Study of Phosphorus Behaviour in Levitated Silicon-Iron Droplets

STUDY OF PHOSPHORUS BEHAVIOUR IN LEVITATED SILICON-IRON DROPLETS

Katherine Le

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Department of Materials Science and Engineering University of Toronto

Study of Phosphorus Behaviour in Levitated Si-Fe Droplets

Katherine Le

Master of Applied Science

Department of Materials Science and Engineering University of Toronto

2016

Abstract

While the treatment of relatively inexpensive ferrosilicon alloys is a potential refining route in order to generate solar grade silicon, phosphorus is one of the more difficult impurities to remove by conventional processing. In this project, electromagnetic levitation was used to investigate the dephosphorization of ferrosilicon alloy droplets exposed to H2-Ar gas mixtures under various experimental conditions including, refining time, temperature (1450°C-1720°C), H2-Ar gas concentrations and flow rate, iron alloying content, and initial phosphorus concentration. Reaction rates increased with higher refining times, temperatures, and H2 gas concentrations. With unknown parameters associated with the kinetics of gas phase reactions, the approach involved comparison of apparent activation energies derived for the chemical reaction and gas diffusion steps of the dephosphorization process. The phosphorus removal rate is thought to be controlled by the interfacial reaction step; further work is required to confirm this conclusion.

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Acknowledgements

I would like to express my gratitude and respect to my supervisor, Prof. Alex McLean for the opportunity to work on this research. I am thankful for his guidance, wisdom and encouragement throughout the course of my studies. He is a truly inspiring person, and a great enabler of new learning opportunities.

I would like to thank Prof. Mansoor Barati for all his support and kindness. His recommendations and advice allowed me to further explore and analyze the significance of my results, and to attain the overall findings reported in this thesis.

I would also like to express my thanks to Dr. Yindong Yang for his unwavering support and constructive input over the course of this thesis, and during my time as an undergraduate in the research group. His knowledge and perspectives in research and industry have been a great source of encouragement and inspiration.

A special thank you to Dr. Paul Wu, for his mentorship in this project. I am indebted to him for his valuable advice, and always being available to share his knowledge and perspectives in research. I would also like to thank past co-investigators on this project, Dr. Wei Yan and Andrew Hue.

I would like to thank Dr. Hiroshi Soda for his advice and wonderful stories. I am also grateful for my colleagues at U of T who have contributed to this work whether it be through experimental preparations and analysis, discussions, suggestions, and support: Dr. Karim Danaei, Sridevi Thomas, Dr. Sherry Esfahani, Dr. Leili Tafaghodikhajavi, Dr. Dawei Yu, Xue Yin, Bennett Yan, Richard Elliott, and Kevin Yu.

Financial assistance from the Natural Science and Engineering Research Council of Canada, the Ontario Graduate Scholarship, and the Department of Materials Science and Engineering at the University of Toronto is gratefully acknowledged.

I am thankful for my family and friends for their unending encouragement and moral support. To my siblings, Helen and David for their patience and reassurance. Finally, to my loving parents who have taught me the values of hard work, discipline, perseverance, and importance of lifelong learning.

TABLE OF CONTENTS

Abstract ...... ii

Acknowledgements ...... iii

CHAPTER 1 ...... 1

Introduction ...... 1

References ...... 3 CHAPTER 2 ...... 4

Background for Proposed Research ...... 4

2.1 Silicon ...... 5 2.2 Solar Grade Silicon Production ...... 8 2.3 Thermodynamics of Phosphorus in Molten Silicon Alloy Systems ...... 20 2.4 Kinetics of Phosphorus Removal from Molten Silicon Alloys ...... 22 References ...... 24 CHAPTER 3 ...... 26

Electromagnetic Levitation ...... 26

3.1 Principle ...... 26 3.2 Review of Experimental Aspects of Levitation Melting ...... 27 3.3 Applications of the Levitation Technique ...... 31 3.4 Advantages of Levitation Melting ...... 37 3.5 Disadvantages of Levitation Melting ...... 38 3.6 Proposed Metallurgical Refining Route ...... 39 References ...... 41 CHAPTER 4 ...... 44

Experimental Considerations...... 44

4.1 Electromagnetic Levitation Apparatus ...... 44 4.2 Materials ...... 48 4.3 Chemical Analysis of Samples: Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) ...... 50 References ...... 52 v

CHAPTER 5 ...... 53

Results and Discussion ...... 53

5.1 Experimental Results ...... 53

5.2 Dephosphorization of Levitated Si-Fe Droplets in H2-Ar gas: Effect of Process Variables ...... 55 5.3 Thermodynamic Study of Si-Fe Dephosphorization under Reducing Gas Atmosphere: FactSage Study ...... 59 5.4 Kinetic Study of Phosphorus Evaporation from Si-Fe Droplets ...... 65 References ...... 77 CHAPTER 6 ...... 78

Conclusions and Future Work ...... 78

6.1 Conclusions ...... 78 6.2 Future Work ...... 79 Appendix A FactSage Equilibrium Reaction Products ...... 80

A.1 Si-Fe-P System – Pure Components ...... 80 A.2 Si-Fe-P System – Commercial Alloy ...... 81

A.3 Gaseous reaction, P, H2 ...... 82

Appendix B Sample Calculation of Mass Transfer Coefficient in Melt Boundary Layer, Km for 1520°C (1793K) ...... 83

LIST OF TABLES

Table 2-1: Typical proportions of impurities in different grades of silicon ...... 6 Table 2-2: Differentiation of Si products by purity ...... 11 Table 2-3: Segregation coefficient values for various impurities found in MG-Si ...... 17

Table 3-1: Summary of measured thermophysical properties of metal alloy systems at TEMPUS Spacelab EML facility ...... 34

Table 4-1: Chemical composition of commercial ferrosilicon (Gerdau) and metallurgical silicon ...... 48 Table 4-2: Impurity concentration of electrolytic iron from Allied Metals (wt.%) ...... 49 Table 4-3: Impurity concentration of silicon (6N purity) from ESPI Metals ...... 49 Table 4-4: Chemical composition of ferrophosphorus from Hiekman Williams & Company (supplier’s analysis, wt. %) ...... 49

Table 5-1: Effect of processing conditions on dephosphorization kinetics ...... 55 Table 5-2: Physical property values used in calculation ...... 68

Table 5-3: Liquid phase mass transfer coefficients, km ...... 68

Table 5-4: Summary of apparent rate constants (interfacial reaction control), ka (cm/s) ...... 70

Table 5-5: Summary of calculated apparent activation energies, Ea (kJ/mol) ...... 71

Table 5-6: Summary of equilibrium constant terms, Keq ...... 75

Table 5-7: Summary of apparent rate constants (gas diffusion control), ka (cm/s) ...... 75

Table 5-8: Summary of calculated apparent activation energies, Ea (kJ/mol) ...... 76

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LIST OF FIGURES

Figure 2-1: Limits of impurity concentrations in p-type silicon for impurities determining threshold of solar cells- 1:-Si; 2:SoG-Si; 3:MG-Si ...... 7 Figure 2-2: Schematic of a Siemens reactor ...... 9 Figure 2-3: Schematic of a fluidized bed reactor ...... 10 Figure 2-4: Ellingham diagram for various metal oxides ...... 13

Figure 2-5: Solubility of P in saturated CaO - CaF2 melts ...... 14 Figure 2-6: Relationship between yield of Si ...... 15 Figure 2-7: Effectiveness of solidification refining on impurity removal ...... 16 Figure 2-8: Solid solubility of elements in silicon ...... 18 Figure 2-9: Temperature dependence of Gibbs free energy change ...... 20 Figure 2-10: Effect of temperature on saturated vapour pressures of pure phosphorus and silicon ...... 21 Figure 2-11: Effect of iron alloying on equilibrium P concentration in molten ...... 22 Figure 2-12: Comparison of apparent mass transfer coefficients of P removal from molten Si ...... 23

Figure 3-1: EML principle ...... 26 Figure 3-2: EMF field distribution within levitation coil ...... 27 Figure 3-3: Progression of levitation coil designs: (a) Single levitation coil, (b) Primary lifting coil with counter winding, (c) Conical coil with counter windings ...... 28 Figure 3-4: Schematic showing proposed metallurgical refining route for SOG-Si production ...... 40

Figure 4-1: Schematic diagram of electromagnetic levitation apparatus ...... 44 Figure 4-2: Schematic diagram of levitation coil ...... 45 Figure 4-3: Schematic diagram of gas flow system ...... 46

Figures 5-1 a to d: Change in phosphorus concentration with time ...... 53 Figures 5-1e: Effect of hydrogen gas concentration under fixed temperature and gas flow rate ...... 53 Figure 5-2: Effect of time and temperature on dephosphorization ...... 56

Figure 5-3: Separation coefficients of P and Fe in molten Si alloys; if βi >1, the impurity i can be separated from base metal. For βi ≤1, impurity removal is difficult ...... 56

Figure 5-4: Effect of H2 gas concentration ...... 57 Figure 5-5: Effect of Fe composition in Si-Fe ...... 57 Figure 5-6: Iso-activity curves of [P] in liquid Si-Fe-P alloys at 1873K ...... 58 Figure 5-7: Mass fraction of P in the vapour phase during vapour-liquid equilibration of Si-P and Si-Fe alloys ...... 58 Figure 5-8: Effect of initial [P] in Si-Fe ...... 58 Figures 5-9 a to b: FactSage Equilibrium reaction products for 76wt.%Si-Fe-P (pure) under various reducing H2-Ar gas conditions...... 60 viii

Figures 5-10 a to e: FactSage Equilibrium reaction products for 76wt. %Si-Fe-P ...... 63

Figure 5-11: FactSage Equilibrium reaction products P and H2 gas species ...... 64

Figures 5-12 a to d: ln(Pt/P0) vs. Time plots ...... 70 Figures 5-13 a to c: Activation energy plots for chemical reaction control conditions ...... 71

Figures 5-14 a to c: (1/Pt)-(1/P0) vs. Time plots ...... 74 Figures 5-15 a to c: Activation energy plots for gas diffusion control conditions ...... 76

LIST OF SYMBOLS

σ Electrical conductivity

µ0 Magnetic permeability ƞ Dynamic viscosity ρ Melt density C Weight concentration

C0 Initial concentration

DP,m Diffusion coefficient of phosphorus in melt (Si-Fe) 푗 Interaction coefficient of j on i 푒푖

Ea Activation energy f Characteristic frequenc ΔG° Standard Gibb’s free energy of formation

Jo Coil current ka Apparent rate constant kB Boltzmann constant

Keq Equilibrium constant

Km Mass transfer coefficient L Characteristic length/melt diameter p* Saturated vapour pressure

[P]i Initial phosphorus concentration

[P]in Phosphorus concentration at gas-metal interface

[P]b Phosphorus concentration in bulk gas

[P]t Phosphorus concentration at time, t R Ideal gas constant

RP Covalent radius of phosphorus r Melt radius T Temperature

Uo Characteristic velocity vm Melt surface velocity x

LIST OF ABBREVIATIONS

EML Electromagnetic levitation EMF Electromagnetic field

ICP-OES Inductively coupled plasma optical emission spectroscopy

PV Photovoltaic MG-Si Metallurgical grade silicon SoG-Si Solar grade silicon e-Si Electronic grade silicon

CHAPTER 1 Introduction

While modern life remains heavily reliant on the use of ubiquitous fossil fuels, in recent times, there has been a rapid shift towards the diversification, development and implementation of renewable energy resources, predicted to sustain well into the future. Still comprising a low proportion in the global energy mix, renewables have become cost competitive with fossil fuels in many energy markets. Solar energy is a promising renewable resource for the future, with the industry experiencing remarkable growth over the last few years. Silicon remains the most dominant PV material in industry due to its natural abundance in the earth and properties upon refinement.

Metallurgical grade silicon (MG-Si) is produced on a large scale through the carbothermic reduction of silica to silicon. It is the precursor material for producing solar (SoG) and electronic (e-Si) grade-silicon, and has a 98% to 99% purity [1,2]. The relative purity of the various grades of silicon is measured in number of “nines” (N), with e-Si requiring a 9N (99.9999999%) purity level, and SoG-Si requiring a purity of 6N to 7N (<1 ppm impurities). In spite of the fact that expensive and energy intensive chemical purification (distillation) processes still dominate the existing production capacity for PV materials, new processes while currently limited, have been in development with the aim of directly producing SoG-Si.

The use of relatively inexpensive MG-Si to directly produce SoG-Si on a large scale is considered to be the most economical method, and an area of interest in which considerable research is being carried out. Such metallurgical refining approaches involve the removal of detrimental impurities in MG-Si, which reduce solar cell efficiency and performance by decreasing the lifetime of the energy carriers in the cell, and disrupting electrical generation [3]. The investigated methods have been found to be selective, with no single method able to remove all impurity elements [1]. Consequently, a combination of refining steps is required in order to achieve required purity levels 2 for SoG-Si. Phosphorus is deemed as one of the most difficult impurity elements to remove from metallurgical silicon by investigated techniques, and has been the focus of several recent studies.

Electromagnetic levitation (EML) refining enables containerless processing of liquid metals. It is an excellent experimental technique for carrying out fundamental investigations of metallurgical reaction processes at elevated temperatures. In this study, an electromagnetic levitation technique is used to investigate the dephosphorization kinetics of ferrosilicon alloy droplets exposed to reducing H2-Ar gas mixtures. The effect of processing parameters on dephosphorization kinetics were studied, which included: refining time, temperature, H2-Ar gas composition and flow rate, iron alloying content in Si-Fe, and initial phosphorus concentration in the alloy. A theoretical thermodynamic study was carried out using FactSage, to determine reaction products of the process under equilibrium conditions. Kinetics of phosphorus removal were evaluated in order to determine the rate limiting step of the process.

References

1. M. D. Johnston, L. T. Khajavi, M. Li, S. Sokhanvaran, and M. Barati, JOM 64, 935 (2012). 2. O. S. Fishmann, ASM Int. 33 (2008). 3. K. Morita and T. Miki, Intermetallics 11, 1111 (2003).

