Calculating Models on the Surface Tension of CaO-FeO-SiO 2 Molten Slags

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1 Research of Materals Scence March 014, Volume 3, Issue 1, PP Calculatng Models on the ace Tenson of --SO Molten Slags Chengchuan Wu 1, )#, Guoguang Cheng 1, ) 1, ), Qq Ma 1) State Key Laboratory of Advanced Metallurgy, Unversty of Scence and Technology Bejng, Bejng , Chna ) School of Metallurgcal and Ecologcal Engneerng, Unversty of Scence and Technology Bejng, Bejng , Chna # Correspondng author, E-mal: wuchengchuan163@163.com Abstract A thermodynamc model has been developed for determnng the surface tenson of --SO molten slags based on the on and molecule coexstence theory (IMCT) of slag structure and Butler s equaton. The temperature and composton dependence of the surface tensons n molten --SO slag systems was reproduced by the present model usng surface tensons and molar volumes of pure oxdes, as well as the mass acton concentratons (actvtes) at the surface and at the bulk phase of the slag component. The evaluated results for the surface tenson show good agreements wth lterature data. The so-surface tenson lnes of --SO slag melt have also been calculated and the effects of slag composton and temperature on the surface tenson were also nvestgated. Keywords: --SO Molten Slags; ace Tenson; the Ion and Molecule Coexstence Theory; Butler s Equaton; Calculatng Model. 1. Introducton The surface tenson of molten slag s one of the most mportant parameters for metallurgy processes, on account of whch s closely related to the phenomena such as ncluson formaton and removng n metal melt, slag foamng, slag-metal emulsfcaton and slag-metal reacton. However, t s dffcult to fnd the approprate surface tenson data of molten slag due to the hgh temperature measurement and the complcated effect of component on surface tenson. Varous models have been developed to predct the surface tenson of molten slag systems. For slag wth complcated nteractons, T. Tanaka et al. [1-3] appled a model consderng the anonc and catonc rad of the component oxdes as the model parameters to descrbe the surface tenson, and H. G. Lee et al. [4] calculated the surface tenson usng crtcally evaluated onc surface dstances of pure oxdes. In addton, these two models are based on Butler s equaton and acheved consstent results compared to the data reported n the lterature. However, all these models are not on account of the actual structures of the slag melt. The coexstence theory of slag structure [5, 6] has been proposed by.m. Chuko and modfed by J. Zhang to express the reacton ablty of components n a slag by the defned mass acton concentraton accordng to the mass acton law, lke the tradtonally appled actvty a of component. The calculated mass acton concentratons of all exsted structural unts or on couples n the slags, lke the tradtonally measured or calculated actvty of components, have been used to predct sulfur dstrbuton and phosphate capacty, and also been used to determne the mass acton concentraton of structural unts n the Ce O 3 and La O 3 contanng slags [7-11], n whch on and molecule coexstence theory (IMCT) corresponds to the coexstence theory of slag structure. G. G. Cheng et al. [1, 13] developed a thermodynamc model for evaluatng the surface tenson of slag melt for consderng the bulk and surface structures of slag melt based on the on and molecule coexstence theory of slag structure as well as Butler s equaton. Ths model s characterzed by the reasonable understandng of the slag structure wth whch t can be smply apply to the mult-component slag melt, because the calculatons are only based on the surface tenson and molar volume of the pure components, the on and molecule coexstence theory and

