Modelling Viscosities of CaO MgO Al 2 O 3 SiO 2 Molten Slags

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1 ISIJ Iteratoal, Vol. 5 (01, No. 3, pp Modellg Vscostes of Al 3 S Molte Slags Guo-Hua ZHANG, 1, Kuo-Chh CHU 1, ad Ke MILLS 3 1 State Key Laboratory of Advaced Metallurgy, Uversty of Scece ad Techology Bejg, Cha. School of Metallurgcal ad Ecologcal Egeerg, Uversty of Scece ad Techology Bejg, Bejg, Cha. E-mal: zgh90@16.com, kcc16@16.com 3 Departmet of Materals, Imperal College, Lodo, SW7 AZ UK. (Receved o August 17, 011; accepted o November 15, 011 A structurally-based vscosty model (usg a few optmzed parameters s proposed to represet vscosty as fuctos of both temperature ad composto for the Al 3 S. The model represets the slag structure through the dfferet types of oyge os formed the melt. Appromate methods for calculatg the cocetratos of these dfferet types of oyge os are proposed ad are the used to descrbe the effect of melt structure o vscosty. The model provdes a good descrpto of the vscosty behavor vared wth composto ad temperature wth the Al 3 S system. Ths cludes pure systems: Al 3 ad S ; bary systems: S, S, Al 3 S ad Al 3; terary systems: S, Al 3 S ad Al 3 S ; quaterary system: Al 3 S. The dfferet roles of ad o vscosty are also dscussed; these ted to dffer melts wth or wthout Al 3. I the absece of Al 3, reduces the vscosty more tha. I cotrast, whe Al 3 s preset, the + os take prorty over + os the charge-compesato of Al os whch leads to the formato of more stable Al 4 tetrahedral structures, whch, tur, results a crease vscosty. However, whe there s eough basc ode ( or preset to geerate o-brdgg oyges, reduces the vscosty more effectvely tha. KEY WRDS: vscosty; brdgg oyge; o-brdgg oyge; alumoslcate melt. 1. Itroducto The vscostes of alumoslcate melts are mportat because of ther dramatc effect o pyrometallurgcal processes ad also because of ther sestvty to the slag structure. For stace, relable vscostes are eeded ( to guaratee smooth operato of the blast furace ( for foamg processg ( for the successful separato of metal ad slag durg the basc oyge steelmakg process ad (v the cotuous castg process where the slag acts as a lubrcat. From the vew pot of the reacto ketcs, most metallurgcal reactos are dffuso-cotrolled ad whch ca be drectly related to the vscosty of the molte slag. Therefore, accurate vscosty values are essetal for the optmzato ad mprovemet of metallurgcal processes. However, obtag data oly by epermetal measuremets are both tme-cosumg ad sometmes accurate (or mpossble because of the dffcultes assocated wth hgh temperature operatos (or the hgh meltg pot of some compostos. Cosequetly, there s a prove eed for a model to estmate the vscosty as a fucto of temperature from the chemcal composto of the slag. It has bee poted out that the term the Arrheus equato coverg the actvato eergy for vscous flow for alumo-slcate melts s a o-lear fucto of composto. 1 Thus the tal addto of basc odes to alumoslcates causes a rapd decrease the actvato eergy of vscosty but ths atteuato becomes less steep as the basc ode cocetratos crease. Amog the dfferet vscosty models, 11 the Rboud et al. model epresses the actvato eergy as a lear addto of compoets; ths ca ot reflect the o-lear varato of actvato eergy wth composto. The Urba model 3 utlzes a polyomal fucto of composto wth a order of 3, whereas Zhag et al. 4,5 epress the actvato eergy as a polyomal fucto of the three types of oyge (troduced by Fcham ad Rchardso 1 wth the hghest order of 3 to descrbe the olear behavor. I our prevous paper, 13 a ew vscosty model was developed to represet the vscosty data of the Fe M S system. Ths model s eteded to clude Al 3 below (.e. the, Al 3 S system, whch s a fudametal system wth great dustral sgfcace.. Model.1. Model Descrpto At a costat pressure, vscosty s maly depedet upo composto ad temperature. Therefore, oe task whe modelg the vscosty s to fd a epresso relatg the vscosty to both composto ad temperature. The Arrheus equato s frequetly used to correlate vscosty wth temperature: lη = la+ E/ RT... (1 It has bee proposed that for Eq. (1, the logarthm of preepoet al parameter (la s a lear fucto of the act ISIJ

