Predicting Oxide Activities in Ca0-Al203-Si02 System by Computer Model Napovedovanje aktivnosti oksidov v sistemu Ca0-Al203-Si02 z računalniškim modelom B. Koroušič, Institut for Metals and Technology, Ljubljana The most important metallurgical effects of ladle treatment of aluminium - killed steels with calcium, are associated vvith the modification of alumina inclusions. For the development of the deoxidation - control model for inclusions, the thermodynamic slag model, based on the Gibbs energy minimization and modelling approaches postuiated from Hastie et al., vvas used to calculate component oxide activities in the system CaO-AI203 and part of the system 3Ca0.AI203-Si02, 12CaO. 7AIPOrSiOP and Ca0.AI203-Si02 a t 1500°C and 160CPC. Key vvords: Slag activities, model computations, Gibbs energy minimization Najpomembnejši metalurški učinki pri uporabi kalcija za obdelavo jekel pomirjenih z aluminijem so povezani z modifikacijo aluminatnih vključkov. Pri razvoju modela za kontrolo vključkov smo uporabili termodinamični model, ki sloni na Gibbsovem modelu minimizacije energije in postulatu, ki ga je postavil Hastie et a/. Izračunavanja aktivnosti oksidnih komponent smo izvršili za sistem 3Ca0.AI203-Si02, 12CaO 7AI?0~-Si09 in Ca0.AI203-Si02 pri temperaturi 150CPC in 160CPC. Ključne besede: aktivnosti žlinder, modelna izračunavanja, Gibbsova energija minimizacije. 1. Introduction In last two decades calcium-based additions are made to molten steel not only for deoxidation and/or desulfurisation pro-poses, but also for the control of inclusion composition and mor-phologv. The ladle metallurgy offers today excellent possibili-ties to control of the cleanness and quality of steels. The most important metallurgical effects of ladle treatment of aluminium-killed steels vvith calcium, are associated vvith the modification of alumina inclusions preventing his precipitation during the continuousllv casting known as nozzle clogging process. Also the role of the syntetic slags Ca0-Al,0rSi02 for the secondarv refining of steel is growing dramatically because of it s excellent refining capabilities. In order to put inclusion engineering into practice. it is essential that the equilibrium relationship betvveen the liquid steel and the corresponding inclusion should be determined. With suitable seleetion of the deoxidation practice (changing ratio Ca/Al) is possible to avoid nozzle clogging, en-suring inclusions vv ith melting points lovver than the steel melt temperature. In this paper are presented equilibrium thermodynamic ac-tivitv of the Al/T, CaO. and SiO, in system CaO-Al,OrSiO:. determined vvith new Gibbs Energy Minimization Model -GEMM (The equilibrium calculation in the GEMM program is a minimization of the integral Gibbs free energy using a Langrangian multiplier method for the constraints) and discussed in relation to their use in deoxidation and calcium treatment control. 2. Thermodvnamic model of oxide phase equilibria -GEMM Many thermodvnamical models are developed in last tvvo decades for the investigation of multiphase equilibria and for thermodynamic predietions of multicomponent high-tempera-ture oxide systems'"'". Calculations involving thermodynamic equilibria in multi-phasc oxide systems are extremely time con-suming, even in the systems vvith relatively fevv components. In recent years, there has been rapid progress in the use of thermo-dynamic models achieving better understanding of many metallurgical, ceramical and chemical systems of commerical significance. This progress has been made possible largely by develop-ments in computer softvvare technology as vvell as the inereasing availability of reliable and comprehensive thermodynamic values compared vvith "hand" calculations vvhich have