# Effect of Mold Flux Containing Ce2O3 on the Contents of Aluminum, Silicon, and Titanium in Incoloy825 Super Alloy

Authors: Geng Xin; Boyang Li; Zhouhua Jiang; Hou Yu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The effect of mold flux containing Ce2O3 on the contents of aluminum, silicon, and titanium in Incoloy825 super alloy was investigated based on the slag-steel interfacial chemical reaction experiment between mold flux and alloy. Firstly, the activity model of the CaO-SiO2-Al2O3-Na2O-MgO-CaF2-Ce2O3 slag system was established according to the ion and molecule coexistence theory (IMCT), and the calculation results show that with the increase of Ce2O3 content in the mold flux, the activity of Al2O3 decreases significantly and the activity of SiO2 decreases and gradually tends to 0. Secondly, thermodynamic calculations of the slag-steel interfacial chemical reaction revealed that the main chemical reaction in this study system is [Ti] + (SiO2) = [Si] + (TiO2). With the increase of Ce2O3 content in the mold flux, the slag-steel interfacial chemical reaction is weakened and the oxidation of Al and Ti in steel is inhibited. Finally, the results of slag-steel reaction experiment show that the increase rate of Al content increases from 1.03% to 10.31%, the increase rate of Si content decreases from 55.95% to 31.25%, and the oxidation rate of Ti content decreases from 33.27% to 20.00% when Ce2O3 content in the mold flux increases from 0% to 15% and the slag-steel reaction for 40 mins.


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## Body

## 1. Introduction

Incoloy825 super alloy is a fully austenitic nickel-based alloy treated by Ti stabilization, which has good resistance to stress corrosion cracking, crevice corrosion, and pitting corrosion [1–3]. Therefore, Incoloy825 is used in corrosion-resistant and extremely hot environments, such as heat exchanger, turbine engine, turbine, nuclear power reactor core, and other important components [4–6].At present, Incoloy825 is mainly smelted using the electroslag remelting (ESR) [7, 8], while it is difficult to use continuous casting for large-scale production. In general, the composition of the commonly used continuous casting mold flux is shown in Figure 1 in region A, its high content of SiO2 is prone to interfacial chemical reactions with the high content of Ti and Al in Incoloy825, as shown in (1). The reaction not only causes oxidation loss of Ti and Al but also leads to changes in the properties of the mold flux, which affects the continuous casting process [9–12].(1)2M+xSiO2=xSi+2MOx.Figure 1
Phase diagram of CaO-SiO2-Al2O3.In order to solve the abovementioned problems, researchers have proposed the use of low-reactive CaO-Al2O3-based mold fluxes with SiO2 ≤ 10 wt% (as shown in region B in Figure 1) for steel grades with serious slag-steel reaction [13–16]. However, the high activity of CaO in the mold fluxes tends to generate high melting point CaTiO3 with TiO2, as shown in Eq. (2). The high melting point minerals will enhance the crystallization ability of the mold flux and affect the penetration of liquid slag into the gap between mold and primary billet shell, resulting in insufficient lubrication ability of the mold flux [17–19]. Therefore, Piao et al. reduced the crystallization temperature and critical cooling rate by adding BaO to the mold flux [20]. But, the liquidus temperature of Incoloy825 is 1646 K which is much lower than that of steel (1803 K), so this slag system is not suitable for Incoloy825 continuous casting production.(2)CaO+TiO2=CaTiO3.Aiming at the oxidation loss of Ti and Al in Incoloy825 and the lubrication problem in continuous casting process, a new type of mold flux based on region C in Figure1 of CaO-SiO2-Al2O3-based mold flux was developed in this paper. The main precipitated phases in this region are melilite, CaAl2Si2O8, and CaSiO3, so the activity of Al2O3 and SiO2 is low and the slag-steel interfacial chemical reaction is weak, which can control the oxidation loss of group elements in the steel. At the same time, the content of SiO2 in mold flux is high, which can ensure the lubricating performance of the mold flux.In order to further prevent the oxidation loss of Ti in steel, TiO2 is often added to the mold flux [21–24]. However, when TiO2 is added into the CaO-SiO2-Al2O3 system, CaSiO3 will be transformed into CaTiO3 [25, 26], as shown in Eq. (3), which will result in low effective activity of TiO2 and increased activity of SiO2. In addition, the lower temperature of the continuous casting process will result in the preferential precipitation of CaTiO3, which has a higher melting point, and this will affect the lubricating ability of the casting agent. As a result, the addition of TiO2 does not work as well as it should.(3)CaSiO3+TiO2=CaTiO3+SiO2.This paper innovatively proposes to add Ce2O3 to the mold flux to form Ce2Si2O7 [27] and CeAlO3 [28], which can effectively reduce the activity of Al2O3 and SiO2 and inhibit the chemical reaction at the slag-steel interface. In addition, the melting point of the main compound Ce2Si2O7 (2043 K) [27] is 200 K lower than that of CaTiO3 (2243 K) [26], which ensures the lubrication performance of mold flux. The research results will provide theoretical basis for low activity mold flux and have important theoretical significance for developing Incoloy825 continuous casting mold flux.


