ISIJ International. Vol. 33 (1993), No. 1, pp. 2-1 1

Mathematical Expression of Slag-Metal Reactions in SteelmakingProcess by Ouadratic Formalism Basedon the Regular Solution Model

Shiro BAN-YA

Faculty of Engineering. Tohoku University, Aza-Aoba, Aramaki. Aoba-ku. Sendai. Miyagi-ken, 980 Japan.

(Received on May79. 1992, accepted in final form on July 19. l992)

During the past three decades manytheoretical treatments have been developed to predict the ther-

modynamicproperties of silicate melts, In this paper, an attempt has been madeto describe the slag-metalreactions in steelmaking process quantitatively by the relation of quadratic formalism based on the regular

solution model, The approximate validity of the model wasquite satisfactory to formulate the reactions of

the oxygen distribution, the ferrous-ferric iron equilibrium, the manganesedistribution, the phosphorusdistribution and the hydroxyl capacity, The prediction of activities of componentsin FetO-CaO-Si02andFetO-MnO-Si02ternaries are aiso in good agreementwith the measurements.

KEYWORDS:slag-metal reaction; steelmaking; quadratic formalism; regular solution model; oxygendistribution; ferrous-ferric equilibrium; manganesedistribution; phosphorus distribution; hydroxyl capacity;

thermodynamics; activity.

1. Introduction

During the past three decades, the available data for

the physico-chemical properties of metallurgical slags

have been exceedingly improved by the efforts of manyInvestigators in the world. Theselected values of activity

and chemical properties for numerousbinary, ternaryand quaternary oxide melts have been compiled andpublished in Germanyl) and Japan.2) However, useful

data in multi-component slags are quite few to describe

the slag-metal reactions in steelmaking process. Manyslag models have been proposed to express the ther-

modynamicproperties of silicate melts. Someof the

models were successful for the mathematical expressionof slag-metal reactions in a restricted range of slag

composition, but the samemodels were inadequate for

the data from other sources obtained at different slag

composition. This is probably due to the fact that theslag models proposed are not enough to evaluate the

interaction energies between the oxides in slag andactivities of slag constituents.

This paper will summarize the outline of our recentstudies for the application of regular solution model to

formulate the activities of slag constituents, the capacities

of slags and slag-metal reactions concerning steelmaking

processes. Theregular solution modelof polymeric meltshas been proposed by J. Lumsdem(1961)3) to expressthe activities of componentsin FeO-Fe203-Si02slag.

Sommerville et al.4) have also showedthat the regular

solution model was applicable to describe the activities

of FeOandMnOin quaternary FeO-MnO-Al203-Si02slag. Recently, the approximate validity of the regular

solution model has been proved for manykinds of

C 1993 ISIJ 2

silicate, phosphate and aluminate slags of multi-

componentsystem by the extensive studies of Ban-yaand his co-workers.2,5~8) According to their works, it

has been shown that the activity coefficient of a com-ponent in multi-component slag can be described bythe relation of quadratic formalism based on the regularsolution model, even if the liquid silicate melt is notstrictly regular solution. The outline of the treatmentswill be described in the next section.

2. Regular Solution Model of Silicate Melts

The most difficult problems related to the nature ofpolymeric melts are the fact that the structure of silicate

anions varies with the amountand the kind of co-existing

cations and temperature. In other words, the extent ofthe polarization of oxygen ion is affected by the valence

and radius of cations. To avoid this difficult question of

the nature of the silicate melts, Lumsden3)has proposedthe application of simple relation of regular behavior for

oxide mixtures. In the model, it is assumedthat all kinds

of cations such as Cu+,Ca2+

.Fe2+

,Fe3+

,Si4+ and P5+

are randomly distributed in the matrix of oxygenanion,

which is a commonanion for all kinds of cations presentin the melts. The composition is expressed with cation

fractions, and the melt is considered to be composedof

oxides of the form such as CuO0.5, CaO,FeO, FeOl.5,

Si02 and P02.5' The activity coefficient of component,i, in a multi-component regular solution is expressed bythe following equations:

Gt=Aj~i =RTlnyi........

...........(1)

c(ijXJ +~~(oeij+0e,k ocJk)XJXk.