traditional-ly been assigned to specialists. A new modelling approach for thermodvnamic predietions of multiphase high-temperature oxide systems developed by J.W. Hastie and D.W. Bonnell" has been extended and applied for the investigation of the binary and ternary systems CaO-A1,0, and Ca0-Al;0,-Si0,. Well-known examples of solution models in current use include, ideal, regular, and the molecular-level associated liquid or cluster models4"71. The basic approach used in the GEMM predietion model is a deseription of non-ide-al mixture and the formation of complex liquids and solids as mixing componenets. This model has a thermodynamic basis and does not rely on assumed molecular or ionic entitics in the liquid phase. The liquid components are not independent molecular species, but are essentially subphases that serve as models for the local associative order-an idea that Schenk himself great-ly expanded some 50 years ago". Although the components are included individualy, it is assumed that in most cases, the components form short range order, and do not necessarily represent diserete molecular, ionic or other structural entities. The component and complex-compo-nent oxides formed are assumed to mix idealy, in accordance with Raoult' law. Henee, thermodvnamie aetivities and apparent mole fractions (X ) are equivalent quantities for this model. In the GEMM-predietion model, the thermodynamie activi-ty of oxides CaO, A1:0„ and SiO, can be calculated from the cor-responding thermodynamic functions. The modelling approach has been validated by comparison with experimental activitv dala. obtained from Taylorsl, Kav'", and recently published data from Fujisavva"", and Nagata"1. While the thermodvnamie data are incomplete they are stili sufficiently extensive to allovv their tise in the performance of common thermodynamical calcula-lions for manv high-temperature slags and other systems. Good agreement between the model predictions and experimental activitv data is obtained. The utility of even sparse experimental data can, in principle, be greatlv enhanced by GEMM optimiza-tion techniques. 3. Thermodynamic data bases Before actual calculations can begin. the necessarv thermo-dynamic data must be collected. For most oxide svstems relevant lo industrial steelmaking practice, the experimental thermody-namic data base are often a variety of somewhat obscure sources or are incomplete. The CaO-AfO, and Ca0-Al,0,-Si0. svstems are an excep-tion, in that there is an adequate thcrmodynamic data base which can be applied lo test the model computations. Such a thermo-dynamical optimization technique offers the important benefit thal it can drastically reduce the need to conduct costlv experi-ments. The Gibbs free energy data for the corresponding oxide phase at 1600"C are given in table I. Table 1: Compounds Gibbs energy of fonnation, negative (kJ/mol) (s)=solid, (l)=liquid Tabela 1: Prosta tvorbena energija nekaterih oksidov, minus (kJ/mol) Components 1873 K(s) 1873 K(l) Al,O, 1089.81 1065.70 CaO 431.08 427.47 SiO, 578.50 - 3Ca0AI,0, 2454.77 - 12Ca07AI,0, 13222.86 13280.00 CaOAl.O, 1564.62 1564.33 Ca02AI,0, 2693.83 2688.12 Ca06AI,0, 7063.18 7051.92 The GEMM-computer program used for calculation of the equilibrium composition, and hence aetivities. utilizes a data base made up of Gibbs energies of formation A(Gf) as a funciton of temperature (T). The free energies of formation A (Gf) are ei-ther known or can be estimated for these complex component liquids and solids. The data for most oxides vvere obtained mainly from data base made by J. Ilastie and Bonnell121. In a fevv instances, the co-efficients lo lite A (Cif) equation have been re-evaluted using nevv thermodv namie data obtained in the literature. 