## 2. Thermodynamic Calculation of Slag-Steel Reaction

### 2.1. Activity Calculation of Elements in Steel and Components in Slag

As previously described, the equations for slag-steel interfacial chemical reaction of Ti and Al in Incoloy825 with CaO-SiO2-Al2O3-based mold flux are shown in Eq. (4), Eq. (6), and Eq. (8).(4)Ti+SiO2=Si+TiO2.(5)ΔG1θ=−3446.49−26.04T,ΔG1=ΔG1θ+RTlnK1=ΔG1θ+RTlnaSi⋅aTiO2aTi⋅aSiO2=ΔG1θ+RTlnfSi⋅wSi%fTi⋅wTi%+RTlnaTiO2aSiO2,(6)4Al+3SiO2=3Si+2Al2O3(7)ΔG2θ=−686233.57+112.20T,ΔG2=ΔG2θ+RTlnK2=ΔG2θ+RTlnaSi3⋅aAl2O32aAl4⋅aSiO23=ΔG2θ+RTlnfSi3⋅wSi%3fAl4⋅wAl%4+RTlnaAl2O32aSiO23.(8)3Ti+2Al2O3=4Al+3TiO2,(9)ΔG3θ=675894.11−190.32T,ΔG3=ΔG3θ+RTlnK3=ΔG3θ+RTlnaAl4⋅aTiO23aTi3⋅aAl2O32=ΔG3θ+RTlnfAl4⋅wAl%4fTi3⋅wTi%3+RTlnaTiO23aAl2O32,where ΔG is the reaction Gibbs free energy, ΔGθis the standard reaction Gibbs free energy, K is the reaction equilibrium constant, aAl2O3, aSiO2, and aTiO2 are the activities of Al2O3, SiO2, and TiO2 in slag, fAl, fSi, and fTi are the activity coefficients of Al, Si, and Ti in steel, which can be calculated by Eq. (10), respectively, and the activity interaction coefficients are listed in Table 1.(10)lgfi=∑eijw%j.Table 1
Activity interaction coefficienteij of the constituent in the present work.
eijAlCrCuMnMoNiSiTiAl0.040 [29]0.045 [29]0.034 [29]-0.0376 [30]Si0.058 [30]−0.021 [31]−0.009 [32]0.132 [29]Ti0.025 [33]0.014 [33]−0.12 [33]0.016 [33]−0.0166 [33]0.048 [31]According to the composition of Incoloy825 (Table2) and equation (10), the activity coefficients and activity of components in steel can be calculated as, fAl = 0.205, aAl = 0.020, fSi = 0.144, aSi = 0.048, fTi = 0.746, and aTi = 0.753. The calculations show that aTi is much greater than aAl, suggesting that Ti is more susceptible to oxidation than Al.Table 2
Chemical composition of the Incoloy825 (mass percentage).
AlCoCrCuMnMoNiSiTiFe0.0960.4420.621.950.463.141.740.3361.01Bal.In order to better understand the role of Ce2O3 in mold flux, aAl2O3 and aSiO2 of S0∼S4 (Table 3) are calculated according to IMCT [34, 35]. On the basis of IMCT, the mole fraction of each oxide could be assigned as b1=nCaOο, b2=nSiO2ο, b3=nAl2O3ο, b4=nNa2Oο, b5=nMgOο, b6=nCaF2ο, and b7=nCe2O3ο to represent the chemical composition of the slag, and each of niοcould be expressed by (11). The relevant compounds and chemical reactions of the present slag are listed in Tables 4 and 5, respectively. The composition of mold fluxes is shown in Table 3.(11)niο=ni∑ni.Table 3
Chemical composition of slag samples in each experimental heat (mass percentage).
SampleCaOSiO2Al2O3MgONa2OCaF2Ce2O3S0303015510100S1303015510105S23030155101010S33030155101015S43030155101020Table 4
Expression of structural units, their mole numbers, and mass action concentrations in 100 g CaO-SiO2-Al2O3-Na2O-MgO-CaF2-Ce2O3 slags based on IMCT.
ItemStructural units (ion or molecule)Mole number of structural unitsniMass action concentration of structural unitsNiSimple ion (5)Ca2++O2−nS1=nCa2+=nO2−NS1=NCaO=2nS1/∑niNa++O2−nS4=2nNa+=nO2−NS4=NNa2O=3nS4/∑niMg2++O2−nS5=nMg2+=nO2−NS5=NMgO=2nS5/∑niCa2++2F−nS6=nCa2+=2nF−NS6=NCaF2=3nS6/∑ni2Ce2++3O2−nS7=2nCe3+=3nO2−NS7=NCe2O3=5nS7/∑niSimple molecule (2)SiO2nS2=nSiO2NS2=NSiO2=nS2/∑niAl2O3nS3=nAl2O3NS3=NAl2O3=nS3/∑niComplex molecule (40)CaO⋅SiO2nC1=nCaO⋅SiO2NC1=NCaO⋅SiO2=nC1/∑ni2CaO⋅SiO2nC2=n2CaO⋅SiO2NC2=N2CaO⋅SiO2=nC2/∑ni3CaO⋅SiO2nC3=n3CaO⋅SiO2NC3=N3CaO⋅SiO2=nC3/∑ni3CaO⋅2SiO2nC4=n3CaO⋅2SiO2NC4=N3CaO⋅2SiO2=nC4/∑niCaO⋅Al2O3nC5=nCaO⋅Al2O3NC5=NCaO⋅Al2O3=nC5/∑niCaO⋅2Al2O3nC6=nCaO⋅2Al2O3NC6=NCaO⋅2Al2O3=nC6/∑niCaO⋅6Al2O3nC7=nCaO⋅6Al2O3NC7=NCaO⋅6Al2O3=nC7/∑ni3CaO⋅Al2O3nC8=n3CaO⋅Al2O3NC8=N3CaO⋅Al2O3=nC8/∑ni12CaO⋅7Al2O3nC9=n12CaO⋅7Al2O3NC9=N12CaO⋅7Al2O3=nC9/∑ni3Al2O3⋅2SiO2nC10=n3Al2O3⋅2SiO2NC10=N3Al2O3⋅2SiO2=nC10/∑niNa2O⋅SiO2nC11=nNa2O⋅SiO2NC11=NNa2O⋅SiO2=nC11/∑niNa2O⋅2SiO2nC12=nNa2O⋅2SiO2NC12=NNa2O⋅2SiO2=nC12/∑ni2Na2O⋅SiO2nC13=n2Na2O⋅SiO2NC13=N2Na2O⋅SiO2=nC13/∑niMgO⋅SiO2nC14=nMgO⋅SiO2NC14=NMgO⋅SiO2=nC14/∑ni2MgO⋅SiO2nC15=n2MgO⋅SiO2NC15=N2MgO⋅SiO2=nC15/∑niNa2O⋅Al2O3nC16=nNa2O⋅Al2O3NC16=NNa2O⋅Al2O3=nC16/∑niNa2O⋅3Al2O3nC17=nNa2O⋅3Al2O3NC17=NNa2O⋅3Al2O3=nC17/∑niNa2O⋅9Al2O3nC18=nNa2O⋅9Al2O3NC18=NNa2O⋅9Al2O3=nC18/∑niMgO⋅Al2O3nC19=nMgO⋅Al2O3NC19=NMgO⋅Al2O3=nC19/∑niCe2O3⋅Al2O3nC20=nCe2O3⋅Al2O3NC20=NCe2O3⋅Al2O3=nC20/∑niCe2O3⋅11Al2O3nC21=nCe2O3⋅11Al2O3NC21=NCe2O3⋅11Al2O3=nC21/∑niCaO⋅Al2O3⋅2SiO2nC22=nCaO⋅Al2O3⋅2SiO2NC22=NCaO⋅Al2O3⋅2SiO2=nC22/∑ni2CaO⋅Al2O3⋅2SiO2nC23=n2CaO⋅Al2O3⋅SiO2NC23=N2CaO⋅Al2O3⋅SiO2=nC23/∑ni2Na2O⋅CaO⋅3SiO2nC24=n2Na2O⋅CaO⋅3SiO2NC24=N2Na2O⋅CaO⋅3SiO2=nC24/∑niNa2O⋅CaO⋅5SiO2nC25=nNa2O⋅CaO⋅5SiO2NC25=NNa2O⋅CaO⋅5SiO2=nC25/∑niNa2O⋅2CaO⋅3SiO2nC26=nNa2O⋅2CaO⋅3SiO2NC26=NNa2O⋅2CaO⋅3SiO2=nC26/∑niNa2O⋅3CaO⋅6SiO2nC27=nNa2O⋅3CaO⋅6SiO2NC27=NNa2O⋅3CaO⋅6SiO2=nC27/∑niCaO⋅MgO⋅SiO2nC28=nCaO⋅MgO⋅SiO2NC28=NCaO⋅MgO⋅SiO2=nC28/∑niCaO⋅MgO⋅2SiO2nC29=nCaO⋅MgO⋅2SiO2NC29=NCaO⋅MgO⋅2SiO2=nC29/∑ni2CaO⋅MgO⋅2SiO2nC30=n2CaO⋅MgO⋅2SiO2NC30=N2CaO⋅MgO⋅2SiO2=nC30/∑ni3CaO⋅MgO⋅2SiO2nC31=n3CaO⋅MgO⋅2SiO2NC31=N3CaO⋅MgO⋅2SiO2=nC31/∑ni3CaO⋅2SiO2⋅CaF2nC32=n3CaO⋅2SiO2⋅CaF2NC32=N3CaO⋅2SiO2⋅CaF2=nC32/∑ni3CaO⋅3Al2O3⋅CaF2nC33=n3CaO⋅2Al2O3⋅CaF2NC33=N3CaO⋅2Al2O3⋅CaF2=nC33/∑ni11CaO⋅7Al2O3⋅CaF2nC34=n11CaO⋅7Al2O3⋅CaF2NC34=N11CaO⋅7Al2O3⋅CaF2=nC34/∑niNa2O⋅Al2O3⋅2SiO2nC35=nNa2O⋅Al2O3⋅2SiO2NC35=NNa2O⋅Al2O3⋅2SiO2=nC35/∑niNa2O⋅Al2O3⋅4SiO2nC36=nNa2O⋅Al2O3⋅4SiO2NC36=NNa2O⋅Al2O3⋅4SiO2=nC36/∑niNa2O⋅Al2O3⋅6SiO2nC37=nNa2O⋅Al2O3⋅6SiO2NC37=NNa2O⋅Al2O3⋅6SiO2=nC37/∑ni2MgO⋅2Al2O3⋅SiO2nC38=n2MgO⋅2Al2O3⋅SiO2NC38=N2MgO⋅2Al2O3⋅SiO2=nC38/∑niNa2O⋅MgO⋅4SiO2nC39=nNa2O⋅MgO⋅4SiO2NC39=NNa2O⋅MgO⋅4SiO2=nC39/∑niNa2O⋅2MgO⋅6SiO2nC40=nNa2O⋅2MgO⋅6SiO2NC40=NNa2O⋅2MgO⋅6SiO2=nC40/∑niTable 5
