Thermochemical Aspects of Boron and Phosphorus Distribution Between Silicon and BaO-SiO2 and CaO-BaO-SiO2 lags

In the production of solar grade silicon by metallurgical route the distribution of B and P between slags and liquid silicon is the most important key issue. The equilibrium and thermochemistry of reactions between liquid silicon and BaO-SiO2 slags and up to 10% BaO-containing CaO-BaO-SiO2 slags is studied through experimental work and using thermodynamic calculations. It is shown that the distribution coefficient of B (LB) is higher for the CaO-BaO-SiO2 slags than that for BaO-SiO2 slags and it is not significantly affected by temperature and composition changes of the slags. In contrast, the distribution coefficient of P (LP) is higher for BaO-SiO2 slags than that for the CaO-BaO-SiO2 slags, and it is higher at lower temperatures. The chemical activities of the dilute solutions of Ba in liquid silicon, and the dilute solutions of B2O3, P2O5 and BaO in the slags are calculated. Moreover, the reaction mechanisms for B, P, Ba and Ca transport between liquid silicon and the slags are explained.


Introduction
Silicon is liberated from its natural oxide form (quartz) through a carbothermic reduction process in submerged electric arc furnace; the product being metallurgical grade silicon (MG-Si), which is further purified to reach solar grade silicon (SoG-Si) quality for PV applications.
The purity of MG-Si isusually above 99% Si and it contains impurities such as Fe, Al, Ti, Ca, B, and P [1], while SoG-Si has much higher purity of above 99.9999 %Si. The majority of SoG-Si feedstock in the market is currently produced from MG-Si through the well known Siemens process or newly developed fluid bed reactor (FBR) technology. In these chemical processes, pure silicon is deposited on rods or silicon seeds from a gas phase, which is produced through the conversion of MG-Si to purified gaseous compounds of silicon; SiHCl3 or SiH4.
The Siemens process in particular is an expensive process with regard to high energy consumption [2,3]. However, the production of SoG-Si through metallurgical refining processes is more energy efficient and environmentally friendly than chemical route which in turn may encourage a faster growth of the global PV market. This has been the motivation for the development of several refining processes, where MG-Si is refined through the combination of sub-processes to produce SoG-Si. Almost all the present impurities in MG-Si except B and P can be effectively removed by directional solidification, which is a final key process step in metallurgical approaches. Boron is the most difficult element to be removed by directional solidification due to its large distribution coefficient between solid and liquid phases, which is KB=0.8 [4]. In order to remove this impurity, many potential processes have been studied such as slag refining, plasma refining, gas refining, solvent refining, leaching, etc. [3] . In particular, the slag refining technique is a part of the only commercial metallurgical process of ELKEM Solar for SoG-Si production, where the dissolved B in silicon is adsorbed to a silicate slag through oxidation. Hence, the potential of slags for B removal is the main important parameter to consider for the process. In this case, the thermodynamic equilibrium for B distribution 3 between liquid silicon and molten slags is studied, which is defined based on the weight percentages of B in the two phases as: The magnitude of LB-value is depending on slag type and composition, temperature, gas phase composition and as it is a quite important parameter it has been extensively studied through many experimental works for many silicate slag systems. For instance, many slags such as CaO-SiO2 [5,6,7,8,9,10], CaO-CaF2-SiO2 [6,8,11,12], CaO-BaO-SiO2 [6], CaO-MgO-SiO2 [5,6,13], CaO-Al2O3--SiO2 [14], CaO-Na2O-SiO2 [14,15], Al2O3-CaO-MgO-SiO2 [16], Al2O3-BaO-SiO2 [16] and Al2O3-CaO-MgO-SiO2 [16] , Na2O-SiO2 [17] and CaO-Na2O-SiO2 slags [18] have been studied experimentally. In general L B is increased with increasing temperature as been observed through the studies using CaO-SiO 2 slags [6], CaO-CaF 2 -SiO 2 slags [6,12], and CaO-Na 2 O-SiO 2 slags [14,15]. The relationship between L B and slag chemical composition is complicated and L B in a wide range from 0.3 for CaO-SiO 2 slags to 9.3 [6] for CaO-Al 2 O 3 -SiO 2 slags [14] have been reported by different researchers. Inspecting the literature data it is seen that the measured L B values for a given slag system are not in agreement. For instance, the reported L B values by Teixeira et al. [8] using CaO-SiO 2 slags are in the range of 2 to 5.5, L B is in the minimum at CaO/SiO 2 =0.85 and it is increased with both decreases and increases of the slag basicity. However, much narrower L B range for the same slag system has been observed in which L B is not significantly affected by the slag chemical composition and it is increaseed minimally from 2.2 to 2.5 with increasing the basicity from 0.6 to 1.3 [9] . It has to be noticed that the analysis of B in low concentrations in both Si and slag phases is a challenge and this issue may be a reason for observing different results in similar 4 experiments, in addition to other sources of errors. The recent studies on using Na 2 O-SiO 2 [17] and CaO-Na 2 O-SiO 2 [18] slags have shown that when Na 2 O-containog slags are contacted with silicon the dissolved B is also gasified in the form of sodium metaborate (Na 2 B 2 O 4 ) due to its relative high vapor pressure in the system as its mechanism has been explained. [17,18] In the present study the distribution of B and also P between silicon and BaO-SiO 2 and CaO-BaO-SiO 2 slags is studied. In addition to B distribution, the P distribution between slags and silicon is studied as it is more concentrated in the silicon phase and it may affect further silicon purification processes, i. e. acid leaching. The involved reactions for the mass transport of Ba, Ca, B and P between the silicon and slag phases are studied. The thermodynamic activities of the solute elements in the silicon and slag phases are determined through applying the fundamental thermochemical approaches, employing thermodynamic tables and software.