4. Results Cu0-Al203 Svstcm The CaO-AUO, system is one of the fundamental systems of the calcium-based slags and non-metallic inclusions, and there have been manv reports on the thermodynamics of this system. Much of the published information on lite thermodvnamie properties for some binarv aluminates has been based on vvork conducted and published in 1960's. Extrapolation of these data to steelmaking temperatures ntav introduce large errors. espe-c i a 11 y for a particular composition range. The CaO and AKO, activitv data shovvn in figure 1 are con-sistent vvith the bulk of literature experimental data at T=1600' C. Electromotive force (emf) and cell-activity data have recentlv been obtained by Fujisavva et al"" covering a vvide range of com-positions. Our model activitv data at T = I500"C have been com-pared vvith recently published data by Nagata et al"1 and as is shovvn in figure 2. Good agreement betvveen the model predic-tion and experimental activitv data for a vv ide range of composition is demonstrated. SVSTEM Ca0-Al203 T = '530 °C a(CqO)(s)-Modeli -a (CaO) - Nagata a (AI2O3) (s) - Modeli a (AI2O3)- Nagata 0,001 3 1 12:7 _I__i_ 1:1 _j_ 1:2 1:6 0 10 20 30 40 50 60 70 30 90 10C Al703 (mol/%) Figure t: Model dependance of computed activitv data in CaO-A I.O, at T=I500"C. Slika t: Modelna izračunavanja aktivnosti oksidov v sistemu CaO-AI.O, pri T=I500"C O < O o o 0,001 30 40 50 60 A1203 (mol/%) Figure 2: Model dependance of computed activitv data in CaO-AKO,, at T=1600"C Slika 2: Modelna izračunavanja aktivnosti oksidov v sistemu CaO-Al,Q, pri T=1600"C SVSTEM Ca0-Al203-Si02 (3Ca0-AI;03) mol % SiO2 0,0001 oooooi -a (A1203) (s)-Modeil O a {AI2O3) - Taylor 10 20 mol % SiO2 Fig. 3a o a O 0,1 > t! < 0,01 Ca0-AI203-Si02 System The control and prevention of multiphase in CaO-AKO,-SiO, and a suitable deoxidation practice should be applied to avoid undesirable alumina inclusions, thcy are not deformable and. besides, provoke tundish no/zle blockage problems. In order to determine oxygen und sulphur contents in molten steel and the conditions for aluminate and solid sulphide coprecipitation during casting, the knowledge of the activitv of CaO, AUO, and SiO, 111 molten slag and inclusions is important. One of the main advantages in the used model is the treatment as a high order sys- Fig. 3c Figure 3: Model computed dala of CaO, Al,O, and SiO, in CaO-AI,OrSiO: system for 3CaO.AfO, composition and T=1600"C Slika 3: Modelna izračunavanja CaO. Al,O, in SiO, v sistemu CaO-A 1,0,-SiO; za sestavo 3CaO.AfO< pri T=1600"C SYSTEM Ca0-Al203 -Si02 (12CaO-7 Al203 ) c 0 1 / T 1600°C - - a (/ 0 a (/ M203) (s) M203) - Tt -Modeli iylor 0 10 20 30 40 50 mol % Si02 Fig. 4a tem at high temperatures where extrapolation of thermodynam-ic dala may introduce large errors. For CaO-Al,OrSiO, system, several experimental studies of activity measurement and phase - diagram determination are reported in the literature*1. But. because of experimental difficulties, large discrepancies are observed between different experimental works. Tha activitv of [SVSTEM Ca0-Al203-5i02 (3CaO -Al^Og)] 20 mol % Si02 Fig. 3b T = 1600°C - a (CaO) (s)-Modeli o a (CaO) - Taylor mol % Si02 Fig. 4b SYSTEM Ca0-Al2d3-Si02 (CaO AI2O3) T = 1600°C - a (t 0 a ( U203) (s) M2O3) - Ta -Modeli y lor 0 10 20 30 40 50 mol % Si02 Fig. 5a F'g- 4c Fig. 5b and alumina were calculated in ali of liquidus domains. The com-positions are expressed in mole fractions of CaO, A1015 and SiO,. The reason for choosing A1015 rather then A1,0, is because in the basic melts, A 1,0, give rise to tvvo foreign ions AlO2", vvheres SiO, gives rise onlv to one SiO4". Thermodynamic activ-ities calculated using Gemm - computer program are shovvn in figures 3 - 5. Experimental activity data for the Ca0-Al,0;-Si0, system