SiO2 is a more acidic oxide compared with Al2O3 [35], increasing the SiO2 content of slag results in a more acidic slag i.e. lower concentration of oxygen ions. Thus, further increase in SiO2/Al2O3 ratio decreases LB values. In other words, when PO2 surpasses a critical value, LB decreases due to stronger effect of basicity drop. The highest LB recorded in the present work, by changing the oxygen potential of slag, is 5.3 at SiO2/Al2O3 ratio of 3. The critical oxygen potential (PO2, critical) is defined as the oxygen potential at which the highest removal can be achieved. In other words, the balance between oxygen potential and the concentration of oxygen ions results in the highest partition ratio at this point. Therefore, PO2 at SiO2/Al2O3 ratio of 3 is considered as the PO2, critical for B removal. PO2 for all slag compositions in this study are presented in Table 3. These values are calculated from the equilibrium constant (k ¼ aSi.PO2/aSiO2) for Si/SiO2 equilibrium (Eq. (5)). By obtaining the equilibrium constant of Eq. (5) (from HSC 5.1 thermodynamic database), activity coefficient of silicon in molten Si-Fe (0.977) [36] and activity of silica for various compositions of CaO-SiO2-Al2O3 ternary [37], PO2 for each slag composition was calculated. PO2, critical for B removal process is calculated as approximately 9 1018 atm in this study. 3.3. Effect of basicity According to Eq. (3), concentration of oxygen ions, which is represented by slag basicity, is another crucial factor that is used for improving B removal. To investigate the effect of basicity on partition ratio of B, Al2O3 content of slag was fixed at 15 wt% while the CaO/SiO2 ratio was varied. Slags 4 and 8e12 in Table 1 were chosen for this purpose. Partition ratio results are shown in Table 1 and Fig. 5. Increasing the CaO content of slag provides higher concentration of oxygen ions (Eq. (4)) which is beneficial for B removal. Nevertheless, excessive amounts of basic oxides decrease the oxygen potential because of their great affinity for SiO2. As a result of this conflictive relationship between basicity and oxygen potential
Table 2 Partition ratio of B (LB) as a function of holding time for 20 wt% CaO-65 wt% SiO215 wt% Al2O3. Holding time (h)
2
4
6
8
LB
0.24
0.69
1.08
1.08
Fig. 3. Partition ratio of B (LB) as a function of holding time.
Fig. 4. Partition ratio of B (LB) as a function of SiO2/Al2O3 ratio.
of slag, it is expected to observe a negative parabola when LB values are plotted against CaO/SiO2 ratio. However, as shown in Fig. 5, B partition ratio increases exponentially when the CaO/SiO2 ratio of slag changes in the range of 0.31e1.125. The highest value of LB, which is equal to 11.4, is achieved at the maximum ratio of CaO/ SiO2. In other words, the slag with the highest basicity is the most successful in removal of B. The slag with the highest CaO/SiO2 ratio has the lowest oxygen potential. However, PO2 values for different slag compositions presented in Table 3 show that even the lowest PO2 value which corresponds to the slag with the highest CaO/SiO2 ratio, is higher than PO2, critical (1.40 1017 vs. 9.01 1018). This implies that the expected maximum value of LB cannot be observed in the range of CaO/SiO2 ratio in this study. 3.4. Isolating the effect of basicity As stated before, B is removed according to the reaction presented in Eq. (3). Equilibrium constant (K1) of this reaction is presented in Eq. (6). C1 is a constant applied for converting the mass percent of BO3 3 to mass percent of B in slag phase. (B) and [B] are also representative of concentration of B in slag and alloy, respectively. Eq. (6) can be rearranged to obtain the partition ratio of B (Eq. (7)), where K3 represents the equilibrium constant of Si/SiO2 equilibrium (Eq. (5))
K1 ¼
aBO3 3
3=4 aB aO2
3=2 aO2
¼
C1 ðBÞgBO3 3
3=4
3=2
½B gB PO2 aO2
(6)
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Table 3 Optical basicity, oxygen potential, normalized distribution, and borate capacity for CaO-Al2O3-SiO2 ternary system at 1600 C. L
Slag 1 2 3 4 5 6 7 8 9 10 11 12
DB
PO2 17
1.69 10 1.50 1017 1.25 1017 9.01 1018 6.29 1018 2.80 1018 1.77 1018 8.11 1017 6.14 1017 3.95 1017 2.11 1017 1.40 1017
0.624 0.627 0.632 0.640 0.648 0.664 0.672 0.560 0.579 0.598 0.618 0.663
Fig. 5. Partition ratio of B (LB) as a function of CaO/SiO2 ratio.
3=4 3=2 3=2 ðBÞ K1 gB PO2 aO2 K1 gB aO2 K3 aSiO2 3=4 ¼ LB ¼ ¼ ½B C1 gBO3 C1 gBO3 aSi 3
3
3.47 10 4.06 1012 1.52 1013 3.23 1013 3.67 1013 2.54 1013 3.04 1013 1.27 1012 1.18 1012 2.71 1012 4.88 1012 4.99 1013
1.87 1015 2.18 1015 8.18 1015 1.74 1016 1.97 1016 1.37 1016 1.63 1016 6.84 1014 6.36 1014 1.46 1015 2.62 1015 2.68 1016
Fig. 6. Normalized distribution of B vs. optical basicity of slag for different systems.