Chemical reaction formulas of possibly formed complex molecules.
ReactionΔGiθ (J/mol)ReferenceNiCa2++O2−+SiO2=CaO⋅SiO2−21757−36.82T34NC1=KC1N1N22Ca2++O2−+SiO2=2CaO⋅SiO2−102090−24.27T34NC2=KC2N12N23Ca2++O2−+SiO2=3CaO⋅SiO2−118826−6.69T35NC3=KC3N13N23Ca2++O2−+2SiO2=3CaO⋅2SiO2−236814+9.62T35NC4=KC4N13N22Ca2++O2−+Al2O3=CaO⋅Al2O359413−59.41T34NC5=KC5N1N3Ca2++O2−+2Al2O3=CaO⋅2Al2O3−16700−25.52T34NC6=KC6N1N32Ca2++O2−+6Al2O3=CaO⋅6Al2O3−22594−31.80T34NC7=KC7N1N363Ca2++O2−+Al2O3=3CaO⋅Al2O3−21757−29.29T34NC8=KC8N13N312Ca2++O2−+7Al2O3=12CaO⋅7Al2O3617977−612.12T34NC9=KC9N112N373Al2O3+2SiO2=3Al2O3⋅2SiO2−4354−10.47T34NC10=KC10N22N332Na++O2−+SiO2=Na2O⋅SiO2−299349+55.32T36NC11=KC11N2N42Na++O2−+2SiO2=Na2O⋅2SiO2−279094+23.19T36NC12=KC12N22N422Na++O2−+SiO2=2Na2O⋅SiO2−517220+124.22T36NC13=KC13N2N42Mg2++O2−+SiO2=MgO⋅SiO223849−29.71T34NC14=KC14N2N52Mg2++O2−+SiO2=2MgO⋅SiO2−56902−3.35T34NC15=KC15N2N522Na++O2−+Al2O3=Na2O⋅Al2O3−247971+44.6T36NC16=KC16N3N42Na++O2−+3Al2O3=Na2O⋅3Al2O3−282626+35.28T36NC17=KC17N33N42Na++O2−+9Al2O3=Na2O⋅9Al2O3−295918+25.18T36NC18=KC18N39N4Mg2++O2−+Al2O3=MgO⋅Al2O3−18828−6.28T34NC19=KC19N3N52Ce3++3O2−+Al2O3=Ce2O3⋅Al2O3−60241−14.19T37NC20=KC20N3N72Ce3++3O2−+11Al2O3=Ce2O3⋅11Al2O349332−80.56T37NC21=KC21N311N7Ca2++O2−+Al2O3+2SiO2=CaO⋅Al2O3⋅2SiO2−13816−55.26T36NC22=KC22N1N22N32Ca2++O2−+Al2O3+SiO2=2CaO⋅Al2O3⋅SiO2−61961−60.29T36NC23=KC23N12N2N322Na++O2−+Ca2++O2−+3SiO2=Na2O⋅CaO⋅3SiO2−672020 + 62.8T36NC24=KC24N1N23N422Na++O2−+Ca2++O2−+5SiO2=Na2O⋅CaO⋅5SiO2−443841+63.84T36NC25=KC25N1N25N42Na++O2−+2Ca2++O2−+3SiO2=Na2O⋅2CaO⋅3SiO2−607293+125.68T36NC26=KC26N12N23N42Na++O2−+3Ca2++O2−+6SiO2=Na2O⋅3CaO⋅6SiO2−837543+219.7T36NC27=KC27N13N26N4Ca2++O2−+Mg2++O2−+SiO2=CaO⋅MgO⋅SiO2−124683+0.77T35NC28 = KC28N1N2N5Ca2++O2−+Mg2++O2−+2SiO2=CaO⋅MgO⋅2SiO2−80−51.88T34NC29=KC29N1N22N52Ca2++O2−+Mg2++O2−+2SiO2=2CaO⋅MgO⋅2SiO2−73638−63.29T34NC30=KC30N12N22N53Ca2++O2−+Mg2++O2−+2SiO2=3CaO⋅MgO⋅2SiO2−205016−31.80T34NC31=KC31N13N22N53Ca2++O2−+2SiO2+Ca2++2F−=3CaO⋅2SiO2⋅CaF2−255180−8.2T34NC32=KC32N13N22N63Ca2++O2−+3Al2O3+Ca2++2F−=3CaO⋅3Al2O3⋅CaF2−44492−73.15T38NC33=KC33N13N33N611Ca2++O2−+7Al2O3+Ca2++2F−=11CaO⋅7Al2O3⋅CaF2−228760−155.8T38NC34=KC34N111N37N62Na++O2−+Al2O3+2SiO2=Na2O⋅Al2O3⋅2SiO2−370572.02+9.98T36NC35=KC35N22N3N42Na++O2−+Al2O3+4SiO2=Na2O⋅Al2O3⋅4SiO2−440860+101.36T36NC36=KC36N24N3N42Na++O2−+Al2O3+6SiO2=Na2O⋅Al2O3⋅6SiO2−425604+19.38T36NC37=KC37N26N3N42Mg2++O2−+2Al2O3+5SiO2=2MgO⋅2Al2O3⋅5SiO2−14422−14.81T34NC38=KC38N25N32N522Na++O2−+Mg2++O2−+4SiO2=Na2O⋅MgO⋅4SiO2−306210−1.2T36NC39=KC39N24N4N52Na++O2−+2Mg2++O2−+6SiO2=Na2O⋅2MgO⋅6SiO2−312061−33.06T36NC40=KC40N26N4N52According to the description of IMCT, the formulas for calculating the activity of (12) components are established as follows:(12)NS1+NS2+...+NC40=∑Ni=1,b1=1/2NS1+NC1+2NC2+3NC3+NC5+NC6+NC7+3NC8+12NC9+NC22+2NC23+NC24+NC25+NC26+3NC27+NC28+NC29+2NC30+3NC31+3NC32+3NC33+11NC34∑ni,b2=NS2+NC1+NC2+NC3+2NC4+2NC10+NC11+2NC12+NC13+NC14+NC15+2NC22+2NC23+3NC24+5NC25+3NC26+6NC27+NC28+2NC29+2NC30+2NC31+2NC32+2NC35+4NC36+6NC37+5NC38+2NC39+6NC40∑ni,b3=NS3+NC5+2NC6+6NC7+NC8+7NC9+3NC10+NC16+3NC17+9NC18+NC19+NC20+11NC21+NC22+NC23+2NC24+3NC33+7NC34+NC35+NC36+NC37+2NC38∑ni,b4=13NS4+NC11+NC12+NC13+NC16+NC17+NC18+NC25+NC26+NC27+NC35+NC36+NC37+2NC38+NC39+6NC40∑ni,b5=12NS5+NC14+NC15+NC19+NC28+NC29+NC30+NC31+NC39+2NC40∑ni,b6=13NS6+NC32+NC33+NC34∑ni,b7=17NS7+NC20+NC21∑ni.The system of nonlinear equations from (12) is solved using MATLAB software, which allows the solution of NS1 to NS7, that is, solving for the concentration of the action of each group element.The addition of Ce2O3 to the mold flux has an important effect on aAl2O3 and aSiO2 as shown in Figure 2. With the increase of Ce2O3 content in mold flux, aAl2O3 decreases significantly and aSiO2 decreases and gradually tends to 0, indicating that the reactivity of both Al2O3 and SiO2 in the mold flux is weakened.Figure 2
Influence of (w) (Ce2O3) on the activity of Al2O3 and SiO2.This is because Ce2O3 is able to form compounds such as CeAlO3 and Ce2Si2O7 with Al2O3 and SiO2, respectively [27, 28], reducing the activity of Al2O3 and SiO2. In addition, when the content of Ce2O3 in the mold flux is 20%, aSiO2 approaches 0.


