Multiple Slag Operation on Boron Removal from Metallurgical-Grade

Article pubs.acs.org/IECR

Multiple Slag Operation on Boron Removal from Metallurgical-Grade Silicon Using Na2O‑SiO2 Slags Ming Fang,† Chenghao Lu,† Liuqing Huang,† Huixian Lai,† Juan Chen,† Xiaobing Yang,† Jintang Li,† Wenhui Ma,‡ Pengfei Xing,§ and Xuetao Luo*,† †

College of Materials, Xiamen University, Xiamen 361005, People’s Republic of China Faculty of Materials and Metallurgical Engineering, Kunming University of Science and Technology, Kunming 650093, People’s Republic of China § School of Materials and Metallurgy, Northeastern University, Shenyang 110004, People’s Republic of China ‡

ABSTRACT: The removal of boron from metallurgical-grade silicon by Na2O-SiO2 slag refining was investigated. The final content of boron in refined silicon was examined under different conditions of temperature, slag composition, holding time, mass ratio of slag to silicon, and slag refining times. The content of boron in silicon decreased from 10.6 to 0.65 ppmw by slag treatment in one time, and increasing slag refining times was beneficial for removing boron at the conditions of the small mass ratio of slag to silicon and short holding time. Moreover, the removal mechanism of boron was also discussed. The primary removal mechanism of boron was that a large amount of boron was oxidized and then volatilized to the atmosphere in the form of boron oxides. The mass transfer coefficient of boron from silicon to slag was connected with the radius of silicon droplet in the slag refining process.

1. INTRODUCTION Providing a source of clean and sustainable energy to address environmental issues, solar energy has attracted enormous attention in recent years due to its potential applications in commercial products. Silicon-based photovoltaic industry plays a crucial role in meeting the world’s need for solar energy.1−3 In this decade, multicrystalline silicon has captured over 90% of the commercial solar cells, but metallurgical-grade silicon (MGSi, purity 99%) as feedstock often fails to fulfill the requirement of low-consumption solar-grade silicon (SOG-Si, purity 99.9999%).4 Hence, developing a low cost technology to purify MG-Si has become a critical problem in industrial application. To meet the increasing demands on the low-consumption method in producing SOG-Si, physical metallurgy as an efficient and effortless technology has been carried out to purify MG-Si by plenty of researchers.5 Most metal impurities can be eliminated by directional solidification,6 acid leaching,7 and solvent refining.8 But these methods have no effect on removing boron from MG-Si as boron has high segregation coefficient and low vapor pressure. So far, slag refining9 is considered as a promising method to remove boron from MGSi. In the previous investigations, various kinds of slag like binary SiO2−CaO/Na2O,10−12 ternary SiO2−CaO−Al2O3/ MgO/BaO/Li2O/CaF2,2,5,13,14 and quaternary SiO2−CaO− Al2O3−MgO15 were performed to refine MG-Si. SiO2 was the most suitable slag composition for oxidizing because the equilibrium between SiO2 and Si could provide sufficient oxygen potential, which was beneficial for improving the removal efficiency of boron from MG-Si.15 Thereinto, CaOSiO2 system, which had been commonly employed in the steelmaking industry, could be chosen to remove nonmetallic boron impurity from MG-Si.10 Generally, some additives, such as Li2O, CaF2, Al2O3, MgO, or BaO, were added in CaO-SiO2 © 2014 American Chemical Society

to increase the slag basicity and decrease the slag viscosity. Wu et al.5 acquired an excellent removal efficiency of boron by adding Li2O in CaO-SiO2, and the minimum concentration of boron was 1.3 ppmw when the mass ratio of slag to silicon was 4. Similarly, Cai et al.14 added CaF2 to decrease the melting point and viscosity of CaO-SiO2 slag, and the concentration of boron was successfully reduced from 15 to 1.1 ppmw when the mass ratio of slag to silicon was 3. Some innovative technologies on slag refining were designed to obtain a good result on the removal of boron. Nishimoto and Morita16 employed gas blowing and injection to advance the removal efficiency of boron in the slag refining process. They found that the best elimination of boron was obtained under Cl2 treatment due to the formation of volatilized boron chlorides. More recently, applying slag refining on Si−Sn melt to eliminate boron was carried out by Ma et al.17 It not only increased the partition ratio of boron but also decreased the required amount of slag. But one significant obstacle of this approach was that it was difficult to separate silicon from Si−Sn melt by physical method. Although great effort on boron removal had been achieved in the preceding investigation, the concentration of boron in single-pass refined silicon was much higher than the acceptable content in SOG-Si. Up to now, multiple slag operation is considered as a viable way to reduce the boron concentration below 0.3 ppmw. A fundamental requirement for multiple slag operation is that slag has much less density as compared to the liquid silicon. The density of liquid silicon was 2.56 g/cm3.18 Some silicate slags, such as CaO-SiO2,19 MnO-SiO2,20 and Received: Revised: Accepted: Published: 12054

