Modeling the viscosities of alumino-silicate melts

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1 Modelg the vscostes of alumo-slcate melts Guo-Hua Zhag 1,* ad Kuo-Chh Chou 1, 1 School of Metall. ad Ecologcal Egeerg, Uversty of Scece ad Techology Beg, Beg 10008, Cha State Key laboratory of Advaced Metallurgy, Uversty of Scece ad Techology Beg, Beg 10008, Cha Abstract: The structurally based vscosty model for alumoslcate melts has developed, whch the fluece of melt structure o vscosty has epressed by the deftos of dfferet types of oyge os: ( brdgg oyge S, boded to S + os ( o-brdgg oyge S, boded to S + o ad cato from basc ode, ( free oyge, boded to os, (v brdgg oyge, boded to a Al + o charge compesated by cato ; (v o-brdgg oyge Al,, boded to the metal cato ad Al+ o charge compesated by cato ; (v oyge Al, boded to a Al + o whch s ot charge compesated. A systematc method s proposed to calculate umbers of these oyge os. Accordg to the calculato results of the vscosty model, t has bee foud that the abltes of basc odes decreasg vscosty follow the order: Fe>M>Ca>Mg, whe Al s absece. The vscostes of quary, quarterary, terary, bary ad uary systems volvg Mg, Ca, Fe, M, Al ad S compoets have bee calculated by the preset model wth all the mea devatos ot great tha 0%. Furthermore, t dcates the better precso of the preset model tha that of other models for the same systems. Keywords: Vscosty, model, alumo-slcate melt, structure base 1. Itroducto Vscosty s a mportat physcal property for alumo-slcate melts because of ther dramatc effect o pyrometallurgcal processes ad sestvty to the slag structure. For stace, relable vscostes are requred ( to guaratee smooth operato of the blast furace ( for the successful separato of metal ad slag durg the basc oyge steelmakg process ( for foamg processg ad (v the cotuous castg process where the slag acts as a lubrcat, etc.. From the vewpot of reacto ketcs, most pyrometallurgcal reactos are cotrolled by vscosty determed dffuso process molte slags. 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 because of the dffcultes assocated wth hgh temperature operatos. Cosequetly, the method of model estmato becomes very mportat. May vscosty models are proposed to estmate vscosty of alumoslcate melts [1-10]. Though these models are successful to some etet, may shortcomgs stll est: ( The applcato rages of these models are very arrow. They ca oly obta good estmato results or ear the composto (or temperature rage, whch the model parameters are optmzed, whle the results wll be accurate whe away from the rage. ( For alumoslcate melts

2 cotag several basc odes, these vscosty models ca ot well represet the vscosty varato tedecy wth composto. Sometmes, a verse tedecy wth the epermetal fdg may be gve []. ( These models ca ot be eteded to the vscosty estmato of ode systems wthout S. Therefore, much work stll should be doe o the vscosty model.. Requremets to vscosty model At costat pressure, vscosty s determed by temperature ad chemcal composto of molte slags. Modellg vscosty s fdg a reasoable epresso to descrbe the relatoshp betwee vscosty ad temperature as well as composto. Geerally, vscosty model must fulfll the followg four requremets: ( Vscosty s sestve to the structure of alumoslcate melts, ad dfferet compoets (acdc ode, e.g. S ; basc ode, e.g. Ca ad Mg; amphoterc ode, e.g. Al have dfferet flueces o the structure. Thereby, vscosty model should be bult based o a reasoable descrpto to the structure of alumoslcate melts. However, the emprcal models by Rboud [1], Urba [6], Kodratev [7], NPL [], Ray [5], etc., dd t cosder the fluece of melt structure o the vscosty. ( Geerally, the temperature depedece of vscosty ca be descrbed by the Arrheus equato [11] E η = Aep( RT or Weyma equato [1] E η = ATep(, whch there s a lear relato betwee the logarthm of pre-epoet RT factor la ad actvato eergy E whch s called the temperature compesato effect ad s a commo rule the felds of vscosty, ketcs, electrcal coductvty ad dffuso coeffcet [1]. Therefore, the compesato effect should also be take to cosderato the vscosty model, whle t s ot cosdered vscosty models of Rboud [1], NPL [], KTH [], Nakamoto [], Ida [10], etc.. ( It has bee poted out that the actvato eergy of vscosty s a o-lear fucto of composto for bary slcate melts ad shows a abrupt crease ear pure slca [1]. Cosequetly, vscosty model should reflect the olear varato behavor of actvato eergy wth composto. Amog the dfferet vscosty models, the polyomal fuctos wth the hghest order of were utlzed by dfferet authors to descrbe the relato betwee actvato eergy ad composto: =1 model of Rboud [1] ; = model of Shu [9] ; = models of Urba [6], Kodratev [7] ad Zhag [8]. (v Al s a amphoterc ode, whch ehbts as a basc ode uder the codto of low bascty, ad as a acdc ode uder the codto of hgh bascty. Furthermore, Al + ca form 5 Al tetrahedro, ad replace the posto of S whe the bascty s hgher a proper rage. As the covalece of alumum o s +, whch s less tha that of slco o whe t s the posto of S, therefore a etra cato s eeded to compesate the charge balace. The cato of basc ode ca act as the charge-compesator, e.g. Ca + ad Na +, etc.. However, t s foud that dfferet catos have dfferet abltes of compesatg Al + os [15], so vscosty model should cosder the dfferet orders of dfferet catos whe compesatg Al + os. However, o model ca dstgush ths ablty of charge compesato ecept NPL model [] whch acheves ths goal accordg to the dfferet optcal bascty values of dfferet basc odes. However, ths way has defect for the reaso that NPL model may basc odes has the same optcal bascty values