CHAPTER 2 Background for Proposed Research

Solar energy has experienced rapid growth over the past few years, as a result of increased innovation in technology and usage, and investment for installed capacity for electricity generation. This progress follows a tumultuous decade, in which silicon used for PV cells experienced a shortage with skyrocketing market prices of up to $450/kg (2005-2008), to an oversupply situation, with a record low price level for polysilicon (2012-2014) [1]. In spite of new developments in semiconductor materials for solar cells, specifically for thin-film technologies containing compounds such as cadmium telluride, copper indium gallium selenide, or gallium arsenide, crystalline silicon still remains the dominant material for solar cells. Over 90% of PV cells currently produced are silicon based [2]. The availability, quality and cost of silicon feedstock is of paramount importance for the development of the photovoltaic sector in the future global energy mix.

This chapter presents an overview of silicon materials and refining processes for photovoltaic cells. Processes include conventional chemical methods, and alternative metallurgical refining methods to achieve impurity removal. Research involving the thermodynamics and kinetics of impurities in metallurgical silicon and ferrosilicon alloys is examined, to better understand and apply alternative metallurgical refining routes.

2.1 Silicon Silicon is the second most abundant element in the earth’s crust. Due to its affinity to oxygen,

silicon exists in nature as silica (SiO2) or in the form of silicates (MeSiOx). The natural abundance of silicon, and properties upon refinement make it an ideal material for solar cells. Challenges in developing efficient silicon technologies are associated with the costly and energy intensive purification steps of crude (metallurgical) silicon. This results in silicon material comprising approximately 45-50% of the total cost of a typical crystalline-silicon module [3]. With demand for the technology expected to grow, greater volumes of silicon raw material will be required to meet capacity requirements and as such, the development of more energy-efficient and cost- effective methods is imperative.

2.1.1 Metallurgical grade silicon and ferrosilicon Both metallurgical grade silicon (MG-Si) and ferrosilicon (FeSi) are produced industrially through the carbothermic reduction of quartz (silicon dioxide) in a submerged electric arc furnace (Figure 2.1) at temperatures above 2000°C. A general equation of the overall reaction that occurs in the production of MG-Si is shown as follows:

SiO2 + 2C = Si + 2CO (g) [2] (2.1)

The majority of world production of MG-Si and FeSi is used in the steel, aluminum alloying, and silicone industries, with a small proportion of the supply used as feedstock for the semiconductor industry.

The MG-Si produced is typically of 98% to 99% purity [4]. The impurities that remain in MG-Si and FeSi include: Al, Ca, Ti, Mn, Mg, Cr, Cu, Ni and V, which are generally in the 100 to 1000ppm mass range or above [5]. Other impurities such as S, B, and P are usually present in the 10-100ppm range or below [5]. The major source of impurities are from the raw materials used, specifically the reducing agents containing coke, charcoal, petroleum, lignite, and wood chips [6]. The detrimental effect of these impurity elements is dependent on the use of the alloys. Dissolved impurity elements such as S, P, O, N, C, H greatly affect the final quality of steel products [5]. High grade silicon stainless steel, containing 5-6 mass% Si [5], have stricter requirements on cleanliness, thus, alloy additions such as FeSi and MG-Si, containing high impurity levels become more unfavourable. For the production of solar-grade and semiconductor-grade silicon, impurity 6 refinement to minimum requirement levels is necessary. The typical proportions of impurities present in the different grades of silicon are shown in Table 2-1 [7,8].

Table 2-1: Typical proportions of impurities in different grades of silicon

Metallurgical Grade Si, MG-Si Solar Grade Si, SoG-Si Electronic Grade Si, e-Si Element (ppm) (ppm) (ppm) 99.9999 % (6N pure) Si* 98-99 % 99.9999999 % (≥ 9N pure) 99.99999 % (7N pure) Fe 2000 - 3000 < 0.3 < 0.01 Al 1500 - 4000 < 0.1 < 0.0008 Ca 500 - 600 < 0.1 < 0.003 C 600 < 3 < 0.5 O 3000 < 10 Ti 160 - 200 < 0.01 < 0.003 Cr 50 - 200 < 0.1 B 40 - 80 < 0.3 < 0.0002 P 20 - 50 < 0.1 < 0.0008

Price (USD/kg) 1.80-2.75 18-20 40-60 * Si content in mass % 2.1.2 Semiconductor grade silicon Semiconductor grade silicon (e-Si) is a high purity material (9N, impurities of <1ppb) used in the electronics industry. The conversion of MG-Si to e-Si involves a chemical method known as the Siemens Process. The process is based on chemical vapour deposition, in which MG-Si is converted to a volatile silicon compound (silicon tetrachloride), distilled, and is subsequently decomposed into high purity elemental silicon.

2.1.3 Solar grade silicon Various chemical and pyrometallurgical routes are available to refine MG-Si to required impurity levels for PV applications. Historically, solar-grade silicon was supplied commercially through the use of expensive electronic-grade silicon scrap, which was also of much higher purity than necessary for their function. The increase in demand for solar silicon in the mid to late 2000s resulted in serious shortages in supply, and skyrocketing prices, which severely hampered growth in the industry, along with innovations in production methods. With the new wave of growth in the industry expected to sustain long-term, innumerable opportunities exist for innovation in material production processes. Current industrial and pyrometallurgical routes for refining MG-Si to SoG-Si are discussed in the subsequent section (2.2).

Given the purity requirement for SoG-Si being between 6N to 7N (99.9999% to 99.99999% purity, < 1 parts per million impurities) [4], the refinement of MG-Si is crucial. Impurities have varying effects on performance of SOG-Si cells. Work carried out by Hopkins and Rohatgi [9] (Figure 2- 1), comparing the concentration of impurities on efficiency showed that certain impurities have less effects on cell efficiency than others.

Figure 2-1: Limits of impurity concentrations in p-type silicon for impurities determining threshold of solar cells- 1:-Si; 2:SoG-Si; 3:MG-Si [9] 8

2.2 Solar Grade Silicon Production

2.2.1 Chemical processes for silicon production Modified Siemens process – Trichlorosilane (TCS)

Polycrystalline Si with manufacturing objective of PV applications is produced by a Modified Siemens method, which employs the original Siemens reaction method developed in the 1960s for semiconductor grade silicon. Currently, 90% of installed polysilicon capacity is produced by this technology [1].

The method consists of the production of trichlorosilane (TCS) from metallurgical grade silicon, purification of silicon through distillation and condensation, and decomposition in a thermal chemical vapour deposition (CVD) reactor [1]. Detailed steps of the process are presented as follows [1]:

Hydrogen chloride reacts with MG-Si to produce TCS (300-350°C at 1-5 bars).

Si (s) + 3HCl (g)  SiHCl3 (g) + H2 (g) (2.2)

Silicon tetrachloride (STC) is also produced during the production of TCS as a side reaction. While

STC may be recycled in a closed loop process by reacting with H2 at 1000°C, this requires large amounts of energy.

Si(s) + 4HCl(g) = SiCl4 + 2H2 (2.3)

SiCl4 + H2 = SiHCl3 + HCl (2.4)

Subsequent purification of the volatile TCS occurs through a two-step process in which heavier impurity components are removed by distillation, followed by the removal of volatile gas components, producing an ultra-high purity stream of TCS. The gas is transferred into a Siemens

reactor with H2 comprising inverted U-shaped silicon rods (Figure 2-2) heated to 1100°C. The TCS

flowing past the rods react with H2, and subsequent decomposition of pure Si occurs over the heated rods.

2SiHCl3 (+H2) → Si + 2HCl + SiCl4 (+H2) (2.5) 9

Figure 2-2: Schematic of a Siemens reactor [10] The main issues that arise from the Siemen process include [11,12]: 1) High energy requirements of the process in that it requires two power supplies –one used to preheat the silicon seed rods, and the second to superheat the rods by conduction 2) The process produces low yields of approximately 25% due to the fact that the SiCl4 by- product is more favourable 3) High costs resulting from equipment and energy requirements 4) Production of hazardous gases at high temperatures

Fluidized bed reactor (FBR) – Silane

The fluidized bed reactor (FBR) process which involves the use of a silane (SiH4) feed-gas is a challenger to the Siemens process, with less than 10% of global polysilicon output generated through this method [1].

The process involves the introduction of silane and hydrogen feed gas into a bed reactor containing MG-Si seeds which are semi- continuously loaded from the top. The ascending gases decompose, and pure Si is deposited onto the bed of fine particle silicon seeds (800-1000°C), producing granular silicon. As the Si seeds reach a certain size, they become too heavy to remain suspended by the fluidized bed, and are pushed downwards by gravity, where they are Figure 2-3: Schematic of a fluidized bed reactor [1] collected and removed from the reactor.

SiH4 (+H2) → Si + 2H2 (+H2) (2.6)

As a continuous operation, this permits the simultaneous introduction and removal of feed and exhaust gases, and seed particles and product granules. Advantages of this process include lower capital and operating costs (lower energy consumption). However, production economics of this process are still in early development. In addition, this process is less efficient than the Siemens process with respect to potential contamination sources including metals, carbon and oxygen. Comparison of purity levels between the two chemical methods Siemens and FBR as well as the Upgraded Metallurgical Grade (silicon) (UMG) process are displayed in Table 2-2 [1].

Table 2-2: Differentiation of Si products by purity

Current commercial processes to produce silane include the Union Carbide process and Ethyl Corporation process.

Union Carbide Process: This method consists of the redistribution of trichlorosilane through fixed bed columns, followed by distillation of reactants and products to form silane.

2SiHCl3 = SiH2Cl2 + SiCl4 (2.7)

3 SiH2Cl2 = SiH4 + 2SiHCl3 (2.8)

Ethyl Corporation Process: The process consists of the hydrogenation of silicon tetrafluoride, a by-product of the fertilizer industry, to silane, by aluminum metal hydrides. The resulting AlMF4 may be sold to the aluminum industry for metal recovery.

SiF4 + AlMH4 = SiH4 + AlMF4, M being Li or Na (2.9)

2.2.2 Metallurgical processes for silicon production Over the past few decades, various techniques have been developed to directly refine MG-Si to SoG-Si, with the purpose of reducing reliance on costly, high purity processes [4].

Acid Leaching

Acid leaching is a low cost hydrometallurgical method which can be used as an initial treatment step for MG-Si purification. Studies have found that most impurities in solid MG-Si exist in grain boundaries due to their small segregation coefficient values (ratio between impurity element concentration in solidifying crystal and melt) and thus, low solid solubility [13,14]. Consequently, the acid leaching method involves the crushing of solid MG-Si into fine powder (50-100µm), followed by acid treatment. Acid solution that may be used include combinations of HCl, HNO3,

H2SO4, or HF. Parameters influencing the degree of impurity removal include: leaching time and temperature, particle size, concentration and combination of acid mixtures [15].

Work by Dietl demonstrated that the technique was successful in removing many metal impurities (Mn, Ti, Fe, Al, Ca), with impurities eliminated down to several orders of parts per million [16]. However, removal of doping elements B and P was not as effective, owing to their large segregation coefficients. Early work by Elkem disclosed the removal rate of phosphorus in MG- Si to be 90% effective [2]. Overall, as a standalone process, acid leaching is unable to produce silicon with acceptable impurity levels for solar cells, and thereby requires the combination of other refining techniques.

Slag Refining

Slag refining employs the addition of fluxes to oxidize impurity elements, followed by dissolution into a slag phase [4]. The reactions involved in this process are dependent on thermodynamic stabilities of oxide compounds. From the Ellingham diagram for oxides (Figure 2-4), it can be noted that Al, Mg, Ba, and Ca impurities are more readily oxidized than silicon due to their high oxygen affinities, producing minimal losses in Si [4]. From Figure 2-4, it can be seen that phosphorus and boron are more noble than silicon, and thus have limited slag removal capacity. Investigations have focused on examining the effect of basicity and oxygen potential to Figure 2-4: Ellingham diagram for various maximize the removal of phosphorus metal oxides [4] and boron impurities.

The distribution coefficient, LM is a commonly used quantifier describing the extent and effectiveness of impurity removal by slag refining. LM denotes the concentration (wt.%) ratio of impurity M, in the slag phase (M) to that in the metal phase [M]:

(푀) 퐿 = (2.10) 푀 [푀]

Studies have shown that the removal of P and B from the melt to the slag phase occurs through oxidation reactions, in which acidic oxide complexes are formed and subsequently absorbed in the slag layer. The dissociation of basic oxides in the slag phase, such as CaO, BaO and Na2O, to provide oxygen ions promotes the removal of P and B from the silicon melt. Boron reacts to form 3- a stable boron oxide complex, and is absorbed into the slag as borate (BO3 ). Depending on oxygen potential in the system, phosphorus will dissolve as either a phosphate ion (high oxygen potential) or phosphide ion (low oxygen potential).

2- 3- [B] + (3/2) O + (3/4) O2  (BO3 ) (2.11)

2- 3- [P] + (3/2) O + (5/4) O2  (PO4 ) (high pO2) (2.12)

2- 3- [P] + (3/2) O  (P ) + (3/4) O2 (low pO2) (2.13)

Investigations have been carried out to examine the

effects of oxygen potential (pO2) and basicity on distribution of phosphorus equilibrated between silicon and calcium oxide (CaO) based slags [4].Calcium oxide based slags are traditionally used in the steel industry for the dephosphorization of molten iron. Tabuchi and Sano [17] measured the

solubility of phosphorus in CaO-CaF2 melts, equilibrated under various oxygen partial pressures. It was observed that low oxygen pressures resulted in the increase of phosphorus solubility in slag as Figure 2-5: Solubility of P in saturated Ca3P2 [2,4] (Figure 2-5). However, the addition of CaO - CaF2 melts [17] CaO in excess resulted in increased Ca concentration in Si, which caused the reduction of P from slag, and its subsequent conversion back into the molten silicon through ternary interactions [2,4]. Although slag treatment of MG-Si has proven to be successful in removing a range of impurities, its use for phosphorus removal is not as favourable.