is particularly sparse and disparate8"3"41. Very good agreement betvveen the model and experiment data for the silica- Figure 4: Model computed data of CaO, Al,O, and SiO, in CaO-Al,OrSiO, system for 12Ca0.7AI,0, composition and T=1600"C Slika 4: Modelna izračunavanja CaO, Al,O, in SiO, v sistemu CaO-Al ,(),-SiO, za sestavo 12Ca0.7Al,0, pri T=1600"C CaO, Al.O,. and SiO, in CaO-Al,OrSiO, molten slag at 1500"C vvas measured by Rein and Chipman in 1963 and 1965131. The ac-tivity data determined the activity of silica by cquilibrium vvith a metallic phase, of carbon - saturated iron vvith silicon in solution. By integration of the Gibbs - Duhem lavv. the activitics of lime 0,01 o in 0,001 0,0001 SYSTEM Ca0-Al203-Si02 (CaP-A^Ps) 0,00001 0 10 20 30 mol % Si02 Fig. 5c Figure 5: Model computed data ofCaO, AUO, and SiO, in CaO-AKOrSiO, system for CaO.AbO, composition and T=1600"C Slika 5: Modelna izračunavanja CaO, Al,O, in SiO, v sistemu CaO-Al,0,-Si0, za sestavo CaO.AfO, pri T=f600"C activities and computed thermodynamic activity data for A1:0, and CaO at 1600"C is demonstrated. 5. Conclusion The Gibbs energy minimization model (GEMM) is used with the corresponding thermodynamical data base to calculate the predicted composition of solids, liquids (non-ideal solu-tions), and the vapour phase. The calculated composition of the CaO, Al20,, and SiO, are taken as the activity. Numerous comparisons between model and the experimental activities in the systems CaO-AkO, and CaO-Al:0,-Si02 at different temperatures have confirmed the realia-bility of this approximation. Considering the large number of the data base components, and the cumulative errors in the thermodynamic functions. the possihility exists that the present data base is not unique. However, as has been pointed out by J. Hastie and D. Bonnell", the author expects that some future modifications of the data base will be relatively ntinor. 6. References " Eriksson, G.: Chem. Scripta 8, 100, (1975) 21 Gaye, H„ D. Coulombet: Irsid PCM-RE. 1064. March, 1984 " Hastie. J.W„ Horton, W. S„ Plante, E.R., and Bonnell, D.W.: Thermodynamic Models of Alkali Vapor Transport in Silicate Systems, IUPAC Conf., Chemistry of Materials at High Temperature, Harwel, U.K.. August 1981: High Temp.-High Pres. 14, 669, (1982) 41 Ansara, I.: The modern computer applications in thermody- namics, Mattech '90, June 14-15 (1990), Helsinki 51 Lin, P.L., Pelton, A.D. Bale,C.W„ and Thompson, W.T.: CALPHAD 4. 47(1980) 61 Sundman, B.: Thermo-calc course, Mattech '90, June 14-15 (1990), Helsinki 71 Barin, 1„ G. Eriksson, F. Sauert, M. Zeitler. B. Witting, W. Schmidt: Equitherm, Databank and computer program for thermodynaniic calculation, Privat comunication (1990) 81 Verein Deutscher Eisenhiittenleute (Hrsg.) Schlackenatlas; Dusseldorf Verlag Stahleisen (1981) '" Kay, D.A.R.. S.V. Subramanian and R. V. Kumar: Inclusions in Calcium Treated Steels, Proceedings of the Second International Symposium on the Effects and Control of Inclusions and Residuals in Steels, 25th Conference of Metallurgist, Toronto, (1986) C1M "" Fujisavva, T., Ch.Yamauchi. H.Sakao: Activity of CaO and A1,03 in CaO-CaS slags satturated with CaS and the equilib-rium between the slags and molten iron alloys at 1873 K. The Sixth Internat. Iron and Steel Congress, Vol.I, 201-208 (1990) 111 Nagata, K„ J. Tanabe, and K.S. Goto: Activities of Calcium oxide in CaO-based Inclusions, measured by galvanic cells, The Sixth Intern. Iron and Steel Congress, Vol. 1, 217-224 (1990) 121 Hastie, J., D.W.Bonnell: A predictive phase equilibrium model for multicomponent oxide mixtures Part II. Oxide of Na-K-Ca-Mg-Al-Si, High Temperature Science, Vol. 19, (1985) 275-306 131 Rein, R.H., J. Chipman: J. Trans. Metali. Soc. AIME 233,415 (1965).