December 29, 2013 May 22, 2014 July 3, 2014 July 3, 2014 dx.doi.org/10.1021/ie404427c | Ind. Eng. Chem. Res. 2014, 53, 12054−12062

Industrial & Engineering Chemistry Research

Article

Table 1. Experimental Conditions in the Present Study experiment

composition (wt %)

temp

(1)

Na 2O/SiO2 = 2.0

1823 K

slag/silicon (wt %) 1

holding time 30 min

slag refining times 1

(2)

Na 2O/SiO2 = 2.0

1873 K

1

30 min

1

(3)

Na 2O/SiO2 = 2.0

1923 K

1

30 min

1

(4)

Na 2O/SiO2 = 2.0

1973 K

1

30 min

1

(5)

Na 2O/SiO2 = 2.0

2023 K

1

30 min

1

(6)

Na 2O/SiO2 = 2.0

1973 K

1

10 min

1

(7)

Na 2O/SiO2 = 2.0

1973 K

1

20 min

1

(8)

Na 2O/SiO2 = 2.0

1973 K

1

40 min

1

(9)

Na 2O/SiO2 = 2.0

1973 K

1

50 min

1

(10)

Na 2O/SiO2 = 2.0

1973 K

1

60 min

1

(11)

Na 2O/SiO2 = 2.0

1973 K

1

70 min

1

(12)

Na 2O/SiO2 = 2.0

1973 K

1

80 min

1

(13)

Na 2O/SiO2 = 0.5

1973 K

1

30 min

1

(14)

Na 2O/SiO2 = 1.0

1973 K

1

30 min

1

(15)

Na 2O/SiO2 = 1.5

1973 K

1

30 min

1

(16)

Na 2O/SiO2 = 2.5

1973 K

1

30 min

1

(17)

Na 2O/SiO2 = 3.0

1973 K

1

30 min

1

(18)

Na 2O/SiO2 = 3.5

1973 K

1

30 min

1

(19)

Na 2O/SiO2 = 4.0

1973 K

1

30 min

1

(20)

Na 2O/SiO2 = 2.0

1973 K

0.5

30 min

1, 2, 3

(21)

Na 2O/SiO2 = 2.0

1973 K

1.0

30 min

1, 2, 3

(22)

Na 2O/SiO2 = 2.0

1973 K

1.5

30 min

1, 2, 3

(23)

Na 2O/SiO2 = 2.0

1973 K

2.0

30 min

1, 2, 3

(24)

Na 2O/SiO2 = 2.0

1973 K

2.5

30 min

1, 2, 3

Figure 1. Schematic of the experimental process.

FexO-SiO2,21 have much higher density than liquid silicon, which are inconvenient for continuous operation during the furnace run. Bockris et al.22 indicated that the density of Na2OSiO2 slag varied in the range of 2.16−2.21 g/cm3 by changing the composition of Na2O from 11 to 60 mol %. Hence, Na2OSiO2 was considered as an appropriate slag for multiple slag operation. Yin et al.12 demonstrated that the removal efficiency of boron from MG-Si could be improved by adding Al2O3 in Na2O-SiO2 slags. Moreover, the thermodynamic and kinetic behaviors of boron between silicon and Na2O-SiO2 slags were analyzed by Safarian et al.23 Despite the great effort involved in these investigations, the concentration of boron in refined silicon was much higher than 0.3 ppmw. Herein, multiple slag operation with Na2O-SiO2 slags was performed to reduce the boron concentration below 0.3 ppmw. The removal capacity of boron was assessed at varying temperature, slag composition, holding time, mass ratio of

slag to silicon, and slag refining times, and the removal mechanism of boron was also discussed.

