{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Non UBC","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Materials Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"Aggregated Source Repository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Citation":[{"label":"Citation","value":"Processes 11 (7): 2065 (2023)","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#identifierCitation","classmap":"oc:PublicationDescription","property":"oc:identifierCitation"},"iri":"https:\/\/open.library.ubc.ca\/terms#identifierCitation","explain":"UBC Open Collections Metadata Components; Local Field; Indicates a bibliographic reference for the resource if it has been previously published."}],"Creator":[{"label":"Creator","value":"Taposhe, Golam Ismot Ara","attrs":{"lang":"","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."},{"label":"Creator","value":"Tafaghodi, Leili","attrs":{"lang":"","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"Date Available","value":"2023-08-01T18:11:08Z","attrs":{"lang":"","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"Date Issued","value":"2023-07-11","attrs":{"lang":"","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Description":[{"label":"Description","value":"A hybrid process of slag and solvent refining was used to remove boron and phosphorus from silicon. Quaternary slag of CaO-Al\u2082O\u2083-SiO\u2082-Na\u2082O was employed to remove boron (B) and phosphorus (P) from Si-20 wt% Fe alloy at 1300 \u00b0C. A slag-to-metal ratio of one was used at different reaction times. The mass transfer coefficient of B and P in the slag and alloy phases was calculated to determine the rate-limiting step. The mass transfer coefficients of B in the alloy and slag phases were 6.6 \u00d7 10\u2212\u2077 ms\u2212\u00b9 and 2.8 \u00d7 10\u2212\u2077 ms\u2212\u00b9, respectively. The mass transfer coefficients of P in the alloy and slag phases were determined to be 7.5 \u00d7 10\u2212\u2078 ms\u2212\u00b9 and 3.5 \u00d7 10\u2212\u2077 ms\u2212\u00b9, respectively. The rate-limiting stage of the slag\u2013alloy reaction kinetics was mass transport in the liquid slag for B and mass transport in the alloy phase for P.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"Digital Resource Original Record","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/85364?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"Full Text","value":"Citation: Taposhe, G.I.A.; Khajavi,L.T. Kinetic Analysis of Boron andPhosphorus Removal from Si-FeAlloy by CaO-Al2O3-SiO2-Na2O Slag.Processes 2023, 11, 2065. https:\/\/doi.org\/10.3390\/pr11072065Academic Editor: Prashant K.SarswatReceived: 9 May 2023Revised: 4 July 2023Accepted: 6 July 2023Published: 11 July 2023Copyright: \u00a9 2023 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https:\/\/creativecommons.org\/licenses\/by\/4.0\/).processesArticleKinetic Analysis of Boron and Phosphorus Removal from Si-FeAlloy by CaO-Al2O3-SiO2-Na2O SlagGolam Ismot Ara Taposhe 1,* and Leili Tafaghodi Khajavi 21 Department of Materials Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada2 Department of Materials Science and Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada;tafaghodi@mcmaster.ca* Correspondence: taposhe@mail.ubc.caAbstract: A hybrid process of slag and solvent refining was used to remove boron and phosphorusfrom silicon. Quaternary slag of CaO-Al2O3-SiO2-Na2O was employed to remove boron (B) andphosphorus (P) from Si-20 wt% Fe alloy at 1300 \u25e6C. A slag-to-metal ratio of one was used at differentreaction times. The mass transfer coefficient of B and P in the slag and alloy phases was calculatedto determine the rate-limiting step. The mass transfer coefficients of B in the alloy and slag phaseswere 6.6 \u00d7 10\u22127 ms\u22121 and 2.8 \u00d7 10\u22127 ms\u22121, respectively. The mass transfer coefficients of P in thealloy and slag phases were determined to be 7.5 \u00d7 10\u22128 ms\u22121 and 3.5 \u00d7 10\u22127 ms\u22121, respectively. Therate-limiting stage of the slag\u2013alloy reaction kinetics was mass transport in the liquid slag for B andmass transport in the alloy phase for P.Keywords: silicon; boron; phosphorus; slag refining; kinetics1. IntroductionUltra-pure silicon (9 N) for electronic applications is produced by chemical vapordeposition techniques such as the Siemens method. Considering the high energy intensityof these processes and the difference in silicon purity required for application in micro-electronics and in photovoltaics (6\u20137 N), developing processes for the mass productionof silicon for photovoltaic applications has been the subject of much investigation [1\u20135].Metallurgical techniques have been particularly focused on because of their scalability. Slagrefining is one of the metallurgical processes applicable to Si purification. Slag refininginvolves the oxidation and dissolution of impurities in the slag phase. For example, Boxidizes to form borate, and P oxidizes to produce phosphate or phosphide. Later, theseoxides dissolve in slag. Several investigations were carried out on binary slags, such asSiO2-CaO [6], SiO2-MgO [7], and SiO2-Na2O [8], ternary slags, such as CaO-SiO2-CaCl2 [9],CaO-SiO2-MgO, and SiO2-Al2O3-MgO [2], and quaternary slags like CaO-SiO2-Al2O3-MgO [2] and CaO-SiO2-Al2O3-CaF2 [10]. However, the removal of B and P is still one ofthe main challenges in the slag refining of Si. Solvent refining involves alloying silicon witha metal that has a higher affinity for B and P compared to the affinity of silicon for B andP. Alloying metals like Al [11\u201315], Cu [16,17], and Fe [18\u201320] were