### 2.2. Thermodynamic Analysis of Slag-Steel Reaction

In order to investigate the effect of adding Ce2O3 to mold flux on the slag-steel interfacial chemical reaction, aCe2O3, aAl2O3, and aSiO2are calculated by IMCT and fAl, fSi, and fTi in steel were brought into Eq. (6), Eq. (9), and (2) to obtain the reaction Gibbs free energy of Eq. (4), Eq. (6), and Eq. (8). The composition of steel and mold fluxes is shown in Tables 2 and 3, respectively, and the calculation results are shown in Figure 3.Figure 3
Gibbs free energy of the slag-steel interface chemical reaction with different Ce2O3 contents.As shown in Figure3, Ce2O3 component is added to the mold flux, and ΔG1 is the minimum compared with ΔG2 and ΔG3. Therefore, the main slag-steel interfacial chemical reaction is [Ti] + (SiO2) = [Si] + (TiO2), and the secondary reactions are the following: 4[Al] + 3(SiO2) = 3[Si] + 2(Al2O3) and 3[Ti] + 2(Al2O3) = 4[Al] + 3(TiO2). The reason is that aTi is much greater than aAl, so Ti in steel is more susceptible to oxidation. With the increase of Ce2O3 content in mold flux, ΔG1, ΔG2, and ΔG3 gradually increase, of which ΔG1 increases the most. This is because Ce2O3 in the mold flux is combined with Al2O3 and SiO2, which reduces the activities of Al2O3 and SiO2 and weakens the slag-steel interfacial chemical reaction and inhibits the oxidation loss of Ti and Al in steel.It can be seen from Figure3 that CaO-SiO2-Al2O3-based slag system will inevitably cause the oxidation of Al and Ti in steel, and the TiO2 generated into the mold flux will lead to a change in the trend of each reaction. In order to better understand the trend of each reaction at the slag-steel interface, the influence of different TiO2 contents on the slag-steel interfacial chemical reaction was calculated, where the calculation results of S0 slag system are shown in Figure 4.Figure 4
Gibbs free energy of the slag-steel interface chemical reaction with different TiO2 contents for S0.As shown in Figure4, when w(TiO2) is less than 0.5%, ΔG1 and ΔG3 increase rapidly, and when w(TiO2) is more than 0.5%, ΔG1 and ΔG3 increase slowly and gradually tend to equilibrium. This is due to the fact that TiO2 generated by slag-steel interfacial chemical reaction causes a significant increase in the activity of TiO2 and the interfacial chemical reactions of Eq. (4) and Eq. (8) are inhibited. However, there is no TiO2 in the interfacial chemical reaction of Eq. (6), but with the increase of TiO2 content in the mold flux, the mass percentage of Al2O3 and SiO2 in the mold flux is changed, which makes Eq. (9) change to some extent, so ∆G2 decreases slightly. When w(TiO2) is 3%, at this time ΔG3 is 0, the reaction Eq. (10) reaches an equilibrium state, and ΔG1 and ΔG2 are close. The slag-steel interfacial chemical reactions are the following: [Ti] + (SiO2) = [Si] + (TiO2) and 4 [Al] + 3 (SiO2) = 3 [Si] + 2 (Al2O3). However, when more TiO2 components are added to the protective slag, TiO2 will combine with CaO to form CaTiO3. On the one hand, the actual activity of TiO2 in the mold flux is small; on the other hand, the binding ability of CaO with Al2O3 and SiO2 is reduced, which makes the activity of Al2O3 and SiO2 increase, which is not conducive to reducing the oxidation of Al and Ti in steel.