2. EXPERIMENTAL SECTION 2.1. Materials. The feedstock, MG-Si containing 10.6 ppmw boron was provided by Run Xiang Co., Ltd., China. Slags of the Na2O-SiO2 system with different Na2O/SiO2 ratios were prepared for removing boron from MG-Si, and Na2O was obtained by thermal decomposition of Na2CO3 at high temperature. The average particle sizes of the Na2CO3 and SiO2 powders were both 500 μm. 2.2. Methods. Before slag refining experiment, Na2CO3 and SiO2 powders were mixed uniformly by ball-milling, and this mixture was dried at 393 K for 24 h. Afterward, the mixed slag and MG-Si were placed in an intermediate frequency induction furnace. A heating rate of 30 K/min was applied from room temperature to the required melt temperature under the 12055

dx.doi.org/10.1021/ie404427c | Ind. Eng. Chem. Res. 2014, 53, 12054−12062


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atmosphere (air). Slag refining experiments were done at five temperatures, 1823, 1873, 1923, 1973 and 2023 K, respectively. Table 1 lists the experimental conditions in the present study. The experimental procedure is depicted in Figure 1. There are five steps in the experimental procedure. Step 1: Silicon and Na2O-SiO2 slag were held at the required melt temperature for a certain period of time to ensure complete melting, mixing and slagging. Step 2: Turning off the electrical power of the furnace, the melt was separated into two layers after 2 min standing, and the upper layer was liquid slag because it has less density than silicon at 1823−2023 K.22 Step 3: Removing the upper slag layer away from the liquid silicon by a high-purity graphite plate. Step 4: Sampling liquid silicon and slag by alumina tube (inner diameter: 10 mm, length: 100 mm). Step 5: Turning on the electrical power of the furnace and repeating slag operation. After each slag experiment, the liquid silicon and slag were dumped into another high-purity graphite crucible for quenching. After cooling to room temperature, the solid silicon and slag were detached from the graphite crucible and prepared for chemical analysis. 2.3. Analysis. The concentration of boron in silicon and slag was detected by inductively coupled plasma mass spectrometry (ICP-MS, Optima 2000 DV, PerkinElmer Inc., US). An electron probe microanalyzer (EPMA, JXA-8100, Jeol Ltd., Japan) was applied to observe the microstructure of sample. Analysis conditions were 2 × 104 V accelerating voltage and 2 × 10−9 A current.

Figure 2. CB and silicon yield at different temperature, slag refining times = 1; slag/silicon mass ratio = 1.

3. RESULTS The partition ratio of boron (LB) between silicon and slag is calculated as eq 1. LB =

Figure 3. Change of CB in treated silicon and slag, Na2O/SiO2 mass ratio = 2; slag refining times = 1; slag/silicon mass ratio = 1.

C(B) C[B]

(1)

where C(B) and C[B] represent the concentration of boron in slag and silicon after slag refining, respectively. Generally, LB is used to evaluate the removal efficiency of boron, but it has no direct relevance with the final concentration in treated silicon when boron is both removed to the slag phase and the gas phase. Herein, the final concentration of boron is applied to characterize the removal mechanism of boron. 3.1. Effect of Temperature on Boron Removal and Silicon Yield. Experiments 1 to 5 were designed to study the effect of temperature on boron removal and silicon yield. As exhibited in Figure 2, it can be observed that the temperature have an obvious effect on boron removal and silicon yield. When the temperature increases from 1823 to 2023 K, the final concentration of boron decreases from 0.96 ppmw to 0.62 ppmw, and the yield of silicon decreases from 87.2 to 66.1 wt %. Two reasons can explain the loss of silicon. One is that silicon volatilized to the atmosphere at high temperature. The other one is that silicon reacted with SiO2 or Na2O in the slag refining process. 3.2. Effect of Holding Time on Boron Removal. According to the results from Figure 2, it is apparent that the yield of silicon sharply decreases when the holding temperature is up to 1973 K; moreover, the final concentration of boron decreases to below 0.7 ppmw at 1973 K. Hence, the holding temperature of slag refining is determined at 1973 K. The holding time variation with boron concentration in treated silicon and slag is shown in Figure 3 (experiment 4 and