examined by previousresearchers. Even though these metals could remove B and P to various degrees, a suitableconcentration of impurities for solar applications is yet to be achieved [21]. Therefore, ahybrid process including slag and solvent refining is proposed to facilitate B and P removal.The process involves using slag to remove B and P from a silicon alloy, followed by con-trolled cooling to obtain high-purity silicon phases while leaving the residual B and P inthe alloy phase.Understanding the thermodynamics and kinetics of B and P distribution between theslag and alloy phases is crucial for process control. A significant number of investigationswere carried out on the thermodynamic analysis of Si refining [18,19,22\u201328]. However,kinetic analysis on the mass transfer of B and P between the alloy and slag phases isProcesses 2023, 11, 2065. https:\/\/doi.org\/10.3390\/pr11072065 https:\/\/www.mdpi.com\/journal\/processesProcesses 2023, 11, 2065 2 of 13very limited. The kinetics of B mass transfer have been investigated using CaO-SiO2 andCaO-SiO2-MgO slags for refining Si-containing 250 ppm B [29]. The reaction temperaturewas between 1600 \u25e6C and 1650 \u25e6C. The mass transfer coefficient in CaO-SiO2 slag wasdetermined to be 1.2 and 2.1 \u00d7 10\u22126 ms\u22121 for the slag to Si ratios of 1 and 2, respectively.For CaO-SiO2-MgO slag, the mass transfer coefficient was reported to be 3.2 \u00d7 10\u22126 ms\u22121.However, the rate-determining step was not determined in this study. Transport kineticsand equilibrium studies were carried out between ferrosilicon (Si-50\u201385 wt% Fe) dopedwith 300 ppm B and slag (CaO-SiO2) with a variable reaction time at 1600 \u25e6C [30]. The Bmass transfer coefficient value between the alloy and the slag phase was determined to be1.43\u20131.8\u00d7 10\u22126 ms\u22121 with the variable alloy composition in the range of 50\u201385 wt% Fe. Themass transfer rate of B between ferrosilicon and slag increased marginally with ferrosiliconiron concentration. The rate-limiting step was assumed to be the mass transfer in the slagphase because the viscosity of the ferrosilicon alloy is several orders of magnitude lowerthan that of the slag.Kinetic analysis of B removal from Si metal was investigated with binary CaO-SiO2and ternary CaO-SiO2-Al2O3 slags [31]. The mass transfer coefficients in the binary slagwere 2.24 \u00d7 10\u22126 ms\u22121, 2.59 \u00d7 10\u22126 ms\u22121, and 2.82 \u00d7 10\u22126 ms\u22121 at 1500 \u25e6C, 1550 \u25e6C,and 1600 \u25e6C. For ternary slag of CaO-SiO2-Al2O3, the mass transfer coefficients weredetermined to be 1.49 \u00d7 10\u22126 ms\u22121, 1.86 \u00d7 10\u22126 ms\u22121, and 2.13 \u00d7 10\u22126 ms\u22121. The masstransfer coefficient slightly decreased when the Al2O3 content of the slag was increasedfrom 9.59 wt% to 15.9 wt%.Different slag systems, namely, CaO-SiO2-Al2O3-(CaF2) and Na2SiO3-CaO-SiO2, wereused to refine Si containing an initial B concentration of 13\u201325 ppm. The refining processwas carried out at 1800 \u25e6C [32]. The mass transfer coefficients in the above slag phasesare 1.19 \u00d7 10\u22126 and 10.1 \u00d7 10\u22126 ms\u22121, respectively. It was also reported that the masstransfer in the slag phase was the rate-determining step. The CaO-SiO2 binary slag was alsoemployed to refine Si containing 300 ppm B at 1600 \u25e6C [33]. The mass transfer coefficientvalue was estimated at 1.4 \u00d7 10\u22126 ms\u22121. Using CaO-SiO2-TiO2 slag and Si-100 ppm B at1600 \u25e6C [34] resulted in a mass transfer coefficient of 5.2\u00d7 10\u22126 ms\u22121. The CaO-SiO2-K2CO3ternary mixture was employed to examine the kinetics of B removal from Si-22 ppmw B at1600 \u25e6C [35]. The mass transfer coefficient was measured for various slag compositions.The maximum mass transfer coefficient reported was 25.2 \u00d7 10\u22126 ms\u22121. The mass transferin the ternary slag was determined to be the rate-limiting step of boron transfer.CaO-SiO2-CaCl2 was used to refine Si-3.6 ppm B at 1600 \u25e6C and 1650 \u25e6C [36]. At1600 \u25e6C, the mass transfer coefficient value was found to be 5.2 \u00d7 10\u22126 ms\u22121, while at1650 \u25e6C, the value was 6.6 \u00d7 10\u22126 ms\u22121. Kinetic analysis of B removal from Si-22 ppmw Bwas also performed with CaO-SiO2 and CaO-SiO2-K2CO3 slag at 1550 \u25e6C [37]. For CaO-SiO2-K2CO3 slag, the mass transfer coefficient value was reported as 2.43 \u00d7 10\u22125 ms\u22121,which is significantly higher than the value of 3.16 \u00d7 10\u22126 ms\u22121 for CaO-SiO2. It wasreported that addition of K2CO3 results in higher B mass transport in the slag phase.The Li2O-SiO2 binary slag was used to investigate removal kinetics from Si-8.6 ppmB at 1700 \u25e6C [38]. However, the mass transfer coefficient value was comparatively low,i.e., 2.3 \u00d7 10\u22128 ms\u22121 compared to the previous research. Similar to the other investigations,mass transfer in the slag phase was found to be the rate-limiting step.With the final goal of determining the rate-limiting step, this manuscript examines thekinetics of B and P removal from Si-20 wt% Fe alloy by CaO-SiO2-Al2O3-Na2O quaternaryslag. The refining process was carried out at 1300 \u25e6C, which is lower than the previousinvestigations. The lower refining temperature will contribute to the lower energy con-sumption of the process. The mass transfer coefficients of B and P in the slag and the alloyphase were determined. The rate-limiting step for B and P removal was determined fromthe experimental analysis.Processes 2023, 11, 2065 3 of 132. Materials and Methods2.1. Alloy