## 2.1. Activity Calculation of Elements in Steel and Components in Slag

As previously described, the equations for slag-steel interfacial chemical reaction of Ti and Al in Incoloy825 with CaO-SiO2-Al2O3-based mold flux are shown in Eq. (4), Eq. (6), and Eq. (8).(4)Ti+SiO2=Si+TiO2.(5)ΔG1θ=−3446.49−26.04T,ΔG1=ΔG1θ+RTlnK1=ΔG1θ+RTlnaSi⋅aTiO2aTi⋅aSiO2=ΔG1θ+RTlnfSi⋅wSi%fTi⋅wTi%+RTlnaTiO2aSiO2,(6)4Al+3SiO2=3Si+2Al2O3(7)ΔG2θ=−686233.57+112.20T,ΔG2=ΔG2θ+RTlnK2=ΔG2θ+RTlnaSi3⋅aAl2O32aAl4⋅aSiO23=ΔG2θ+RTlnfSi3⋅wSi%3fAl4⋅wAl%4+RTlnaAl2O32aSiO23.(8)3Ti+2Al2O3=4Al+3TiO2,(9)ΔG3θ=675894.11−190.32T,ΔG3=ΔG3θ+RTlnK3=ΔG3θ+RTlnaAl4⋅aTiO23aTi3⋅aAl2O32=ΔG3θ+RTlnfAl4⋅wAl%4fTi3⋅wTi%3+RTlnaTiO23aAl2O32,where ΔG is the reaction Gibbs free energy, ΔGθis the standard reaction Gibbs free energy, K is the reaction equilibrium constant, aAl2O3, aSiO2, and aTiO2 are the activities of Al2O3, SiO2, and TiO2 in slag, fAl, fSi, and fTi are the activity coefficients of Al, Si, and Ti in steel, which can be calculated by Eq. (10), respectively, and the activity interaction coefficients are listed in Table 1.(10)lgfi=∑eijw%j.Table 1
Activity interaction coefficienteij of the constituent in the present work.
eijAlCrCuMnMoNiSiTiAl0.040 [29]0.045 [29]0.034 [29]-0.0376 [30]Si0.058 [30]−0.021 [31]−0.009 [32]0.132 [29]Ti0.025 [33]0.014 [33]−0.12 [33]0.016 [33]−0.0166 [33]0.048 [31]According to the composition of Incoloy825 (Table2) and equation (10), the activity coefficients and activity of components in steel can be calculated as, fAl = 0.205, aAl = 0.020, fSi = 0.144, aSi = 0.048, fTi = 0.746, and aTi = 0.753. The calculations show that aTi is much greater than aAl, suggesting that Ti is more susceptible to oxidation than Al.Table 2
Chemical composition of the Incoloy825 (mass percentage).
AlCoCrCuMnMoNiSiTiFe0.0960.4420.621.950.463.141.740.3361.01Bal.In order to better understand the role of Ce2O3 in mold flux, aAl2O3 and aSiO2 of S0∼S4 (Table 3) are calculated according to IMCT [34, 35]. On the basis of IMCT, the mole fraction of each oxide could be assigned as b1=nCaOο, b2=nSiO2ο, b3=nAl2O3ο, b4=nNa2Oο, b5=nMgOο, b6=nCaF2ο, and b7=nCe2O3ο to represent the chemical composition of the slag, and each of niοcould be expressed by (11). The relevant compounds and chemical reactions of the present slag are listed in Tables 4 and 5, respectively. The composition of mold fluxes is shown in Table 3.(11)niο=ni∑ni.Table 3
Chemical composition of slag samples in each experimental heat (mass percentage).
SampleCaOSiO2Al2O3MgONa2OCaF2Ce2O3S0303015510100S1303015510105S23030155101010S33030155101015S43030155101020Table 4
Expression of structural units, their mole numbers, and mass action concentrations in 100 g CaO-SiO2-Al2O3-Na2O-MgO-CaF2-Ce2O3 slags based on IMCT.
ItemStructural units (ion or molecule)Mole number of structural unitsniMass action concentration of structural unitsNiSimple ion (5)Ca2++O2−nS1=nCa2+=nO2−NS1=NCaO=2nS1/∑niNa++O2−nS4=2nNa+=nO2−NS4=NNa2O=3nS4/∑niMg2++O2−nS5=nMg2+=nO2−NS5=NMgO=2nS5/∑niCa2++2F−nS6=nCa2+=2nF−NS6=NCaF2=3nS6/∑ni2Ce2++3O2−nS7=2nCe3+=3nO2−NS7=NCe2O3=5nS7/∑niSimple molecule (2)SiO2nS2=nSiO2NS2=NSiO2=nS2/∑niAl2O3nS3=nAl2O3NS3=NAl2O3=nS3/∑niComplex molecule (40)CaO⋅SiO2nC1=nCaO⋅SiO2NC1=NCaO⋅SiO2=nC1/∑ni2CaO⋅SiO2nC2=n2CaO⋅SiO2NC2=N2CaO⋅SiO2=nC2/∑ni3CaO⋅SiO2nC3=n3CaO⋅SiO2NC3=N3CaO⋅SiO2=nC3/∑ni3CaO⋅2SiO2nC4=n3CaO⋅2SiO2NC4=N3CaO⋅2SiO2=nC4/∑niCaO⋅Al2O3nC5=nCaO⋅Al2O3NC5=NCaO⋅Al2O3=nC5/∑niCaO⋅2Al2O3nC6=nCaO⋅2Al2O3NC6=NCaO⋅2Al2O3=nC6/∑niCaO⋅6Al2O3nC7=nCaO⋅6Al2O3NC7=NCaO⋅6Al2O3=nC7/∑ni3CaO⋅Al2O3nC8=n3CaO⋅Al2O3NC8=N3CaO⋅Al2O3=nC8/∑ni12CaO⋅7Al2O3nC9=n12CaO⋅7Al2O3NC9=N12CaO⋅7Al2O3=nC9/∑ni3Al2O3⋅2SiO2nC10=n3Al2O3⋅2SiO2NC10=N3Al2O3⋅2SiO2=nC10/∑niNa2O⋅SiO2nC11=nNa2O⋅SiO2NC11=NNa2O⋅SiO2=nC11/∑niNa2O⋅2SiO2nC12=nNa2O⋅2SiO2NC12=NNa2O⋅2SiO2=nC12/∑ni2Na2O⋅SiO2nC13=n2Na2O⋅SiO2NC13=N2Na2O⋅SiO2=nC13/∑niMgO⋅SiO2nC14=nMgO⋅SiO2NC14=NMgO⋅SiO2=nC14/∑ni2MgO⋅SiO2nC15=n2MgO⋅SiO2NC15=N2MgO⋅SiO2=nC15/∑niNa2O⋅Al2O3nC16=nNa2O⋅Al2O3NC16=NNa2O⋅Al2O3=nC16/∑niNa2O⋅3Al2O3nC17=nNa2O⋅3Al2O3NC17=NNa2O⋅3Al2O3=nC17/∑niNa2O⋅9Al2O3nC18=nNa2O⋅9Al2O3NC18=NNa2O⋅9Al2O3=nC18/∑niMgO⋅Al2O3nC19=nMgO⋅Al2O3NC19=NMgO⋅Al2O3=nC19/∑niCe2O3⋅Al2O3nC20=nCe2O3⋅Al2O3NC20=NCe2O3⋅Al2O3=nC20/∑niCe2O3⋅11Al2O3nC21=nCe2O3⋅11Al2O3NC21=NCe2O3⋅11Al2O3=nC21/∑niCaO⋅Al2O3⋅2SiO2nC22=nCaO⋅Al2O3⋅2SiO2NC22=NCaO⋅Al2O3⋅2SiO2=nC22/∑ni2CaO⋅Al2O3⋅2SiO2nC23=n2CaO⋅Al2O3⋅SiO2NC23=N2CaO⋅Al2O3⋅SiO2=nC23/∑ni2Na2O⋅CaO⋅3SiO2nC24=n2Na2O⋅CaO⋅3SiO2NC24=N2Na2O⋅CaO⋅3SiO2=nC24/∑niNa2O⋅CaO⋅5SiO2nC25=nNa2O⋅CaO⋅5SiO2NC25=NNa2O⋅CaO⋅5SiO2=nC25/∑niNa2O⋅2CaO⋅3SiO2nC26=nNa2O⋅2CaO⋅3SiO2NC26=NNa2O⋅2CaO⋅3SiO2=nC26/∑niNa2O⋅3CaO⋅6SiO2nC27=nNa2O⋅3CaO⋅6SiO2NC27=NNa2O⋅3CaO⋅6SiO2=nC27/∑niCaO⋅MgO⋅SiO2nC28=nCaO⋅MgO⋅SiO2NC28=NCaO⋅MgO⋅SiO2=nC28/∑niCaO⋅MgO⋅2SiO2nC29=nCaO⋅MgO⋅2SiO2NC29=NCaO⋅MgO⋅2SiO2=nC29/∑ni2CaO⋅MgO⋅2SiO2nC30=n2CaO⋅MgO⋅2SiO2NC30=N2CaO⋅MgO⋅2SiO2=nC30/∑ni3CaO⋅MgO⋅2SiO2nC31=n3CaO⋅MgO⋅2SiO2NC31=N3CaO⋅MgO⋅2SiO2=nC31/∑ni3CaO⋅2SiO2⋅CaF2nC32=n3CaO⋅2SiO2⋅CaF2NC32=N3CaO⋅2SiO2⋅CaF2=nC32/∑ni3CaO⋅3Al2O3⋅CaF2nC33=n3CaO⋅2Al2O3⋅CaF2NC33=N3CaO⋅2Al2O3⋅CaF2=nC33/∑ni11CaO⋅7Al2O3⋅CaF2nC34=n11CaO⋅7Al2O3⋅CaF2NC34=N11CaO⋅7Al2O3⋅CaF2=nC34/∑niNa2O⋅Al2O3⋅2SiO2nC35=nNa2O⋅Al2O3⋅2SiO2NC35=NNa2O⋅Al2O3⋅2SiO2=nC35/∑niNa2O⋅Al2O3⋅4SiO2nC36=nNa2O⋅Al2O3⋅4SiO2NC36=NNa2O⋅Al2O3⋅4SiO2=nC36/∑niNa2O⋅Al2O3⋅6SiO2nC37=nNa2O⋅Al2O3⋅6SiO2NC37=NNa2O⋅Al2O3⋅6SiO2=nC37/∑ni2MgO⋅2Al2O3⋅SiO2nC38=n2MgO⋅2Al2O3⋅SiO2NC38=N2MgO⋅2Al2O3⋅SiO2=nC38/∑niNa2O⋅MgO⋅4SiO2nC39=nNa2O⋅MgO⋅4SiO2NC39=NNa2O⋅MgO⋅4SiO2=nC39/∑niNa2O⋅2MgO⋅6SiO2nC40=nNa2O⋅2MgO⋅6SiO2NC40=NNa2O⋅2MgO⋅6SiO2=nC40/∑niTable 5