Vaporization Techniques

Vaporization techniques have been employed for impurity removal from silicon due to its low volatility. The technique facilitates impurity removal by promoting the evaporation of relatively high vapour- pressure species from a molten bath, subsequently forming elemental vapour, or a volatile compound [4]. Effectiveness of the process is also dependent on bath temperature, molten bath size, surface area exposed to the vacuum, and system pressure. Vacuum refining has been found to be one of the most promising methods of refining MG-Si to SoG-Si, and has been shown to provide a close control of the melt composition and Figure 2-6: Relationship between yield of Si and P content attained at 1823K temperature while simultaneously preventing (initial P content of 2.5x10-3 mass %) [19] undesired contamination by reactive gases [18]. With this technique, removal of problematic impurity elements such as phosphorus and boron has been readily achieved. One study using the electron beam melting method resulted in over 99% of metallic elements removed, and over 98% of phosphorus removed (0.4 ppmw P) [4]. However, these removal rates required higher beam power, and lower total pressure. The rate of dephosphorization was also found to be proportional to temperature at the reaction interface and beam power applied, which eventually led to substantial silicon losses through vaporization [4]. From the various vaporization techniques which were investigated, including electron beam melting, and reactive gas/plasma injection, it was revealed that reaching acceptable concentrations of P or B impurities in SoG-Si resulted in high unfavourable losses in Si as vapour, due to requirements of high beam power or large gas volumes, respectively [19] (Figure 2-6). In addition, such techniques are costly due to high energy requirements, limited by small batch sizes, and associated complexities in operation.

Solidification Refining

The premise of solidification refining is based on differences in solubility limits of impurities in solid silicon compared with the liquid phase. During the process, impurity elements advance through a solid-liquid front to one end of an ingot [2], in which impurities that are less soluble in the solid phase are rejected into liquid phase. The portion that is last to solidify is concentrated with impurities, while the portion of the ingot that solidifies first will have fewer impurities than the starting material. The effectiveness of solidification refining is estimated by the segregation coefficient, and change in impurity concentration (Figure 2-7) [20]. The segregation coefficient, ki describes the ratio between the concentration of an impurity element, i, in the solidifying crystal and liquid phase respectively, shown in Equation 2.14 [21]:

퐶푖 푖푛 푠표푙푖푑 푠푖푙푖푐표푛 푘푖 = (2.14) 퐶푖 푖푛 푚푒푙푡

As shown in Figure 2-7 and Table 2-3, solidification refining is effective for the majority of impurities in silicon –specifically ones with low segregation coefficients (less than 10-5) [20]. The method produces a negligible effect on impurities with high segregation coefficients such as B (0.8) and P (0.35), which show only a slight decrease in impurity content, even after applying solidification refinement twice. From Figure 2-7, given that most impurity elements require two passes, this method is unfavourable due to high costs and energy intensive requirements. As a result, a metallurgical refining route to produce solar-grade silicon should involve a combination of metallurgical refining steps Figure 2-7: Effectiveness of solidification refining with directional solidification employed as on impurity removal [20] last step in the purification process.

Table 2-3: Segregation coefficient values for various impurities found in MG-Si [13,22]

Solvent Refining

The solvent refining process involves the recrystallization of a supersaturated melt, based on the segregation behaviour of impurity elements. For metallurgical silicon purification, the process involves the alloying of silicon with a metal that can act as an impurity trapper during solidification [4]. During the process, the Si-metallic alloy is kept above the liquidus and slow cooled, producing pure silicon crystal precipitates from the melt and rejecting impurities to the liquid alloy phase, also known as the solidification front [4]. When the amount of Si solidifying out of the melt has been depleted, the alloy is quenched, from which the purified and impurity rich eutectic phase can be separated. With the high segregation coefficient of P and B impurity elements (seen in Figure 2-7 and Table 2-3), the candidate alloying metal would be expected to have a high affinity for the elements, and low solid solubility in silicon [4]. Figure 2-8 shows the relationship between solid solubility and distribution coefficients for elements found in silicon [4]. Several solvent refining studies have been carried out for the Al-Si, Cu-Si, Fe-Si, Sn-Sb-Si, Ni-Si, and Ga-Si systems, and are presented in several reviews [4,15], [22,23]. The studies have shown varying efficiencies in impurity removal for different elements.

Figure 2-8: Solid solubility of elements in silicon as a function of segregation coefficient [4] 19

Fe-Si System Iron is a favourable solvent element due to its low solid solubility in silicon compared to both Cu and Al, and high affinity for phosphorus and boron impurity elements deemed to be more difficult to remove by other metallurgical refining techniques. Its relative abundance, low cost, and potential to be recycled (ferrosilicon, FeSi2) and used in the steel industry is also advantageous. The low segregation coefficient of iron (8x10-6), as shown in Figure 2-8 enables its subsequent separation from the final purified Si material through directional solidification. In using iron alloying, Esfahani [23] applied a combination of solvent refining and physical separation to purify MG-Si, obtaining a total removal of 98.8% from the process. An optimal crushing size for the separation of Si dendrites was determined. Samples were quenched at a range of temperatures above and below the eutectic (1207oC). It was found that impurity removal was significantly higher for samples quenched above the eutectic temperature, with over 90% removal achieved for all elements except Cr (80%) and P (57%). Tafaghodikhajavi [15] applied solvent refining to investigate the distribution coefficient of phosphorus and boron in silicon and the iron alloy melts. They found that the process was 2-3 times more effective than the conventional solidification refining process in removing P and B impurities. From the distribution coefficient values obtained, the removal percentage of phosphorus calculated at temperatures from 1210-1310°C ranged from 62.2% to 84.1%. Removal percentage of boron from silicon ranged from 65.1% to 70.5% for the same temperature range.

2.3 Thermodynamics of Phosphorus in Molten Silicon Alloy Systems Miki et al. [19] studied the thermodynamics of phosphorus in molten silicon contained in a graphite crucible, and determined the Gibbs free energy change of phosphorus dissolution into molten silicon for the temperature range 1723K to 1848K (Figure 2-9). They accomplished this by equilibrating the molten phosphorus alloy with a controlled phosphorus partial pressure expressed as follows [19]: 1 P2 (g) = (P) (mass%, in Si) (2.15) 2 ΔGo = -139,000 (±2000) + 43.4 (±10.1T) (J/mol) (2.16)

Figure 2-9: Temperature dependence of Gibbs free energy change for phosphorus dissolution in silicon

Monatomic phosphorus gas dissolved into molten silicon was calculated as [19]:

P (g) = (P) (mass%, in Si) (2.17) ΔGo = -387,000 (±2000) + 103 (±10.1T) (J/mol) (2.18)

The research demonstrated the possibility of achieving phosphorus removal from silicon by vacuum treatment, through the free evaporation of phosphorus.

In examining evaporative losses of phosphorus from molten silicon, investigations by Wei et al. [24] demonstrated phosphorus removal by vacuum distillation to be a viable method, owing to the large difference in saturated vapour pressures between phosphorus and silicon. The saturated pressure for pure phosphorus and silicon is written as:

∗ −1 푙표푔푝푝 = 2740 푇 + 9.965 (2.19)

∗ −1 푙표푔푝푆푖 = −20900 푇 − 0.565 푙표푔푇 + 12.905 (2.20)

For the temperature range 1350K to 2150K, the saturated vapour pressures for phosphorus and silicon are plotted in Fig. 2-10.

Figure 2-10: Effect of temperature on saturated vapour pressures of pure phosphorus and silicon [24]

The results in Figure 2-10 are indicative of the tendency that drives the rate of phosphorus evaporation over silicon, rather than a quantitative measure. Nevertheless, in developing experimental approaches to achieve phosphorus removal, it is important to note the increase in silicon vaporization tendency at elevated temperatures.

Ueda et al. [25], investigated the interaction coefficients of phosphorus in silicon alloys under a controlled phosphorus partial pressure. The activity coefficient of phosphorus in the Si-Fe alloy, showed a maximum value at a certain composition due to strong interaction between silicon and iron, resulting in decreased phosphorus content in the alloy (Figure 2-11). Consequently, the possibility for dephosphorization of silicon alloyed with iron was demonstrated. The 퐹푒 corresponding first order interaction coefficient was 푒푃 = 0.199 [25].

Figure 2-11: Effect of iron alloying on equilibrium P concentration in molten -1 Si-Fe at 1723K and PP2= 1.84 x 10 Pa [25]

2.4 Kinetics of Phosphorus Removal from Molten Silicon Alloys The dephosphorization process involves the following steps which may determine the rate of reaction: 1) Mass transport of phosphorus in the liquid metal to the melt boundary layer.

2) Formation of adsorbed P atoms or P2 molecules from P atoms on the liquid surface,

followed by chemical evaporation of phosphorus (as P or P2) at the melt-gas interface. 3) Gas phase mass transport of phosphorus within the gas boundary layer.

Based on the Hertz-Knudsen-Langmuir Estimated equation, the rate constant for monatomic from Eq. 2.21 phosphorus evaporation may be expressed as follows [26]:

100 푀푃 ∆퐺°1 푘1 = √ exp ( ) (2.21) 휌푆푖 2휋푅푇 푅푇

Research on phosphorus removal from silicon by vacuum induction refining and electron Figure 2-12: Comparison of apparent mass transfer coefficients of P removal from molten Si [26] beam melting was summarized by Sasaki et al. [26] Apparent mass transfer coefficients for monatomic phosphorus evaporation, along with estimated values from Equation 2.21, are compared in Figure 2-12. While there are notable differences between reported values from experimental work, the estimated coefficient line from Equation 2.21 shows reasonable agreement with the overall results.

Possible reasons for the discrepancies between higher k1 values and those estimated from Equation 2.21 were suggested by Sasaki et al. [26]:

 P evaporation as both P and P2  Temperature inhomogeneity of molten Si, specifically the local temperature at the Si surface which may have been higher than estimated, resulting in preferential evaporation of P  Evaporation enhancement of P due to the fact that it is a surface-active element and therefore concentrates at the surface of molten Si  Deviations at high operating temperatures caused by mass transport of P in molten Si or the gas phase

Work carried out by Shi et al. [27], Zheng et al. [18], and Safarian et al. [28], considered an overall mass transfer coefficient based on first-order kinetics, from which they concluded that the possible rate limiting steps were a combination of chemical reaction and mass transport. 24

References

1. G. Bye and B. Ceccaroli, Sol. Energy Mater. Sol. Cells 130, 634 (2014). 2. D. Lynch, Jom 61, 41 (2009). 3. Giorgio Simbolotti, (2013). 4. M. D. Johnston, L. Tafaghodikhajavi, M. Li, S. Sokhanvaran, and M. Barati, JOM 64, 935 (2012). 5. O. S. Klevan, Removal of C and SiC from Si and FeSi during Ladle Refining and Solidification, The Norweigian University of Science and Technology, n.d. 6. Kirk-O, editor , in Kirk-Othmer Encycl. Chem. Technol. (John Wiley & Sons, New York, 2005), p. 535. 7. B. S. Xakalashe, (2011). 8. PV Insights, (2015). 9. R. H. Hopkins and A. Rohatgi, J. Cryst. Growth 75, 67 (1986). 10. A. Luque and S. Hegedus, Handbook of Photovoltaic Science and Engineering Title, 2nd ed. (John Wiley & Sons, 2011). 11. O. S. Fishmann, ASM Int. 33 (2008). 12. M. Sumiya, T. Akizuki, K. Itaka, and M. Kubota, 4, 2012 (2012). 13. B. R. Bathey and M. C. Cretella, J. Mater. Sci. 17, 3077 (1982). 14. J. M. Juneja and T. K. Mukherjee, Hydrometallurgy 16, 69 (1986). 15. L. Tafaghodikhajavi, Thermodynamics of Impurity Removal in Solvent Refining of Silicon, Ph.D Thesis, University of Toronto, 2015. 16. J. Dietl, Sol. Cells 10, 145 (2983). 17. S. Tabuchi and N. Sano, Metall. Trans. B 15, 351 (1984). 18. S.-S. Zheng, W.-H. Chen, J. Cai, J.-T. Li, C. Chen, and X.-T. Luo, Metall. Mater. Trans. B 41, 1268 (2010). 19. T. Miki, K. Morita, and N. Sano, Metall. Mater. Trans. B 27B, 937 (2000). 20. K. Morita and T. Miki, Intermetallics 11, 1111 (2003). 21. T. Yoshikawa and K. Morita, J. Cryst. Growth 311, 776 (2009). 22. K. Visnovec, Refining of Silicon During Its Solidification From a Cu-Si Melt by Refining of 25

Silicon During Its Solidification From a Cu-Si Melt, M.A.Sc. Thesis, University of Toronto, 2011. 23. S. Esfahani, Solvent Refining of Metallurgical Grade Silicon Using Iron, M.A.Sc. Thesis, University of Toronto, 2010. 24. K. Wei, W. Ma, Y. Dai, B. Yang, D. Liu, and J.-F. Wang, Trans. Nonferrous Met. Soc. China 17, 1022 (2007). 25. S. Ueda, K. Morita, and N. Sano, 1 (1997). 26. H. Sasaki, Y. Kobashi, T. Nagai, and M. Maeda, Adv. Mater. Sci. Eng. 2013, (2013). 27. S. Shi, W. Dong, X. Peng, D. Jiang, and Y. Tan, Appl. Surf. Sci. 266, 344 (2013). 28. J. Safarian and M. Tangstad, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 43, 1 (2012).

CHAPTER 3 Electromagnetic Levitation

3.1 Principle Electromagnetic levitation (EML) is a containerless, high-temperature processing technique that can be used to refine and investigate fundamental properties of liquid alloy systems. When a metal or conductor is placed in an alternating high-frequency electromagnetic field, eddy currents are induced in the conductive material, which subsequently cause inductive heating of the sample through ohmic resistive losses (Joule heating) [1]. In the levitation apparatus, the electrical field is produced by passing a high frequency alternating current through a water cooled copper coil, designed to produce field patterns that allow for droplet stability and temperature control. The interaction between the applied field and induced currents produces a repulsive electromagnetic (Lorentz) force against gravity, which holds and suspends the solid or liquid specimen in a state of stable equilibrium, Figure 3-1.