PreparationThe master alloy was prepared with 80 wt% Si and 20 wt% Fe with the addition of Band P as impurities. The crucible containing 150 g of the powder mixture was first heatedat 3.2 \u25e6C\/min up to 600 \u25e6C, followed by heating up to 1600 \u25e6C at the rate of 1 \u25e6C\/minin a vertical tube furnace. The sample was kept for 10 h to complete melting. Then, thetemperature was decreased to 600 \u25e6C (at a rate of 1 \u25e6C\/min) followed by further cooling toroom temperature at the rate of 3.2 \u25e6C\/min. The heating, melting, and cooling processeswere carried out in an Ar environment. The master alloy was ground by a grinder. Anamount of 5 g of the master alloy was taken to conduct each experiment. The initial B andP concentration of the alloy is important for performing the kinetic analysis. Therefore, theinitial concentration of B and P in each sample was measured using ICP-OES (inductivelycoupled plasma optical emission spectrometry). The model of the equipment used in thecurrent investigation was Varian 725-ES.Prior to ICP-OES analysis, 0.1 g of the alloy was chemically digested with an acidmixture containing 2 mL H2SO4, 5 mL HNO3, and a dropwise addition of HF. The initialconcentration of B and P was measured 3 times to obtain reliable values.2.2. Slag PreparationThe optimum composition for maximum removal of B and P from the Si-Fe alloy wasdetermined by the authors and has been reported in previous publications [22,23]. Theoptimum impurity removal at 1300 \u25e6C was achieved at CaO\/SiO2 of 1.5, SiO2\/Al2O3 of2, and 10 wt% Na2O for the quaternary slag. Considering the previous findings, 45 wt%CaO-30 wt% SiO2-15 wt% Al2O3-10 wt% Na2O was chosen as the slag composition toexamine B and P removal kinetics at 1300 \u25e6C. An amount of 5 g of slag was premelted in analumina crucible for 4 h at 1600 \u25e6C. The heating and cooling rates were similar to that ofthe alloy. The Ar atmosphere was maintained in the vertical tube furnace throughout theslag preparation process.2.3. Experimental ProcedureThe schematic and physical image of the tube furnace and the experimental setup areshown in Figure 1. Considering the 1:1 alloy to slag ratio, 5 g of the master alloy was addedto 5 g of the premelted slag in the alumina crucible. The alumina crucible was placed ina graphite crucible and suspended from the upper cap of the furnace. The sample washeated at 3.2 \u25e6C\/min to 600 \u25e6C\/min, followed by 1 \u25e6C\/min to 1500 \u25e6C, and kept at 1500 \u25e6Cfor 2 h. Later, the sample was cooled to 1300 \u25e6C at the rate of 1 \u25e6C\/min. The reactiontemperature was 1300 \u25e6C, while the reaction time was varied between 2 and 8 h for kineticinvestigations. After the selected reaction time, the lower cap was opened, and the lowerrefractory plug was pulled out. The entire sample was quenched in a bucket of water whichwas placed under the furnace. A diamond cutter was used to obtain the cross-section ofthe crucible containing the sample and also to separate the alloy and slag physically. Thephysical separation approach involves separating the phases manually by applying slightpressure to the interface of the alloy and slag. An amount of 0.1 g of the quenched groundalloy was taken for chemical analysis to measure B and P concentration, using a similardigestion technique for the alloy described in Section 2.1. The final concentration of B andP was measured by ICP-OES.Processes 2023, 11, 2065 4 of 13Processes 2023, 11, x FOR PEER REVIEW 4 of 14    (a) (b) Figure 1. (a) Schematic and (b) physical image of the vertical tube furnace. 3. Results 3.1. Mass Transfer Control Kinetic Model The removal of B and P from the alloy phase involves three steps. First is the transport of B and P in the alloy phase, the second is the oxidation and dissolution reactions at the interface, and the last step is the transport in the slag phase. The reactions at the interface are expected to be fast as the reaction temperature is 1300 \u00b0C. Therefore, it is logical to assume that the rate-controlling step should be the transport of B and P in the alloy or the slag phase. The results of the experimental work described above were used to find the rate-limiting steps for B and P. Assuming a first-order reaction, the rate of change of the concentration of impurities, I (I = B or P) in the alloy and slag phase, is given by Equations (1) and (2). \u2212 d[I]dt =  AV\u0b45 K\u0b45([I]\u0b60 \u2212 [I]\u0b67) (1)   d(I)dt =  AV\u0bcc K\u0bcc((I)\u0b67 \u2212 (I)\u0b60) (2)Here, A stands for the slag\u2013alloy interface area (m2), VA and vs stand for the alloy and slag volumes (m3), and [I] and (I) stand for the impurities\u2019 concentrations (ppmw) in the alloy and slag phase, respectively. Interface and bulk are denoted by the subscripts \u201ci\u201d and \u201cb\u201d. The mass transfer coefficients (ms\u22121) of impurities in the alloy and slag phases are KA and KS, respectively.  Considering the equilibrium condition of impurities\u2019 distribution at the interface of the alloy and slag phase, the partition ratio, LI, which is the ratio of the impurity Figure 1. (a) Schematic and (b) physical image of the vertical tube furnace.3. Results3.1. Mass Transfer Control Kinetic ModelThe removal of B and P from the alloy phase involves three steps. First is the transportof B and P in the alloy phase, the second is the oxidation and dissolution reactions at theinterface, and the last step is the transport in the slag phase. The reactions at the interfaceare expected to be fast as the reaction temperature is 1300 \u25e6C. Therefore, it is logical toassume that the rate-controlling step should be the transport of B and P in the alloy or theslag phase. The results of the experimental work described above were used to find therate-limiting steps for B and P.Assuming a first-order reaction, the rate of change of the concentration of impurities, I(I = B or P) in the alloy and slag phase, is given by Equations (1) and (2).