2 Butler s equaton. Ths model has also been used to smply predct the surface tenson of -SO, MnO-SO and -MnO-SO slag melt. In the present work, a further verfcaton of the above model was attempted for predctng the surface tensons of the --SO slag systems. The calculated surface tenson results were compared wth the data reported n the lterature. In addton, to understand the effects of component on the surface tenson, the so-surface tenson curves of --SO ternary slag were also compared.. Thermodynamc model for estmaton of the surface tenson of molten slag.1 Butler s Equaton Among varous models suggested by prevous researchers for the predcton of surface tenson of lqud solutons, the present model also based on the Butler s equaton. The surface tenson ( ) of the molten slag system s calculated from Eq.(1): Pure RT a ln (1) A a Where subscrpt refer to the followng component:,, or SO. Superscrpts and ndcate the surface and bulk phase, respectvely. R s the gas constant and T s the absolute temperature. Where a and a Pure are the actvtes of the component at the surface phase and at the bulk phase, respectvely. s the surface tenson of the pure molten component. And A s the molar surface area n a monolayer of pure molten component, whch can be fgure out by Eq. (): A L V () 1/ 3 / 3 0 Where 0 s Avogadro s number, V molar volume of the pure molten component, L correcton factor resultng from the surface structure and usually set to be 1 for the molten salts and onc oxde mxtures by Tanaka et al.. Hypotheses The classc hypotheses about the on and molecule coexstence theory of slag structure are descrbed n detal elsewhere [5, 6]. However, the key ponts of ths model are that the surface layer s also obeyng the hypotheses of the on and molecule coexstence theory of slag structure, and the relaton between surface tenson of molten slag and mass acton concentratons of components at the surface phase and at the bulk phase conforms to Butler s equaton, whch can be summarzed as follows: (a) The type of structural unts at the surface phase of the studed --SO slag systems s the same as at the bulk phase of molten slag, composed of smple ons such as Ca +, Fe + and O -, smple molecule SO, and complex molecules as alumnates. (b) There are dynamc equlbrum chemcal reactons between smple ons, smple molecules and complex molecules, takng slcate formaton reacton for example: Me O SO Me SO 4 (3) (c) The chemcal reactons of formng complex molecules as shown n Eq. (3) obey the mass acton law, and Eq.(4) can be gotten: K MeSO4 Me SO 4 MeO SO (4) Where Me SO4, MeO and SO are surface mass acton concentratons (surface actvtes) of MeO, whch

3 exsted as on couples ( Me + O ), SO and Me SO 4, respectvely; K s chemcal reacton equlbrum constant of Eq. (1), whch can be calculated by K exp G RT. Me SO4 r m, MeSO4 (d) The relaton between surface tenson of slag melt and mass acton concentratons of components at the surface phase and at the bulk phase conforms to Butler s equaton: Pure RT ln (5) A Where and are the mass acton concentratons (actvtes) of the component at the surface phase and at the bulk phase, respectvely. Takng --SO slag melt as an example, Eq. (5) can be expressed as Eq. (6)-(8): Pure RT --SO ln (6) A Pure RT --SO ln (7) A RT (8) Pure --SO SO ln ASO SO SO.3 The mass acton concentratons calculatng model of --SO The mass acton concentraton of the structural unt s defned as a rato of the equlbrum mole number of structural unt to the total equlbrum mole numbers of all structural unts accordng to IMCT, and all structural unts n the form of smple ons, smple molecules, and complex molecules can be calculated by n. The Me n O 3 such as on- par (Me + +O - ), should be calculated by MeO Me n n Me, MeO O, MeO nmeo., MeO O, MeO n n The mole numbers of, and SO n 100g of total slag mass were defned as b n, 1 b n and a1 nso respectvely. The symbols of the mass acton concentratons for all structure unts were lsted as followng: 1, SO, 3. The total equlbrum mole number of all structural unts n the --SO slag can be expressed as: n n1 n n3 n4 n5 n6 n (mol). 7 Mass equlbrum formulas were lsted below: b1 n (9) a1 n (10) b n (11) 1 (1) Therefore, the Table.1 and equaton (9)-(1) are the governng equatons of the developed thermodynamc model for calculatng mass acton concentratons of structural unts or on couples n the --SO slag. TABLE 1 EXPRESSIO OF STRUCTURAL UITS, THEIR MOLE UMBERS AD MASS ACTIO COCETRATIOS OF