Figure 3-1: EML principle [1] 27

3.2 Review of Experimental Aspects of Levitation Melting There are various parameters which operate in combination to provide and control droplet temperature and stability during any given experiment.

3.2.1 Coil design & levitation force Coil design for levitation melting is essential to provide adequate lifting force, induction heating, and droplet stability; however, proper selection of design for a given experimental system is generally derived empirically. Figure 3-2 depicts the electromagnetic force (EMF) field and reverse coil configuration suitable for levitation determined by Price [2], and reported by Jenkins et al. [3]. Based on this configuration, a levitated droplet will tend to sit in position of minimum field strength, point A. Stable droplet levitation depends on static and dynamic elements [4,5]. Static stability involves the balance of electromagnetic, gravitational and surface tensional forces, while

dynamic stability is concerned with oscillations Figure 3-2: EMF field distribution within from the interacting forces [5]. levitation coil [2,3]

The general progression of coil designs are shown in Figure 3-3, from a single coil (Fig. 3-3a), a cylindrical shape with counter windings (Fig. 3-3b), to multiple concentric counter windings (Fig. 3-3c)). The addition of a counter wound loop above the single primary loop (Fig. 3-3b) offered increased droplet stability by creating a radial restoring force, and additional axial stability [6]. The conical helix-type design (Fig. 3-3c), comprising multiple primary and counter windings was found to be capable of levitating and melting a variety of metals (Al, Ti, Cu etc.), and thus became a standard design for most EML processing work [6]. 28

Figure 3-3: Progression of levitation coil designs: (a) Single levitation coil, (b) Primary lifting coil with counter winding, (c) Conical coil with counter windings [6]

Studies carried out by Okress et al. [7], Harris and Jenkins [3], as well as Kermanpur et al. [8] have provided theoretical and experimental background for coil design, through investigations based on horizontal turns, coil angle, sample weight and vertical position, as well as effects of lifting force and droplet temperature profiles.

Factors affecting levitation force that result in increased field strength in relation to coil design, are outlined below [5]:

(i) Increasing the number of coil turns per unit length (ii) Increasing applied coil current (iii) Decreasing coil diameter, allowing for more turns per unit length – 1/8in. tubing of 0.020in. wall, the smallest size that could be adequately cooled; however, volume of material is restricted (iv) Coil turn angle: Through experimentation with solid metal spheres, Price et al. found that a coil with a semi-cone angle of 30°-40° resulted in a maximum levitating force [2]. Larger angles were found to decrease lateral stability of the droplet [2].

3.2.2 Temperature control During the electromagnetic levitation process, the high frequency current to the coil supplies both the lifting force and heating energy to the specimen. Given this interdependency, a host of external parameters is required to maintain and control the steady-state temperature. Factors influencing droplet temperature during levitation refining that are dependent on the characteristics of the levitation system and levitated specimen, were summarized by McLean [9], Zuliani [10], and Wu [11] as follows:

Electrical power supplied to the coil: The magnitude of applied power controls the vertical position of the specimen in the electromagnetic field, which consequently influences the density of electrical flux lines interacting with the specimen, as seen in Figure 3-2. Based on this, an increase in power will increase the levitation force and lift the specimen to a higher position where the field is divergent, and thus decrease the droplet temperature. Conversely, decreasing power results in the droplet positioning lower within the coil, where it will interact with a greater number of flux lines, thus experiencing higher temperature.

Frequency of the applied current: A higher frequency powered generator will increase the eddy currents generated on the near-surface of the specimen. This increases the effective electrical resistance and temperature of the droplet, but also results in decreased lifting force.

Physical properties of the specimen: Material properties including weight, density, electrical conductivity, and magnetic permeability influence the vertical position of the droplet in the electromagnetic field. With increasing electrical conductivity and magnetic permeability, the depth of eddy currents induced and lifting force on the specimen decrease. Thus, an increase in these properties along with weight and density results in the droplet sitting lower in the coil, where it is subject to greater heating.

Coil-specimen coupling distance: As the distance of separation is reduced, the density of field flux lines interacting with the droplet increases. As such, lifting force is increased, and droplet temperature is decreased. The distance between upper and lower sections for a coil system will also affect the specimen position within the coil at an applied current, and subsequently the minimum temperature attainable under the conditions. 30

System atmosphere: For a levitation system with a continuous gas stream, the rate of heat removal is dependent on the heat capacity, thermal conductivity, and gas flow rate through the reaction chamber. The thermal conductivity of a gas varies as a reciprocal of molecular weight. Gases with lower molecular weights such as hydrogen or helium will decrease droplet temperature at a given flow rate due to convective cooling. The direction of gas flow has also been found to affect droplet temperature. McLean et al. [9] investigated the effect of gas flow direction for iron melts under a nitrogen gas atmosphere. With an upward gas flow, particularly at high flow rates (22 L/min), the droplet is lifted to a higher position within the coil where the field strength is lower, and heat input is reduced. The iron droplet temperature was maintained at 1600°C. When the flow was reversed, the specimen is pushed into a lower position within the coil where the field strength is higher. Temperatures between 1900°C to 2200°C were observed. Under reactive gas environments, effects of endothermic and exothermic reactions may lower or raise droplet temperatures.

3.2.3 Temperature measurement Direct temperature measurement of levitated droplets by a submerged thermocouple is not feasible due to the small melt volume, possibility of melt contamination, and high processing temperatures. Early work in levitation melting employed non-contact, disappearing filament infrared (IR) pyrometry, a technique which uses measured radiation emitted from a high temperature surface and emissivity of the object to determine surface temperature. Temperature is inferred from the current of an electrical filament positioned between the observer’s eye and the incandescent object. The filament current is adjusted until it is the same colour –indicating the same temperature [12]. While accurate emissivity data are available for pure metals, it was found that emissivity varied with chemical composition and surface roughness [10,13].

To overcome emissivity effects, two-colour IR pyrometry was developed. The basis of this technique assumes that emissivity remains constant at different wavelengths. The unknown emissivity is eliminated by taking the ratio of the radiant energies of the droplet at two known wavelengths, which are temperature dependent. The technique was further refined by Shiraishi and Ward [14], in which a linear calibration for the pyrometer was taken for the lower temperature range of a melt, and compared against a submerged thermocouple in a crucible arrangement. As 31

such, frequent calibration of two-colour pyrometers is necessary to ensure improved reliability, notably in conditions where emissivity values may differ.

3.2.4 Droplet quenching At the end of a levitation experiment, the droplet may be solidified through several methods [10]. (i) Slow cooling: The droplet may be solidified while remaining in levitation through making adjustments to current and gas flow rate. One such method includes increasing applied power, and purging the chamber with a highly conductive gas (helium or hydrogen). When the power supply is turned off, the sample can be recovered. (ii) Moderate cooling: By shutting off the power supply, the molten sample can be dropped into a mould made from copper or brass, which may be at room temperature or cooled with liquid gas. (iii) Rapid cooling: A rapid quench (105°C/sec) can be obtained by capturing the falling droplet between two copper plates.

3.3 Applications of the Levitation Technique Electromagnetic levitation was first proposed and patented by Muck in 1923 [15]. The technique was investigated in 1952 by Okress et al. [7] with the purpose of achieving simultaneous induction melting of reactive high melting point metals. Since its introduction as a containerless processing technique, levitation melting has undergone considerable development in its use for studying properties of molten metals.

The development of the EML technique –from theory to experimental considerations and practice, under both terrestrial and microgravity conditions have been reviewed by Bakhtiyarov and Siginer in a series of publications [16,17]. Most recently, Gao et al. [18] have summarized applications of EML and the progress of mathematical models over the past 15 years. The reviews delineate inherent difficulties associated with the technique which include maintaining droplet stability, controlling and measuring temperature. To a certain extent, these problems can been addressed through proper selection of coil design, current frequency, power input and field strength, sample weight, and gaseous atmosphere. 32

Techniques based on EML have been developed which include electrostatic levitation (ESL) with combined laser heating, as well as the cold crucible method. ESL with laser heating offers advantages in which heating and levitation control are independent, thus addressing the temperature control and droplet stability issues associated with the conventional EML technique [19]. The technique has been applied to many studies involving physical property measurements of alloys. The cold crucible method, a semi-contact melting technique allows for the processing of a larger sample quantity.

Applications of levitation melting, specifically its use as a small-scale industrial laboratory research tool have included: thermophysical property measurements of liquid metals, determination and evaluation of physico-chemical properties, preparation of high purity alloys and nanomaterial synthesis.

3.3.1 Measurement of thermophysical properties Levitation melting has been applied to the determination of various thermophysical properties of metals such as: heat capacities and enthalpies of fusion, density, surface tension, viscosity, electrical resistivity, and thermal conductivity.

A levitation calorimeter developed by Margrave and Bonnell provided the first general technique for the determination of thermodynamic properties of liquid metals and conductors [20,21]. The technique comprised a modified drop calorimeter in which the furnace was replaced by a levitation system. Enthalpies of fusion and heat capacities were determined for liquid phases of iron, titanium and vanadium, which had not previously been measured. This technique became widely used, and was applied to determine properties for various high temperature metal groups (IVb-VIb) and extended to mixing enthalpy measurements for Fe-V and Fe-Ti alloy systems [22,23].

Levitation has been widely used for density measurements of liquid metals. El-Mehairy and Ward calculated the density of liquid copper and nickel over the temperature range of 1097 to 1827°C and 1149 and 1866°C, respectively [24]. Density was determined by photographically estimating the levitated liquid volume of droplets of a known weight at a given temperature. Without the constraint of a crucible, density measurements over a large temperature range are possible, in addition to measurements below the melting point, given that levitated droplets may be 33

supercooled [14,25]. Using a static magnetic field to surpress surface oscillation, Inatomi et al. performed density measurements of pure silicon droplets, and demonstrated a linear dependence for temperature from 1367K to 1767K [26]. Adachi et al. [27] applied the basis of this technique to density measurements of Si-Ge alloys over the range of 1350K to 1650K.

Surface tension of liquid metals and alloys using levitation have been investigated extensively. Lu and his coworkers pioneered research in this field, through relating frequency and droplet surface oscillations to the Rayleigh equation [28,29]. Results obtained by applying the droplet oscillation technique were found to be higher than measurements from previous work, applying a static sessile technique [30]. Soda et al. [31] conducted surface tension measurements for copper and iron under conditions in which droplet oscillation amplitude was minimized. Results were found to be in good agreement with published data, and as such, the reported discrepancies between the techniques were attributed to oscillation amplitude sensitivity. The levitating drop technique was determined to be a reliable method for surface tension measurements by Keene et al. [32] who compared results from two independent laboratories with data from established methods. Surface tension measurements in undercooled conditions have also been achieved. Zhou et al. [33] performed measurements for undercooled liquid Ti-51at%Al, with a maximum undercooling of 324K (0.19

Tm). Measurements for monotectic Fe-Cu-Mo alloys were performed by Wang et al. [34] with an undercooling range of up to 223K (0.13 Tm).

Fujii et al. [35] pioneered research on shape change and surface oscillation of levitated droplets under microgravity conditions, and demonstrated that improved accuracy of thermophysical property measurements could be achieved under such conditions. Building upon this, Egry et al. [36] carried out extensive research at the TEMPUS Spacelab electromagnetic levitation facility. Under the microgravity conditions, thermophysical properties including specific heat, surface tension, viscosity, density, and electrical resistivity were measured for several metal and alloy systems, summarized in Table 3-1.

Table 3-1: Summary of measured thermophysical properties of metal alloy systems at TEMPUS Spacelab EML facility

Further work by Egry, Brillo et al. [36–39] included surface tensions measurements for Al-Cu- Ag, Cu,-Co-Fe, and Ni-Cu-Fe ternary alloys over a wide temperature range. Egry et al. [36] presented comprehensive reviews for thermophysical measurements of liquid metallic alloys in both terrestrial and microgravity conditions.

3.3.2 Thermochemical studies EML has been widely used in the determination of thermodynamic data. Several studies have been carried out involving levitated molten steel droplets under controlled oxygen potential atmospheres to determine interaction parameters of alloying elements including chromium and vanadium on the activity coefficient of oxygen between 1500°C and 1850°C [40,41]. Due to the presence of steep temperature gradients, the technique is subjected to error caused by thermal diffusion between the metal droplet and gas mixtures. In studies involving the effect of vanadium on oxygen activity in Fe-V droplets under H2O/H2 gas mixtures, Kershaw et al. noted the need to account for thermal diffusion effects for proper comparison with equilibrium ratios calculated from conventional crucible experiments [40]. Sunderland et al. [42] subsequently performed sulphurization studies using H2S/H2 gas mixtures, and developed an expression to quantify thermal diffusion effects from levitation experiments for corresponding thermodynamic and kinetic data derived. With rapid attainment of equilibrium through the EML technique, Caryll and Ward investigated slag-metal equilibria in the Fe-Mn-O system [43]. Results were in agreement with 35

those from crucible experiments [44], and an equation for the standard free energy change for the reaction between the melting point of iron to 1900°C was derived [9].

For kinetic studies, EML offers unique advantages over crucible techniques given that melt geometry and surface area can be accurately defined. Reaction rates can be calculated from experimental results, which may be interpreted in terms of mass transfer theory for gas flowing past a sphere [9]. Large temperature gradients existing between gas and liquid metal phases, as well as mass transfer resulting from strong stirring within the droplet are thought to affect vaporization rates of solutes from the droplet. Beaudhuin et al. [45] applied EML to achieve solute impurity removal in undercooled silicon droplets by controlling partial pressures of ammoniac and hydrocarbon gases. Zuliani and McLean investigated effect of manganese vaporization on the rate of sulphurization from levitated iron droplets under various inert and reactive gas atmospheres [10]. Sulphurization rates were found to be controlled by thermal diffusion and manganese vaporization in the gas phase [46]. Recent work by Wu applied EML to study metallurgical reactions in levitated stainless steel droplets using CO2 as an oxidant [11]. Findings indicated that decarburization rates for alloy melts containing high carbon content were controlled by mass transfer in the gas phase, and experimentally derived coefficients as well as non-dimensional correlations could potentially exhibit temperature gradient dependence. Numerous kinetic studies have been conducted to investigate oxidation reactions [9,11,47] and nitrogen dissolution [48] in steelmaking operations. Work by Siwka et al. applied EML to further investigate nitrogen dissolution in liquid Fe-alloys, Cr, Ni, Co, and V droplets under various pressure and temperature ranges [49,50].