Chemical reaction formulas of possibly formed complex molecules.
ReactionΔGiθ (J/mol)ReferenceNiCa2++O2−+SiO2=CaO⋅SiO2−21757−36.82T34NC1=KC1N1N22Ca2++O2−+SiO2=2CaO⋅SiO2−102090−24.27T34NC2=KC2N12N23Ca2++O2−+SiO2=3CaO⋅SiO2−118826−6.69T35NC3=KC3N13N23Ca2++O2−+2SiO2=3CaO⋅2SiO2−236814+9.62T35NC4=KC4N13N22Ca2++O2−+Al2O3=CaO⋅Al2O359413−59.41T34NC5=KC5N1N3Ca2++O2−+2Al2O3=CaO⋅2Al2O3−16700−25.52T34NC6=KC6N1N32Ca2++O2−+6Al2O3=CaO⋅6Al2O3−22594−31.80T34NC7=KC7N1N363Ca2++O2−+Al2O3=3CaO⋅Al2O3−21757−29.29T34NC8=KC8N13N312Ca2++O2−+7Al2O3=12CaO⋅7Al2O3617977−612.12T34NC9=KC9N112N373Al2O3+2SiO2=3Al2O3⋅2SiO2−4354−10.47T34NC10=KC10N22N332Na++O2−+SiO2=Na2O⋅SiO2−299349+55.32T36NC11=KC11N2N42Na++O2−+2SiO2=Na2O⋅2SiO2−279094+23.19T36NC12=KC12N22N422Na++O2−+SiO2=2Na2O⋅SiO2−517220+124.22T36NC13=KC13N2N42Mg2++O2−+SiO2=MgO⋅SiO223849−29.71T34NC14=KC14N2N52Mg2++O2−+SiO2=2MgO⋅SiO2−56902−3.35T34NC15=KC15N2N522Na++O2−+Al2O3=Na2O⋅Al2O3−247971+44.6T36NC16=KC16N3N42Na++O2−+3Al2O3=Na2O⋅3Al2O3−282626+35.28T36NC17=KC17N33N42Na++O2−+9Al2O3=Na2O⋅9Al2O3−295918+25.18T36NC18=KC18N39N4Mg2++O2−+Al2O3=MgO⋅Al2O3−18828−6.28T34NC19=KC19N3N52Ce3++3O2−+Al2O3=Ce2O3⋅Al2O3−60241−14.19T37NC20=KC20N3N72Ce3++3O2−+11Al2O3=Ce2O3⋅11Al2O349332−80.56T37NC21=KC21N311N7Ca2++O2−+Al2O3+2SiO2=CaO⋅Al2O3⋅2SiO2−13816−55.26T36NC22=KC22N1N22N32Ca2++O2−+Al2O3+SiO2=2CaO⋅Al2O3⋅SiO2−61961−60.29T36NC23=KC23N12N2N322Na++O2−+Ca2++O2−+3SiO2=Na2O⋅CaO⋅3SiO2−672020 + 62.8T36NC24=KC24N1N23N422Na++O2−+Ca2++O2−+5SiO2=Na2O⋅CaO⋅5SiO2−443841+63.84T36NC25=KC25N1N25N42Na++O2−+2Ca2++O2−+3SiO2=Na2O⋅2CaO⋅3SiO2−607293+125.68T36NC26=KC26N12N23N42Na++O2−+3Ca2++O2−+6SiO2=Na2O⋅3CaO⋅6SiO2−837543+219.7T36NC27=KC27N13N26N4Ca2++O2−+Mg2++O2−+SiO2=CaO⋅MgO⋅SiO2−124683+0.77T35NC28 = KC28N1N2N5Ca2++O2−+Mg2++O2−+2SiO2=CaO⋅MgO⋅2SiO2−80−51.88T34NC29=KC29N1N22N52Ca2++O2−+Mg2++O2−+2SiO2=2CaO⋅MgO⋅2SiO2−73638−63.29T34NC30=KC30N12N22N53Ca2++O2−+Mg2++O2−+2SiO2=3CaO⋅MgO⋅2SiO2−205016−31.80T34NC31=KC31N13N22N53Ca2++O2−+2SiO2+Ca2++2F−=3CaO⋅2SiO2⋅CaF2−255180−8.2T34NC32=KC32N13N22N63Ca2++O2−+3Al2O3+Ca2++2F−=3CaO⋅3Al2O3⋅CaF2−44492−73.15T38NC33=KC33N13N33N611Ca2++O2−+7Al2O3+Ca2++2F−=11CaO⋅7Al2O3⋅CaF2−228760−155.8T38NC34=KC34N111N37N62Na++O2−+Al2O3+2SiO2=Na2O⋅Al2O3⋅2SiO2−370572.02+9.98T36NC35=KC35N22N3N42Na++O2−+Al2O3+4SiO2=Na2O⋅Al2O3⋅4SiO2−440860+101.36T36NC36=KC36N24N3N42Na++O2−+Al2O3+6SiO2=Na2O⋅Al2O3⋅6SiO2−425604+19.38T36NC37=KC37N26N3N42Mg2++O2−+2Al2O3+5SiO2=2MgO⋅2Al2O3⋅5SiO2−14422−14.81T34NC38=KC38N25N32N522Na++O2−+Mg2++O2−+4SiO2=Na2O⋅MgO⋅4SiO2−306210−1.2T36NC39=KC39N24N4N52Na++O2−+2Mg2++O2−+6SiO2=Na2O⋅2MgO⋅6SiO2−312061−33.06T36NC40=KC40N26N4N52According to the description of IMCT, the formulas for calculating the activity of (12) components are established as follows:(12)NS1+NS2+...+NC40=∑Ni=1,b1=1/2NS1+NC1+2NC2+3NC3+NC5+NC6+NC7+3NC8+12NC9+NC22+2NC23+NC24+NC25+NC26+3NC27+NC28+NC29+2NC30+3NC31+3NC32+3NC33+11NC34∑ni,b2=NS2+NC1+NC2+NC3+2NC4+2NC10+NC11+2NC12+NC13+NC14+NC15+2NC22+2NC23+3NC24+5NC25+3NC26+6NC27+NC28+2NC29+2NC30+2NC31+2NC32+2NC35+4NC36+6NC37+5NC38+2NC39+6NC40∑ni,b3=NS3+NC5+2NC6+6NC7+NC8+7NC9+3NC10+NC16+3NC17+9NC18+NC19+NC20+11NC21+NC22+NC23+2NC24+3NC33+7NC34+NC35+NC36+NC37+2NC38∑ni,b4=13NS4+NC11+NC12+NC13+NC16+NC17+NC18+NC25+NC26+NC27+NC35+NC36+NC37+2NC38+NC39+6NC40∑ni,b5=12NS5+NC14+NC15+NC19+NC28+NC29+NC30+NC31+NC39+2NC40∑ni,b6=13NS6+NC32+NC33+NC34∑ni,b7=17NS7+NC20+NC21∑ni.The system of nonlinear equations from (12) is solved using MATLAB software, which allows the solution of NS1 to NS7, that is, solving for the concentration of the action of each group element.The addition of Ce2O3 to the mold flux has an important effect on aAl2O3 and aSiO2 as shown in Figure 2. With the increase of Ce2O3 content in mold flux, aAl2O3 decreases significantly and aSiO2 decreases and gradually tends to 0, indicating that the reactivity of both Al2O3 and SiO2 in the mold flux is weakened.Figure 2
Influence of (w) (Ce2O3) on the activity of Al2O3 and SiO2.This is because Ce2O3 is able to form compounds such as CeAlO3 and Ce2Si2O7 with Al2O3 and SiO2, respectively [27, 28], reducing the activity of Al2O3 and SiO2. In addition, when the content of Ce2O3 in the mold flux is 20%, aSiO2 approaches 0.