2 ISIJ Iteratoal, Vol. 5 (01, No. 3 vato eergy (E, whch s referred to as the temperature compesato effect. Thus for the vscosty varato of a pure slca melt, ths lear relato s epressed as follows:.3.. Al 3 S System I the Al 3 S system, there are o basc odes to provde metal catos to charge balace the Al 3+ os. Therel A= k( E ( where the values of E of ad the la of are the Arrheus parameters for pure slca. 13 The parameter, k, ca be obtaed from the vscosty of a specfc bary system M y S. For a mult-compoet system, the value of parameter la s assumed to be the lear addto of the values for the dvdual bary systems wth correcto for the re-ormalzed mole fractos of compoet ecept S. 4,11 Therefore, the parameter k ca be calculated as follows, k = ( k /, S, S... (3 The actvato eergy of vscosty, E Eqs. (1 ( s epressed the followg way to descrbe the olear chage of vscosty wth composto, E =... (4 + α S where o s the umber of other types of oyge ecept brdgg oyge S (these wll be defed the followg sectos, mol. It s ecessary at ths pot to troduce bref descrptos of the dfferet oyge os preset the melt... The Dfferet Types of yge Ios It s ot our teto to determe the dfferet types of oyge os derved from the real structure of alumo-slcate melts, sce ths s eceedgly comple. Istead, the dfferet types of oyge os assocated wth the boded catos are calculated usg a appromate method. I slca melts wthout Al 3, three types of oyge est, amely, ( brdgg oyge S ( o-brdgg oyge S ( free oyge. I melts cotag several basc odes, for the coveece of modelg, the oyge os boded to dfferet metal catos are eglected. For alumo-slcate melts, the codto s more complcated because of the amphoterc ature of Al 3. I order to dscuss the dfferet types of oyge os, t s ecessary to uderstad the dfferet forms of the Al 3+ os preset the melt. A Al 3+ 5 o ca form a Al 4 tetrahedro, ad ca 4 be absorbed to a S 4 ut such as a cha provdg there s eough metal cato preset to charge balace the Al 3+ o. I the preset model, all the Al 3+ os are assumed 5 to form the Al 4 tetrahedro f the mole fracto of basc ode M s hgher tha that of the Al 3. There s a cosderable dspute over the form adopted by a Al 3+ o whe t s ot charge balaced, ad two ma structural models have bee proposed. The coordato model 14,15 cosders ths type of Al 3+ o to be octahedral coordato. Based o the vscosty measuremets for the Al 3 S system, there s some dcatos that hghly-coordated alumum speces may be domat the hghly peralumous lquds (/Al 3 < Lacy 17 poted out the structure of Al 3+ o wth hgh oyge o coordato s eergetcally ustable. Moreover, he suggested the trcluster model whch cosdered that Al 3+ o remaed tetrahedrally-coordated wth a trcluster structure beg formed by Al 3+ os whch were ot charge balaced. Such trclusters are foud to est slca-free calcum alumate crystals 18 ad calcum alumate melts 19 at hgh temperature. Topls et al. 16,0 also showed that ths structure may be domat the peralumous Na Al 3 S ad Al 3 S melts. Zrl et al. 1 provded evdece for ther estece of trclusters Al 3 S melts from molecular dyamcs smulatos. I summary, t s cosdered that the two structures proposed for Al 3+ os (whe ot charge balaced may be both preset the melts, but sometmes oe type may be domat. Based o ths dscusso of the Al 3+ o, t s suggested that the oyge os boded wth the charge balaced Al 3+ o are brdgg oyge, whle those Al 3+ os,whch are ot charge balaced, are cosdered to be a ew type of oyge o, o matter what the form adopted by these Al 3+ os. Therefore, for alumo-slcate melt, s types of oyge os are preset: S, j S,, Al,, Al, ad Al. The brdgg oyge boded