\u2212d[I]dt=AVAKA([I]b \u2212 [I]i) (1)d(I)dt=AVSKS((I)i \u2212 (I)b) (2)Here, A stands for the slag\u2013alloy interface area (m2), VA and vs stand for the alloy andslag volumes (m3), and [I] and (I) stand for the impurities\u2019 concentrations (ppmw) in thealloy and slag phase, respectively. Interface and bulk are denoted by the subscripts \u201ci\u201d and\u201cb\u201d. The mass transfer coefficients (ms\u22121) of impurities in the alloy and slag phases are KAand KS, respectively.Considering the equilibrium condition of impurities\u2019 distribution at the interface of thealloy and slag phase, the partition ratio, LI, which is the ratio of the impurity concentrationProcesses 2023, 11, 2065 5 of 13in slag to that of the alloy at equilibrium, i.e., (I)e[I]e, can be written as the ratio of the impurityconcentration at the interface, i.e., (I)i[I]i(Equation (3)).LI =(I)i[I]i=(I)e[I]e(3)The mass balance equation for impurity I is shown in Equation (4).MA[I]0 +Ms(I)0 = MA[I] +MS(I) (4)Here, MA and MS are the mass (g) of the alloy and slag, respectively. The subscription\u201c0\u201d stands for the initial state. Substituting Equations (3) and (4) into Equations (1) and (2)and integrating them with the initial conditions, [I] = [I]0 and (I) = (I)0, Equations (5) and (6)can be derived.VAA\u00b7MA[I]0 +MS(I)0 \u2212MA[I]eMA[I]0 +MS(I)0\u00b7 ln [I]\u2212 [I]e[I]0 \u2212 [I]e= \u2212KAt (5)VSA\u00b7 MA[I]eMA[I]0 +MS(I)0\u00b7 ln [I]\u2212 [I]e[I]0 \u2212 [I]e= \u2212KSt (6)The derivations of the kinetic equations are available in [39]. For easier understanding,Equations (5) and (6) can be re-written as Equation (7).YA\/S ln Z = \u2212KA\/S t (7)Here, Z is [I]\u2212[I]e[I]0\u2212[I]e and YA\/S depends on the particular rate-determining step. Thatmeans, for the Si-Fe alloy phase, YA =VAA \u00b7MA[I]0+MS(I)0\u2212MA[I]eMA[I]0+MS(I)0, and for the slag,YS =VSA \u00b7MA[I]eMA[I]0+MS(I)0\u00b7 ln [I]\u2212[I]e[I]0\u2212[I]e is constant at any particular time. When t = 0, [I] = [I]0;therefore, YA\/S ln Z = 0. As a result, the linear regression function must pass throughthe origin. The concentration of impurities in the alloy phase reduces with time. As thereaction proceeds, [I] becomes smaller than [I]0 and it continuously decreases. Therefore,YA\/S ln Z has a negative value which decreases with time. This in turn results in the fittedregression line having a negative slope and KA\/S having a positive value. The mass transfercoefficient, KA\/S, is the negative of the slope of the regression line fitted to the YA\/S ln Zversus time (t) data. The rate-determining step can be determined by comparing KA andKS for B and P.3.2. Interfacial Area of Alloy and SlagThe cross-section of the sample including the alloy and the slag phase is shown inFigure 2. Inside the alumina crucible, the slag phase surrounds the alloy as it takes on aspherical shape. The sphere\u2019s diameter is estimated to be 12 mm. The total surface area ofthe alloy sphere was calculated knowing its diameter. However, approximately 1\/6 of thealloy surface area was uncovered by the slag. To determine the estimated interfacial areaof the alloy and the slag for the kinetic study, the uncovered area was subtracted from thealloy\u2019s total area. The estimated interfacial area of the alloy and slag was 3.77 cm2.Processes 2023, 11, 2065 6 of 13Processes 2023, 11, x FOR PEER REVIEW 6 of 14    Figure 2. Cross-section of the quenched sample including the spherical alloy and the surrounding slag phase in an alumina crucible. 3.3. Kinetic Analysis of B Removal Because full composition homogeneity is difficult to achieve, it was expected that there would be some variation in the initial concentration of B in different samples prior to the refining process. As a result, the initial impurity concentration of each sample was determined independently. The average of the initial concentration of B from three sam-ples was taken for experimental analysis. The details of the measurement procedure of the initial B concentration in the alloy and the final concentration of B in the refined alloy were discussed in Section 2. The B concentration of each sample was determined using the av-erage of these three measurements. The experimental results are tabulated in Table 1. Table 1. Initial, final, and normalized concentration of B, YA ln Z, and YS ln Z at 1300 \u00b0C. Sample ID Time (Hours) Initial  [B]Alloy (ppmw) Final  [B]Alloy (ppmw) Normalized [B] YA lnZ YS lnZ 1 2 190.43 82.54 0.43 \u22120.51 \u22120.21 2 3 186.53 68.77 0.37 \u22120.68 \u22120.29 3 4 230.28 82.13 0.36 \u22120.72 \u22120.31 4 5 222.30 66.96 0.30 \u22121.33 \u22120.56 5 6 191.93 54.81 0.29 equilibrium equilibrium 6 8 189.50 55.82 0.29 equilibrium equilibrium Normalized B concentration of the refined alloy to the initial concentration of each sample at different reaction times is shown in Figure 3. It is clear that B removal from the alloy was fast in the first 2 h of the process. As time increases, the concentration of B in the alloy phase decreases. The B transport reached the equilibrium state after 6 h of equilib-rium time.  