(7)
L¼
SXi ni Li SXi ni
(9)
3
As it is obvious in Eq. (7), partition ratio of B is a function of oxygen potential and basicity of slag. Normalized distribution (DB) is a parameter that can be used to remove the effect of oxygen potential from LB. Eq. (8) is used for obtaining DB through normalizing LB values by PO2 at each slag composition. The calculated DB values in this study are listed in Table 3.
DB ¼
CBO3 12
3=4 3=2 ðBÞ aSi K gB aO2 ¼ 1 ½B aSiO2 K3 C1 gBO3
(8)
3
Optical basicity (L) is a parameter directly proportional to the concentration of the negative charge of oxygen ions; thus it is introduced as a measure of slag basicity [38,39]. Eq. (9) can be used for calculating the optical basicity of a multi-component slag. In this equation, Li is the optical basicity of each component of slag, ni is the number of oxygen atoms in each slag component and Xi is the mole fraction of each component. Optical basicity of CaO, SiO2 and Al2O3 was considered as 1, 0.48, and 0.6, respectively [35]. Optical basicity of different slag compositions is presented in Table 3. Fig. 6 shows the relation between DB values and the optical basicity of the slags used in this study. It is clear that by removing the effect of oxygen potential, B distribution represents a direct relation with the basicity of slag. The linear plots are achieved by least-square minimization method. The relation between DB and optical basicity in this study is presented in Eq. (10).
Log (DB) ¼ 15.86 L þ 3.00
(10)
Ma et al. [29] and Li et al. [30] applied slag treatment on alloys of Si-Sn at 1400 C and Si-Cu at 1500 C, respectively. Fig. 6 shows DB values for these systems which were calculated using the data reported in the previous study [40]. DB has a linear relation with optical basicity of slag. According to Eq. (8), there are three variables that can change DB values: 1) K1 which is a function of temperature, 2) aO2- which is a function of slag composition, and 3) aB in Si or alloy which is a function of the alloy composition. Therefore, Lower DB values obtained in the current study can be attributed to the higher purification temperature (1600 C vs. 1500 C and 1400 C), different slag compositions (CaO-SiO2-Al2O3 vs. CaOeSiO2eNa2OeAl2O3 and CaOeSiO2e24mol% CaF2), and different activity coefficients of B (gB in Si-Fe vs. Si-Cu and Si-Sn). Borate capacity is another parameter that is used for isolating the effect of basicity. Borate capacity can be obtained by rearranging Eq. (6) into Eq. (11). Borate capacity values for different slag compositions in the present work are listed in Table 3.
CBO3 ¼ 3
Mass%BO3 3 3=4 aB PO2
3=2
¼
K1 aO2
gBO3 3
(11)
Considering the above equation, borate capacity is only a function of temperature and slag composition and is not dependent on the composition of alloy/metal phase. Therefore, plotting BO3 3
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against optical basicity, it is expected to observe the same equation for all systems that have employed the same temperature and slag composition, regardless of the alloy/metal phase composition. Jakobsson and Tangstad [33] utilized the CaO-SiO2-Al2O3 ternary slag for B removal from silicon metal at 1600 C. Fig. 7 shows the borate capacity values calculated from the results of Jakobsson and Tangstad [33] together with the results of the current study. Borate capacity results of these two studies are in excellent agreement with each other. Eq. (12) shows the relation between borate capacity and optical basicity for CaO-SiO2-Al2O3 system at 1600 C in the composition range examined in the present study.
Ln CBO3 ¼ 36:5 L þ 13:19 3
(12) Fig. 8. Comparing boron removal efficiency for slag refining, solvent refining and combination of slag and solvent refining.
3.5. Comparison with solvent refining and slag refining In order to compare the efficiency of the process used in the current study with that of solvent refining and slag refining, the expected final B content of Si (or alloy) is calculated for all three processes. Fig. 8 shows the minimum and maximum B content of Si (or alloy) calculated from the LB values reported in these processes. For the sake of consistency, the calculations were based on 100 ppm of B in the starting material. The difference between the minimum and the maximum boron content in solvent refining which is shown in Fig. 8, is associated with the variation in the purification temperature. However, changing the slag composition brings about the minimum and maximum values in the slag refining case. Using solvent refining and slag refining boron content can be reduced to as low as ~25 ppm [12] and ~35 ppm [33], respectively. However, the findings of the current study show that combination of solvent refining and slag refining can result in B concentration of ~8 ppm when the slag with the highest LB is utilized. 3.6. Boron removal kinetics Investigating mass transfer of B leads to quantifying its removal rate in the slag refining process. Using the removal rate, the time required for achieving a desired B concentration can be estimated. As it is schematically shown in Fig. 9, removal of dissolved B includes five steps: 1) B is transferred from the bulk of the molten alloy to the slag/alloy interface, 2) SiO2 is transferred from the bulk of molten slag to the slag/alloy interface, 3) At the interface, B is oxidized through a reaction with SiO2 4) Si is transferred from the interface to the bulk of the molten alloy, 5) B2O3 is transferred from the interface to the bulk of the molten slag. Since SiO2 and Si are
among the main components of the slag and the alloy phases, the rate of steps 2 and 4 are not likely to be the limiting steps. Also, since B oxidation reaction (step 3) occurs at high temperature (1600 C), the reaction rate is fast and it is not considered as the rate-determining step. Therefore, steps 1 and 5 are the ones that determine the removal rate of B. According to the two-film theory [41], the mass transfer rate of B can be calculated based on the concentration of B in the alloy. Eq. (13) shows the removal rate where k, A, and V are total mass transfer coefficient, interfacial area between the alloy and the slag, and volume of the alloy, respectively.