experiment 6 to 12). With the refining time increasing, the boron concentration in silicon decreases, and the boron concentration in the treated slag increases. When the holding time is over 40 min, the content of boron in silicon remains unchanged; however, the content of boron in the treated slag decreases because the generated boron oxides volatilized with Na2O to the atmosphere at high temperature. 3.3. Effect of Slag Composition on Boron Removal. With the mass ratio of slag to silicon fixed at 1, the effect of slag composition on boron removal is shown in Figure 4

Figure 4. CB and basicity at different Na2O/SiO2 mass ratio; temperature = 1973 K; holding time = 30 min; slag refining times = 1. 12056



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(experiment 13 to 19). The values of optical basicity increase with the rise of Na2O proportion in slag. According to Duffy and Ingram’s study,24 the values of the optical basicity can be derived by eq 2. Λ=

[B] +

(3)

In each case, Na2O and CO2 are generated by thermal decomposition of Na2CO3 at high temperature; oxygen ions are provided by Na2O and oxygen partial pressure is that resulting from the decomposition of SiO2.

X Na 2On Na 2OΛ thNa 2O + X SiO2nSiO2 Λ thSiO2 X Na 2On Na 2O + X SiO2nSiO2

y x O2 + O2 − → (BOx + y /2 )y − 2 2

(2)

where X is the mole fraction; Λth is the optical basicity of oxide, which can be calculated from pauling electronegativities, Λth (Na2O) = 1.15, Λth (SiO2) = 0.48;25 n is the number of oxygen atom in the molecule, for example, 1 for Na2O, 2 for SiO2. As shown in Figure 4, at the initial stage, the final concentration of boron decreases with the increase of Na2O proportion in slag, and the minimum concentration of boron is 0.65 ppmw when the mass ratio of Na2O to SiO2 is 2. Afterward, a significant increase in the final concentration of boron occurs with the further increase of Na2O proportion. Two factors can explain this phenomenon: (1) Na2O was reduced to Na by silicon at the slag/silicon interface. (2) Na2O volatilized to the atmosphere at high temperature.23

Na 2CO3(s) → Na 2O(s) + CO2 (g)

(4)

Na 2O(s) → 2Na +(1) + O2 −(1)

(5)

SiO2 (s) → Si(l) + O2 (g)

(6)

The oxidation process can be divided into six steps. Step 1: Boron in silicon phase transfers to the silicon boundary; meanwhile, the produced oxygen ion or oxygen partial pressure in slag phase diffuses to the slag boundary. Step 2: Boron, oxygen ion or oxygen partial pressure passes through each boundary. Step 3: The oxidation reaction of boron occurs at the slag/silicon interface. Step 4: The generated boron oxides diffuse from the interface to slag phase. Step 5: Boron oxides continue to diffuse in the slag phase. Step 6: Some boron oxides are evaporated into the air. Diffusion. The diffusion of boron between silicon and slag is described by two-film theory.26,27 Based on this theory, an interface exists between silicon and slag. There is a diffusion boundary layer at each side of the interface, and only molecular diffusion takes place at the interface. The bulk concentration is independent of the refining time, and the equilibrium concentration always exists at the slag/silicon interface. In the initial stage of slag refining, boron diffuses from silicon to slag as the concentration of boron in silicon is higher than that in slag; meanwhile, the produced oxygen ion or oxygen partial pressure diffuses from slag to silicon due to the concentration difference between slag and silicon. If the mass transfer rate is faster than the oxidation rate, boron will diffuse from silicon to slag without oxidation. With the proceeding of slag refining, the diffusion of boron reaches equilibrium when both adsorption ability and oxidation ability of slag reach its limit. Reduction. Ellingham diagrams for the formation of borides of some metal elements are generated using FactSage thermochemical software.18,28 Metal impurities like titanium, iron, nickel, aluminum, and manganese have a higher tendency than silicon to form compounds with boron. Hence, boron coprecipitates with metal impurities to form some different borides, which easily enrich at grain boundaries in the solidification process. This is beneficial for removing boron in the subsequent acid leaching process. 4.2. Oxidation Reaction of Boron Removal. As mentioned above, the removal mechanism of boron is

4. DISCUSSION 4.1. Mechanism of Boron Removal from Silicon. Boron removal from silicon by slag refining is a complex process and its main mechanism is oxidation reaction, which has not yet been clarified. As presented in Figure 5, a schematic of the removal mechanism is modified in this study. There are three different ways to assess the removal mechanism of boron.