3 but the compesatg abltes of the metal catos are dfferet actually, e.g. optcal bascty of L, Ca, Fe ad M usg the same value of 1.. Descrpto of structure of alumoslcate melts Before modellg the vscosty, flueces of dfferet compoets o structure of alumoslcate melts should be epressed quattatvely by a relatvely smple method. I our prevous papers [1, 16], the structure of melts was descrbed the sght of the dfferet types of oyge os. Frstly, the possble estece of oyge os should be defed. I slca melts wthout Al, three types of oyge os est, amely, ( brdgg oyge S, boded wth S + o ( o-brdgg oyge S, boded wth S + o ad metal cato,, ad ( free oyge, boded wth metal cato. I alumoslcate melts, ecept for the referred three types, other three types of oyge os appear, amely, (v brdgg oyge, boded wth a Al + o charge compesated by cato ; (v o-brdgg oyge Al,, boded wth metal cato ad Al+ o compesated by cato ; (v oyge Al, boded to a Al + o whch s ot charge compesated. It should be poted out that free oyge boded wth metal catos ad, ad brdgg oyge boded wth S + o ad compesated Al + o, are ot take to cosderato the above classfcatos. Several thermodyamc models have bee proposed to calculate the umbers of dfferet types of oyge os, such as thermodyamc models by Toop ad Sams [17], ttoello [18], Yokokawa ad Nwa [19], Masso [0], L ad Pelto [1], etc., whle those models ca oly be appled to M-S bary system, ad the etrapolatos to the hgh order systems or systems cotag Al are very hard (or mpossble. Gaye [] developed a cell thermodyamc model whch could be used to S -Al -Fe -Ca-Fe-Mg-M system. Although the cell model provdes better results, t ca ot be appled to the systems cotag alkal odes. The Susa method [] ca oly calculate the umbers of three types of oyge os: o-brdgg oyge S, brdgg oyge S, brdgg oyge. I vew of these facts, a ew method wll be gve based o the followg fve assumptos. Assumpto I: Whe addg basc ode M to a pure slca, the free oyge from M reacts wth the brdgg oyge from S to produce a o-brdgg oyge S S. It s assumed that the equlbrum costat of ths reacto s fte. S : M = 0 ; M S = ; = (1 S S M S < : M

4 = ; M S = ; S S = 0 ( S Assumpto II: 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: frst, calculate S, ad usg Eqs. (1- ad by S assumg the system s a pseudo-bary system. The each term s multpled by the re-ormalzed mole fractos of basc odes (Eqs. ad to calculate the dfferet types of oyge os. = ( (M / ( S S (M ( = ( (M / (M Assumpto III: I M -Al -S system, the addto of basc ode M ca lead to more Al + o beg corporated to the S etwork. It s assumed that the equlbrum costat for the reacto of M z+ o compesatg Al + o s fte. I the case of M / <1, all M act as charge balacers, whereas the case of / M >1, all Al + os form the 5- Al tetrahedros, the etra M act as etwork modfers. Assumpto IV: I the case of M / <1, whe the etra M breaks the brdgg oyge, t s assumed that 5- - the brdgg oyge Al ad S tetrahedro are equvalet, ad the o-brdgg oyge os formed (boded to Al + ad S os are proportoal to the umbers of brdgg oyge Al ad S tetrahedros. The followg cases may be preset, (I / <1 M I ths case, the cotet of M s ot eough to compesate all the Al + os. The umbers of oyge os ca be calculated as follows: = (5 S S = ( (6 Al M = (7 M (II / M >1 ad ( < ( + M S (= I ths case, all the Al + 5- os form Al tetrahedra after the charge compesato by M ; etra M M ca ot break all the brdgg oyge boded to Al + ad S + os. The umbers of other types of