d½B A ¼k ½B ½Be dt V
(13)
Integrating this equation, the relation between the concentration of B in the alloy and time is achieved as Eq. (14).
ln
½B ½Be A t ¼ k V ½Bi ½Be
(14)
Where superscripts “i” and “e” stand for initial and equilibrium concentrations, respectively. Concentration of B at holding time of 8 h is used as the equilibrium concentration. The samples with different holding times, which are presented in Table 2, are utilized for calculating the term on the left side of Eq. (14). For the samples presented in Table 2, the alloy phase was dispersed in the slag phase in the form of small droplets. Fig. 10(a) shows some alloy droplets that were separated from the quenched sample. The droplets diameters are in the range of 1.3e3.0 mm. Sauter mean diameter (d32) [42] of the alloy droplets is calculated using Eq. (15). Calculating d32, the number of the alloy droplets (N) dispersed in slag is estimated using Eq. (16).
d32 ¼
N¼
Sd3i
(15)
Sd2i V
4 3
P
d32 2
3
(16)
Substituting N from Eq. (16), Eq. (14) can be rewritten as Eq. (17).
ln
Fig. 7. Borate capacity as a function of optical basicity of slag.
N P d232 ½B ½Be 6 t ¼ k ¼ k t d32 ½Bi ½Be V
(17)
Eq. (17) can be shown in the form of YlnX ¼ -kt. Fig. 10(b) shows the linear relation between YlnX and time. The total mass transfer
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Fig. 9. Schematic of mass transfer of B from an alloy droplet to molten slag.
Fig. 10. (a) Solid alloy droplets separated from a quenched sample (b) Relationship between YlnX and holding time.
coefficient of B, k, is estimated as 7.48 106 cm/s through finding the slope of the linear plot. Fig. 11 shows the SEM image of one of the alloy droplets. As it is obvious, the droplet is consisted of two phases. EDX results confirm that the dark phase is silicon while the bright one is an alloy of Si and Fe (55 wt% Si e 45 wt% Fe).
4. Conclusions A metallurgical purification route is proposed for removing B from silicon. Partition ratios of B between CaO-SiO2-Al2O3 ternary slags and Si-Fe alloy were measured at 1600 C (1873 K). Oxygen potential and basicity of slag are two competing factors that influence the B removal process. Therefore, a critical oxygen potential value, at which a balance between these two factors is achieved, was calculated. The highest LB value of 11.42 was obtained for the slag with the highest CaO/SiO2 ratio (the most basic slag). Thus, it is proposed that slag with the highest basicity and an oxygen potential equal to PO2, critical can bring about the highest B removal. Effect of basicity was isolated through using two parameters, namely normalized distribution and borate capacity. Normalized distribution and borate capacity were respectively correlated to optical basicity of slag via the following equations: Log (DB) ¼ 15.86 L þ 3.00 and Ln (CBO3 ) ¼ 36.5 L þ 13.19. Total mass transfer co3 efficient of B was estimated as 7.48 106 cm/s. Acknowledgement
Fig. 11. SEM image of a droplet of alloy.
The present work has been partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC, RGPIN-2017-04669).
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Thermodynamics of boron removal in slag refining of Fe-Si alloy Ali Hosseinpour*, Leili Tafaghodi Khajavi University of British Columbia, Materials Engineering Department, Vancouver, British Columbia, V6T 1Z4, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 June 2018 Received in revised form 19 July 2018 Accepted 21 July 2018 Available online 24 July 2018
Two metallurgical purification techniques, namely solvent refining and slag treatment, were combined to remove boron from silicon. Silicon was alloyed with iron and the alloy was subjected to slag treatment by a ternary of CaO-SiO2-Al2O3 at 1600 C (1873 K). Effects of oxygen potential and basicity of slag on boron removal were investigated through changing the SiO2/Al2O3 and CaO/SiO2 ratios, respectively. Results indicate that these two parameters have major effects on partition ratio of boron. A critical oxygen potential value, which yields the highest partition ratio of boron, was calculated as approximately 9 1018 atm. Partition ratio of boron was normalized with oxygen potential at each slag composition in order to isolate the effect of basicity. Borate capacity values were calculated for different slags and it was shown that this parameter is only a function of temperature and slag composition. The kinetics of boron removal was quantified and the total mass transfer coefficient of boron was calculated as 7.48 106 cm/s. © 2018 Elsevier B.V. All rights reserved.