4 --SO SLAGS AT METALLURGICAL TEMPERATURE BASED O THE IO AD MOLECULE COEXISTECE THEORY. Structural unts o Reacton -1 G (J mol ) Mass acton concentraton SO 4 (Ca + +O - )+SO = SO T 4 K1 1 SO 5 (Ca + +O - )+ SO =3 SO T 5 K 1 3 SO 6 3(Ca + +O - 3 )+ SO =3 SO T 6 K3 1 SO 7 (Fe + +O - )+ SO = SO T 7 K4 3.4 Model Establshng From what descrbed above, the sequence of the establshed thermodynamc model for predctng the surface tenson s shown n Fg.1. As shown n Fg.1, where the parameters K s the absolute temperature, and n s the mole number of four components as, and SO n 100 g of --SO slag to represent chemcal composton of the slags. In addton, K j s the chemcal reacton equlbrum constant of formaton complex molecules, IMCT represent the on and molecule coexstence theory of slag structure. In addton, the chemcal reacton equlbrum constant K j of formaton complex molecules and the detal of and calculatng model of --SO slag system based on IMCT can be got from Table 1 [14] Pure. Parameters of and A used n the calculaton are lsted n Table and 3 [1-3]. can be calculated by mole fractons (or mass fracton) of components and the chemcal reacton equlbrum constant of complex molecule based on the on and molecule coexstence theory. Further, and can be calculated by, and A based on the on and molecule coexstence theory and the Butler s equaton. Pure The model stated above can be extends to mult-component slag systems, so long as the bulk phase and the surface phase are both obeyng the hypotheses of IMCT. Sample calculatons have been made for ternary --SO slag system. FIG.1 THE SEQUECE OF THE MODEL FOR THE ESTIMATIO OF THE SURFACE TESIO TABLE. TEMPERATURE DEPEDECE OF THE SURFACE TESIO OF THE PURE COMPOETS Components SO Temperature (K) dependence of surface tenson (m/m) T T T

5 Components TABLE 3. TEMPERATURE DEPEDECE OF THE MOLAR VOLUME OF THE PURE COMPOETS Temperature (K) dependence of molar volume (m 3 /mol) T T 1773 SO T Results and Dscussons At a certan temperature, the calculaton could carry out wth certan slag components usng the governng equatons under the condtons of equlbrum state and the standard state. After lnearzaton, ewton teratve method was used n Matlab software to gan all the mass acton concentratons of each structural unts or on couples. 3.1 Model evaluaton In order to evaluate the performance of the present model, the mean devaton defned as: 1 Calc Mean devaton 1 Expe Expe 100% (13) Where Calc and Expe are the calculated and measured surface tenson, respectvely, and represents the number of the samples. The surface tenson data of melts of fve dfferent compostons n the system --SO were measured n the early publcaton [15], whch has been well represented by the present model. The estmated surface tenson was compared wth the expermental surface tenson data and s shown n Fg.; the mean devaton was found to be 8.08%. Therefore, the present model provdes a good descrpton of the surface tenson varaton of the --SO system wth regard to temperature and composton. FIG. COMPARISO OF THE EVALUATED AD MEASURED SURFACE TESIO FOR THE --SO SYSTEM. 3. Model applcaton The calculated results for the --SO system at 1573 K, 163 K, 1673 K and 1708 K are shown n Fg.3. These results were bascally consstent wth the lterature values at each temperature, although surface tenson s larger estmated by the present model. The so-surface tenson curves n Fg.3, calculated usng the current model,

6 reproduce the composton dependence of surface tenson for the --SO system, and show that ts surface tenson ncreases wth ncreasng content and decreases wth ncreasng SO content. Analyzng the so-surface tenson curves from Fg.3 (a), (b), (c) and (d), t can be seen that surface tenson decreases wth ncreasng temperature. FIG.3 CALCULATED ISO-SURFACE TESIO LIES (M/M) OF MOLTE FEO-CAO-SIO SYSTEM AT (A) 1573 K, (B) 163 K, 4. Conclusons (C) 1673 K AD (D) 1708 K. (1) Based on the on and molecule coexstence theory (IMCT) of slag structure and Butler s equaton, a calculatng model has been developed for determnng the surface tenson of - -SO molten slags. () The evaluated results for the surface tenson from the present model show good agreements wth lterature values n --SO ternary system. The mean devaton of the present model was found to be 8.08%. (3) The so-surface tenson lnes of --SO slag melt have also been calculated. ace tenson of --SO slag decreases wth ncreasng temperature and ncreasng SO content and ncreases wth ncreasng content. REFERECES [1] TAAKA T, KITAMURA T and BACK I A. Evaluaton of ace Tenson of Molten Ionc Mxtures [J]. ISIJ Internatonal, 006,