Experimental procedure
In the present study, specific silicon and slag samples were produced and further interacted at elevated temperatures through the following described methodology.

Materials preparation
Two types of BaO-containing slags were prepared by mixing high purity powders of BaO, CaO and SiO2 powders (+99%) and melting the mixtures in high purity graphite crucibles. The slags were BaO-SiO2 binary slags, and BaO-CaO-SiO2 slags containing up to 10%BaO, the initial compositions for these slags are given in Table 1. All the target slag compositions are in molten state at the target reaction temperatures, according to the related binary and ternary slag systems. The slags were prepared through heating up the mixtures to 1923±30 K (1650±30˚C) 5 and holding for around one hour for complete melting, followed by slow cooling to the room temperature.
High purity electronic grade silicon was doped by B and P elements through mixing with two high purity Si-B and Si-P master alloys, which were containing 500 ppm B and 1300 ppm P, respectively. The applied procedures for making these two master alloys were described previously [19,20]. The silicon mixtures were melted through their heating up to 1823 K (1550˚C) in a high purity graphite crucible in an induction furnace, holding at this temperature for 30 minutes and casting the melt in a water-cooled copper mold to attain a homogeneous silicon regarding the B and P concentrations. As a result, a silicon containing 30±1 ppmw B and 25±0.5 ppmw P was produced as analyzed by a high resolution Inductively Coupled Plasma-Mass Spectrometer (ICP-MS) on four samples. It is worth mentioning that the contamination of silicon by carbon is not significant as the solubility of carbon in silicon is low, i.e. 150 ppm at 1550 ˚C. This small amount of carbon have no significant effect on the chemical properties of B and P components, which is more acceptable when the concentrations are very low as this study.

Silicon and slag interaction
The B-and P-doped silicon sample was added into the slag-containing crucibles, while the slag/silicon mass ratio was fixed equal to 2. Then the crucibles were heated to 1773 K (1500˚C) and 1873 K (1600˚C) in an induction furnace under high purity Ar (99.999%Ar) flow. The samples were hold at the target temperatures for 2 hours, followed by slow cooling to the room temperature. As the electromagnetic forces extensively stir the molten silicon, it causes high mixing of the system and equilibrium is reached in the experiments duration. The solidified samples were then crushed and silicon and slag particles were separated. It is worth mentioning that the solidified silicon and slag phases showed similar configuration in all crucibles (silicon melt is surrounded by slag phase) as observed previously in using Na2O-SiO2 slag [17] indicating complete melting and proper contact of the two phase. The samples were then analyzed for measuring the main components by ICP-MS. In this case, three parallels of each sample were analyzed and then the average compositions were determined.

Results
The results of the experiments are described as follows.