Keywords: Metallurgical techniques Silicon purification Slag treatment Solvent refining Solar grade silicon Boron removal
1. Introduction The utilization of renewable energy sources is one of the main factors that must be considered in discussions of sustainable development. Among the current renewable energy sources, solar power is generally regarded as one of the most appropriate for satisfying the thriving demand. The huge gap between the potential supply of solar energy and the amount that is currently utilized is mostly due to the cost and energy issues associated with the production of solar cells [1,2]. Development of an energy-efficient and cost-effective technology for purification of Si, which is the key raw material in solar cells, can significantly help to narrow this gap [3]. The Siemens process is currently the most widespread industrial method for production of solar grade silicon (SoG-Si). This process involves the conversion of solid metallurgical grade silicon to gaseous compounds, which makes it an energy-intensive route. Also, toxic and corrosive reagents such as gaseous trichlorosilane are used as a precursor in this process. Thus, reducing the environmental impacts and improving the energy efficiency have been the main objectives behind the development of alternative processes for silicon purification [4e7]. Metallurgical purification techniques, that take place in the molten state, fit within the above
* Corresponding author. E-mail address: [email protected] (A. Hosseinpour). https://doi.org/10.1016/j.jallcom.2018.07.246 0925-8388/© 2018 Elsevier B.V. All rights reserved.
objective because of their lower energy consumption and lower cost [8]. The energy consumption of these processes is almost one sixth of Siemens and Siemens-like processes (~130 kW h/kg vs. ~20 kW h/kg) [9]. In addition, the energy payback time of a photovoltaic system using metallurgical route is about 1.1 years while this figure is about 1.3 years for a photovoltaic system using the Siemens process [10]. Metallurgical purification of silicon can lower the lifetime carbon emissions associated with photovoltaics to one-third (21 g C/kWh vs. 6.5 g C/kWh) [11]. Solvent refining is a metallurgical process in which silicon is alloyed with another metal. When the alloy melt is cooled to below the silicon-metal liquidus temperature, impurities with higher affinity for the solvent metal are rejected from the solid silicon and are trapped in the molten alloy phase. The ratio of the concentration of an impurity in liquid phase to that of solid phase is known as the segregation coefficient of the impurity. B is considered as one of the most problematic impurities in Si production because of its high segregation coefficient. A suitable metal for alloying with Si to remove B is one that has low solid solubility in Si and also high affinity for B [8]. Fe [12,13], Al [14e16], Cu [17,18], Mg [19], Sn [20,21], and Ni [22] are some of the alloying agents that have been used for solvent refining of silicon in previous studies. Slag refining is another purification technique which is used for removal of impurities from Si to produce SoG-Si [23e25]. In this method, impurities are removed from silicon through an oxidation reaction. The oxidized impurity is dissolved in the slag phase. Oxidation and dissolution reactions for the removal of B from
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silicon are shown in Eq. (1) and Eq. (2), respectively. Slag components, which are mostly oxides, should be chosen in a way that the melting point of the slag does not exceed the melting point of silicon. Also, the slag should not be miscible with Si and should chemically tend to react with impurities rather than silicon [26]. Elements, such as B, that show higher affinity for silicon than for oxygen cannot be easily oxidized and removed via slag refining. Thus, the slag components should be selected carefully to fulfill all the aforementioned requirements. The overall (oxidation and dissolution) B removal reaction through slag treatment is shown in Eq. (3). [B] þ 3/4 O2 / 1/2 B2O3
(1)
1=2B2 O3 þ 3=2O2 /BO3 3
(2)
2. Experimental 2.1. Materials Silicon powder (crystalline, 140 mesh) with purity of 98.5% and iron powder with purity of 99%, which are the main components of the alloy, were provided by Alfa Aesar CA and SigmaAldrich, respectively. Boron powder (1-mm average) with purity of 99.9% was provided by CERAC. The slag employed in this study consisted of SiO2, Al2O3, and CaO. The first two components were supplied by Alfa Aesar CA and the last one was provided by Fisher Scientific. Sodium hydroxide (NaOH, purity of min 97%, provided by Anachemia), Nitric acid (HNO3, purity of 70%, provided by Anachemia), Sulfuric acid (H2SO4, purity of 95%e98%, provided by Fisher Scientific), and Hydrofluoric acid (HF, purity of 48%, provided by Sigma Aldrich) were also used for digestion of the slag and alloy phases. 2.2. Methods
2
½B þ 3=2O
þ
3=4O2 /BO3 3
(3)