3.3.3 Metal alloy preparation and nanomaterial synthesis Levitation melting is a useful technique for alloy preparation, as it avoids melt contamination, and allows for precise control of chemical composition and good homogeneity. It is suitable for the production of reference alloys, alloys for nuclear target or reactor applications, or melting reactive metals [51]. Morita et al. [52] applied cold crucible electromagnetic levitation melting to prepare 1 kg of uniform composite titanium-tantalum (Ti-15wt.%Ta) alloy from pure base metals, for use in biomedical applications. This was a significant achievement given the known difficulties in the synthesis of Ti and Ta or Nb using conventional arc or induction melting furnaces, owing to their 36

high reactivity at high temperatures, as well as differences in melting point and specific gravity [52]. Sypien et al. [53] applied the technique to prepare Ti-Ni-Fe alloys, for use into investigations of the crystallization process and intermetallic microstructural changes.

In recent times, EML has been applied to the synthesis of nanomaterials. Kermanpur et al. [8] produced pure monodisperse Fe nanoparticles under a He-20%Ar gas atmosphere, through a one- step bulk synthesis method by electromagnetic levitational gas condensation (ELGC). This process involved, the condensation of Fe vapours ascending from the levitated metal droplet by cryogenic He-Ar gas, under atmospheric conditions. The process was estimated to yield a production rate of 10 g/h. This technique was subsequently applied to the synthesis of other nanoparticles including semi-conductor grade ZnO nanorods and nanoparticles [54,55], pure silver for biomedical applications, nickel, iron-oxide, and pure metallic titanium [56,57].

3.3.4 Solidification and undercooling processes In the absence of a crucible, heterogeneous nucleation is avoided, and undercooling can be achieved during the levitation process. These processing features permit investigation into various solidification phenomena including the degree of supercooling, solidification speed, as well as phase selection during crystallization and morphology at different undercooling temperatures. McLean et al. [9] investigated the supercooling phenomena for nickel and iron droplets, reporting 480°C and 420°C supercooling in hydrogen, respectively. Li et al. [58] applied the EML technique to investigate the crystal growth kinetics of a deeply undercooled Zr50Cu50 alloy. The solidification speed was observed and measured by capturing the movement of the solid-liquid interface front, using a high-speed camera. Through this method, they were able to determine interface velocities at specific temperatures, and measure the maximum growth rate during the solidification process at an undercooling of approximately 200K (0.83Tm). From research carried out by Binder et al.

[59] on undercooled Ni2B melts, strong stirring and fluid flow in levitated droplets during EML were found to influence microstructure growth during solidification. Investigations of undercooled Co-Cu alloys revealed that strong stirring during levitation contributed to the formation of Cr-rich dendrites, which was found to be consistent with morphology observed from the rapid solidification of Cu60Co30Cr10 alloy [60–62].

3.4 Advantages of Levitation Melting The levitation melting technique offers several unique advantages and opportunities for materials processing:

Lack of melt contamination: As a containerless processing technique, this effectively eliminates the potential for contamination sources deriving from refractory materials, heterogeneous nucleation of the liquid metals, and better control of material chemistry at high temperatures [63].

Rapid melting: Owing to the small mass involved (approximately one gram), the sample can be melted or heated to the desired temperature within a few seconds to less than one minute. This permits for an increased number of experiments to be carried out, the opportunity to vary more parameters than would normally be practical, and is also expected to enhance the consistency of experimental data. With the absence of a crucible, this eliminates potential issues arising from thermal shock of containers.

Melt stirring and rapid attainment of equilibrium: Strong inductive stirring induced by the applied electromagnetic field allows for melt homogeneity to be retained throughout an experimental run. The large surface area to volume ratio of the droplet exposed to the gas phase, coupled with vigorous inductive stirring, enables the liquid-gas system to reach equilibrium rapidly. Additionally, with constant surface renewal of the solute-depleted layer as a result of melt stirring, the rate of mass transport in the liquid phase is increased.

Spherical geometry: With a well-defined melt geometry and surface to volume ratio, the levitation technique is well suited for kinetic studies, where interpretations can be made based on correlations developed for spherical geometry.

Temperature range: Levitation melting experiments can be conducted over a wide temperature range, where the upper limit is dependent on the degree of droplet vaporization. With the absence of a crucible, heterogeneous nucleation is avoided, and undercooling can be achieved. Gomersall et al. [64] reported undercooling of approximately 400°C during levitation melting of iron and nickel. 38

3.5 Disadvantages of Levitation Melting There are also various limitations associated with the levitation technique:

Temperature control and measurement: Difficulties in temperature control during levitation are generally due to the limitations in electrical equipment used for a given system. With the large surface area to volume ratio and temperature gradient in the gas boundary layer, the applied electromagnetic field may sometimes provide excessive heating to the specimen, leading to vaporization of the droplet. This in turn may cause inaccuracies in temperature measurements. The droplet may be cooled by modifying the flow rate or type of inert gas passing through the system.

Steep temperature gradient in gas boundary layer: At the liquid-gas interface, a steep temperature gradient exists when gases flowing into the system at room temperature interact with the high temperature droplet surface. Consequently, the variation of physical properties existing near the liquid-gas interface of the droplet often creates discrepancies in diffusivity data used for evaluating thermal diffusion effects.

3.6 Proposed Metallurgical Refining Route In examining the various techniques to remove impurities from metallurgical grade silicon, it has been established that the refinement of MG-Si to SoG-Si must involve a combination of techniques to target each of the various impurities, rather than one single technique.

With phosphorus and boron deemed to be the most difficult impurities to remove from MG-Si, research into refining techniques to target these impurity elements will ultimately define the success in producing low-cost solar-silicon by metallurgical means. Morita and Miki have suggested the use of plasma-assisted oxidation for boron removal [65], with an 88% reduction in boron (less than 7ppm) attained through an oxidation slagging method. Several studies previously outlined have achieved dephosphorization through vacuum distillation and electron beam remelting methods. While these vaporization methods for phosphorus and boron have proven to be effective, these processes are generally costly due to high temperature requirements, accompanied by losses in silicon.

Investigation of impurity removal from molten silicon by electromagnetic levitation has yet to be reported; however, the use of the technique for thermophysical property measurements and thermochemical studies show promise in the applicability to containerless materials processing.

By applying EML, dephosphorization under a reducing atmosphere can be investigated, while boron removal can be studied under a controlled oxidizing atmosphere. The proposed metallurgical refining technique in this project involves the use of EML to study impurity behaviour in metallurgical silicon alloys. Phosphorus is the more critical and prevalent of two elements, and is the focus of the EML refining technique investigated in this project. Once dephosphorization can be achieved, the partially refined alloy can be processed by a combination of previously investigated metallurgical techniques to remove remaining impurities to ultimately produce solar- grade silicon. A schematic of the proposed metallurgical refining route is shown in Figure 3-4. 40

Figure 3-4: Schematic showing proposed metallurgical refining route for SOG-Si production

Commercial ferrosilicon is chosen as a starting material for the following reasons:

. Abundance, low cost, and availability from the steel industry. . Ease of levitation compared with MG-Si –which requires an additional pre-heating step. The iron in the silicon-iron alloy provides inductive heating to the sample. . Low solubility of iron in Si, and low segregation coefficient allowing for removal by acid leaching or directional solidification. . Fe has a higher affinity for phosphorus –and this has been shown to enhance P transfer to the iron phase during the solvent refining technique.

In using a hydrogen-argon gas mixture, the argon atmosphere simulates a vacuum effect, similar to the Argon Oxygen Decarburization (AOD) process in the steelmaking process, in which dilution by the inert gas helps to lower the partial pressure of phosphorus gas and accelerate dephosphorization. Based on steelmaking data, the interaction coefficient for the effect of 퐻 hydrogen on phosphorus dissolved in an iron melt is known to be 푒푃 = 0.33 [66]. With the positive interaction coefficient value, hydrogen gas is thought to increase phosphorus activity in the Si-Fe melt, enabling the formation of P-H gaseous species, and thus promoting phosphorus removal.

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44. J. Chipman, Trans. Metall. Soc. AIME 188, 341 (1950). 45. M. Beaudhuin, K. Zaidat, T. Duffar, and M. Lemiti, J. Mater. Sci. 45, 2218 (2010). 46. D. J. Zuliani and a. McLean, Can. Metall. Q. 18, 323 (1979). 47. L. A. Baker, N. A. Warner, and A. E. Jenkins, Trans. Metall. Soc. AIME 230, 1228 (1964). 48. L. A. Greenberg and A. McLean, Trans. Iron Steel Inst. Japan 14, 395 (1974). 49. J. Siwka, ISIJ Int. 48, 385 (2008). 50. J. Siwka and A. Hutny, Metalurgija 48, 23 (2009). 51. C. Ingelbrecht and F. Peetermans, Nucl. Inst. Methods Phys. Res. A 334, 116 (1993). 52. A. Morita, H. Fukui, H. Tadano, S. Hayashi, J. Hasegawa, and M. Niinomi, Mater. Sci. Eng. A 280, 208 (2000). 53. A. Sypien and W. Przybylo, Mater. Sci. Technol. 26, 31 (2010). 54. M. Vaghayenegar, A. Kermanpur, M. H. Abbasi, and H. G. Yazdabadi, Adv. Powder Technol. 21, 556 (2010). 55. M. Vaghayenegar, A. Kermanpur, and M. H. Abbasi, Ceram. Int. 38, 5871 (2012). 56. A. V. Mohammadi and M. Halali, RSC Adv. 4, 7104 (2014). 57. M. Malekzadeh and H. Mohammad, Chem. Eng. J. 168, 441 (2011). 58. L. X. Li, J. L. Zhao, and X. M. Guan, Appl. Mech. Mater. 513-517, 56 (2014). 59. S. Binder, P. K. Galenko, and D. M. Herlach, J. Appl. Phys. 115, 0 (2014). 60. C. Cao, T. Letzig, G. P. Gorler, and D. M. Herlach, J. Alloys Compd. 325, 113 (2001). 61. J. B. Guo, C. De Cao, S. L. Gong, R. B. Song, X. J. Bai, J. Y. Wang, J. B. Zheng, X. X. Wen, and Z. B. Sun, Trans. Nonferrous Met. Soc. China (English Ed. 23, 731 (2013). 62. Z. M. Zhou, W. J. Huang, L. W. Tang, T. Zhou, X. P. Li, J. Luo, C. Y. Peng, and J. Zhan, Adv. Mater. Res. 239-242, 695 (2011). 63. J. K. R. Weber, S. Krishnan, and P. C. Nordine, JOM 43, 8 (1991). 64. D. W. Gomersall, A. McLean, and R. G. Ward, Trans. Metall. Soc. AIME 242, 1309 (1968). 65. K. Morita and T. Miki, Intermetallics 11, 1111 (2003). 66. M. Hino and K. Ito, Thermodynamic Data for Steelmaking, Tohoku Uni (Sendai, 2010).

CHAPTER 4 Experimental Considerations

4.1 Electromagnetic Levitation Apparatus The electromagnetic levitation apparatus used in this work was based on the work of P. Wu [1,2]. A schematic diagram of the electromagnetic levitation facility used in this research is shown in Figure 4-1. The apparatus consists of a quartz tube chamber (15 mm O.D., 13 mm I.D., 304 mm length) a copper levitation coil, a rotatable platform housing a copper mould and alumina rod. The water-cooled levitation coil was wound using 1/8 inch diameter copper tubing. The quartz tube chamber is sealed at the upper end with O-rings attached to an optical grade fused quartz viewing window (2 mm in thickness) to permit temperature measurement from a two-colour infrared (IR) pyrometer. The lower portion of the chamber is inserted into Figure 4-1: Schematic diagram of electromagnetic an O-ring sealed rotatable platform. The levitation apparatus [1] platform cover was made from polycarbonate and polyvinyl chloride materials, while the base plate was made from aluminum. The platform houses a copper mould used for droplet quenching, and an alumina rod for solid sample loading into the levitation zone. 45

4.1.2 Power supply and coil design The power was provided to the coil using an Ameritherm-Ambrell high frequency induction heating system with a rated terminal output of 10 kW and a frequency range from 150 to 400 kHz. Adjustments in applied current allows for the manipulation of the vertical position of the droplet within the levitation coil, and accordingly the amount of heating provided to the sample based on interaction with field flux lines. The corresponding applied power reading based on applied current corresponds to the measured temperature of a sample. A minimum working current to support the droplet in levitation is dependent on sample material, mass, gas flow rate, and coil design.

Figure 4-2 shows a schematic of the five-turn levitation coil used in this work. The coil is a low- angle conical configuration comprising two segments: a lower three-turn primary cone, and an upper inverted cone with two reverse turns. This configuration was found to provide sufficient lifting force and droplet heating to appropriate temperatures (lower cone), and vertical and lateral stability (upper inverted cone) [1].

Figure 4-2: Schematic diagram of levitation coil [1]

4.1.3 Temperature measurement The developments and advantages of two-colour pyrometry have been discussed in Chapter 3. Droplet temperatures were measured with a CHINO IR-CA Q3088 two-colour pyrometer (uncertainty of ±15°C). To perform temperature measurements, the pyrometer is aimed at the optical viewing window at the top of the levitation chamber, from which the droplet can be viewed. The pyrometer contains a control unit which provides continuous temperature readings of the droplet surface. The optical viewing window serves to minimize spectral losses during measurements.