Mass transport between the phases and Ba and Ca distribution
The measured chemical compositions of the slags after interaction with silicon are given in Table 1. The chemical composition changes in this table show that there is significant mass transport between the two phases so that the concentrations of Ba, Ca and Si in the slags are significantly different compare to the initial slag concentrations. However, no significant changes in the main slag components is observed for the experiments 8, 9 and 12. This may indicate that the slags 8 and 9 are in almost equilibrium with molten silicon. However, experiment 10 result may indicate that BaO in low concentrations has a high affinity into the CaO-SiO2 slags (with CaO/SiO2 =0.67) and it is not reduced at 1500˚C when up to 2.5 %BaO exists in the slag. The measured concentrations of Ba in silicon interacted with the binary BaO-SiO2 slags (Fig.1 ) show that the solubility of Ba in silicon is increased with increasing the slag basicity (BaO/SiO2 ratio), indicating there is larger driving force for the mass transport of Ba from the barium-silicate slags into the liquid metal for higher basicities. Moreover, the amount 7 of Ba in silicon is depending on the process temperature. Fig. 1 shows that more Ba is transferred from the slags into silicon at the higher temperature, while there is slightly different trends at the two temperatures for Ba concentration dependence on basicity changes.
The measured concentrations for experiments 9 to 14 show that the mass transport of both Ca and Ba from the slag into the silicon occurs; Ca for CaO-SiO2 slags and the both elements in CaO-BaO-SiO2 slags. Fig. 2 shows that Ba transfer into liquid silicon is increased with increasing the concentration of BaO in the initial slag for a given temperature and initial CaO/SiO2 ratios. Regarding the concentrations in Table 1, there is significant reduction in basicity ((wt%CaO+wt%BaO)/wt%SiO2) when BaO exists in the slag, and considerable reductions of BaO and CaO occurs, which is accompanied with Si transfer as SiO2 into the slag. According to Table 1 and Figs. 1 and 2, the transfer of Ba and Ca into liquid silicon for a given initial chemical composition is significantly higher at 1873 K (1600˚C) than 1773 K (1500˚C). Figure 3 shows the relationship between XBa/XCa molar ratio and XBaO/XCaO molar ratio in metal and slag phases, respectively. A direct relationship between these concentration ratios in the two phases is observed and larger XBa/XCa ratio for higher BaO concentrations in the initial ternary slags. However, it is observed that for a given BaO/CaO ratio there is higher Ba/Ca ratio in the metal phase at the lower temperature, evident of CaO reduction at 1873 K (1600˚C) is significantly more than that at 1773 K (1500˚C). It is worth noting that Ca and Ba transferred into the silicon are easily removed by directional solidification in the integrated solar silicon process. 8

The distribution of phosphorus
The distribution coefficient of P between the slag and silicon phases (LP) can be calculated based on the measured P concentrations in the two phases using the following expression: (2) Figure 4 shows the relationship between LP and basicity for the binary BaO-SiO2 slags in contact with silicon. Obviously, the LP value is depending on temperature and it is larger for lower temperatures. Moreover, LP is not significantly depending on the basicity, and it is increased or decreased minimally with basicity changes, however, different trends for the two temperatures are observed. The distribution of P between CaO-(BaO)-SiO2 slags and silicon in However, the LP change with basicity change is not significant at 1873 K (1600˚C). This may show that the introduction of small amount of BaO into CaO-SiO2 slag is beneficial for P removal. However, the both diagrams in Figs. 6 and 7 indicate that the effect of temperature on P distribution is the main parameter. It is worth mentioning that LP for 20%Al2O3-BaO-SiO2 slags for BaO/SiO2 between 0.45 to 1.3 was studied by Johnston and Barati [16] and the measured LP between 0.1 to 0.2 at 1773 K (1500˚C), which is lower than the LP in this study.