Eq. (3) indicates that the concentration of oxygen ions and partial pressure of oxygen (PO2) are crucial factors to enhance B removal. These two factors are represented by slag basicity and oxygen potential, respectively. Eqs. (4) and (5) show the reactions in which oxygen ions and oxygen molecules, required for B removal, are produced. Basic oxides such as CaO, have a great affinity for SiO2 in slag. Thus, increasing the CaO content of slag leads to lower activity of SiO2 which in turn results in a decline in PO2. In other words, slag basicity and oxygen potential are two counterbalancing factors and it is impossible to increase them simultaneously [27]. CaO (or any other basic oxide such as BaO, Na2O etc.) / Ca2þ þ O2
(4)
SiO2 / Si þ O2
(5)
Partition ratio of an impurity, which is shown by LI and is defined as the ratio of concentration of an impurity in slag to that of silicon, is a crucial factor for evaluating the efficiency of impurity removal via slag refining. Numerous studies have been conducted on increasing the partition ratio of B (LB) through changing the slag composition. Low partition ratios of B are attributed to an inevitable decrease in oxygen potential while increasing the slag basicity. Among all the binary, ternary and quaternary slags used, the highest partition ratio of B (5.5) was reported for a binary slag consisting of SiO2-48.3 mol% CaO at 1823 K (1550 C) [28]. Therefore, a combination of solvent and slag refining has been proposed as a route for improving the partition ratio of B [29e31]. It is worthwhile noting that simultaneous employment of two high temperature processes, i.e. solvent and slag refining is beneficial from the perspective of process energy efficiency. In the current work, Fe was employed as the alloying agent for Si purification. Iron is a favorable choice as the solid solubility of iron in silicon is significantly lower than most of the other solvent metals [32]. This will result in less residual iron in the purified silicon. Additionally iron is not expensive and has the advantage that the by-product of the process, ferrosilicon, can be used in other metallurgical processes. Various compositions within the CaOSiO2-Al2O3 ternary system were utilized as the slag phase. LB values were measured between slag and Si-Fe alloy at 1873 K (1600 C). The effect of basicity on partition ratio values was isolated through two parameters: normalized distribution and borate capacity. Finally, a kinetic analysis of the B removal process was carried out and the total mass transfer coefficient of B was calculated.
Si-20 wt% Fe alloy was made at 1600 C. The sample was held at this temperature for 10 h to provide enough time for preparing a homogeneous alloy. B was also added to the alloy as the impurity in the starting material. The prepared alloy was then crushed and ground for subsequent high temperature experiments. Five grams of pre-melted Si-Fe alloy was charged in an alumina crucible together with 5 g of the desired composition of CaO-SiO2-Al2O3 slag. The crucible was suspended form the upper cap of a vertical tube furnace and heated to 1600 C. Through some preliminary experiments, the holding time required for reaching equilibrium between the slag and the alloy was determined as 8 h. To avoid the oxidation of the samples, argon was purged into the furnace with the flow rate of ~4 lit/h. Fig. 1 shows the schematic of suspension of the sample from the upper cap of the furnace. After equilibrium, the lower cap was opened and the sample was quickly released from the top cap and quenched in a water bath that was placed under the furnace. Fig. 2 shows the temperature profile of the samples in slag/ alloy equilibrium experiments. For each quenched sample, the slag was separated from the alloy and each phase was ground and digested for chemical analysis. 0.1 g of the alloy phase was charged in a Teflon beaker containing 2 ml of H2SO4 and 5 ml of HNO3. HF was also added drop by drop to the beaker until the alloy was completely digested. The beaker was kept in a water/ice bath during the whole digestion process to avoid a sudden increase of the solution temperature. Finally, the solution was diluted with distilled water to prepare it for analysis. 0.3 g of the ground slag was mixed with 4.5 g of NaOH. The mixture was charged in a zirconium crucible (highly resistant to corrosion) and placed in the furnace. It was maintained at 450 C for 2 h followed by slow cooling to room temperature. 0.1 g of the ground fused slag was digested in 5 ml of diluted HNO3. B content of the alloy and the slag were measured by inductively coupled plasma optical emission spectrometry (ICP-OES). 3. Results and discussion 3.1. Determining the equilibrium time Mass transfer occurs slower in slags with higher viscosity because diffusivity is inversely proportional to viscosity [33]. In other words, the slag with the highest viscosity takes the longest time to reach equilibrium. Table 1 shows different slag compositions that were used in the current study. Since decreasing the CaO content of slag results in higher viscosity [34], slag 8 with the lowest CaO content was chosen for determining the equilibrium
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547
Fig. 1. Schematic of the furnace setup used for high temperature experiments.
Table 1 Composition of the slags equilibrated with Si-Fe alloy.
Fig. 2. Temperature profile for alloy/slag equilibrium experiments.