5 oyge os are calculated as follows: = ( M Al S = ( M Al Al, S + S + S (8 (9 S = S (10 S (III M / >1 ad = Al (11 ( > ( + M S I ths case, all the Al + os form 5- Al tetrahedra; the basc ode M cotet s suffcet to break all the brdgg oyge, ad all the oyge os boded to Al + ad S + os are o-brdgg oyge. = (1 S S 8 = (1 = 5 (1 M S Assumpto V: Dfferet metal catos have dfferet abltes of charge-compesatg Al + o. The prorty order ca be defed by Parameter I (epressed by the coulombc force betwee the cato ad oyge ao s troduced to characterze the abltes of dfferet catos, Q I = ( r + r Z+ - M (15 where Q s the covalece of M z+ o; r Z+ ad r - are the raduses of M ad oyge os, respectvely. Whe there M s several basc odes alumoslcate melt, for stace, as addg basc ode (M to (M -Al -S melt, the cato wth the hgher prorty wll substtute the posto of. It s assumed the equlbrum costat of substtuto reacto of o for o s fte. The followg cases may be preset, (IV + < (M (M Ths s smlar to case (I, the calculato s carred out as follows: = (16 S S

6 = ( (17 Al Al (M (M = (18 Al, (M = (19 Al, (M (V <, + > ad (M (M (M + (M (M < ( S + I ths case, os frst compesate the Al + os; ay Al + 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 oyge os. S ( (M (M Al = + S + S (M = ( (M + (M Al Al, + S ( Al (M = ( (M + (M Al Al, + S (0 (1 ( S = ( S S = ( Al, (M = ( Al, Al (M (5 (VI > ad (M + < ( + (M (M S I ths case, all Al + os are charge-compesated by os; ad ay ecess ted to form o-brdgg oyge os but are suffcet cocetratos to break all the brdgg oyge os. S ( (M Al = S + S (6

7 S = (M S + S (7 = ( (M Al + S (8 = (M + S (9 S S = (0 S S = (1 (VII > ad (M + > ( + (M (M S I ths case, all the Al + os are compesated by os; the ad ay ecess ca break all the brdgg oyge boded to Al + ad S + os to form the o-brdgg oyge os. = (M 8 (M Al + (M ( = 8 (M + (M Al (M ( S = (M S (M Al + (M ( S = S (M + (M Al (M (5 Al, S = (M Al (6 Al, S = (M (7 (VIII < ad (M + > ( + (M (M S

8 I ths case, os frst charge-compesate Al + os. Ay Al + os ot compesated by os wll be charge-balaced by os. Ay ecess ca be used to break all the brdgg oyge to form the o-brdgg oyge os. 8 = (8 (M = 8( (9 Al (M S = (0 S Al, S = (M + (M Al (1 I the eve hgher system, umbers of dfferet types of oyge os ca also be calculated followg the above method. After obtag the umbers of oyge os, the ew vscosty model wll gve et secto.. Model The temperature depedece of vscosty s descrbed by the Arrheus law, where η s the vscosty, dpa S lη = la + E / RT ( ; A s the pre-epoet factor, dpa S ; E s the actvato eergy, J/mol; R s the gas costat, 8.1 J/(mol K ; T s the absolute temperature, K. The compesato effect betwee the logarthm of pre-epoet factor la ad actvato eergy E s epressed as follows: l A= ke ( ( where costats of ad 17.7 are used to descrbe the vscosty of pure S. For multcompoet systems, parameter k ca be calculated as follows, = ( k ( k/, S, S The actvato eergy E Eq. ( s epressed usg the equato E = + ' S ' (5 where S s the umber of brdgg oyge boded wth S + o; ' s the umber of other type of oyge o; parameter ' descrbes the deformg ablty of bod aroud the oyge o ' relatve to the dfferet types of oyge os, 5 types of parameters: S,, S. Correspodg to Al,, Al, ad Al, are assged to descrbe the deformg ablty of bods aroud, S,, ad Al, respectvely. Al

9 5. The applcato of the ew model Table 1 Values of model parameters 5 k 10 S Al, Al, Mg Al, Ca Fe Al, Ca Mg Ca Fe M Al Table Mea devatos for dfferet vscosty models (% Systems Rboud Urba Kodratev Ida NPL Ray Nakamoto Preset model Al Mg-S Ca-S Fe-S Mg-Fe-S Ca-Mg-S Ca-Fe-S Ca-M-S Ca-Fe-M-S Ca-Mg-M-S Al -S Ca-Al Mg-Al -S Ca-Al -S Fe-Al -S M-Al -S Ca-Fe-Al Ca-Mg-Al -S Ca-Fe-Al -S Ca-Mg-Fe-Al -S * the blak dcates the system ca ot be calculated for the absece of parameters; represets the mea devato s hgher tha 1000%. The vscostes of alumoslcate systems volvg the compoets of Mg, Ca, Fe, M, Al, S have