wth S 4+ o ad Al 3+ o smultaeously has bee eglected as the treatmet for free oyge boded wth dfferet metal catos. I the followg secto, parameters α S, α, j α Al,, α Al, ad α Al are assged to descrbe the moblty of,, Al,, j S Al, ad Al, respectvely, relatve to that for the brdgg oyge S. It has bee poted out 13 that the tradtoal thermodyamc models, e.g. Toop ad Sams, ttoello 3 etc., have ther ow defects calculatg the umber of dfferet types of oyge os. I ths paper, a smple method has bee proposed ad wll be eteded to the melt cotag Al 3. The detals are gve as follows..3. The lculatos of Numbers of Dfferet Types of yge Ios.3.1. M S System Whe addg basc ode M to the pure slca, the free oyge from M reacts wth the brdgg oyge S from S to produce a o-brdgg oyge S. It s assumed that the equlbrum costat of ths reacto s fte (Assumpto I. Therefore, the umbers of dfferet types of oyge ca be calculated as follows, : S S M = 0; = ; = M S M S S < M :... (5 = ; ; = 0... (6 M S S S S For a system cotag several basc odes ( M -S, the umbers of dfferet types of oyge os ca be calculated by the radom mg rule (Assumpto II: frst, calculate S, S ad usg Eqs. (5 (6 ad by assumg the system s a pseudo-bary system. The each term s multpled to accout for the re-ormalzed mole fractos of basc odes (Eqs. (7 ad (8. = ( ( M / S S ( M... (7 = ( ( M / ( M... (8 01 ISIJ 356

3 ISIJ Iteratoal, Vol. 5 (01, No. 3 fore, all the Al 3+ os are regarded as Al. There are two types of oyge os ths bary system: Al, S, wth the amouts beg calculated as follows: Al S = 3 Al3 = S... (9... ( M Al 3 S System I M Al 3 S system, the addto of basc ode (M ca lead to more Al 3+ o beg corporated to the S etwork. It s assumed that the equlbrum costat for the reacto of M compesatg Al 3 s fte (Assumpto III. I the case of / M < 1, all M Al 3 act as charge balacers, whereas the case of / > 1, all Al 3+ M Al 3 5 os form the Al 4 tetrahedros, ad ay etra M act as etwork modfers. Whe breakg the brdgg 5 oyge, t s assumed that the brdgg oyge Al 4 4 ad S 4 tetrahedro are equvalet, ad the o-brdgg oyges formed (boded to Al 3+ ad S 4+ os are proportoal to the umbers of brdgg oyge Al 4 5 ad 4 S 4 tetrahedros (Assumpto IV. The followg cases may be preset, (I M/ < 1 Al3 I ths case, the cotet of M s ot eough to compesate all the Al 3+ os. Therefore there are o o-brdgg oyges ( whether boded to S 4+ os or Al 3+ os. The umbers of oyge os ca be calculated as follows: = S... (11 S = 3(... (1 Al Al3 M... (13 Al, M (II M/ > 1 ad Al3 ( M ( I ths case, all the Al 3 < S + Al3 5 os form Al 4 tetrahedra after the charge compesato by M ; ay etra M (= M ca ot break all the brdgg oyge boded Al to Al 3+ ad S 4+ os. The umbers of other types of oyge os are calculated as follows: S = (... (14 M Al S + = ( M Al Al, S Al3 Al (15 S = S... (16 S Al,... (17 Al, (III M/ > 1 ad ( ( M > S + I ths case, all the Al 3 Al3 5 os form Al 4 tetrahedra; the basc ode M cotet s suffcet to break all the brdgg oyge, ad all the oyge os boded to Al 3+ ad S 4+ os are o-brdgg oyge. S S = 8 S Al, = 5 M S Al3... (18... (19... ( Al 3 S System I ths quaterary system, there are two basc odes: ad, whch ca be used to charge-compesate Al 3+ os. I the vscosty models reported by Urba, 3 Kodratev et al. 4 ad Nakamoto et al., 5 ad play smlar roles the compesato of Al 3+ os. However, ths s ureasoable because of the strog teracto of the + o wth other os because of ts small radus (relatve to that of the + o. Thermochemcal 6,7 ad spectroscopc data 8,9 have show that + os have prorty over + o for charge compesato of the Al 3+ o. Therefore, whe addg to Al 3 S melts, the + os ted to replace those + os provdg charge compesato to Al 3+ os. It s assumed that the equlbrum costat of substtuto reacto of + o for + s fte (Assumpto V. The followg stuatos may be preset durg the calculato, (IV < Al 3 Ths s smlar to case (I, the calculato s carred out as follows: =... (1 S S = 3( Al Al3 Al, Al,... (... (3... (4 (V <, > Al3 ad < ( S + I ths case, + os frst compesate the Al 3+ os; ay Al 3+ os ot charge-compesated by + os wll be charge-balaced by + os. Ay ecess + os wll be used for etwork breakg but are suffcet to break all the brdgg oyges.... (5... (6 ( = ( +.. (7 Al,... (8... (9... (30 (VI > Al 3 ad < ( S + I ths case, all Al 3+ os are charge-compesated by + 3 os; ad ay ecess ted to form o-brdgg oyges but are suffcet cocetratos to break all the brdgg oyge. = ( + S = ( + Al, S = S S Al, Al, S Al3 S Al3 S = 4( Al, S Al, ISIJ