Samples
CaO (wt%)
Al2O3 (wt%)
SiO2 (wt%)
LB
1 2 3 4 5 6 7 8 9 10 11 12
40 40 40 40 40 40 40 20 25 30 35 45
5 7 10 15 20 30 35 15 15 15 15 15
55 53 50 45 40 30 25 65 60 55 50 40
0.9 1.0 3.2 5.3 4.6 1.7 1.5 1.1 0.8 1.4 1.5 11.4
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time between the alloy and the slag. Equilibrium experiments were performed with holding times of 2, 4, 6 and 8 h. Results for these experiments are shown in Table 2 and Fig. 3. Partition ratio of B increases with increasing the holding time. However, it levels off after a specific time which indicates that the slag/alloy equilibrium has been reached. Considering the results presented in Fig. 3, holding time of 8 h was chosen for equilibrium experiments. 3.2. Effect of oxygen potential In order to investigate the effect of oxygen potential on B removal from Si-Fe alloy, CaO content of slag was kept constant at 40 wt% while SiO2/Al2O3 ratio was changed. For this purpose, slag compositions 1 to 7 in Table 1 were chosen. Results of these experiments are presented in Table 1 and Fig. 4. B removal reaction (Eq. (3)) shows that PO2 is one of the factors that can enhance B removal. Thus, it is expected to observe an increase in LB values by increasing the SiO2 content of slag. Fig. 4 shows that the expected trend is achieved at SiO2/Al2O3 ratios smaller than 3. However further increase in SiO2/Al2O3 ratio leads to a decline in LB values. Since SiO2 is a more acidic oxide compared with Al2O3 [35], increasing the SiO2 content of slag results in a more acidic slag i.e. lower concentration of oxygen ions. Thus, further increase in SiO2/Al2O3 ratio decreases LB values. In other words, when PO2 surpasses a critical value, LB decreases due to stronger effect of basicity drop. The highest LB recorded in the present work, by changing the oxygen potential of slag, is 5.3 at SiO2/Al2O3 ratio of 3. The critical oxygen potential (PO2, critical) is defined as the oxygen potential at which the highest removal can be achieved. In other words, the balance between oxygen potential and the concentration of oxygen ions results in the highest partition ratio at this point. Therefore, PO2 at SiO2/Al2O3 ratio of 3 is considered as the PO2, critical for B removal. PO2 for all slag compositions in this study are presented in Table 3. These values are calculated from the equilibrium constant (k ¼ aSi.PO2/aSiO2) for Si/SiO2 equilibrium (Eq. (5)). By obtaining the equilibrium constant of Eq. (5) (from HSC 5.1 thermodynamic database), activity coefficient of silicon in molten Si-Fe (0.977) [36] and activity of silica for various compositions of CaO-SiO2-Al2O3 ternary [37], PO2 for each slag composition was calculated. PO2, critical for B removal process is calculated as approximately 9 1018 atm in this study. 3.3. Effect of basicity According to Eq. (3), concentration of oxygen ions, which is represented by slag basicity, is another crucial factor that is used for improving B removal. To investigate the effect of basicity on partition ratio of B, Al2O3 content of slag was fixed at 15 wt% while the CaO/SiO2 ratio was varied. Slags 4 and 8e12 in Table 1 were chosen for this purpose. Partition ratio results are shown in Table 1 and Fig. 5. Increasing the CaO content of slag provides higher concentration of oxygen ions (Eq. (4)) which is beneficial for B removal. Nevertheless, excessive amounts of basic oxides decrease the oxygen potential because of their great affinity for SiO2. As a result of this conflictive relationship between basicity and oxygen potential
Table 2 Partition ratio of B (LB) as a function of holding time for 20 wt% CaO-65 wt% SiO215 wt% Al2O3. Holding time (h)
2
4
6
8
LB
0.24
0.69
1.08
1.08
Fig. 3. Partition ratio of B (LB) as a function of holding time.
Fig. 4. Partition ratio of B (LB) as a function of SiO2/Al2O3 ratio.
of slag, it is expected to observe a negative parabola when LB values are plotted against CaO/SiO2 ratio. However, as shown in Fig. 5, B partition ratio increases exponentially when the CaO/SiO2 ratio of slag changes in the range of 0.31e1.125. The highest value of LB, which is equal to 11.4, is achieved at the maximum ratio of CaO/ SiO2. In other words, the slag with the highest basicity is the most successful in removal of B. The slag with the highest CaO/SiO2 ratio has the lowest oxygen potential. However, PO2 values for different slag compositions presented in Table 3 show that even the lowest PO2 value which corresponds to the slag with the highest CaO/SiO2 ratio, is higher than PO2, critical (1.40 1017 vs. 9.01 1018). This implies that the expected maximum value of LB cannot be observed in the range of CaO/SiO2 ratio in this study. 3.4. Isolating the effect of basicity As stated before, B is removed according to the reaction presented in Eq. (3). Equilibrium constant (K1) of this reaction is presented in Eq. (6). C1 is a constant applied for converting the mass percent of BO3 3 to mass percent of B in slag phase. (B) and [B] are also representative of concentration of B in slag and alloy, respectively. Eq. (6) can be rearranged to obtain the partition ratio of B (Eq. (7)), where K3 represents the equilibrium constant of Si/SiO2 equilibrium (Eq. (5))
K1 ¼
aBO3 3
3=4 aB aO2
3=2 aO2
¼
C1 ðBÞgBO3 3
3=4
3=2
½B gB PO2 aO2
(6)
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Table 3 Optical basicity, oxygen potential, normalized distribution, and borate capacity for CaO-Al2O3-SiO2 ternary system at 1600 C. L
Slag 1 2 3 4 5 6 7 8 9 10 11 12
DB
PO2 17
1.69 10 1.50 1017 1.25 1017 9.01 1018 6.29 1018 2.80 1018 1.77 1018 8.11 1017 6.14 1017 3.95 1017 2.11 1017 1.40 1017
0.624 0.627 0.632 0.640 0.648 0.664 0.672 0.560 0.579 0.598 0.618 0.663
Fig. 5. Partition ratio of B (LB) as a function of CaO/SiO2 ratio.