10 bee smulated our prevous papers [1, 16, ], wth the optmzed parameters show Table 1. Parameters k, ad are optmzed (M -S system; ad k Al are optmzed Al -S system; Al, ad Al, are S Al optmzed (M -Al -S terary system; s optmzed (M -(M -Al -S system. It should be Al, poted out that parameter (=Mg, Ca, M are calculated by T m, Fe 1. ( T m, (where T m s the meltg pot of Fe compoet for the absece of data (M -S system wth the slca cotet lower tha 1/ ecept Fe-S system [1] ; k ad S are optmzed Ca-M-S system for the weak compatblty of vscosty data from dfferet refereces M-S system [8]. The systems of Ca-Mg-S, Ca-Fe-S, Mg-Fe-S, Ca-Mg-M-S, Ca-Fe-M-S, Al, Ca-Al, Ca-Fe-Al are ot partcpated to the parameters optmzato, ad the vscosty estmato of these systems are doe by the parameters optmzed other systems. The mea devato (defed as = 1 η -η N N, mea, cal 100%, where, cal = 1 η, mea η ad η, mea are the estmated ad measured vscostes, respectvely, ad N represets the umber of the samples s used to evaluate the calculatg result of the preset model. The mea devatos of our model ad models of Rboud [1], Urba [6], Kodratev [7], Ida [10], NPL [], Ray [5] ad Nakamoto [] are gve Table, from whch t ca be see that our model has the strogest ablty for vscosty estmato, eve for the system wthout S. 6. Dscussos (1 I order to see clearly the dfferet flueces of dfferet basc odes (Fe, M, Mg ad Ca o vscosty, the theoretcal vscosty varatos (estmated by the preset model of the Mg-S, Ca-S, M-S, Fe-S four bary systems wth the mole fracto of S at 187K are gve Fg. 1, from whch the vscosty of melts at the same temperature ad composto follow the order: Fe-S <M-S <Ca-S <Mg-S, or the ablty of basc odes to decrease vscosty follows the order: Fe>M>Ca>Mg, whe Al s absece. The same order s also obtaed by Zhag [8] ad Shu [9].

11 10 9 Mg-S 粘度 /dpa.s Ca-S M-S Fe-S S Fg.1 The flueces of dfferet metal odes o the vscosty of M-S bary system at 187K ( The preset model ca fulfll all the four requremets: dfferet types of oyge os are defed to descrbe the structure of alumoslcate melts, ad a systematc method s proposed to calculated the umbers of dfferet types of oyge os; the compesato effect betwee the logarthm of pre-epoet la ad actvato eergy of vscosty E s take to cosderato the preset model. Meawhle, order to corporate the vscosty estmato of pure slca, oly oe parameter s eeded the compesato relatoshp; the recprocal fucto s utlzed to epress the olear behavor betwee actvato eergy of vscosty ad composto; a prorty order s set for dfferet metal catos whe charge compesatg Al + o based o the coulombc force betwee the cato ad oyge ao. However, oe of the other vscosty models cosder all the four requremets. So, the preset model has strog ablty for vscosty estmato, whch ca be see from Table. 7. Coclusos New vscosty method s proposed based o defg dfferet types of oyge os to descrbe the structure of alumoslcate melts. Ad fve assumptos are suggested to calculate the umbers of these oyge os. Whe several basc odes est the Al cotag melts, dfferet prortes are determed for dfferet metal catos whe charge compesatg Al + o, accordg to the coulombc force betwee cato ad oyge ao. Accordg to the comparsos of dfferet models calculatg the vscostes of alumoslcate melts volvg Mg, Ca, Fe, M, Al, S compoets, t s cocluded that the preset model has the strogest ablty for vscosty estmato. Ackowledgemet The authors wsh to thak the Chese Natural Scece Foudato for ther kd support uder the cotract Refereces [1] P.V. Rboud, Y. Rou, L.D. Lucas, H. Gaye. Improvemet of cotuous castg powders. Fachber. Huettepra. Metallweter Verarb., 1981, 19 (10, p [] K.C. Mlls, S. Srdhar. Vscostes of romakg ad steelmakg slags. Iromakg Steelmakg, 1999, 6 (, p6-68. [] S.C. Du, J. Bygde, S. Seetharama. Model for estmato of vscostes of comple metallc ad oc melts.

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