Figure 5. Schematic of mechanism of boron removal from MG-Si.

Oxidation. The oxidation reaction of boron removal from silicon is considered as follows:13,15 Table 2. Oxidation Reactions between SiO2 and Boron no.

reactions

temp (K)

(7)

1 1 [B](s or l) + SiO2 (s or l) → Si(s or l) + BO(g) 2 2

1500−2000

(8)

[B](s or l) + SiO2 (s or l) → Si(s or l) + BO2 (g)

1500−2000

(9)

1 1 2[B](s or l) + SiO2 s or l → Si(s or l) + B2O(g) 2 2

1500−2000

(10)

2[B](s or l) + SiO2 s or l → Si(s or l) + B2O2 (g)

1500−2000

(11)

2[B](s or l) +

3 3 SiO2 s or l → Si(s or l) + B2O3(g) 2 2 12057

1500−2000



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considered as an oxidation reaction, which takes place at the slag/silicon interface. Boron may be oxidized by SiO2 or Na2O due to the different activities of SiO2 and Na2O in slag. Table 2 lists the possible oxidation reactions between SiO2 and boron in the slag refining process, and the calculated standard Gibbs free energies of these reactions are shown in Figure 6. Thermodynamic data are taken from NIST-JANAF.29

Figure 7. ΔGΘ of reactions 14 to 18 between Na2O and boron.

ΔG19 = ΔG θ19 + 2.303RTlg

[P(BmOn)/P θ ]αNa 2n αBmα Na 2On

(20)

Θ

In Figure 6, the ΔG values of reactions 7 to 11 are positive in the temperature range of 1700 to 2000 K. As shown in Figure 7, the ΔGΘ values of reactions 14 to 18 (except reaction 16) are negative in this temperature range. By comparing the ΔGΘ values of reactions 7 to 11 and 14 to 18, boron is more inclined to react with Na2O than SiO2 when the activity Na2O is equal to that of SiO2 in the slag refining process. Only under the high activity of SiO2 in Na2O-SiO2 slag, boron in silicon can be oxidized by SiO2. 4.3. Rate of Boron Oxidation. In Figure 7, boron in silicon can be oxidized into BO, BO2, B2O2, and B2O3 by Na2O under the standard state conditions, and the preferential order of boron oxides is B2O3 > B2O2 > BO2 > BO from 1700 to 2000 K. Hence, B2O3 is the most thermally stable product in the slag refining process. In this study, the oxidation rate of reaction 18 can be used to represent the overall rate of boron oxidation. In Figure 3, the changes of CB in silicon can be applied to calculate the rate of reaction 18. This reaction may be a first-order reaction or a second-order reaction. If this reaction is a first-order reaction, the rate of boron oxidation can be written as follows:

Figure 6. ΔGΘ of reaction 7 to 11 between SiO2 and boron.

Reactions from 7 to 11 can be expressed by following equation: n n m[B](s or l) + SiO2 (s or l) → Si(s or l) + BmOn(g) 2 2 (12)

The Gibbs free energy of reaction 12 is written as following: ΔG12 = ΔG

θ 12

+ 2.303RTlg

[P(BmOn)/P θ ]αSi n /2 αBmαSiO2 n /2

(13)

As the initial content of boron in silicon is very low, in eq 13, silicon can be regarded as pure substance. The activity of silicon is considered to be 1 (αSi = 1), which is chosen as the activity standard state in the molten slag, αB and P(BmOn)/Pθ are related with the initial content of boron in silicon. Table 3 lists the possible oxidation reactions between Na2O and boron, and Figure 7 shows the calculated standard Gibbs free energies of these reactions. Thermodynamic data are taken from NIST-JANAF.29 Reactions from 14 to 18 can be expressed by following equation:

r=

ln

−dC[B] dt

C[B]0 C[B]