The distribution of boron
The measured concentrations of B between the slag and metal phases were used to calculate the distribution coefficient of B between the two phases by Eq. (1) and the results for the BaO-SiO2 slags and CaO-BaO-SiO2 slags are shown in Figs. 6 and 7, respectively. These figures 9 show that LB is significantly lower for BaO-SiO2 slags than that for low BaO-containing CaO-SiO2 slags. LB is in the range of 0.85 to 1.35 for BaO-SiO2 slags, while for the other slag is in the range of 2.0 to 2.4. On the other hand, the relationship between the LB and basicity in these slags is different. It is worth mentioning that Suzuki et al. [6] measured lower LB-values for using CaO-10%BaO-SiO2 slags at 1723K ( 1450˚C) and the obtained LB between 1.45 to 1.9 for (CaO+BaO)/SiO2 ratios between 0.8 to1.3, which are higher basicity range than the present study. As seen in Fig. 6, when the binary BaO-SiO2 slag is contacted with liquid silicon, the LB value is showing smaller value when the basicity is close to unity. However, for other studied basicities, up to around 30% higher LB-value is observed. Moreover, LB-value is higher for higher temperature for a given slag composition, meaning that more B is possible to be removed from silicon at higher temperatures, this may be the reason of obtaining higher LBvalues in this study than Suzuki et al. [6]. The changes of LB with basicity for the CaO-(BaO)-SiO2 slags in Fig. 7 show that LB is not significantly affected by the introduction of small amount of BaO into the CaO-SiO2 slag. Moreover, it is difficult to see a clear effect of temperature and LB-value in a short range of 2.1±0.1 at 1600˚C, and 2.2±0.2 at 1500˚C. This insignificant temperature dependence of LB is in agreement with literature for CaO-SiO2 slag systems [27]. In contrast to LP parameter, LB is more dependent on the slag composition and less on process temperature.

Discussion
The obtained results presented in the previous section are discussed and they are used to determine some thermodynamics parameters in the studied slag-metal systems.

Mass transport of Ba into silicon and its chemical activity
When the binary BaO-SiO2 slag reacts with the high purity liquid silicon, a portion of Ba is transferred into the molten silicon through the following reaction: In addition, when a BaO-CaO-SiO2 ternary slag is contacted with silicon, chemical reaction (4) takes place simultaneously in the system, yielding some dissolved Ca in the silicon melt: The measured slag concentrationsat two different temperatures show that reaction (3) As observed above, there is a large negative deviation from ideal solution for the silicon-rich Si-Ba solutions and due to the low chemical activity of Ba, the chemical reaction (3) proceeds when the BaO-SiO2 slags are contacted with silicon, which causes significant Ba transport into the liquid silicon as shown in Fig. 1. The more Ba transport from the slag into silicon at higher temperatures for a given slag composition is mainly attributed to the higher activity of BaO in the slags at higher temperatures, while the other chemical activities in chemical reaction (3) are less temperature dependent. In other word, there is a larger driving force for the chemical reaction (3) at higher temperatures. However, not significant BaO transport to silicon when the concentration of BaO is low in CaO-BaO-SiO2 is due to the low chemical activity of BaO in the slag, which causes small Ba transfer into Si (Fig. 2). Obviously, equilibrium is established by small BaO concentration in the slag, i.e. 2.5wt%BaO, while it occurs with more Ba transfer at higher concentrations and temperatures.

Chemical activity of BaO in low BaO-containing CaO-SiO2 slags
The mass transport of Ba through chemical reactions (3) The concentration of Ba in liquid silicon is low and dilute solutions of Ba in silicon are in contact with the slags containing low BaO concentrations. Assuming no significant interaction between dissolved Ba and Ca in silicon, we may calculate the chemical activities of Ba in silicon using the above calculated ° for Ba in liquid silicon. On the other hand, as the concentration of BaO in the slags is low and XBaO < 0.034 according to Table 1, it is a fair approximation to consider the thermodynamics data for binary CaO-SiO2 slags to calculate the chemical activity of SiO2 in the slags. Based on the activity data for SiO2 in CaO-SiO2 system by Rein and Chipman [26], which are reliable as compared with literature previously [27], aSiO2 can be estimated around 0.8 and 0.85 at 1773 K (1500˚C) and 1873 K (1600˚C), respectively.
Assuming the activity of silicon solvent as unity, we can calculate the chemical activity of BaO in the slag phases as shown in Fig. 10 for the two temperatures. The calculated results give