4 ISIJ Iteratoal, Vol. 5 (01, No. 3 = ( S S =... (31... (3... (33... (34 (VII > Al 3 ad > ( S + I ths case, all the Al 3+ os are compesated by + os; the ad ay ecess ca break all the brdgg oyge boded to Al 3+ ad S 4+ os to form the obrdgg oyges. Al3 = 8... (37 Al,... (38... (39... (40 (VIII < Al 3 ad > ( S + I ths case, + os frst charge-compesate Al 3+ os. Ay Al 3+ os ot compesated by + os wll be chargebalaced by + os. Ay ecess ca be used to break all the brdgg oyge to form the o-brdgg oyges. = 8... (43 Al, = 8(... (44 Al,... (45... (46.4. The ptmzato of Model Parameters The followg parameters are eeded for the S Al3 S S Al3 S = ( Al, Al, = S S S S =... (35 S Al, Al,... (36 S Al, Al, S S = 8 Al3 S S Al3 Al3 Al3 Al, S =... (41 Al, S =.... (4 S S Al, Al, S = + Al 3 S system, to descrbe the depedecy of vscosty o temperature ad composto: k, k ad k Al, are related to the relatoshp betwee the pre-epoet factor ad the actvato eergy of vscosty. The parameters, α ad α, descrbe the deformg ablty of the bod aroud the free oyge boded to a + o or + o. Smlarly, α Al, descrbes the deformg ablty of bod aroud oyge boded to a Al 3+ o whch s ot charge balaced; α S ad α S, descrbe the deformg ablty of bod aroud obrdgg oyge boded wth S 4+ o ad + o or + o, respectvely ad α Al, ad α Al, ( =,, descrbe the deformg ablty of the bod aroud the brdgg oyge boded wth Al 3+ o compesated by a o, ad the bod aroud the o-brdgg oyge boded wth a o ad a o compesated Al 3+ o. Lastly, α Al, descrbes the deformg ablty of a bod aroud the o-brdgg oyge boded wth a + o ad a Al 3+ o compesated by a + o. For the above 13 parameters, k ad α S ( =, are optmzed usg the vscosty data for (M S bary systems; k Al ad α Al are optmzed usg data for the Al 3 S bary system ad α Al, ad α Al, from data for the (M Al 3 S terary system. Fally, the values for α Al, are optmzed usg data for the Al 3 S quaterary system. It ca be see Eqs. (5 ad (6 volve the optmzato of parameters α ad α ad requre vscosty data for (M S compostos where S 1/3. However, there are o data the lterature for ether the S or S systems because of the hgh meltg pots ths compostoal rage. I our prevous paper, 13 α ad α were calculated by Tm, Fe 1. α = ( αfe (where T m s the meltg pot of pure Tm, ode, ad the value of α Fe ca readly be optmzed by usg the data for the low meltg, Fe S system for compostos where S 1/3. Therefore, oly 11 parameters eed to be optmzed. The optmzed parameters are gve Table 1. The vscosty at a specfc temperature ad composto ca be calculated usg Eqs. (1 (4. 3. Results I order to evaluate the performace of the preset model, N 1 mea cal the mea devato defed as η η, -, 100% N = 1 ηmea, (where η,cal ad η,mea are the calculated ad measured vscosty, respectvely, ad N represets the umber of the samples s used. Table 1. Values of model parameters for the Al 3 S system. k α α Al, k α α S α Al, k Al α Al α S α Al, α Al, α Al, ISIJ 358