= K1C[B]

(21)

= K1t

(22)

where K1 is the rate constant of first-order reaction, C[B] is the content of boron in silicon with different refining time t, C[B]0 is the initial content of boron in silicon. If this reaction is a

m[B](s or l) + n Na 2O(s or l) → 2n Na(l) + BmOn(g) (19)

The Gibbs free energy of reaction 19 is written as follows: Table 3. Oxidation Reactions between Na2O and Boron no.

reactions

temp(K)

(14)

[B](s or l) + Na 2O(s or l) → 2Na(l) + BO(g)

1500−2000

(15)

[B](s or l) + 2Na 2O(s or l) → 4Na(l) + BO2 (g)

1500−2000

(16)

2[B](s or l) + Na 2O(s or l) → 2Na(l) + B2O(g)

1500−2000

(17)

2[B](s or l) + 2Na 2O(s or l) → 4Na(l) + B2O2 (g)

1500−2000

(18)

2[B](s or l) + 3Na 2O(s or l) → 6Na(l) + B2O3(g)

1500−2000

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Figure 8. Plots of ln(C[B]0/C[B]) and 1/C[B] vs time according to Figure 3

second-order reaction, the following equation can be used to describe the rate of boron oxidation. r=

dC[B] dt

= K 2C[B]2

1 1 − = K2t C[B] C0

(23)

(24)

where K2 is the rate constant of second-order reaction. According to the data in Figure 3, the C[B] in silicon remains unchanged after the refining time over 40 min, which illustrates that the dissolution of boron in slag reaches a saturation state. Equations 22 and 24 are used to fit the experimental data in the range from 0 to 40 min. The rate constants of first-order reaction and second-order reaction with different refining time are shown in Figure 8a,b, respectively. We can draw a conclusion that the oxidation reaction is a second-order reaction, and the rate constant can be calculated by the slope of the line in Figure 8b, which is 6.725 × 10−4 ppm−1 s−1. 4.4. Mass Transfer Coefficient of Boron from Silicon to Slag. Sampling of the molten slag and silicon was a difficult task during the furnace run. Alumina tube was inserted into the melt at high temperature and sample was taken. To retain the state of melt, the liquid sample was immediately quenched to room temperature in water. The cooled sample then was cut into ten slices with 20 × 20 × 5 mm3, and each slice was embedded in epoxy resin and polished by 2500 rpm high speed polisher. After that, an electron probe microanalyzer (EPMA) was used to analyze the number and radius of silicon droplet in each slice. The typical micromorphology of melt is shown in Figure 9. A lot of silicon particles with different size dispersed in slag. The reason for this phenomenon was that silicon droplets created by magnetic stirring had not sufficient time to merge together as the cooling rate was so fast at the quenching process. Smaller spherical silicon particle ranged from 10 to 100 μm, while larger silicon particle with irregular shape ranged from 100 to 500 μm. The average diameter of silicon droplet was calculated by averaging the number and radius of silicon droplet, which was less than 100 μm. For the calculation of mass transfer coefficient of boron, there are two steps to consider: Step 1: Boron in liquid silicon transfers to the silicon boundary; step 2: Boron passes through the silicon boundary layer and diffuses in the slag/silicon interface.

Figure 9. Micromorphology of melt; Na2O/SiO2 mass ratio = 2; temperature = 1973 K; slag/silicon mass ratio = 2.

In step 1, since the diameter of silicon droplet is less than 100 μm, silicon droplet can be considered as a rigid particle when it quickly moves in the molten slag. In this case, the internal recycle in silicon droplet can be ignored and molecular diffusion is the main way for the mass transfer in silicon droplet. When the radius of silicon droplet is very small and slag refining time is sufficiently long, the mass transfer coefficient of boron in silicon droplet (kB) can be expressed as following: D kB ≈ B (25) r where DB is the diffusion coefficient of boron in liquid silicon and r is the radius of silicon droplet.