Mass transport of Ca
As mentioned above, when silicon is contacted with the CaO-BaO-SiO2 ternary slag, the partial silicothermic reduction of CaO from slag occurs through reaction (4) simultaneously with BaO reduction. As BaO is more readily reduced due to considerably larger K3 value compared to K4 value, i.e. 4000 larger at 1773 K (1500˚C), there will be larger extent of Ba transfer than Ca transfer from the slag into the melt, as seen in Fig. 3. In addition to reactions (3) and (4), the other reaction that can show equilibrium in the system regarding these components is: Ca + (BaO) = Ba + (CaO) K8 = (at 1773 K) = 65.74 (8) 14 This reaction at equilibrium condition may yield: The term in the parenthesis is a constant value for a given temperature and depending on the

Phosphorous distribution thermochemistry
Although a couple of chemical reactions may occur for the oxidation of the dissolved P in silicon or the reduction of its oxide from the slag, the equilibrium can be studied considering the following reaction for the both BaO-SiO2 and CaO-BaO-SiO2 slags: The chemical activity of P in liquid silicon, aP, can be calculated for different measured chemical compositions considering the phosphorous activity coefficients as °= 0.47 and °= 0.49 at 1500˚C and 1600˚C, respectively. [28] Activities of SiO2 in the slags for the given chemical compositions at equilibrium in Table 1 can be determined by the outlined approach above for BaO-SiO2 slags and the literature data for low BaO-containing CaO-SiO2 slags. [22][23][24][25] Employing the HSC Chemistry thermodynamic software for calculating the changes in the reaction constant, 10 , the activity of P2O5 can be calculated for the both types of slags as shown against the P2O5 molar fraction in Fig. 11.
The calculated activities for P2O5 in the slags can be used to determine the activity coefficient of dilute solutions of P2O5 in the slags. This yields 2 5°= 2 × 10 −32 and 2 5°= 1 × 10 −30 for illustrated system in Figure 11 for BaO-SiO2 slags at 1500˚C and 1600˚C, respectively.
Similarly for low BaO containing CaO-SiO2 slags at 1773 K (1500˚C) and 1873 K (1600˚C), 2 5°= 4 × 10 −33 and 2 5°= 3 × 10 −31 are obtained, respectively. Although these very small activity coefficients for P2O5 in the slags are obtained, not significant phosphorous is removed from silicon into the slag, which is due to the very small reaction constant for chemical reaction (10).
The other type of chemical reaction for P transport from silicon to the adjacent slag is the formation of barium phosphide according to the following reaction: 16 2 P + 3 Ba = Ba3P2 K12 (at 1773 K) = 3.7 × 10 5 (12) The chemical activity of Ba3P2 in the slags can be calculated using the above calculated chemical activities for P and Ba and this yields larger activities for this compound compared to the calculated P2O5 activities. This may indicate that the formation of P2O5 is a more stable form than Ba3P2 in the slag. However, in order to study the thermodynamics of P removal from silicon in BaO-SiO2 system through these mechanisms, the following overall chemical reaction can be considered: Ba3P2 + 4(SiO2) = 3(BaO) + (P2O5) + 4Si K13 (at 1773 K) = 1.6 × 10 -21 (13) Considering the equilibrium constant for this reaction, K 13, we may write: Based on the above calculated chemical activities for SiO2 and BaO and considering Raoultian behavior for silicon, the right part of Eq. (14) can be calculated as illustrated in Figure 12 for two temperatures. It is found observed that for all the experiments ( 2 5 indicating that P2O5 is the more stable P-containing phase in the slag. Therefore, we may conclude that the mechanism of P adsorption into the slag is through the chemical reaction (10). 17 The distribution of P, and in another word, the extent of P transfer between the two phases is depending on the type of slag as observed in Figs. 4 and 5. Considering chemical reaction (10), the formation of P2O5 is in relation with the source of oxygen in the system (SiO2), and therefore there must be a higher rate of P oxidation from silicon for lower basicity. For a given slag composition, observing lower LP value at higher temperature is attributed to the increase of P2O5 activity in the slag, while the activity of P in liquid silicon is not significantly changed by temperature change. On the other hand, the value of LP is dependent on the basicity and the structure of slag and as P2O5 is an acidic agent in the slag, LP is expected to be increased with increasing basicity. This is observed for the BaO-SiO2 slag, while it is less dependent on basicity for CaO-BaO-SiO2 at 1873 K (1600˚C The magnitude of the reaction constants K15, K16, and K17 indicates that for the slags in