4.1.4 Gas flow system Shown in Figure 4-3 is the schematic of the gas flow system used in this work. To remove moisture in the high purity gas, the stream, flowing through thermoplastic tubing, was passed through a drierite column. Control of gas flowrates (volumetric flow) was maintained by flowmeters. Flowmeters were calibrated through the use of a bubble column. If more than one gas source was used, the streams were merged by passing through a gas mixer. Gases were directed out of the reaction chamber to an exhaust system.

Due to the steep temperature gradients during levitation, fuming of the droplet occurred. As a result, a downward gas flow was chosen for this system to avoid fume deposition on the optical glass window used during temperature measurement.

Figure 4-3: Schematic diagram of gas flow system 47

4.1.5 Experimental procedure – Levitation of silicon-iron alloy droplets Silicon-iron alloy samples were cut into 0.6–0.7 gram (± 0.01) pieces. A specimen is placed onto the alumina charging rod, raised to a position between the upper and lower cones of the coil, and the levitation chamber sealed. The apparatus is purged with the reaction/inert gas for 1-2 minutes. The system is checked for leaks prior to commencing experiments. Upon application of electrical power to the coil, the solid specimen levitates, generally within 900°C to 1000°C, and the charging rod is retracted as soon as stable levitation of the solid specimen is attained. The specimen may reach molten state in under one minute, and manipulated to the desired temperature depending on the magnitude of the applied current. For different gas and material compositions, preliminary trials are necessary to establish operating parameters for applied current and power, corresponding to droplet temperature. After a designated reaction time, the rotatable platform is turned so that the copper mould is positioned below the coil. Once power is turned off, the droplet falls and is quenched in the mould. The quenched specimen is collected for subsequent sample analysis.

4.1.6 Experimental conditions investigated The effect of the following experimental conditions were examined in this work to investigate the dephosphorization behaviour of silicon-iron alloy droplets exposed to a reducing H2-Ar gas atmosphere:

. Refining time (5-60 minutes) . Refining temperature (1450°C, 1520C, 1620C, 1720°C)

. H2-Ar gas composition (0%H2-Ar bal. to 100% H2) . Gas flow rate (0.25-1.2 L/min) . Iron alloying in Si-Fe (Si-25wt%Fe, Si-15wt.%Fe) . Initial phosphorus concentration (60-500 ppm)

Experiments carried out were grouped as follows:

. Commercial Si-25wt.%Fe containing 0.0225 wt% P 1450°C-1720°C, 5-60 minutes

- 0.5 L/min  5%, 50%, 100% H2-Ar (bal.), 100% Ar - 1.2 L/min  5%, 25%, 50%Ar (bal.), 100% Ar 48

. Commercial Si-25wt.%Fe containing 0.0510 wt% P 1520°C, 5-40 minutes

- 0.5 L/min, 50% H2-Ar (bal.) . Commercial Si-25wt.%Fe containing 0.0120 wt% P 1520°C, 5-40 minutes

- 0.5 L/min, 50% H2-Ar (bal.) . Commercial Si-25wt.%Fe containing 0.0060 wt% P 1520°C, 5-40 minutes

- 0.5 L/min, 50% H2-Ar (bal.) . Commercial Si-15wt.%Fe containing 0.0510 wt% P 1520°C, 5-40 minutes

- 0.5 L/min, 50% H2-Ar (bal.)

4.2 Materials

4.2.1 Si-Fe alloy specimens Chemical analysis (supplier’s) of the commercial ferrosilicon and metallurgical silicon specimens used in this work are provided in Table 4-1.

Table 4-1: Chemical composition of commercial ferrosilicon (Gerdau) and metallurgical silicon

(wt.%) Si Fe Al Ca C P B Cr Si-Fe 76 balance 1.3 -- 0.096 0.022 -- -- Si-Fe 84 balance -- 0.832 -- 0.022 -- 0.120 MG-Si 99 0.4 0.2 0.1 -- 0.004 0.002 --

The chemical compositions of reagents used are provided in Tables 4-2 to 4-4.

Table 4-2: Impurity concentration of electrolytic iron from Allied Metals (wt.%)

C Si Mn P S Cr Ni Mo V W Co 0.0015 0.0005 <0.0001 0.0001 0.0022 0.0015 0.0026 <0.0001 <0.0001 <0.0001 0.002 Al Ti Pb B Nb Cu N O As Sb Sn 0.0045 <0.0001 0.0002 <0.0001 <0.0001 0.0006 0.0044 0.0267 <0.0001 <0.0001 <0.0001

Table 4-3: Impurity concentration of silicon (6N purity) from ESPI Metals (supplier's analysis, ppm)

Ca Fe Mn P S Cr Ni Zn V K <0.005 0.005 0.001 0.002 0.06 0.002 <0.005 <0.03 0.0004 0.011 Al Ti Mg B Na Cu Li As Cl Co 0.007 0.0007 0.001 0.025 0.011 0.004 0.002 0.051 0.45 0.0006

Table 4-4: Chemical composition of ferrophosphorus from Hiekman Williams & Company (supplier’s analysis, wt. %)

P Mn Ti V Si Cr Ca Mg C S 26.16 1.04 0.76 0.19 0.48 0.074 0.02 0.012 0.04 0.011

Alloy preparation of varying compositions (Si-25wt% Fe; various P concentrations) were prepared by placing predetermined amounts of reagents in a high purity alumina crucible. Electrolytic iron and 6N purity silicon were added to commercial alloys to produce material with lower P concentrations. Ferrophosphorus was added to dope alloys with higher P concentrations (groups containing 0.051wt% P). The crucibles and their contents were heated in an induction furnace in which an inert argon atmosphere was maintained. After approximately 15 minutes, alloy samples were taken by suction through quartz tubes, which were immediately quenched, producing 4 mm diameter rod-shaped specimens. Material prepared in smaller crucibles were removed from the furnace and quenched due to the fact that they were too small for the suction sampling method. Material from these crucibles were cut and sectioned using a ceramic wet tile saw fitted with a 10 cm diameter diamond blade. 50

4.2.2 Gases The following gases were used in this work – supplied by Linde Canada:

. 50wt% H2-Ar (bal.)

. 5% H2-Ar (bal.)

. 100% H2 – Grade 5.0 . 100% Ar – Grade 5.0

4.3 Chemical Analysis of Samples: Inductively Coupled Plasma- Optical Emission Spectrometry (ICP-OES) iCAP 6300 ICP-OES was used to analyze the phosphorus impurity content of initial and processed ferrosilicon samples. Sample preparation consisted of crushing the raw or quenched samples into fine powder using a marble mortar and pestle. Based on Dulski [3], HF acid must be used when

digesting material containing silicon, while HNO3 must be used for digestion of iron-based samples. For each sample group approximately 0.2 g was digested in a 20 mL mixture of acids.

The volume ratio used was 2:1:1 hydrofluoric acid (HF, 48 wt.%), nitric acid (HNO3, 70 wt.%), and de-ionized water, respectively. The digestions were carried out using Teflon beakers, which were covered and heated to approximately 60°C for 30 minutes. The digested samples were diluted to 40 mL in a graduated cylinder, and subsequently transferred to 15 mL tubes for ICP analysis. A blank solution was prepared using the sample acid ratios and dilution factor. The following calibration standards were prepared from stock solution: 0.01 pm, 0.1ppm, 1ppm, 10ppm, 100ppm (stock solution). The calculation for conversion of a given impurity element (analyte) in solution to the amount in the solid sample is provided as follows:

푚푔 퐶′ [ ]×퐷푖푙푢푡푒푑 푉표푙푢푚푒 [퐿]×1000 퐶 [푝푝푚] = 푠표푙푢푡푖표푛 퐿 , 푠표푙푖푑 퐹푒푆푖 푊푒푖푔ℎ푡 표푓 퐷푖푔푒푠푡푒푑 푆푎푚푝푙푒 [푔]

where C’ is the difference between the element concentration in solution and blank solution.

4.3.1 Principle of operation ICP-OES is an analytical technique which allows for the detection of trace elements in solution. The machine is comprised of two parts – the ICP torch and optical spectrometer. Liquid samples are introduced into the machine through a nebulizer where they form into, and are subsequently broken down in a plasma torch into charged ions. Argon gas purged into a radio frequency generator is used to produce the plasma. Exited ions recombine with electrons in the plasma, producing radiation at characteristic wavelengths. A diffraction grating separates the component wavelengths in the optical spectrometer, and light intensities are measured with a photomultiplier. Intensities obtained can be compared with those of previously measured ones. From this, elemental concentrations can be determined from interpolation of calibration lines. The average of three measurements are taken by the machine to obtain a final concentration for each sample.

References

1. P. Wu, Y. Yang, M. Barati, and A. McLean, High Temp. Mater. Process. 33, 1 (2014). 2. C. P. Wu, An Investigation of Metallurgical Reactions with Levitated Droplets, Ph.D. Thesis, University of Toronto, 2015. 3. T. R. Dulski, A Manual for the Chemical Analysis of Metals (American Society for Testing and Materials, West Conshohocken, PA, 1996).

CHAPTER 5 Results and Discussion

5.1 Experimental Results Experimental results presented in Figures 5-1a to 5-1d demonstrate the decrease in phosphorus

concentration as a function of time under the different temperature, H2 gas compositions, and flow rate conditions. The rate of phosphorus removal appears to follow first-order reaction kinetics. Further analysis of the experimental results is provided in the subsequent sections of this chapter.

Figures 5-1 a to d: Change in phosphorus concentration with time under various experimental conditions investigated 54

Plots from Figures 5-1 a to c of experimental sets carried out under the same temperature and flow rates of 1520°C and 0.5 L/min respectively, for different hydrogen gas concentrations are reproduced in the combined plot in Figure 5-1e below. Maximum [P] removal rates of 12%,

39%, and 56% were attained under the 5%, 50%, and 100% H2-Ar gas conditions, respectively.

With the removal rate for the 100% H2-Ar conditions observed to be higher than the percent increase in gas composition from 50% H2-Ar, it is speculated that thermal diffusion effects may influence the dephosphorization rates of levitated droplets. The presence of a steep temperature gradient between the liquid metal-gas interface of the levitated droplet may result in varied flow patterns and physical properties in the gas across the boundary layer, which often creates discrepancies in evaluating thermal diffusion effects. Further experimental work is required to evaluate the effect and implications of thermal diffusion on the reaction kinetics of the process.

Figure 5-1e: Effect of hydrogen gas concentration under fixed temperature and gas flow rate 5.1.1 Reproducibility of experiments Given the high temperature nature and time required for experiments, it is generally not customary to repeat all experimental time points. In this study, the experimental set at 1520°C,

0.5 L/min, 50%H2-Ar, 5-60 min, was repeated three times. The relative standard deviation for the phosphorus concentration of the samples in the chosen set were below 3%. This error was thereby applied to the rest of the experimental sets performed. 55

5.2 Dephosphorization of Levitated Si-Fe Droplets in H2-Ar gas: Effect of Process Variables

The effects of various experimental conditions on phosphorus (P) removal from ferrosilicon droplets were examined in this work. To measure dephosphorization rates under different operating conditions, experiments were carried out for various time periods (5 to 60 minutes). A summary of the effect of experimental conditions investigated is outlined in Table 5-1.

Table 5-1: Effect of processing conditions on dephosphorization kinetics

Experimental Condition Rate of Reaction Reaction Step Affected Liquid phase transport Temperature Increases Chemical reaction Gas phase transport H Gas Concentration Increases 2 Chemical reaction Liquid phase transport Initial P concentration Increases

5.2.1 Effect of refining temperature and time

Figure 5-2 shows results for the phosphorus removal rate ([P]t/P]i]), where [P]t denotes the

phosphorus concentration at time t, and [P]i represents the initial phosphorus concentration of the alloy. The data presented show the increase in phosphorus removal rate with temperature. The removal of phosphorus increases with both time and temperature. Upon approaching the equilibrium time point, the reaction becomes mass transfer limited in the liquid phase. It is observed that an equilibrium time point exists at approximately 45 minutes, for which the concentration of phosphorus remains constant, independent of increasing refining time. Higher processing temperature results in lower final [P] content, with a 72% rate of removal achieved after 40 minutes of levitation at 1720°C. With the continual and increased mass transport of P to the interface, the chemical reaction limited regime, which involves the transition of P to adsorbed and gaseous states, is eventually reached. However, processing at higher temperature is unfavourable from an economical and energy efficiency standpoint. Furthermore, with the predicted saturated vapour pressure behaviour of silicon known to increase significantly at temperatures above the melting point (Fig 2-10), processing at higher temperature would result in

silicon vaporization losses. The theoretical separation coefficient value, β푖, describes the relative distribution of an impurity, i, and solvent (i.e. Si) between gas and liquid phases, calculated based 56

on the activity coefficients of the elements from binary systems [1]. Based on this theory, it was shown that [P] can be effectively removed from a silicon melt (solvent) by evaporation, while in a Si melt containing Fe, Si would be lost to the gas phase to a greater extent (Figure 5-3) [1].