## 2.2. Thermodynamic Analysis of Slag-Steel Reaction

In order to investigate the effect of adding Ce2O3 to mold flux on the slag-steel interfacial chemical reaction, aCe2O3, aAl2O3, and aSiO2are calculated by IMCT and fAl, fSi, and fTi in steel were brought into Eq. (6), Eq. (9), and (2) to obtain the reaction Gibbs free energy of Eq. (4), Eq. (6), and Eq. (8). The composition of steel and mold fluxes is shown in Tables 2 and 3, respectively, and the calculation results are shown in Figure 3.Figure 3
Gibbs free energy of the slag-steel interface chemical reaction with different Ce2O3 contents.As shown in Figure3, Ce2O3 component is added to the mold flux, and ΔG1 is the minimum compared with ΔG2 and ΔG3. Therefore, the main slag-steel interfacial chemical reaction is [Ti] + (SiO2) = [Si] + (TiO2), and the secondary reactions are the following: 4[Al] + 3(SiO2) = 3[Si] + 2(Al2O3) and 3[Ti] + 2(Al2O3) = 4[Al] + 3(TiO2). The reason is that aTi is much greater than aAl, so Ti in steel is more susceptible to oxidation. With the increase of Ce2O3 content in mold flux, ΔG1, ΔG2, and ΔG3 gradually increase, of which ΔG1 increases the most. This is because Ce2O3 in the mold flux is combined with Al2O3 and SiO2, which reduces the activities of Al2O3 and SiO2 and weakens the slag-steel interfacial chemical reaction and inhibits the oxidation loss of Ti and Al in steel.It can be seen from Figure3 that CaO-SiO2-Al2O3-based slag system will inevitably cause the oxidation of Al and Ti in steel, and the TiO2 generated into the mold flux will lead to a change in the trend of each reaction. In order to better understand the trend of each reaction at the slag-steel interface, the influence of different TiO2 contents on the slag-steel interfacial chemical reaction was calculated, where the calculation results of S0 slag system are shown in Figure 4.Figure 4
Gibbs free energy of the slag-steel interface chemical reaction with different TiO2 contents for S0.As shown in Figure4, when w(TiO2) is less than 0.5%, ΔG1 and ΔG3 increase rapidly, and when w(TiO2) is more than 0.5%, ΔG1 and ΔG3 increase slowly and gradually tend to equilibrium. This is due to the fact that TiO2 generated by slag-steel interfacial chemical reaction causes a significant increase in the activity of TiO2 and the interfacial chemical reactions of Eq. (4) and Eq. (8) are inhibited. However, there is no TiO2 in the interfacial chemical reaction of Eq. (6), but with the increase of TiO2 content in the mold flux, the mass percentage of Al2O3 and SiO2 in the mold flux is changed, which makes Eq. (9) change to some extent, so ∆G2 decreases slightly. When w(TiO2) is 3%, at this time ΔG3 is 0, the reaction Eq. (10) reaches an equilibrium state, and ΔG1 and ΔG2 are close. The slag-steel interfacial chemical reactions are the following: [Ti] + (SiO2) = [Si] + (TiO2) and 4 [Al] + 3 (SiO2) = 3 [Si] + 2 (Al2O3). However, when more TiO2 components are added to the protective slag, TiO2 will combine with CaO to form CaTiO3. On the one hand, the actual activity of TiO2 in the mold flux is small; on the other hand, the binding ability of CaO with Al2O3 and SiO2 is reduced, which makes the activity of Al2O3 and SiO2 increase, which is not conducive to reducing the oxidation of Al and Ti in steel.


## 3. Experiment and Results of Slag-Steel Reaction

### 3.1. Experimental Process

To simplify the desulfurization kinetic model, the following assumptions are needed: in order to further study the effect of the content of Ce2O3 in mold flux on the changes of Al, Si, and Ti contents of Incoloy825 alloy, the slag-steel experiments of Incoloy825 and mold flux with different Ce2O3 contents were carried out. The Incoloy825 used in the experiment was smelted in a 25 kg vacuum induction furnace, and the ingots were cut into small pieces by wire cutting. The surface of the sample was angularly ground to remove the oxide from its surface to ensure the accuracy of the experiment. The compositions are shown in Table 2.According to Figure1(c), the CaO-SiO2-Al2O3-based mold fluxes were designed, and the appropriate fluxes were added. Using analytical grade CaO, SiO2, Al2O3, MgO, Na2CO3 (instead of Na2O), CaF2, and Ce2C3O9 (instead of Ce2O3) as raw materials (purity >99%), CaO, MgO, and Ce2C3O9 powders were calcined in a muffle furnace at 873 K for 2 h to remove moisture. The chemical compositions of mold flux used in the experiment are shown in Table 3.A vertical MoSi2 resistance furnace was used to carry out slag-steel reaction equilibrium experiment. The schematic diagram of the experimental device used is shown in Figure 5. The furnace body is made of corundum tubes with an inner diameter of 90 mm and a length of 1000 mm. The temperature of the furnace is measured by a B thermocouple (Pt-30% Rh/Pt-6% Rh), and the temperature deviation can be kept within 2 K in the temperature uniform zone (100 mm).Figure 5
Schematic diagram of the experimental resistance furnace.The experimental process is as follows: first, 500 g of treated Incoloy825 was put into MgO-crucible, which was covered with graphite crucible, and then put into a MoSi2 resistance furnace, and argon (purity is 99%) was introduced at a flow rate of 1 L/min. Then, the temperature of the resistance furnace was raised to 1693 K at 5 K/min, and the constant temperature was maintained for about 30 mins to ensure the complete melting of the alloy in the furnace. Appropriately increased argon flow rate to ensure the atmosphere environment in the furnace during sampling, and the molten steel was sucked by a quartz tube with an inner diameter of 6 mm and recorded as 0 #. Finally, 100 g slag was added to the surface of the molten metal. After the slag was melted for 10, 20, 30, and 40 minutes, respectively, samples 1 # to 4 # were extracted from the molten metal, and a certain amount of slag samples was dipped at the same time. The cooled steel samples and slag samples were put into sample bags and marked with serial numbers.


### 3.2. Experimental Results and Discussion

Figure6 shows the changes of Al, Si, and Ti in Incoloy825 with time during the experiment. The mold fluxes with different Ce2O3 contents have great influence on the contents of Al, Si, and Ti in Incoloy825. As shown in Figures 6(a)-6(d), the Al content is basically unchanged for 20 mins before the reaction and slightly increases for 20 mins to 40 mins after the reaction. The change of Al content in S4 slag system is most obvious, as shown in Figure 6(e), and the increase rate of Al content in steel is from 1.03% to 35.05%. Eq. (6) and Eq. (8) are carried out synchronously, where the content of Al maintains a dynamic equilibrium. As the activity of SiO2 decreases, the reactivity of Eq. (6) becomes weaker, so the concentration of Al increased with time.Figure 6
Changes of Al, Si, and Ti contents with time in Incoloy825: (a) S0, (b) S1, (c) S2, (d) S3, and (e) S4.
(a)(b)(c)(d)(e)It can be seen from Figures6(a)-6(e) that with the increase of slag-steel interfacial chemical reaction time, the content of Si in steel gradually increases and the content of Ti gradually decreases. The increase rate of Si content is from 55.95% to 19.35%, and the decrease rate of Ti content is from 33.27% to 20.00% when the increase of Ce2O3 content in the mold flux and the slag-steel reaction for 40 mins. The minimum oxidation loss of Ti appeared in slag S3 because the activity of Ti in steel will reduce the stable Ce2O3 in the mold flux, as shown in Eq. (13). The aCe2O3 and Ce contents in IMCT are brought into (14), and the calculated results are shown in Figure 7.(13)3Ti+2Ce2O3=4Ce+3TiO2,(14)ΔG4θ=755431.34−188.79T,ΔG4=ΔG4θ+RTlnK4=ΔG4θ+RTlnaCe4⋅aTiO23aTi3⋅aCe2O32=ΔG3θ+RTlnfCe4⋅wCe%4fTi3⋅wTi%3+RTlnaTiO23aCe2O32.Figure 7
Gibbs free energy of the slag-steel interface chemical reaction with different Ce2O3 contents.With the increase of Ce2O3 content in mold flux, ΔG4 decreases gradually. When w(Ce2O3) is more than 15%, ΔG4 is less than 0. At this time, Eq. (13) has a chemical reaction at the slag-steel interface. The reaction will lead to the oxidation of Ti and decrease the content of Ti in steel, so the content of Ce2O3 in mold flux should be less than 15%.