Chemical activity of boron oxide
It is generally accepted in literature that boron exists in the silicate slags in the form of oxide B2O3. As there is always significant amount of silicon oxide in the slag in contact with liquid silicon, the equilibrium can be studied considering the following reaction for the both studied binary and ternary silicate slags: 2 B + 3/2 (SiO2) = (B2O3) + 3/2 Si K18 (at 1773 K) = 9.3×10 -2 (18) and the chemical activity of B2O3 at equilibrium can be expressed as: The chemical activity of B in molten silicon can be calculated using the data literature, [29] which yields °= 3.87 and °= 3.65 at 1773 K (1500˚C) and 1873 K (1600˚C), respectively.
It is a fair approximation to consider Raoutian behavior for silicon solvent, and we can consider aSi equal to its molar faction, which is close to unity. Employing the HSC Chemistry thermodynamic software for calculating the changes in the reaction constant, 18 , the activity of B2O3 can be calculated for the both types of slags as presented against the B2O3 concentration in Fig. 13 for typical conditions. The calculations here yield the following expressions for the activity coefficient of B2O3 in specific BaO-SiO2 slags at different temperatures: For the above expressions LB=1 was considered, which is a fair approximation (Fig. 6) and the calculations for the experimental points are well correlated in Fig. 13. Similarly, the following expressions are obtained for low BaO-containing CaO-BaO-SiO2:

Boron removal mechanism
When a boron-containing silicon melt is contacted with a BaO-SiO2 slag, the oxidation of the dissolved boron occurs, assuming smaller initial B2O3 than equilibrium concentration in the slag. The oxidation can occur via the chemical reaction (18) or via the following reaction: Calculating the changes in the standard Gibbs energy for chemical reactions (18) and (24), ∆ 18° and ∆ 24°, we find that pure oxides of Si and Ba are stable in contact with pure B.
However, when BaO-SiO2 slag containing is contacted with the liquid silicon containing small amounts of B, the mass transfer of B from silicon into the slag occurs due to the very small 20 activity coefficient of B2O3 in the slag. We can determine the reaction mechanism for B oxidation through calculating the changes in Gibbs energy of reactions (18) and (24): In order to find out the reaction with lower Gibbs energy independent of the concentrations of B and B2O3 in the two phases, we can obtain the following equations by rearranging the above equations: Obviously, the magnitude of F18 and F24 for given process conditions will show that which chemical reaction occurs for B oxidation from thermodynamics point of view; the reaction with lower F-value. Figure 14 shows the calculated F18 and F24 values for different given Ba concentrations in silicon and for a wide composition range of BaO-SiO2 slags at 1773 K (1500˚C) and 1873 K (1600˚C) using the above determined activities for the involved species.
As seen, for a large slag composition range up to 60% SiO2 and up to 0.04 wt% Ba in silicon the chemical reaction (24) (24) is the one involved in B oxidation.

Conclusions
The interactions of B-and P-doped silicon with BaO-SiO2 slags and low BaO containing CaO-BaO-SiO2 at 1773 K (1500˚C) and 1873 K (1600˚C) were studied, and the main conclusions for our temperature and compositions can be summarized as:  The distribution coefficient of B for BaO-SiO2 slags is LB=2.2±0.2, which is higher than that for low BaO-containing CaO-SiO2 slags (LB=1.1±0.2), and LB is not significantly affected by temperature and composition changes of the slags.
 The distribution coefficient of P, LP, is in the ranges of 0.25-0.7, which is significantly smaller than LB. However, LP is higher for BaO-SiO2 slags than that for low BaO-containing CaO-SiO2 slags, and LP is higher at lower temperatures.
 The mass transfer of Ba from slag into liquid silicon occurs through silicothermic reduction, which causes dilute solutions of Ba in silicon, and the temperature dependence of the activity coefficient of Ba in silicon can be presented by Eq. (6).
 The mass transport of P from silicon into the silicate slags is through oxidation by SiO2 and the formation of P2O5 is dominant compared to formation of Ba3P2. Although very small chemical activity for P2O5 in slags is calculated, P is not significantly removed from silicon.

22
 Boron is removed from silicon through oxidation by BaO from the slag at high BaO concentrations and until the Ba concentration in silicon reaches an specific concentration.
Further B removal occurs through oxidation by SiO2 in the slag.             ) and composition of BaO-SiO2 slags in equilibrium with silicon containing low P concentrations, symbols: calculated using experimental data.