Figure 5-2: Effect of time and temperature on dephosphorization

Figure 5-3: Separation coefficients of P and Fe in molten Si alloys; if βi >1, the impurity i can be separated from base metal. For βi ≤1, impurity removal is difficult [1]

5.2.2 Effect of hydrogen partial pressure The effect of hydrogen gas composition on dephosphorization behaviour is shown in Figure 5-4 for the two different flow rates investigated (0.5 L/min and 1.2 L/min). The general trend for both cases shows a positive correlation between a higher reductant (H2) partial pressure on the rate of dephosphorization. Further work is required to identify and quantify the reaction products in order to confirm whether the mechanism of phosphorus removal from ferrosilicon occurs by evaporation of

P or P2 gas species– as indicated from the FactSage modelling study, or by chemical reaction with the hydrogen gas atmosphere to form P-H gas species. Figure 5-4: Effect of H2 gas concentration 5.2.3 Effect of iron content in Si-Fe Based on the results plotted in Fig. 5-5, increasing iron alloying content is observed to impede phosphorus removal. This effect is likely due to the strong affinity of Fe for P, than Si for P, which has been verified from this research by the calculated iso-activities of dilute [P] in ternary Si-Fe-P systems in Fig. 5-6, and work by Khajavi et al. [2]. This effect was further confirmed through theoretical vapour-liquid phase equilibria calculations carried out for Si-P and Si-Fe-P alloys [1]. The theoretical mass fractions of P in the vapour phase Figure 5-5: Effect of Fe composition in Si-Fe during vapour-liquid equilibration of Si-P and Si- 15wt.%Fe-P alloys, with initial [P] contents ranging from 0.1 to 1000 ppm are presented in Fig. 5- 7. It is shown that a larger amount of P volatizes from Si-P melts compared to Si-Fe-P alloys. Additionally, it is observed that at higher [P] concentrations, a greater proportion of P reports to the gas phase. 58

Figure 5-6: Iso-activity curves of [P] in liquid Figure 5-7: Mass fraction of P in the vapour phase during Si-Fe-P alloys at 1873K [2] vapour-liquid equilibration of Si-P and Si-Fe alloys [1]

5.2.4 Effect of initial phosphorus concentration in Si-Fe

In examining the effect of initial phosphorus concentration in the levitated ferrosilicon droplets (Fig. 5-8), it is observed that a lower initial concentration results in a lower dephosphorization tendency under the experimental conditions investigated. With a lower initial concentration of phosphorus, and [P] depletion as the reaction proceeds, the overall rate is expected to be controlled by mass transfer in the liquid metal. The observed dephosphorization rates for the higher Figure 5-8: Effect of initial [P] in Si-Fe initial [P] concentrations is promising for steel operations, specifically the opportunity to refine high grade steels. For such operations, control of alloying elements such as chromium, nickel and silicon is critical, and under oxidizing environments, there is risk for loss of these elements, due to preferential oxidation compared with phosphorus. Sano et al. demonstrated that high reducing CaC2-CaF2 fluxes could be applied to the dephosphorization of high-chromium stainless steel [3]. Thus, as shown from this experimental work, the potential to process the material under a reducing environment would enable the alloying elements to be retained in the metal. 59

5.3 Thermodynamic Study of Si-Fe Dephosphorization under Reducing Gas Atmosphere: FactSage Study

FactSage was used to predict products of the ferrosilicon dephosphorization reaction under equilibrium conditions. The purpose of this study was to obtain a qualitative assessment of the possible gas reaction products formed, due to the inherent difficulties associated with measuring gas vapour species produced under experimental conditions. The study was carried out for the pure

and commercial Si-Fe-P, and P-H2 gas systems. To carry out the Equilibrium calculation model, the following databases containing the systems of interest were selected: pure solids (FSPS), steel alloy- FSstel, and miscellaneous substances- FTmisc (liquid iron with dilute [P] solute).

5.3.1 Si-Fe-P System – Pure components The process parameters investigated for the equilibrium study of the Si-Fe-P pure component system are listed as follows:

. 76wt.%Si –Fe-P (P – 0.022 wt.%)

. Gas atmosphere (open system) – 100% Ar, 5% H2-Ar, 25% H2-Ar, 50% H2-Ar, 100% H2 . Temperatures – 1380°C, 1450°C, 1550°C, 1650°C

The initial temperature of 1380°C was chosen, as this is the approximate melting temperature of the ferrosilicon alloy, followed by temperatures of approximately 100 degree increments. Results displaying the proportions of equilibrium products in mole percent are summarized in Figures 5- 9a to 5-9e (complete results can be found in Appendix A.1). Under the 0% to 50% hydrogen gas

conditions (Fig. 5-9a to d), P2 gas is the dominant product species formed, followed by the

formation of P gas for the 0% and 5% H2 cases. With increasing temperatures, there is an

increasing trend in P gas species formed, due to dissociation of P2 gas. Increasing the proportion

of H2 gas in the system resulted in an increase of P-H species formed, with PH2 observed to be the

dominant P-H gas species in the 25% and 50% H2-Ar cases, followed by PH3. Under the 100% H2

atmosphere (Fig. 5-9e), PH3 and PH2 are the dominant gas products formed, with PH3 gas in higher proportion at the lower temperature limit. Given that PH gas does not form a stable compound, this reaction product shown in the mix is thought to be a secondary or intermediary reaction product under the given equilibrium simulation conditions. 60

Figures 5-9 a to b: FactSage Equilibrium reaction products for 76wt.%Si-Fe-P (pure) under various reducing H2-Ar gas conditions.

Figures 5-9 c to e: FactSage Equilibrium reaction products for 76wt. %Si-Fe-P (pure) under various reducing H2-Ar gas conditions 62

5.3.2 Si-Fe-P System – Commercial alloy The process parameters investigated for the equilibrium study of the Si-Fe-P commercial alloy system are listed as follows:

. 76wt.%Si –Fe (C- 0.096%, P- 0.022%, Al- 1.3%)

. Gas atmosphere (open system) – 100% Ar, 5% H2-Ar, 25% H2-Ar, 50% H2-Ar, 100% H2 . Temperatures – 1380°C, 1450°C, 1550°C, 1650°C

Equilibrium products in mole percent are summarized in Figures 5-10a to 5-10e (complete results can be found in Appendix A.2). Results show a CHP gas species (possible reaction intermediate) as the dominant product in all conditions investigated for the commercial Si-Fe alloy, followed by

P2 gas species. While the reaction for CHP formation is unclear, this result is a possible indication of the role of carbon in dephosphorization enhancement. Given the positive interaction coefficient 퐶 value of carbon on phosphorus in iron melts (푒푃 =0.051 [4]) this could indicate the effect of carbon on increasing [P] activity in the melt under the reducing H2 conditions, subsequently promoting its evaporation as P2 gas.

Figures 5-10 a to e: FactSage Equilibrium reaction products for 76wt. %Si-Fe-P (commercial) under various reducing H2-Ar gas conditions 64

5.3.3 P, H2 Gaseous reaction

Equilibrium reaction conditions for P and H2 gas species were simulated to determine the dominant reaction product formed, and it is seen that (excluding H2) P2 followed by P4 gas species are formed under such conditions for the temperatures investigated (Figure 5-11, Appendix A.3).

Figure 5-11: FactSage Equilibrium reaction products P and H2 gas species

5.4 Kinetic Study of Phosphorus Evaporation from Si-Fe Droplets

Based on the thermodynamic study performed (Section 5.3), the P2 gas species was chosen as the theoretical reaction product in this work, to be carried through into assumptions for the kinetic evaluation of experimental results.

5.4.1 Fundamental considerations According to kinetic principles, the phosphorus removal rate may be assessed by estimating an apparent rate constant. The general expression for the rate of phosphorus evaporation is expressed as follows:

푑[푃] 퐴 푅푎푡푒 = − = 푘 (푃 − 푃 )푛, (5.1) 푑푡 푉 푒

where [P] is the concentration of phosphorus at time t, [P]e is the equilibrium concentration of phosphorus, A is the melt surface, V is the melt volume, n is the reaction order, and k is the apparent rate constant.

The rate constant is a function of temperature (T) based on the Arrhenius equation:

−퐸 푘 = 푘 exp ( 푎), (5.2) 푃 표 푅푇

Where, ko is the frequency factor, and Ea is the apparent activation energy for phosphorus evaporation from the melt.

For a first order reaction, Equation 5.1 is expressed as follows (assuming [P]e is negligible ~ 0):

푑[푃] 퐴 − = 푘 [푃] (5.3) 푑푡 1 푉

Similarly, a second-order reaction (i.e. evaporation of P2) is defined as follows:

푑[푃] 퐴 − = 푘 [푃]2 (5.4) 푑푡 2 푉 66

Experimental results presented in Figures 5-1a to 5-1d in Section 5.1 demonstrate the decrease in phosphorus concentration as a function of time, with the rate of phosphorus removal following first-order reaction kinetics. The dephosphorization process involves the following steps:

1. Liquid phase transport of P to the metal-gas interface. 2. Surface desorption reaction of P species at the interface. 3. Gaseous diffusion of P within the gas boundary layer.

From consideration of the experimental results, values of the apparent rate constant (ka) and the activation energy (Ea) for the chemical reaction and gaseous diffusion steps were obtained and compared. Apparent rate constants were determined by obtaining the slope of the linear portions of plots for phosphorus concentration as a function of time (Figures 5-1a to 5-1d). Methods applied based on transport principles to calculate reaction parameters of interest are discussed in the subsequent sections.

5.4.2 Mass transport of phosphorus in the liquid phase

The mass transfer coefficient for the liquid phase transport of phosphorus in the melt boundary layer can be calculated by applying a rigid flow model developed by Machlin, describing the behaviour of a melt in the vicinity of reaction surfaces under vacuum conditions [5]. The equation is expressed as follows:

ퟏ ퟖ푫 풗 푲 = ( 푷,풎 풎)ퟐ (5.5) 풎 흅 풓

Where: r: Melt radius vm: Velocity of streamline flow on the melt surface, related to melt stirring and applied current

Dp,m: Diffusion coefficient of phosphorus in Si-Fe melt

The melt surface velocity, vm, is calculated by a characteristic velocity term describing inductively stirred melts, U0, developed by Szekely et al.:

vm = Uo x Surface Area (5.6) 67

(5.7)

Where: L: characteristic length (melt diameter) f: characteristic frequency

Jo: coil current σ, electrical conductivity ρ: melt density

µ0: magnetic permeability

The diffusion coefficient of phosphorus in the ferrosilicon melt is estimated by the Stokes-Einstein equation [6], modified for considering unequal molecular mass effects of [P] (m1) and Si-Fe (m2):

ퟏ 풌푩푻 ퟏ 풎ퟏ ퟐ 푫푷,풎 = ( + ) (5.8) ퟒ흅ƞ푹푷 ퟐ ퟐ풎ퟐ

Where: kB : Boltzmann constant T: Melt temperature Ƞ: Dynamic viscosity

Rp: Covalent radius of phosphorus m1, m2: molecular mass of solute and solvent

The physical property values used for the calculations of this model summarized in Table 5-2, were based on the experimental conditions, and operating parameters of the electromagnetic levitation furnace. The liquid phase mass transfer coefficient values calculated from 1450°C to 1720°C are summarized in Table 5-3. With the relatively high computed value for the melt surface velocity (0.137 cm/s) with respect to the droplet diameter (0.716 cm), and constant surface renewal from induction stirring, the rate of dephosphorization is not expected to be impeded by liquid phase transport. 68

Table 5-2: Physical property values used in calculation

Characteristic frequency, f 3.2x105 Hz Coil current, Jo 310 A Electrical conductivity, σ 1.82x106 s/m Melt density, ρ 3.2 g/cm3 -6 Magnetic permeability, µ0 1.257x10 H/m

-23 2 2 Boltzmann constant, kB 1.38x10 m ·kg/s ·K Melt temperature, T 1723K, 1793K,1893K,1993K Dynamic viscosity, Ƞ 0.32x106 Pa·s -10 Covalent radius of phosphorus, Rp 106 pm or 1.6x10 m

Melt radius, r 3.58x10-3 m 2 Diffusion coefficient, Dp,Si-Fe Varies with temperature (m /s) -3 Melt surface velocity, vm 1.37x10 m/s

*Detailed calculations can be found in Appendix B.

Table 5-3: Liquid phase mass transfer coefficients, km

Experimental Mass Transfer Temperature Coefficient, km (cm/s)

1450°C 4.82x10-4 1520°C 4.94x10-4 1620°C 5.05x10-4 1720°C 5.18x10-4

5.4.3 Interfacial reaction – Phosphorus evaporation

The surface desorption reaction of P species at the melt interface to form P2 gas is represented by the general equation for the rate of phosphorus evaporation (Eqs. 5.1). With the removal of phosphorus shown to obey first order kinetics, by plotting the integrated form of Eq. 5.3, an apparent rate constant can obtained from the slopes of the linear portions of the plotted curves.

푑[푃] 퐴 Recall: − = 푘 [푃] (5.3) 푑푡 1 푉 Integrating Eq. 5.3, we obtain:

푃푡 퐴 푙푛 ( ) = 푘푝 푡 (5.9) 푃푖 푉

Where: [P]t and [P]i correspond to the phosphorus concentration at a given time point and the initial phosphorus concentration, respectively; A/V denotes the surface area to volume ratio of the droplet.

Plots for ln [P]t/[P]i vs. time from Equation 5.9 for the various reaction conditions are shown in Figures 5-12a to 5-12d. Apparent rate constants for the interfacial reaction of phosphorus, are obtained from the slope of the plots. From the values reported in Table 5-4, it is shown that the apparent rate constant increases with higher temperatures and hydrogen gas composition.