## 3.1. Experimental Process

To simplify the desulfurization kinetic model, the following assumptions are needed: in order to further study the effect of the content of Ce2O3 in mold flux on the changes of Al, Si, and Ti contents of Incoloy825 alloy, the slag-steel experiments of Incoloy825 and mold flux with different Ce2O3 contents were carried out. The Incoloy825 used in the experiment was smelted in a 25 kg vacuum induction furnace, and the ingots were cut into small pieces by wire cutting. The surface of the sample was angularly ground to remove the oxide from its surface to ensure the accuracy of the experiment. The compositions are shown in Table 2.According to Figure1(c), the CaO-SiO2-Al2O3-based mold fluxes were designed, and the appropriate fluxes were added. Using analytical grade CaO, SiO2, Al2O3, MgO, Na2CO3 (instead of Na2O), CaF2, and Ce2C3O9 (instead of Ce2O3) as raw materials (purity >99%), CaO, MgO, and Ce2C3O9 powders were calcined in a muffle furnace at 873 K for 2 h to remove moisture. The chemical compositions of mold flux used in the experiment are shown in Table 3.A vertical MoSi2 resistance furnace was used to carry out slag-steel reaction equilibrium experiment. The schematic diagram of the experimental device used is shown in Figure 5. The furnace body is made of corundum tubes with an inner diameter of 90 mm and a length of 1000 mm. The temperature of the furnace is measured by a B thermocouple (Pt-30% Rh/Pt-6% Rh), and the temperature deviation can be kept within 2 K in the temperature uniform zone (100 mm).Figure 5
Schematic diagram of the experimental resistance furnace.The experimental process is as follows: first, 500 g of treated Incoloy825 was put into MgO-crucible, which was covered with graphite crucible, and then put into a MoSi2 resistance furnace, and argon (purity is 99%) was introduced at a flow rate of 1 L/min. Then, the temperature of the resistance furnace was raised to 1693 K at 5 K/min, and the constant temperature was maintained for about 30 mins to ensure the complete melting of the alloy in the furnace. Appropriately increased argon flow rate to ensure the atmosphere environment in the furnace during sampling, and the molten steel was sucked by a quartz tube with an inner diameter of 6 mm and recorded as 0 #. Finally, 100 g slag was added to the surface of the molten metal. After the slag was melted for 10, 20, 30, and 40 minutes, respectively, samples 1 # to 4 # were extracted from the molten metal, and a certain amount of slag samples was dipped at the same time. The cooled steel samples and slag samples were put into sample bags and marked with serial numbers.


## 3.2. Experimental Results and Discussion

Figure6 shows the changes of Al, Si, and Ti in Incoloy825 with time during the experiment. The mold fluxes with different Ce2O3 contents have great influence on the contents of Al, Si, and Ti in Incoloy825. As shown in Figures 6(a)-6(d), the Al content is basically unchanged for 20 mins before the reaction and slightly increases for 20 mins to 40 mins after the reaction. The change of Al content in S4 slag system is most obvious, as shown in Figure 6(e), and the increase rate of Al content in steel is from 1.03% to 35.05%. Eq. (6) and Eq. (8) are carried out synchronously, where the content of Al maintains a dynamic equilibrium. As the activity of SiO2 decreases, the reactivity of Eq. (6) becomes weaker, so the concentration of Al increased with time.Figure 6
Changes of Al, Si, and Ti contents with time in Incoloy825: (a) S0, (b) S1, (c) S2, (d) S3, and (e) S4.
(a)(b)(c)(d)(e)It can be seen from Figures6(a)-6(e) that with the increase of slag-steel interfacial chemical reaction time, the content of Si in steel gradually increases and the content of Ti gradually decreases. The increase rate of Si content is from 55.95% to 19.35%, and the decrease rate of Ti content is from 33.27% to 20.00% when the increase of Ce2O3 content in the mold flux and the slag-steel reaction for 40 mins. The minimum oxidation loss of Ti appeared in slag S3 because the activity of Ti in steel will reduce the stable Ce2O3 in the mold flux, as shown in Eq. (13). The aCe2O3 and Ce contents in IMCT are brought into (14), and the calculated results are shown in Figure 7.(13)3Ti+2Ce2O3=4Ce+3TiO2,(14)ΔG4θ=755431.34−188.79T,ΔG4=ΔG4θ+RTlnK4=ΔG4θ+RTlnaCe4⋅aTiO23aTi3⋅aCe2O32=ΔG3θ+RTlnfCe4⋅wCe%4fTi3⋅wTi%3+RTlnaTiO23aCe2O32.Figure 7
Gibbs free energy of the slag-steel interface chemical reaction with different Ce2O3 contents.With the increase of Ce2O3 content in mold flux, ΔG4 decreases gradually. When w(Ce2O3) is more than 15%, ΔG4 is less than 0. At this time, Eq. (13) has a chemical reaction at the slag-steel interface. The reaction will lead to the oxidation of Ti and decrease the content of Ti in steel, so the content of Ce2O3 in mold flux should be less than 15%.


## 4. Conclusions

The effect of mold flux containing Ce2O3 on the contents of aluminum, silicon, and titanium in Incoloy825 super alloy was studied. The results are as follows:(1)
The activity model of CaO-SiO2-Al2O3-Na2O-MgO-CaF2-Ce2O3 slag system was established based on the ion and molecule coexistence theory. The calculation results show that with the increase of Ce2O3 content in the mold flux, the activity of Al2O3 decreases significantly and the activity of SiO2 decreases and gradually tends to 0.(2)
In the present study system, the main slag-steel interfacial chemical reaction is as follows: [Ti] + (SiO2) = [Si] + (TiO2), and the secondary reactions are as follows: 4[Al] + 3(SiO2) = 3[Si] + 2(Al2O3) and 3[Ti] + 2(Al2O3) = 4[Al] + 3(TiO2).(3)
The results of slag-steel reaction experiment show that the increase rate of Al content increases from 1.03% to 10.31%, the increase rate of Si content decreases from 55.95% to 31.25%, and the oxidation rate of Ti content decreases from 33.27% to 20.00% when Ce2O3 content in the mold flux increases from 0% to 15% and the slag-steel reaction for 40 mins.(4)
With the increase of Ce2O3 content in the mold flux, the slag-steel interfacial chemical reaction is weakened, and the oxidation loss of Ti and Al in steel is inhibited. When the content of Ce2O3 in mold flux is more than 15%, the following chemical reaction will occur at the slag-steel interface: 3[Ti] +2(Ce2O3) = 4[Ce] +3(TiO2), which will aggravate the oxidation loss of Ti in steel, so the content of Ce2O3 in the mold flux should be less than 15% [36–38].



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*Source: 5314863-2022-10-11.xml*