Figure 2. Cross-section of the quenched sample including the spherical alloy and the surroundingslag phase in an alumina crucible.3.3. Kinetic Analysis of B RemovalBecause full composition homogeneity is difficult to achieve, it was expected thatthere would be some variation in the initial concentration of B in different samples priorto the refining process. As a result, the initial impurity concentration of each sample wasdetermined independently. The average of the initial concentration of B from three sampleswas taken for experimental analysis. The details of the measurement procedure of theinitial B concentration in the alloy and the final concentration of B in the refined alloy werediscussed in Section 2. The B concentration of each sample was determined using theaverage of these three measurements. The experimental results are tabulated in Table 1.Table 1. Initial, final, and normalized concentration of B, YA ln Z, and YS ln Z at 1300 \u25e6C.Sample ID Time (Hours)Initial[B]Alloy(ppmw)Final[B]Alloy(ppmw)Normalized[B] YA lnZ YS lnZ1 2 190.43 82.54 0.43 \u22120.51 \u22120.212 3 186.53 68.77 0.37 \u22120.68 \u22120.293 4 230.28 82.13 0.36 \u22120.72 \u22120.314 5 222.30 66.96 0.30 \u22121.33 \u22120.565 6 191.93 54.81 0.29 equilibrium equilibrium6 8 189.50 55.82 0.29 equilibrium equilibriumNormalized B concentration of the refined alloy to the initial concentration of eachsample at different reaction times is shown in Figure 3. It is clear that B removal fromthe alloy was fast in the first 2 h of the process. As time increases, the concentration ofB in the alloy phase decreases. The B transport reached the equilibrium state after 6 h ofequilibrium time.Processes 2023, 11, 2065 7 of 13Processes 2023, 11, x FOR PEER REVIEW 7 of 14    Figure 3. Normalized B concentration in the refined alloy vs. time at 1300 \u00b0C. Based on the experimental results, B concentration after 6 h is chosen as the equilib-rium concentration, [B]e. The mass transfer coefficient of B in the alloy phase was calcu-lated using the kinetic model described in Section 3.1. The YA ln Z values are plotted as a function of time in Figure 4. The mass transport coefficient of B in the alloy is determined from the slope of the linear regression fitted to the plotted data points. The KA was found to be 6.6 \u00d7 10\u22127 ms\u22121. To the best of the authors\u2019 knowledge, the mass transfer coefficient of B in Si-20 wt% Fe has not previously been reported.   0.00.20.40.60.81.01.20 2 4 6 8 10Time (hours)Normalized [B] AlloyFigure 3. Normalized B concentration in the refined alloy vs. ti e at 1300 \u25e6C.Based ri ental results, B concentration after 6 h is chosen as the equilibriumconcentration, [B]e. The mass transfer coefficient of B in the alloy phase was c lculatedusing the kinetic model described in S ct on 3.1. The YA ln Z va ues are plotted as a functionof time in Figure 4. The mass transpor coefficient of B in he alloy is determined f om theslope of the linear regr ssion fitted to th pl ted data points. The KA was found to be6.6 \u00d7 10\u22127 ms\u22121. To the best of the authors\u2019 knowledge, the mass transfer coefficient of Bin Si-20 wt% Fe has not previously been reported.Processes 2023, 11, x FOR PEER REVIEW 8 of 14     Figure 4. The YA ln Z vs. time for B mass transfer kinetics in the Si\u221220 wt% Fe. The mass transfer coefficient of B in the slag phase was determined via a similar ki-netic model. The acquired YS ln Z values versus time are plotted in Figure 5. The slope of the linear regression function is used to determine the mass transfer coefficient of B in the slag. The KS was calculated to be 2.8 \u00d7 10\u22127 ms\u22121, which is less than the KA of 6.6 \u00d7 10\u22127 ms\u22121. Therefore, it is concluded that B removal is governed by B mass transfer in the slag.   -2.4-2-1.6-1.2-0.8-0.400 1 2 3 4 5 6Time (hours)Y AlnZKA=6.6 \u00d7 10-7 ms-1R\u00b2 = 0.92Figure 4. The YA ln Z vs. time for B mass transfer kinetics in the Si\u221220 wt% Fe.The mass transfer coefficient of B in the slag phase was determined via a similar kineticmodel. The acquired YS ln Z values versus time are plotted in Figure 5. The slope of thelinear regression function is used to determine the mass transfer coefficient of B in the slag.The KS was calculated to be 2.8 \u00d7 10\u22127 ms\u22121, which is less than the KA of 6.6 \u00d7 10\u22127 ms\u22121.Therefore, it is concluded that B removal is governed by B mass transfer in the slag.Processes 2023, 11, 2065 8 of 13Processes 2023, 11, x FOR PEER REVIEW 9 of 14     Figure 5. The YS ln Z vs. time for B mass transfer kinetics in the 45 wt% CaO\u221230 wt% SiO2\u221215 wt% Al2O3\u221210 wt% Na2O phase. In a previous investigation, the mass transfer coefficients of B in the slag containing 46 wt% CaO-38.1 wt% SiO2-15.9 wt% Al2O3 were determined to be 1.23 \u00d7 10\u22126 ms\u22121 at 1500 \u00b0C, 1.38 \u00d7 10\u22126 ms\u22121 at 1550 \u00b0C, and 1.83 \u00d7 10\u22126 ms\u22121 at 1600 \u00b0C [31]. In a different research study, Si metal was refined with 65 wt% Na2O-35 wt% SiO2 slag. The mass transfer coeffi-cient of B in the slag at 1650 \u00b0C was found to be 5.8 \u00d7 10\u22128 ms\u22121 [40]. The current slag con-tains 45 wt% CaO-30 wt% SiO2-15 wt% Al2O3-10 wt% Na2O, and the mass transfer coeffi-cient of B was found to be 2.8 \u00d7 10\u22127 ms\u22121.  