5 ISIJ Iteratoal, Vol. 5 (01, No M S Bary System ad S Terary System I the early publcato, 13 the vscosty data of S, S ad S systems has bee well represeted by the preset model. The vscosty decreases quckly wth addtos of M hgh S rage, whle the varato becomes getly wth the gradual decrease of the S cotet. The model s capable of epressg the o-lear chage of the actvato eergy for vscous flow wth composto. 3.. Al 3 S Bary System Ross et al. 30 ad Urba et al. 31 measured the vscosty of slags the Al 3 S system, wth the S mole fracto rage of The epermetal data were optmzed to yeld values of, parameters k Al ad α Al. The estmated values are compared agast epermetal values Fg. 1; the mea devato was foud to be 30.5%. Although the devato s larger ths case, t s reasoable gve the epermetal error s large due to the hgh temperatures ad hgh vscostes volved at hgh S compostos. The varatos of vscosty wth mole fracto of S at 16 ad 6 K are show Fg., from whch t ca be see that the preset model provdes a good descrpto of the vscosty for the Al 3 S system Al 3 System The vscosty of pure Al 3 at dfferet temperatures ca be calculated by the preset model by etedg the Al 3 S system to the lmtg case of mole fracto of S equal to 0 wth the parameters obtaed Al 3 S systems. The estmated values were compared wth measured values due to Urba et al. 3 ad Ross et al. 30 ad are show Fg. 3; the mea devato was foud to be 4.8%. Therefore, the preset model ca determe the temperature depedece of vscosty for pure Al 3 ad S (the model are proposed based o the data of pure S Al 3 S Terary System The Al 3 S system s a fudametal ad mportat slag system pyrometallurgy process, thus a study of ths system s partcularly mportat. May researchers e.g. Topls et al., 16 Kozakevtch et al., 33 Mach et al., 34 Yasukouch et al., 35 Scarfe et al., 36 Blls et al., 37 Johase et al. 38 ad Kta et al. 39 have measured the vscosty of ths system at dfferet composto pots, wth the mole fracto of Al 3 varyg from 0.03 to The parameters α Al, ad α Al, were optmzed usg more tha 500 groups of vscosty data. The estmated vscosty was compared wth the epermetal vscosty data ad s show Fg. 4; the mea devato was foud to be 1.1%. Fg. 1. Comparso of the estmated ad measured vscosty for the Al 3 S system. Fg. 3. Comparso of the estmated ad measured vscosty for Al 3. Fg.. The vscosty for Al 3 S system at 16 K ad 6 K as a fucto of composto. Fg. 4. Comparso of the estmated ad measured vscosty for the Al 3 S system ISIJ

6 ISIJ Iteratoal, Vol. 5 (01, No. 3 I order to obta a clear uderstadg of the chage of vscosty wth composto, the so-vscosty cotours at K are gve Fg. 5 ad are compared wth the epermetal data due to Topls et al. 16 ad Kozakevtch et al.. 33 It ca be see from Fg. 9, that the vscosty ehbts a mamum at the composto of /Al 3 = 1 for a costat mole fracto of S. Epermetal measuremets reported by Topls et al. 16 ad Kozakevtch et al. 33 ad theortcal estmato by Urba 3 all dcate the presece of a mamum ear /Al 3 = 1 but ehbt a lttle devato o the peralumous sde. The slght dfferece the posto of the mamum may result from the segmet method whe calculatg the umbers of oyge os Al 3 Bary System The vscosty behavor of the Al 3 system wth composto has proved dffcult to study epermetally due to the fact that the low-meltg rego s costrcted to a arrow compostoal rage; thus research o ths system has bee lmted, ad the vscosty results are sometmes parado. 4 At the same temperature, results of Ross et al. ehbt a mamum ear /Al 3 = 1 wth the chage of cotet for data, whle the vscostes measured by Urba et al. decrease mootoously as creasg the cotet of. From the amphoterc behavor of Al 3, a vscosty mamum mght esst wth the gradually addto of to pure Al 3, whch has also be proved by the vscosty model of Urba. 3 The preset model also gves a mamum for the treatmet of dfferet types of oyge os. So, t s atcpated that the results of Ross should be close to the calculated values by the preset model. The vscosty of ths system ca be calculated by the preset model by etedg the Al 3 S system to cover the lmtg case of mole fracto of S equal to 0. The estmated vscosty values are compared wth measured values reported by Ross et al. 30 ad Urba et al. 40 Fg. 6; the mea devato was foud to be 5.7%: 38.4% for Urba s data ad 17.1% for Ross s data Al 3 S Terary System