3=4 3=2 3=2 ðBÞ K1 gB PO2 aO2 K1 gB aO2 K3 aSiO2 3=4 ¼ LB ¼ ¼ ½B C1 gBO3 C1 gBO3 aSi 3
3
3.47 10 4.06 1012 1.52 1013 3.23 1013 3.67 1013 2.54 1013 3.04 1013 1.27 1012 1.18 1012 2.71 1012 4.88 1012 4.99 1013
1.87 1015 2.18 1015 8.18 1015 1.74 1016 1.97 1016 1.37 1016 1.63 1016 6.84 1014 6.36 1014 1.46 1015 2.62 1015 2.68 1016
Fig. 6. Normalized distribution of B vs. optical basicity of slag for different systems.
(7)
L¼
SXi ni Li SXi ni
(9)
3
As it is obvious in Eq. (7), partition ratio of B is a function of oxygen potential and basicity of slag. Normalized distribution (DB) is a parameter that can be used to remove the effect of oxygen potential from LB. Eq. (8) is used for obtaining DB through normalizing LB values by PO2 at each slag composition. The calculated DB values in this study are listed in Table 3.
DB ¼
CBO3 12
3=4 3=2 ðBÞ aSi K gB aO2 ¼ 1 ½B aSiO2 K3 C1 gBO3
(8)
3
Optical basicity (L) is a parameter directly proportional to the concentration of the negative charge of oxygen ions; thus it is introduced as a measure of slag basicity [38,39]. Eq. (9) can be used for calculating the optical basicity of a multi-component slag. In this equation, Li is the optical basicity of each component of slag, ni is the number of oxygen atoms in each slag component and Xi is the mole fraction of each component. Optical basicity of CaO, SiO2 and Al2O3 was considered as 1, 0.48, and 0.6, respectively [35]. Optical basicity of different slag compositions is presented in Table 3. Fig. 6 shows the relation between DB values and the optical basicity of the slags used in this study. It is clear that by removing the effect of oxygen potential, B distribution represents a direct relation with the basicity of slag. The linear plots are achieved by least-square minimization method. The relation between DB and optical basicity in this study is presented in Eq. (10).
Log (DB) ¼ 15.86 L þ 3.00
(10)
Ma et al. [29] and Li et al. [30] applied slag treatment on alloys of Si-Sn at 1400 C and Si-Cu at 1500 C, respectively. Fig. 6 shows DB values for these systems which were calculated using the data reported in the previous study [40]. DB has a linear relation with optical basicity of slag. According to Eq. (8), there are three variables that can change DB values: 1) K1 which is a function of temperature, 2) aO2- which is a function of slag composition, and 3) aB in Si or alloy which is a function of the alloy composition. Therefore, Lower DB values obtained in the current study can be attributed to the higher purification temperature (1600 C vs. 1500 C and 1400 C), different slag compositions (CaO-SiO2-Al2O3 vs. CaOeSiO2eNa2OeAl2O3 and CaOeSiO2e24mol% CaF2), and different activity coefficients of B (gB in Si-Fe vs. Si-Cu and Si-Sn). Borate capacity is another parameter that is used for isolating the effect of basicity. Borate capacity can be obtained by rearranging Eq. (6) into Eq. (11). Borate capacity values for different slag compositions in the present work are listed in Table 3.
CBO3 ¼ 3
Mass%BO3 3 3=4 aB PO2
3=2
¼
K1 aO2
gBO3 3
(11)
Considering the above equation, borate capacity is only a function of temperature and slag composition and is not dependent on the composition of alloy/metal phase. Therefore, plotting BO3 3
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against optical basicity, it is expected to observe the same equation for all systems that have employed the same temperature and slag composition, regardless of the alloy/metal phase composition. Jakobsson and Tangstad [33] utilized the CaO-SiO2-Al2O3 ternary slag for B removal from silicon metal at 1600 C. Fig. 7 shows the borate capacity values calculated from the results of Jakobsson and Tangstad [33] together with the results of the current study. Borate capacity results of these two studies are in excellent agreement with each other. Eq. (12) shows the relation between borate capacity and optical basicity for CaO-SiO2-Al2O3 system at 1600 C in the composition range examined in the present study.
Ln CBO3 ¼ 36:5 L þ 13:19 3
(12) Fig. 8. Comparing boron removal efficiency for slag refining, solvent refining and combination of slag and solvent refining.