In silicate slags, tetrahedral units of SiO44\u2212 form when the Si4+ ion is surrounded by four O2\u2212 ions [41\u201343]. Complex silicate networks are formed by these tetrahedral units in the form of chains, sheets, and 3D structures. Higher SiO44\u2212 content of the slag typically results in higher polymerization which in turn leads to higher viscosity. Cations such as Ca2+ and Na+ are network breakers that hinder slag polymerization. Therefore, the pres-ence of basic oxides such as CaO and Na2O generally results in lower viscosity. Higher temperature also results in lower slag viscosity of silicate slag. Cations such as Al3+ can fit into the polymeric structure of the silicate slags. However, the charge balance needs to be maintained. For example, in the current study, a Na+ ion close to an Al3+ will play the charge-balancing role. It has been shown that the temperature affects the mass transfer coefficient of boron in CaO-SiO2 and CaO-SiO2-Al2O3 slags [31]. Higher temperature results in lower viscosity that favors B transport and increases the mass transfer coefficient in the slag phase. The influence of molecular properties of silicate slags such as CaO-SiO2-MgO was investigated using Raman spectroscopy [44]. The investigation reveals that the presence of CaO pro-motes B transport while MgO does not have an impact on B removal. The ionic structure of slag affects its thermophysical properties. Similarly, B mass transfer value is directly influenced by the ionic structure of the slag phase. Current re-search is based on CaO-SiO2-Al2O3-Na2O quaternary slag which has a different ionic struc-ture than the previous binary (Na2O-SiO2) and ternary slags (CaO-SiO2-Al2O3). The reac-tion temperature in this investigation is also lower, 1300 \u00b0C, than the previous work. Thus, it is difficult to compare the current evaluated KS value with the previous research. It might be concluded that the mass transfer coefficient depends on the ionic structure and the temperature of the slag. However, it would be prudent to conduct more refining ex-periments with the goal of increasing the mass transport coefficient of B in the slag.    -1.0-0.8-0.6-0.4-0.20.00 1 2 3 4 5 6Time (hours)Y Sln ZKs= 2.8 \u00d7 10-7 ms-1R\u00b2 = 0.93i . S ln Z vs. ti e for ss t i ti i t t t i 2 15 tl2 3\u221210 wt% Na2O phase.i ti , t f r ffi i ts ft a -38.1 t SiO2-15.9 wt% Al2O3 w re d termined to be 1.23 \u00d7 10\u22126 ms\u22121 at1500 \u25e6C, 1.38 \u00d7 10\u22126 ms\u22121 at 1550 \u25e6C, and 1.83 \u00d7 10\u22126 ms\u22121 at 1600 \u25e6C [31]. In a differentresearch study, Si metal was refined ith 65 wt% Na2O-35 wt% SiO2 slag. The mass transferoefficient of B in the slag at 1650 \u25e6C was f und to be 5. \u00d7 10\u22128 ms\u22121 [40]. The curre tslag contains 45 wt% CaO-30 wt% SiO2-15 wt% Al2O3-10 wt% Na2O, and the mass transfercoefficient of B was found to be 2.8 \u00d7 10\u22127 ms\u22121.In silicate slags, tetrahedral units of Si 44\u2212 for hen the Si4+ ion is surrounded byfour 2\u2212 ions [41\u201343]. Complex silicate networks are formed by these tetrahedral units inthe for of chains, sheets, and 3 structures. igher Si 44\u2212 content of the slag typicallyresults in higher polymerization which in turn leads to higher viscosity. Cations suchas Ca2+ and Na+ are network breakers that hinder slag polymerization. Therefore, thepresence of basic oxides such as CaO and Na2O generally results in lower viscosity. Highertemperature also results in lower slag viscosity of silicate slag. Cations such as Al3+ canfit into the polymeric structure of the silicate slags. However, the charge balance needs tobe maintained. For example, in the current study, a Na+ ion close to an Al3+ will play thecharge-balancing role.It has been shown that the temperature affects the mass transfer coefficient of boron inCaO-SiO2 and CaO-SiO2-Al2O3 slags [31]. Higher temperature results in lower viscositythat favors B transport and increases the mass transfer coefficient in the slag phase. Theinfluence of molecular properties of silicate slags such as CaO-SiO2-MgO was investi-gated using Raman spectroscopy [44]. The investigation reveals that the presence of CaOpromotes B transport while MgO does not have an impact on B removal.The ionic structure of slag affects its thermophysical properties. Similarly, B masstransfer value is directly influenced by the ionic structure of the slag phase. Currentresearch is based on CaO-SiO2-Al2O3-Na2O quaternary slag which has a different ionicstructure than the previous binary (Na2O-SiO2) and ternary slags (CaO-SiO2-Al2O3). Thereaction temperature in this investigation is also lower, 1300 \u25e6C, than the previous work.Thus, it is difficult to compare the current evaluated KS value with the previous research.It might be concluded that the mass transfer coefficient depends on the ionic structureand the temperature of the slag. However, it would be prudent to conduct more refiningexperiments with the goal of increasing the mass transport coefficient of B in the slag.Processes 2023, 11, 2065 9 of 133.4. Kinetic Analysis of P RemovalThe initial concentration of P in the master alloy was determined using a similarmethod as B. The final concentration of P in the refined alloy and slag were also measuredby ICP-OES analysis. The final concentration was later normalized with the average of thethree initial concentrations of the samples. The experimental findings, YA ln Z, and YS ln Zare shown in Table 2.Table 2. Initial, final, and the normalized concentration of P, YA ln Z, and YS ln Z at 1300 \u25e6C.Sample No Time (Hours)Initial[P]Alloy(ppmw)Final[P]Alloy(ppmw)Normalized [P] YA lnZ YS lnZ1 2 224.30 213.54 0.95 \u22120.03 \u22120.122 3 178.10 159.60 0.90 \u22120.06 \u22120.303 4 232.20 204.00 0.88 \u22120.09 \u22120.414 5 178.90 150.90 0.84 \u22120.17 \u22120.825 6 189.35 155.70 0.82 equilibrium equilibrium6 8 172.45 140.99 0.82 equilibrium equilibriumThe normalized value indicates the change in the concentration of P in the refinedalloy with respect to time as shown in Figure 6. As time increases, the concentrationof P decreases and reaches the equilibrium state after 6 h. However, the change in Pconcentration was not as significant as B.Processes 2023, 11, x FOR PEER REVIEW 10 of 14   3.4. Kinetic Analysis of P Removal The initial concentration of P in the aster alloy as deter ined using a si ilar ethod as B. The final concentration of P in the refined alloy and slag ere also easured by I - S a alysis. e fi al co ce tratio  as later or alize  it  t e average of t e t ree i itial c ce trations of the samples. The experimental findings, YA ln Z, and YS ln Z are shown in Table 2.    ,       , A    S l   at 130  \u00b0C. Sample No Time (Hours) Initial  [P]Alloy (ppmw) Final  [P]Alloy (ppmw) Normalized [P] YA lnZ YS lnZ 1 2 224.30 213.54 0.95 \u22120.03 \u22120.12 2 3 178.10 159 60 0. 0 0.06 0.30 3 4 232.20 204.00 0.88 \u22120.09 \u22120.41 4 5 178.90 150.90 0.84 \u22120.17 \u22120.82 5 6 189.35 155.70 0.82 equilibriu  equilibriu   8 . 5 1  0.  equili  equili  The normalized value indicates the change in the concentration of P in the refined alloy with respect to time as shown in Figure 6. As time increases, the concentration of P decreases and reaches the equilibrium state after 6 h. However, the change in P concen-tration was not as significant as B.   Figure 6. Normalized P concentration in the refined alloy vs. reaction time at 1300 \u00b0C. The first-order kinetic model was implemented to find the mass transfer coefficient value for P in the alloy phase at 1300 \u00b0C. The YA ln Z values were calculated and shown in Figure 7. The mass transfer coefficient value of P in the alloy phase was determined using the slope of the linear regression line. The mass transfer coefficient of P in the Si-20 wt% Fe alloy was found to be 7.5 \u00d7 10\u22128 ms\u22121 at 1300 \u00b0C. 0.00.20.40.60.81.01.20 2 4 6 8 10Normalized [P] AlloyTime (hours)i r . r li c c tr ti i t r fi ll s. r cti ti t \u25e6 .- r ti l l t t ffil i ll \u25e6 . ln Z values ere calc late a s ii r . tr f r ffi i t l f i t ll s t r i it e sl e f t e li ear regression line. The mass transfer coefficient of P in the Si-20 wt% Fealloy was found to be 7.5 \u00d7 10\u22128 ms\u22121 at 1300 \u25e6 .Processes 2023, 11, 2065 10 of 13Processes 2023, 11, x FOR PEER REVIEW 11 of 14    Figure 7. The YA ln Z plot vs. time for P mass transfer kinetics in the Si\u221220 wt% Fe phase. The mass transfer coefficient of P in the slag phase was also calculated using a similar kinetic model. The estimated YS ln Z with respect to time is plotted in Figure 8. The data points are fitted to a linear regression function as illustrated in the aforementioned figure. The mass transfer coefficient in the slag was calculated using the slope of the regression line. The mass transfer coefficient of P in the quaternary slag of CaO-SiO2-Al2O3-Na2O was found to be 3.5 \u00d7 10\u22127 ms\u22121 at 1300 \u00b0C. The mass transfer coefficient in slag, KS, for P is greater than the mass transfer coefficient of P in the alloy phase, KA, indicating that P transfer in the alloy is the rate-limiting step for P removal in refining Si-20 wt% Fe alloy with CaO-SiO2-Al2O3-Na2O slag at 1300 \u00b0C.   -0.3-0.2-0.10.00 1 2 3 4 5 6Time (hours)Y Aln ZKA= 7.5 \u00d7 10-8 ms-1 R2 = 0.94Figure 7. The YA ln Z plot vs. time for P mass transfer kinetics in the Si\u221220 wt% Fe phase.The mass transfer coefficient of P in the slag phase was also calculated using a similarkinetic model. The estimated YS ln Z with respect to time is plotted in Figure 8. The datapoints are fitted to a linear regression function as illustrated in the aforementioned figure.The mass transfer coefficient in the slag was calculated using the slope of the regressionlin . The mass transfer coefficient of P in the quaternary slag of CaO-SiO2-Al2O3-Na2Owas found to be 3.5 \u00d7 10\u22127 ms\u22121 at 1300 \u25e6C. The m ss transfer coefficient in slag, KS, for Pis greater than the mass transfer coefficient of P in the alloy phase, KA, indicating that Ptransfer in the alloy is the rate-limiting step for P removal in refining Si-20 wt% Fe alloywith CaO-SiO2-Al2O3-Na2O slag at 1300 \u25e6C.Processes 2023, 11, x FOR PEER REVIEW 12 of 14     Figure 8. The YS ln Z vs. time of P mass transfer kinetics in the 45 wt% CaO\u221230 wt% SiO2\u221215 wt% Al2O3\u221210 wt% Na2O phase. The findings of a previous work on the Si-Cu refining process with CaO-SiO2-CaCl2 slag at 1550 \u00b0C determined the P mass transfer coefficient in the slag to be 2.55 \u00d7 10\u22126 ms\u22121 [45]. This value is approximately an order of magnitude higher than the P mass transport coefficient which was found in the current study. The difference is most likely attributed to the variation in slag composition and temperature. The data on the mass transfer of P in Si or Si alloy is extremely scarce. The P mass transfer coefficient in Si-20 wt% Fe is ob-tained based on the experimental results of the current investigation. However, further research should be conducted to examine the mass transfer coefficient of P in other Si alloys as well as the slags, particularly to correlate the P mass transfer coefficient to the slag physiochemical characteristics and ionic structure. 