t=

r r2 = kB DB

(26)

where t is the diffusion time of boron in silicon droplet. The diffusion coefficient of boron in liquid silicon is 2.4 ± 0.7 × 10−4 cm2/s,30 and the radius of silicon droplet is less than 50 μm in the slag refining process. Thus, the diffusion time of boron in silicon droplet can be ignored. In step 2, since the thickness of slag/silicon interface is neglectable compared to the radius of silicon droplet, the 12059



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diffusion time of boron in the slag/silicon interface is extremely short. Therefore, the major factor that affects the mass transfer of boron is that boron passes through the silicon boundary layer. Assuming that the concentration of boron outside the silicon boundary layer region is constant, the concentration gradient of boron in silicon boundary layer can be expressed as follows: dC[B] dy

=

C(B) − C[B]

y=0

δc′

(27)

where δc′ is thickness of the effective boundary layer. The fluid velocity is zero at the slag/silicon interface (y = 0), and the diffusion flux of boron is expressed as follows: JB = −DB

dC[B] dy

Figure 10. Relationship between f(%B) and holding time. (28)

y=0

D JB = B (C[B] − C[B]′) δc′

5000 μm. This result shows that the size of silicon droplet has a large influence on the mass transfer coefficient. Some literatures on the mass transfer coefficient of boron have been reported. In Nishimoto and Morita’s study,16 the rate of boron removal was depended on the rate of mass transport in the molten slag, and the mass transfer coefficient of boron from silicon to slag was determined to be 1.4 × 10−4 cm/s. Similarly, Krystad et al.31 found that the mass transfer coefficient of boron was ranged in the order of 1.2−2.1 × 10−4 cm/s and was largely influenced by the mass ratio of slag to silicon and slag composition. According to eq 36, KB′ decreases with the decrease of silicon droplet size. Therefore, boron shows a tendency to be oxidized at small size of silicon droplet because the contact area between silicon droplet and slag increases with decreasing silicon droplet size. 4.5. Multiple Slag Operation on Boron Removal. In previous studies,2,14 based on the law of mass conservation, the boron redistribution between silicon and slag can be expressed as follows:

(29)

where C[B]′ is the equilibrium concentration of boron. In the slag refining process, the diffusion flux of boron can be written as JB = −

D V dC[B] = B (C[B] − C[B] ′) S dt δc′

(30)

where S is the surface area of silicon droplet, V is the volume of silicon droplet, and the differential function of the boron concentration can be derived from eq 30: dC[B] dt

=−

S DB (C[B] − C[B]′) V δc′

(31)

KB′ is introduced as the mass transfer coefficient of boron from silicon droplet to slag, which can be expressed as follows: kB′ =

DB δc′

MSiC[B]0 + MSC(B)0 = MSiC[B]p + MSC(B)p (32)

where Msi and Ms represent the amount of silicon and slag, ignoring the mass loss of silicon and slag in the slag refining process; C[B]0 and C(B)0 indicate the initial content of boron in silicon and slag; C[B]p and C(B)p depict the content of boron in silicon and slag after slag refining, respectively. From the foregoing, boron was oxidized at the slag/silicon interface and some different boron oxides were generated, which could volatilize to the atmosphere. Moreover, the remaining boron oxide could further react with Na2O to form some complexes, such as Na2B2O4, Na2B4O7, and Na2B6O10,22,23 which also easily transferred to the atmosphere in the slag refining process. Hence, the mass conservation of boron can be rewritten in eq 38.

Combining with S = 4πr2 and V = 4πr3/3, we have dC[B] dt

= −3

kB′ (C[B] − C[B]′) r

(33)

Integrating eq 33 and changing C[B] to mass percents of boron [%B], then, eq 33 can be written as follows: log

[%B]0 − [%B]′ k′ =3 B t [%B] − [%B]′ 2.303r

(34)

where [%B]0 and [%B]′ are the initial concentration and equilibrium concentration of boron, respectively. f(%B) = log(([%B]0 − [%B]′)/([%B] − [%B]′)). Based on the data in Figure 3, a linear function of f(%B) varying with t is given in Figure 10. KB′ can be calculated by the slope of this line, which is 9.5442 × 10−4 s−1. 3

kB′ = 9.5442× 10−4 2.303r

kB′ = 3.66338 × 10−4 ∼ 10−6cm/s

(37)