The parameters α Al, ad α Al, for the Al 3 S system were optmzed usg the vscosty data of Topls et al., 16 Mach et al., 41,4 Johase et al., 38 Reblg et al. 43 ad Mzoguch et al.. 44 The calculated values are compared wth epermetal values Fg. 7; wth the mea devato was foud to be 1.0%. The so-vscosty cotours for K are gve Fg. 8, from whch t ca be see that a vscosty mamum occurs the rego where / Al 3 > 1. Ths fdg s supported by Topls et al. from the vscosty measumets for the Al 3 S system. Topls et al. cocluded that the + o has a weak ablty to charge-compesate Al 3+ os. However, the preset model t s assumed all + wll compesate Al 3+ os, provdg there s eough Al 3+ os preset. Moreover, the posto of the vscosty mamum s cosstet wth epermetal fdgs accordg to the adjustmet of parameters α Al, ad. α Al, Fg. 5. Iso-vscosty cotours for the Al 3 S system at K. ( Ref. 16; ( Ref. 33; ( so-vscosty cotours calculated wth the preset model; ad (--- the lqudus Al 3 S Quaterary System The Al 3 S quaterary system s a very mportat slag system. Durg the romakg process a blast furace, the prmary compoets of the slag are,, Al 3 ad S. Also the refg process of steelmakg, the ma costtuets of the slag are,, Al 3 ad S, whch some s added to protect the slag lg from corroso. Ths system has bee wdely Fg. 6. Comparso of the estmated ad measured vscosty for the Al 3 system. Fg. 7. Comparsos of the estmated ad measured vscosty for the Al 3 S system. 01 ISIJ 360

7 ISIJ Iteratoal, Vol. 5 (01, No. 3 studed because of ts dustral mportace wth measuremets due to Scarfe et al., 36 Johase et al., 38 Kta et al., 39 Km et al., 45,46 Lee et al., 47 Mach et al. 41,4,48 ad Mshra et al. 49 etc. at dfferet compostos wth the mole fracto of Al 3 ragg from The vscosty of may hgh Al 3 composto pots have also bee measured due to ts mportace to the creasg use of alumous ore romakg. I ths system, there are two cato + ad + o whch ca compesate Al 3+ os; the + o has prorty charge-compesato. The parameter α Al, was optmzed usg about 600 groups of the vscosty data. The estmated values are compared wth by epermetal data Fg. 9; the mea devato was foud to be 18.4%. The preset model provdes a good descrpto of the vscosty varato of the Al 3 S system wth regard to temperature ad composto. 4. Dscussos (1 It s foud that 13 has a stroger ablty to decrease vscosty tha the absece of Al 3, ad ths fdg s also supported by the work of Zhag et al., 4 Mlls et al. 6 ad Shu et al.. 11 e possble reaso may be Fg. 8. Iso-vscosty cotours the Al 3 S system at K. ( Ref. 16; ( so-vscosty curves calculated wth the preset model; ad (--- the lqudus. that the bod aroud o-brdgg oyge coected to a + o s stroger tha that for a + o. Ths may be due to the fact that the radus of the + o s smaller tha that of the + o, whch leads to the larger teracto of + o wth oyge o. Ths ca also be see from the magtudes of the parameters of α S (= ad α S (= 7.4 whch dcate that the deformg ablty of obrdgg oyge boded wth + o s greater tha that for the + o. Dfferet from the deformg ablty of o-brdgg oyge, the deformg ablty of brdgg oyge boded wth Al 3+ o compesated by + o s stroger tha that compesated by + o, whch ca be see from the optmzed parameters: α S = < α S = 7.4; α Al, = < α Al, = 7.115; α Al, = > α Al, = Sce the bascty of s hgher tha that of, t may be cocluded that the basc ode wth the hgher bascty wll lead to ( a weaker bod aroud the o-brdgg oyge boded to a metal cato M, ad ( a stroger bod aroud the brdgg oyge boded to a Al 3+ o compesated by a M o. I other words, the bascty of basc ode plays a paradocal role vscosty, where a ode wth hgh bascty ca decrease the vscosty by formg weaker bod aroud o-brdgg oyge. However, t ca also crease the vscosty by partcpatg the charge compesato of Al 3+ o to form a more stable tetrahedral structure. ( I order to uderstad how s the curret model s predcto dfferet from the esstg oes. The vscostes of dfferet systems are calculated by the vscosty models, ad the mea devatos of dfferet models for dfferet systems are gve Table. It should be poted out that the data of S, S ad S ca be foud our prevous paper. 