7 46(3): [] AKAMOTO M, KIYOSE A, TAAKA T, et al. Evaluaton of the ace Tenson of Ternary Slcate Melts Contanng Al O 3,,, MgO or MnO [J]. ISIJ Internatonal, 007, 47(1): [3] HAAO M, TAAKA T, KAWAMOTO M, et al. Evaluaton of ace Tenson of Molten Slag n Mult-component Systems [J]. ISIJ Internatonal, 007, 47(7): [4] CHOI J Y and LEE H G. Thermodynamc Evaluaton of the ace Tenson of Molten -SO -Al O 3 Ternary Slag [J]. ISIJ Internatonal, 00, 4(3): 1-8 [5] Zhang J. Coexstence theory of slag structure and ts applcaton to calculaton of oxdzng capablty of slag melts [J]. J Iron & Steel Res., Int., 003, 10(1): 1-10 [6] ZHAG Jan, CHEG Guoguang, WAG Ljun, et al. Computatonal Thermodynamcs of Metallurgcal Melts and Solutons [M], Metallurgcal Industry Press Bejng, Chna, 007, p41-45, n chnese [7] X.M. Yang, J.S. Jao, R.C. Dng, C.B. Sh, and H.J. Guo. A Thermodynamc Model for Calculatng Sulphur Dstrbuton Rato between -SO -MgO-Al O 3 Ironmakng Slags and Carbon Saturated Hot Metal Based on the Ion and Molecule Coexstence Theory [J]. ISIJ Internatonal, 009, 49(1): [8] C. C. Wu, G.G. Cheng, H. Long, et al. A Thermodynamc Model for Evaluaton of Mass Acton Concentratons of Ce O 3 -contaned Slag Systems Based on the Ion and Molecule Coexstence Theory [J]. Hgh Temperature Materals and Processes. 013, 3(3): [9] C. C. Wu, G.G. Cheng. Calculatng model of mass acton concentraton for the La O 3 -Al O 3 -CaF refnng slag system for electroslag remeltng [J]. Journal of Iron and Steel Research,013, 5(9):3-7. n chnese [10] C. C. Wu, G.G. Cheng, H. Long. Calculatng model of acton concentraton of slag systems contanng Ce O 3 [J]. The Chnese Journal of onferrous Metals. 013, 3(10): n chnese [11] X.M. Yang, C.B. Sh, M. Zhang, J.P. Duan, and J Zhang. A Thermodynamc Model of Phosphate Capacty for -SO -MgO--Fe O 3 -MnO-Al O 3 -P O 5 Slags Equlbrated wth Molten Steel durng a Top-Bottom Combned Blown Converter Steelmakng Process Based on the Ion and Molecule Coexstence Theory [J]. Metallurgcal and Materals Transactons B, 011, 4B (5): [1] Cheng G G, Lao B. Calculaton Model for ace Tenson of Slag Melt [J]. J Iron & Steel Res., Int., 1999, 6(): 17-0 [13] L Z J, Cheng G G, Sh C X. Calculaton Model of Interfacal Tenson for Slag Melt and Alloy Melt [J]. Journal of the Chnese rare earth socety, 006, 4(Spec Issue): 7-31 [14] Bale C W, Chamand P, Degterov S A, et al. FactSage theraachemcal software and databases [J]. Calphad- Computer Couplng of Phaec Dagrams and Thermochemstry, 00, 6(): [15] DAVID SKUPIE, D.R. GASKELL. The ace Tensons and Foamng Behavor of Melts n the System --SO [J]. Metallurgcal and Materals Transactons B, 000, 31B (5): Authors Chengchuan Wu (1988- ), male, ph.d.canddate, research nterests are manly n the area of metallurgcal process for specal steel and rare-earth steel