4. Conclusions The kinetic analyses of B and P removal from Si-20 wt% Fe alloy have been carried out using a quaternary slag of 45 wt% CaO-30 wt% SiO2-15 wt% Al2O3-10 wt% Na2O at 1300 \u00b0C. The normalized B concentration in the refined alloy phase showed a relatively high B removal rate at the beginning of the refining process. The removal rate gradually drops, resulting in the equilibrium state in 6 h. The mass transfer coefficient for B in the alloy phase was found to be 6.6 \u00d7 10\u22127 ms\u22121 and in the slag phase it was 2.8 \u00d7 10\u22127 ms\u22121. Therefore, it was concluded that B distribution between the alloy and the slag was con-trolled by the B transport in the slag phase. On the other hand, the P removal rate from the alloy was relatively small and P concentration reached the equilibrium state after 6 h of reaction time. The P mass transfer coefficient values in the alloy and slag phase were determined to be 7.5 \u00d7 10\u22128 ms\u22121 and 3.5 \u00d7 10\u22127 ms\u22121, respectively. Therefore, it was con-cluded that P transport in the alloy phase is slower than the slag phase, resulting in the P transfer in the alloy being the rate-limiting step for P removal. In summary, comparing the mass transfer coefficients of B in the alloy and the slag, the rate-limiting step for B removal was found to be the B transport in the slag phase. However, the rate-limiting step for P was P transfer in the alloy. The findings provide evidence for the mechanisms of the removal of B and P from Si-Fe alloy. Author Contributions: Conceptualization, L.T.K.; methodology, L.T.K. and G.I.A.T.; software, G.I.A.T.; validation, L.T.K. and G.I.A.T.; formal analysis, G.I.A.T.; investigation, L.T.K. and G.I.A.T.; resources, L.T.K.; data curation, G.I.A.T.; writing\u2014original draft preparation, G.I.A.T.; writing\u2014-1.4-1.1-0.7-0.40.00 1 2 3 4 5 6KS= 3.5 \u00d7 10-7 ms-1 R2 = 0.93Y Sln ZTime (hours)Figure 8. The YS ln Z vs. time of P mass transfer kinetics in the 45 wt% CaO\u221230 wt% SiO2\u221215 wt%Al2O3\u221210 wt% Na2O phase.The findings of a previous work on the Si-Cu refining process with CaO-SiO2-CaCl2 slagat 1550 \u25e6C determined the P mass transfer coefficient in the slag to be 2.55 \u00d7 10\u22126 ms\u22121 [45].This value is approximately an order of magnitude higher than the P mass transport coefficientwhich was found in the current study. The difference is most likely attributed to the variationProcesses 2023, 11, 2065 11 of 13in slag composition and temperature. The data on the mass transfer of P in Si or Si alloyis extremely scarce. The P mass transfer coefficient in Si-20 wt% Fe is obtained based onthe experimental results of the current investigation. However, further research should beconducted to examine the mass transfer coefficient of P in other Si alloys as well as theslags, particularly to correlate the P mass transfer coefficient to the slag physiochemicalcharacteristics and ionic structure.4. ConclusionsThe kinetic analyses of B and P removal from Si-20 wt% Fe alloy have been carriedout using a quaternary slag of 45 wt% CaO-30 wt% SiO2-15 wt% Al2O3-10 wt% Na2O at1300 \u25e6C. The normalized B concentration in the refined alloy phase showed a relatively highB removal rate at the beginning of the refining process. The removal rate gradually drops,resulting in the equilibrium state in 6 h. The mass transfer coefficient for B in the alloy phasewas found to be 6.6 \u00d7 10\u22127 ms\u22121 and in the slag phase it was 2.8 \u00d7 10\u22127 ms\u22121. Therefore,it was concluded that B distribution between the alloy and the slag was controlled by theB transport in the slag phase. On the other hand, the P removal rate from the alloy wasrelatively small and P concentration reached the equilibrium state after 6 h of reaction time.The P mass transfer coefficient values in the alloy and slag phase were determined to be7.5 \u00d7 10\u22128 ms\u22121 and 3.5 \u00d7 10\u22127 ms\u22121, respectively. Therefore, it was concluded that Ptransport in the alloy phase is slower than the slag phase, resulting in the P transfer in thealloy being the rate-limiting step for P removal. In summary, comparing the mass transfercoefficients of B in the alloy and the slag, the rate-limiting step for B removal was found tobe the B transport in the slag phase. However, the rate-limiting step for P was P transferin the alloy. The findings provide evidence for the mechanisms of the removal of B and Pfrom Si-Fe alloy.Author Contributions: Conceptualization, L.T.K.; methodology, L.T.K. and G.I.A.T.; software, G.I.A.T.;validation, L.T.K. and G.I.A.T.; formal analysis, G.I.A.T.; investigation, L.T.K. and G.I.A.T.; resources,L.T.K.; data curation, G.I.A.T.; writing\u2014original draft preparation, G.I.A.T.; writing\u2014review and edit-ing, L.T.K.; visualization, L.T.K. and G.I.A.T.; supervision, L.T.K.; project administration, L.T.K.; fund-ing acquisition, L.T.K. All authors have read and agreed to the published version of the manuscript.Funding: The present work has been partially supported by the Natural Sciences and EngineeringResearch Council of Canada (NSERC, RGPIN-2017-04669).Data Availability Statement: Data contained in the article are available in Tables 1 and 2.Conflicts of Interest: The authors declare no conflict of interest.References1. Johnston, M.D.; Khajavi, L.T.; Li, M.; Sokhanvaran, S.; Barati, M. High-temperature refining of metallurgical-grade silicon: Areview. JOM 2012, 64, 935\u2013945. [CrossRef]2. Johnston, M.; Barati, M. Distribution of impurity elements in slag-silicon equilibria for oxidative refining of metallurgical siliconfor solar cell applications. Sol. Energy Mater. Sol. Cells 2010, 94, 2085\u20132090. [CrossRef]3. Hosseinpour, A.; Tafaghodi Khajavi, L. Slag refining of silicon and silicon alloys: A review. Miner. Process. Extr. Metall. Rev. 2018,39, 308\u2013318. [CrossRef]4. Thomas, S.; Barati, M.; Morita, K. 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