13 From Table, t ca be see that the preset model have a stroger ablty of estmatg the vscosty Al 3 S system, cludg the pure compoet, bary system, terary system ad quaterary system, relatve to other models. Especally for Al 3 bary system, oe of the models ecept ours ca gve a well estmato. Whe costructg the vscosty model, all the models ot adopt the vscosty data of Al 3 system, so the estmato effect for ths system ca embody the etrapolato ablty of model. The preset model stll ca gve a well result. The reasos for the larger devatos for other models may be: the model by Rboud et al. does t cosder the o-lear varato of actvato eergy of vscosty wth the composto; models Fg. 9. Comparso of the estmated ad measured vscosty for the Al 3 S system. Table. The mea devatos of dfferet models (%. systems Ref. Ref.3 Ref.50 Ref.51 Ref.9 Preset Al S * S * Al 3 S Al S * Al 3 S Al 3 S Al 3 S ISIJ

8 ISIJ Iteratoal, Vol. 5 (01, No. 3 based o Urba 3,50 cosder so lttle structure factor, ad represet the vscosty data by optmzg lots of parameters, that leads to the arrow applcato rages; models based o the optcal bascty 51 ecouter dffcultes whe dealg wth the system cotag Al 3 for ts amphoterc behavor. 5. Coclusos A model (based o the classfcatos of oyge os s proposed to descrbe the vscosty behavor of the Al 3 S system. The model uses oly 11 parameters whch are derved by are optmzato of the epermetal data. The followg coclusos ca be draw: (1 The structure of alumo-slcate melts are defed terms of the dfferet types of oyge os preset, the cocetratos of these dfferet oyge os ca be calculated o the bass of the assumptos (I V. It provdes be a smple ad coveet way to study alumo-slcate melts. ( The preset model provdes a good descrpto of the vscosty behavor of pure compoets: S ad Al 3; bary systems: S, S, Al 3 S ad Al 3; terary systems: S, Al 3 S ad Al 3 S ; quaterary systems: Al 3 S. (3 The calculated results obtaed wth the model dcate a vscosty mamum occurs the rego where / Al 3 > 1 for Al 3 S melts wth a costat S cotet, whereas, the mamum occurs the rego where /Al 3 = 1 for the Al 3 S system. (4 has a stroger ablty to decrease vscosty tha slcate melts wthout Al 3. However, whe Al 3 s preset, there are two aspects: frstly, + os takes prorty (over + os charge-compesatg Al 3+ os ad ted to form more stable tetrahedral structures ad thereby cause a crease vscosty; secodly, cotrast, ca decrease vscosty more tha by formg weaker bods aroud the o-brdgg oyge. Ackowledgemet The authors wsh to thak the Chese Natural Scece Foudato for ther kd support uder the cotract , ad the Key Lab of Ecologc & Recycle Metallurgy, Mstry of Educato. Nomeclature η vscosty, dpas A the pre-epoetal factor, dpas E the actvato eergy of vscosty, J/mol R the gas costat, J/(mol K T the absolute temperature, K k parameter for correlatg the actvato eergy of vscosty E ad the pre-epoetal factor A S S Al, j Al, mole fracto of compoet brdgg oyge, boded to a S 4+ o o-brdgg oyge, boded to both a S 4+ o ad a metal cato, free oyge, boded wth metal cato brdgg oyge, boded to a Al 3+ o charge balaced by cato o-brdgg oyge, boded wth the metal cato j ad Al 3+ o charge balaced by cato oyge boded to a Al 3+ o whch s ot charge balaced the umber of dfferet type of oyge o α parameter for descrbg the moblty of oyge o relatve to the moblty of S Al REFERENCES 1 J. D. Mackeze: Chem. Rev., 56 (1956, 455. P. V. Rboud, Y. Rou, L. D. Lucas ad H. Gaye: Facber. Hüttepra. Metallweter Verarb., 19 (1981, G. Urba: Steel Res., 58 (1987, L. Zhag ad S. Jahashah: Metall. Mater. Tras. B, 9B (1998, L. Zhag ad S. Jahashah: Metall. Mater. Tras. B, 9B (1998, K. C. Mlls ad S. 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