MSiC[B]0 + MSC(B)0 = MSiC[B]p + MSC(B)p + M Bx Oy

(38)

On the right side of this equation, MsiC[B]p represents the residual boron in the refined silicon; MsC(B)p indicates the remaining boron in the treated slag; MBxOy denotes the mass loss of boron oxides. As shown in Figure 3, the content of boron in MG-Si decreases from 10.6 ppmw to 0.65 ppmw after slag refining, and the residual content of boron in the treated slag is 0.5 ppmw. Hence, the diffusion and reduction of boron capture a small proportion in the slag refining process. A large

(35)

(r = 50 ∼ 5000 μm) (36) −4

In eq 36, KB′ is varied in the range of 3.66338 × 10 ∼ 10−6 cm/s when the radius of silicon droplet changes from 50 to 12060



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investigated. The experimental results indicated that the oxidation reaction of boron at the slag/silicon interface was the principal removal mechanism. This oxidation reaction was a second-order reaction, and the oxidation rate was 6.725 × 10−4 ppm−1s−1. The oxidation products volatilized to the atmosphere or reacted with Na2O to form Na2B2O4, Na2B4O7, and Na2B6O10, which could transfer to the atmosphere. Moreover, the diffusion and reduction of boron also occurred in the slag refining process. The mass transfer of boron from silicon droplet to slag (KB′) was varied in the range of 3.66338 × 10−4∼10−6 cm/s when the radius of silicon droplet changed from 50 to 5000 μm. Multiple slag operation was performed to reduce the boron content below 0.3 ppmw. Increasing slag refining times could improve the removal efficiency of boron at the conditions of the small mass ratio of slag to silicon and short holding time. When the mass ratio of slag to silicon was 1 and the refining time was 30 min, the removal efficiency of boron with slag refining in once, twice and three times was 93.87%, 96.96%, and 98.68%, respectively.

amount of boron volatilizes to the atmosphere in the form of boron oxides. This illustrates that the principal removal mechanism of boron is oxidation reaction at the slag/silicon interface. According to the mass balance of boron in eq 38, LB is not suitable to evaluate the removal efficiency of boron. We choose η to replace LB in this study. η=

C[B]p C[B]0

(39)

The relationship between the final content of boron and slag refining times can be described as the following expression. C[B]p = C[B]0

ηn (1 + A)n

n = (1, 2, 3)

(40)

where A is the mass ratio of slag to silicon and n is the number of slag refining times. Figure 11 indicates the effects of mass ratio of slag to silicon and slag refining times on boron removal (experiment 20 to

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-592-2188503. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the Key Jointed Foundation of the National Science Foundation of China-Yunnan (U1137601) and the National Natural Science Foundation of China Nos. 51334004 and 51204143.

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Figure 11. Relationship between the final content of boron and slag refining times; Na2O/SiO2 mass ratio = 2; temperature = 1973K; holding time = 30 min.

ABBREVIATIONS MG-Si = metallurgical-grade silicon SOG-Si = solar-grade silicon ppmw = parts per million weight REFERENCES

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24). The content of boron sharply decreases with increasing mass ratio from 0.5 to 1.5, but further increase of mass ratio results in a slight decrease on the boron removal. This can be attributed to that both oxidation ability and adsorption ability of slag reach its limit. Hence, only increasing the mass ratio of slag to silicon or prolonging the holding time (Figure 3) cannot significantly improve the removal efficiency of boron. To meet the acceptable content of boron in SOG-Si, slag operation has to be repeated one or two times. Moreover, the final content of boron decreases with increasing slag refining times. When the mass ratio of slag to silicon is 1 and the refining time is 30 min, the removal efficiency of boron with slag refining in once, twice and three times is 93.87%, 96.96%, and 98.68%, respectively. Therefore, multiple slag operation can be used as a feasible method to remove boron from silicon at the conditions of the small mass ratio of slag to silicon and short holding time.

5. CONCLUSIONS Na2O-SiO2 slag was implemented to remove boron from MGSi, and the conditions of temperature, slag composition and holding time were determined by analyzing the result of ICPMS. Moreover, the removal mechanism of boron was also 12061



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Multiple Slag Operation on Boron Removal from Metallurgical-Grade

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