By plotting the apparent rate constants as a function of reciprocal temperature, apparent activation energies were obtained for the 50%H2-Ar (Flow rate: 0.5 L/min, 1.2 L/min), 5%H2-Ar (Flow rate:

0.5 L/min, 1.2 L/min (partial fit)), and 25%H2-Ar (Flow rate: 1.2 L/min) data sets, displayed in Figures 5-13a to 5-13c and summarized in Table 5-5. The values obtained are within the reasonable range for the chemical reaction control mechanism. The results are also in reasonable agreement with literature results for the dephosphorization of MG-Si under vacuum induction refining conditions. Yuge et al. calculated an activation energy of 130 kJ/mol, while Safarian et al. obtained a value of 213 kJ/mol. 70

Figures 5-12 a to d: ln(Pt/P0) vs. Time plots

Table 5-4: Summary of apparent rate constants (interfacial reaction control), ka (cm/s)

Experimental ka (cm/s) Experimental ka (cm/s) Conditions Conditions 0.5 L/min 1.2 L/min -5 -5 50%H2-Ar, 1450°C 1.53x10 50%H2-Ar, 1450°C 1.54x10 -5 -5 50%H2-Ar, 1520°C 2.35x10 50%H2-Ar, 1520°C 3.03x10 -5 -5 50%H2-Ar, 1620°C 2.72x10 50%H2-Ar, 1620°C 5.95x10 -5 -5 50%H2-Ar, 1720°C 4.26x10 50%H2-Ar, 1520°C 4.83x10

-5 -6 100%H2, 1520°C 5.30x10 25%H2-Ar, 1520°C 7.38x10 -5 25%H2-Ar, 1620°C 1.10x10 -6 5%H2-Ar, 1520°C 6.48x10 -5 -6 5%H2-Ar, 1620°C 1.05x10 5%H2-Ar, 1520°C 3.75x10 -5 -6 5%H2-Ar, 1720°C 2.37x10 5%H2-Ar, 1620°C 4.86x10

Figures 5-13 a to c: Activation energy plots for chemical reaction control conditions

Table 5-5: Summary of calculated apparent activation energies, Ea (kJ/mol)

Experimental Activation Condition Energy, Ea (kJ/mol)

0.5 L/min, 50%H2-Ar 100 1.2 L/min, 50%H2-Ar 126 0.5 L/min, 5%H2-Ar 192

5.4.4 Gas diffusion of phosphorus in the gas boundary layer

The gas diffusion of phosphorus (P2) through the gas boundary layer can be expressed as follows:

푑[푃] 퐴퐷 − = 푃 − 푃 (5.10) 푑푡 푉훿 푖푛 푏 Where:

A/V: Melt geometry

D: Diffusion coefficient of P2 in H2-Ar

δ: Boundary layer thickness

Pin and Pb: Phosphorus concentration at the gas-metal interface (as P2), and bulk gas at the boundary layer edge, respectively. The concentration at Pb is assumed to be negligibly low.

Miki et al. described the thermodynamics of this process as shown in Reaction Equation 5.11 and change in Gibbs Standard Free Energy given in Equation 5.12 [7].

(5.11)

(5.12)

At low concentrations of P, the activity coefficient is assumed to be unity, accordingly, the relationship between phosphorus in molten silicon and equilibrium partial pressure of diatomic phosphorus is expressed as follows:

[%푃] −∆퐺° 1/2 = 푒푥푝 [ ] = 퐾푒푞 (5.13) 푃푃2 푅푇

Where Keq is the equilibrium constant derived from Equation 5.12. Substituting Eq. 5.13 into Eq. 5.10, and integrating:

2 푑[푃] 퐴퐷 [%푃] − = ( ) ( ) 푑푡 푉훿 퐾푒푞

1 1 퐴퐷 − = 2 푡 (5.14) [푃] [푃0] 푉훿퐾푒푞

Equation 5.14 can be plotted using experimental results, shown in Figures 5-14a to 5-14c. With the lack of data available to calculate D and δ, the apparent rate constant in this case has been

2 퐴퐷퐾푒푞 1 1 defined as kg= , taken from the slope of the plot for − vs. time (Eq. 5.14). The 푉훿 푃푡 푃0 equilibrium constant term, Keq (summary in Table 5-6), corresponding to a given experimental temperature is multiplied out of the slopes for each of the data sets plotted to obtain the gas phase apparent rate constants. The results for the apparent rate constants, ka, are summarized in Table 5- 7. As a basis of comparison with results from the chemical reaction control step (Section 5.4.3), apparent activation energies were determined from the gas diffusion rate constants for the 50%H2-

Ar (Flow rate: 0.5 L/min, 1.2 L/min) and 5%H2-Ar (Flow rate: 0.5 L/min) data sets, displayed in Figures 5-15a to 5-15c, and summarized in Table 5-8. Based on the fact that typical gas phase controlled reactions yield low positive activation energies, the large negative values obtained indicate that it is more likely that interfacial reaction rather than gas diffusion, would be the rate limiting step for the dephosphorization process.

Figures 5-14 a to c: (1/Pt)-(1/P0) vs. Time plots 75

Table 5-6: Summary of equilibrium constant terms, Keq

Temperature Keq

1450°C 88.52 1520°C 60.60 1620°C 37.03 1720°C 23.78

Table 5-7: Summary of apparent rate constants (gas diffusion control), ka (cm/s)

Experimental ka Conditions 0.5 L/min 3 50%H2-Ar, 1450°C 3.13x10 3 50%H2-Ar, 1520°C 2.74x10 3 50%H2-Ar, 1620°C 1.33x10 3 50%H2-Ar, 1720°C 1.10x10

2 5%H2-Ar, 1520°C 5.71x10 2 5%H2-Ar, 1620°C 4.70x10 2 5%H2-Ar, 1720°C 3.57x10

3 100%H2, 1520°C 4.88x10

1.2 L/min 3 50%H2-Ar, 1450°C 4.09x10 3 50%H2-Ar, 1520°C 3.74x10 3 50%H2-Ar, 1620°C 1.71x10 2 50%H2-Ar, 1720°C 8.63x10

Figures 5-15 a to c: Activation energy plots for gas diffusion control conditions

Table 5-8: Summary of calculated apparent activation energies, Ea (kJ/mol)

Experimental Activation Condition Energy, Ea (kJ/mol)

0.5 L/min, 50%H2-Ar -122 1.2 L/min, 50%H2-Ar -103 0.5 L/min, 5%H2-Ar -173

References

1. W. Yan, Y. Y, W. Chen, M. Barati, and M. A, Unpubl. Manuscript, Univ. Sci. Technol. Beijing, Univ. Toronto (2015). 2. L. T. Khajavi and M. Barati, High Temp. Mater. Process. 31, 627 (2012). 3. N. Sano and H. Katayama, Proc. 1st Int. Chromium Steel Alloy. Congr. 2, 25 (1992). 4. M. Hino and K. Ito, Thermodynamic Data for Steelmaking, Tohoku Uni (Sendai, 2010). 5. E. S. Machlin, Trans. Metall. Soc. AIME 218, 314 (1960). 6. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (John Wiley & Sons, Madison, Wisconsin, 1960). 7. T. Miki, K. Morita, and N. Sano, Metall. Mater. Trans. B 27B, 937 (2000).

CHAPTER 6 Conclusions and Future Work

6.1 Conclusions

1. Using electromagnetic levitation, dephosphorization of molten 76wt.% Si-Fe alloys

containing 0.0060-0.0510 wt. % P was achieved under a reducing H2-Ar gas atmosphere.

Investigations were carried out at 1450°C (1723K) to 1720°C (1993K) with H2-Ar gas

mixtures containing 5% to 100% H2, at flow rates of 0.5 and 1.2 L per minute.

2. Effects of increased time, temperature, hydrogen gas concentration, and initial phosphorus concentration in Si-Fe were found to promote phosphorus removal.

3. Increased iron content in the Si-Fe alloy (26wt.% Fe vs. 15wt.% Fe in Si) was found to impede phosphorus removal. This is likely due to the stronger affinity of Fe for P than Si for P. Theoretical calculations for vapour-liquid phase reactions of Si-Fe-P and Si-P alloys between 1420°C (1693K) and 1600°C (1873K) demonstrated a larger proportion of phosphorus volatizing from Si-P melts compared to Si-Fe-P alloys.

4. Thermodynamic modelling of the Si-Fe dephosphorization reaction under equilibrium conditions predicted the formation of diatomic phosphorus gas to be the dominant product species.

5. The results obtained for phosphorus removal from molten Si-Fe are consistent with a first order reaction. The apparent activation energy obtained for phosphorus evaporation at

1520°C (1793K) under a 50%H2-Ar gas atmosphere was Ea=100kJ/mol.

6. It is concluded that the rate of phosphorus removal from levitated droplets is controlled by the interfacial reaction step. However further work is required to confirm this conclusion. 79

6.2 Future Work

1. Further work is required to verify the mechanism of dephosphorization from Si-Fe alloy droplets. It would be beneficial to study and identify the chemical form of dephosphorization reaction products occurring in the system to confirm results from the thermodynamic modelling and to evaluate potential environmental impacts.

2. Levitation of Si-Fe and Si alloy droplets under a reduced system pressure should be carried out to investigate how this might influence phosphorus removal rates.

3. The effect of iron concentration in ferrosilicon should be further investigated in order to determine the extent to which iron influences the removal of phosphorus.

4. The influence of thermal diffusion on dephosphorization kinetics of ferrosilicon alloy droplets should be further evaluated. Analysis of hydrogen dissolution in levitated specimens can be carried out to determine solute interaction parameters.

5. Thermodynamics of phosphorus dissolution in molten Si-Fe and Si alloys should be investigated under an atmosphere of controlled phosphorus potential. However modifications in the design of the levitation system would be necessary in order to conduct this type of study.

6. The effect of levitation refining on the removal of other impurity elements from Si-Fe and Si alloys under different controlled gas atmospheres should be investigated. Material losses during this processing technique should also be evaluated.

Appendix A FactSage Equilibrium Reaction Products

A.1 Si-Fe-P System – Pure Components . 76wt.%Si –Fe-P (P – 0.022 wt.%)

Results – Reaction products at equilibrium conditions in mol. % (Total 100%)

100% Ar P2 P P4 1380°C 92.3 7.7 1.0E-06 1450°C 88.3 11.7 8.7E-07 1550°C 80.6 19.4 7.0E-07 1650°C 70.7 29.3 5.5E-07

5% H2 P2 P PH2 PH PH3 1380°C 78.7 6.6 6.8 6.2 1.7 1450°C 75.8 10.1 5.8 7.4 1.0 1550°C 69.4 16.7 4.5 8.9 0.5 1650°C 61.0 25.3 3.5 10.0 0.2

25% H2 P2 PH2 PH3 PH P 1380°C 51.7 22.5 12.3 9.1 4.3 1450°C 53.2 20.4 7.8 11.6 7.1 1550°C 51.7 16.9 4.1 14.8 12.5 1650°C 47.4 13.5 2.2 17.4 19.6

50% H2 P2 PH2 PH3 PH P 1380°C 34.8 30.2 23.4 8.7 2.9 1450°C 38.1 29.2 15.8 11.7 5.1 1550°C 39.6 25.9 8.9 16.0 9.6 1650°C 38.0 21.6 4.9 19.7 15.8

100% H2 PH3 PH2 P2 PH P 1380°C 37.5 34.2 19.7 7.0 1.7 1450°C 27.5 35.9 23.4 10.2 3.1 1550°C 24.3 31.7 24.3 13.9 5.9 1650°C 10.0 31.2 27.4 20.1 11.4

A.2 Si-Fe-P System – Commercial Alloy . 76wt.%Si –Fe (C- 0.096%, P- 0.022%, Al- 1.3%) Results – Reaction products at equilibrium conditions in mol. % (Total 100%)

100% Ar P2 P CP 1380°C 91.8 8.2 0.002 1450°C 87.7 12.3 0.005 1550°C 79.8 20.2 0.022 1650°C 69.9 30.0 0.075

5% H2 CHP P2 PH2 P PH PH3 1380°C 72.8 21.1 2.0 1.9 1.8 0.48 1450°C 77.6 16.7 1.4 2.3 1.7 0.23 1550°C 82.4 12.0 0.8 3.1 1.6 0.09 1650°C 85.3 8.8 0.5 3.8 1.5 0.04

25% H2 CHP P2 PH2 PH3 PH P 1380°C 79.5 10.3 4.8 2.6 1.9 0.9 1450°C 84.3 8.1 3.3 1.3 1.9 1.1 1550°C 88.6 5.8 2.0 0.5 1.7 1.5 1650°C 91.0 4.2 1.2 1.6 1.8 0.2

50% H2 CHP P2 PH2 PH3 PH P 1380°C 78.4 7.2 6.7 5.1 1.9 0.6 1450°C 84.4 5.7 4.7 2.5 1.9 0.8 1550°C 89.3 4.1 2.8 1.0 1.8 1.0 1650°C 91.9 3.0 1.8 0.4 1.6 1.3

100% H2 CHP PH3 PH2 P2 PH P 1380°C 74.3 9.8 8.9 4.8 1.8 0.4 1450°C 82.3 4.9 6.4 4.0 1.8 0.6 1550°C 88.7 2.9 4.0 1.9 1.7 0.7 1650°C 92.0 0.8 2.5 2.1 1.6 0.9

A.3 Gaseous reaction, P, H2

Results – Reaction products at equilibrium conditions in mol. % (Total 100%)

H2 P2 P4 PH2 H PH3 PH P 1450°C 67.4 31.3 1.2 0.016 0.015 0.010 0.006 0.002 1550°C 67.0 32.4 0.6 0.035 0.020 0.011 0.008 0.006 1650°C 66.7 32.8 0.3 0.077 0.024 0.019 0.013 0.006

Appendix B Sample Calculation of Mass Transfer Coefficient in Melt Boundary Layer, Km for 1520°C (1793K)

1/2 Machlin’s rigid flow model: Km = (8DP,m*vm/πr)

Dp,m: diffusion coefficient of phosphorus in melt est. by Stokes-Einstein equation; modified for considering unequal molecular mass effects of P (m1), SiFe (m2) T: melt temperature (varied 1723 K to 1993K)

m k T 1 p D  B (  )1/2 , P(m) 4R 2 2m p SiFe

-23 -10 kB = 1.38x10 ; Rp, covalent radius of P= 106 pm or 1.6x10 m; Ƞ, dynamic viscosity= 0.32 x 106 Pa·s

-7 2 Dp(m) = 0.25 x 10 m /s

vm: velocity of streamline flow (relative to current and EML stirring);

vm = Uo(characteristic velocity) x Surface Area

6 Jo, coil current = 310 A; σ, electrical conductivity (calculated) = 1.82x10 s/m; 5 3 -6 f = 3.2x10 Hz; ρ=3.2g/cm ; µ0, magnetic permeability = 1.2566x10 H/m; L, melt diameter = 0.00716 m

-3 Uo = 8.519 x 10 m/s

-3 -4 2 -6 vm = 8.519x10 m/s * 1.61x10 m = 1.37x10 m/s

1/2 -6 -4  Km = (8*DP,m*vm/π*r) = 4.94x10 m/s (4.94x10 cm/s) at 1520°C