3.5. Comparison with solvent refining and slag refining In order to compare the efficiency of the process used in the current study with that of solvent refining and slag refining, the expected final B content of Si (or alloy) is calculated for all three processes. Fig. 8 shows the minimum and maximum B content of Si (or alloy) calculated from the LB values reported in these processes. For the sake of consistency, the calculations were based on 100 ppm of B in the starting material. The difference between the minimum and the maximum boron content in solvent refining which is shown in Fig. 8, is associated with the variation in the purification temperature. However, changing the slag composition brings about the minimum and maximum values in the slag refining case. Using solvent refining and slag refining boron content can be reduced to as low as ~25 ppm [12] and ~35 ppm [33], respectively. However, the findings of the current study show that combination of solvent refining and slag refining can result in B concentration of ~8 ppm when the slag with the highest LB is utilized. 3.6. Boron removal kinetics Investigating mass transfer of B leads to quantifying its removal rate in the slag refining process. Using the removal rate, the time required for achieving a desired B concentration can be estimated. As it is schematically shown in Fig. 9, removal of dissolved B includes five steps: 1) B is transferred from the bulk of the molten alloy to the slag/alloy interface, 2) SiO2 is transferred from the bulk of molten slag to the slag/alloy interface, 3) At the interface, B is oxidized through a reaction with SiO2 4) Si is transferred from the interface to the bulk of the molten alloy, 5) B2O3 is transferred from the interface to the bulk of the molten slag. Since SiO2 and Si are
among the main components of the slag and the alloy phases, the rate of steps 2 and 4 are not likely to be the limiting steps. Also, since B oxidation reaction (step 3) occurs at high temperature (1600 C), the reaction rate is fast and it is not considered as the rate-determining step. Therefore, steps 1 and 5 are the ones that determine the removal rate of B. According to the two-film theory [41], the mass transfer rate of B can be calculated based on the concentration of B in the alloy. Eq. (13) shows the removal rate where k, A, and V are total mass transfer coefficient, interfacial area between the alloy and the slag, and volume of the alloy, respectively.
d½B A ¼k ½B ½Be dt V
(13)
Integrating this equation, the relation between the concentration of B in the alloy and time is achieved as Eq. (14).
ln
½B ½Be A t ¼ k V ½Bi ½Be
(14)
Where superscripts “i” and “e” stand for initial and equilibrium concentrations, respectively. Concentration of B at holding time of 8 h is used as the equilibrium concentration. The samples with different holding times, which are presented in Table 2, are utilized for calculating the term on the left side of Eq. (14). For the samples presented in Table 2, the alloy phase was dispersed in the slag phase in the form of small droplets. Fig. 10(a) shows some alloy droplets that were separated from the quenched sample. The droplets diameters are in the range of 1.3e3.0 mm. Sauter mean diameter (d32) [42] of the alloy droplets is calculated using Eq. (15). Calculating d32, the number of the alloy droplets (N) dispersed in slag is estimated using Eq. (16).
d32 ¼
N¼
Sd3i
(15)
Sd2i V
4 3
P
d32 2
3
(16)
Substituting N from Eq. (16), Eq. (14) can be rewritten as Eq. (17).
ln
Fig. 7. Borate capacity as a function of optical basicity of slag.
N P d232 ½B ½Be 6 t ¼ k ¼ k t d32 ½Bi ½Be V
(17)
Eq. (17) can be shown in the form of YlnX ¼ -kt. Fig. 10(b) shows the linear relation between YlnX and time. The total mass transfer
A. Hosseinpour, L. Tafaghodi Khajavi / Journal of Alloys and Compounds 768 (2018) 545e552
551
Fig. 9. Schematic of mass transfer of B from an alloy droplet to molten slag.
Fig. 10. (a) Solid alloy droplets separated from a quenched sample (b) Relationship between YlnX and holding time.
coefficient of B, k, is estimated as 7.48 106 cm/s through finding the slope of the linear plot. Fig. 11 shows the SEM image of one of the alloy droplets. As it is obvious, the droplet is consisted of two phases. EDX results confirm that the dark phase is silicon while the bright one is an alloy of Si and Fe (55 wt% Si e 45 wt% Fe).
4. Conclusions A metallurgical purification route is proposed for removing B from silicon. Partition ratios of B between CaO-SiO2-Al2O3 ternary slags and Si-Fe alloy were measured at 1600 C (1873 K). Oxygen potential and basicity of slag are two competing factors that influence the B removal process. Therefore, a critical oxygen potential value, at which a balance between these two factors is achieved, was calculated. The highest LB value of 11.42 was obtained for the slag with the highest CaO/SiO2 ratio (the most basic slag). Thus, it is proposed that slag with the highest basicity and an oxygen potential equal to PO2, critical can bring about the highest B removal. Effect of basicity was isolated through using two parameters, namely normalized distribution and borate capacity. Normalized distribution and borate capacity were respectively correlated to optical basicity of slag via the following equations: Log (DB) ¼ 15.86 L þ 3.00 and Ln (CBO3 ) ¼ 36.5 L þ 13.19. Total mass transfer co3 efficient of B was estimated as 7.48 106 cm/s. Acknowledgement
Fig. 11. SEM image of a droplet of alloy.
The present work has been partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC, RGPIN-2017-04669).
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