..,...(2)RTln yi =~. ?jk

ISIJ International, Vol. 33 (1993). No, 1

Table l. Interaction energy between cations of major componentsin steelmaking slag, aij. (J)

ij

Fe2+

Fe3+

Mn2+

Ca2+

2+MgSi4 +

p5 +

A13+

Fe2+ Fe3+ Mn2+ Ca2+ Mg2+ Si4 + p5+ A13+

- 18660

+7 IIO

-31 380

+33 470-41 840

- 31380-41 OOO

- 18 660

- 56480-95810-2930

+32 640

+ 14 640

- 161 080

+7 i lO

- 56480

- 92050

+61 920-75310

- 84940

- 83 680

-3 i 380

-95 810-92050

- IOO420

- 133 890

- 251040

- 154 810

+33 470

- 2930

+61 920

- IOO420

- 66 940

- 37 660-71 130

-41 840

+32 640-75 310

- 133 890

- 66 940

+83 680

- 127610

-31 380

+ 14640

- 84 940

- 251040

- 37 660

+83 680

-261 500

-41 OOO

- 161 080

- 83 680

- 154810-71 130

- 127610-261 500

G,~)E~:co~c:,

oo

8

7

6

5

4

3

2

Fe - O

Si-O

(~e

\-o

fo

4(~

o

(l

O

O 4O IOO20 60 80

--> mo[•/. Si02

Fig. l. Coordinationnumberofcationinbinarysilicatemelts.

Where, Xi is cation fraction, and c(ij is the interaction

energy betweencations, i.e., (i cation)-O-a cation). Thereference state of the activity in this case is taken tohypothetical pure liquid, which has regular nature.Therefore, the activity coefficient of a component i, in

multi-component slag can be written with the functionof slag composition and temperature by Eq. (2), if thesilicate melts have regular nature.

In this model, it is not so rough approximation toignore the polymerization/de-polymerization of silicate

anions. However, the assumption of randomdistributionof cations in the matrix of oxygenanion in silicate meltsis a rough approximation in the treatment. Becauseit is

known that the coordination number of cations for

oxygen ion takes 4, 6or 8by the lonic radius of cations.

According to the extensive studies of Wasedaet al.,9)

however, the coordination numbersof cations for oxygenions were about 4 to 5 in the middle composition ofbinary silicate melts as shownin Fig. 1. Therefore, it is

considered that there is a wide range of regular naturein the middle composition of silicate melts containing

manykinds of cations. Manyexperimental results haveshownus that the activity coefficient of silicate melts canbe approximately expressed with the following Eq. (3),

if this melts is not strictly regular solution:

RTlnyi =~oe,JXj2 + (c(,j + c(ik - ocjk)XjXk + I', .

...(3)•• ~~ -

jkwhere I' is the conversion factor of activity coefficient

betweenhypothetical regular solution and real solution.This is similar to quadratic formalism of metallic solutionproposed by Darken.lo) Furthermore, a fairly good

Table 2. Interaction energy betweencations of other com-ponents.

(i cation)-a cation) aij (J) (i cation)a cation) c(ij (J)

Li + _Si4+ - 142 130 H+_Li + +1500Na+_Fe2+ + 19 250 H+_Na+ +9750Na+_Fe3+

- 74 890 H+_K+ + 13 520Na+Si4 +

- II1290 H+Mg2+ +15800Na+_p5+ -50210 H+_Ca2+ + 15 100K+ _Si4+ - 81 030 H+_Mn2+ - 8230Ti4 +Ca2+

- 167360 H+A13+ - 24400Ti4+Mn2+ - 66 940 H+_Si4+ +30oooTi4 +Fe2+

- 37 660 H+_p5+ +7700Ti4 +_Fe3+ + 1260Ti4 +_Si4+ + 104600

Table 3. Conversion factors of activities.

Reaction Free energy change (J)

Fe*O(/ )+ (1 - t)Fe(s or I)=FeO(R.S.)Si02( p-tr) =Si02(R.S.)Si02( p-cr) =Si02(R.S.)Si02(/ )=Si02(R.S.)

MnO(s)=MnO(R.S.)MnO(!)=MnO(R.S.)Na20(!)=2NaOo.5(R.S.)

CaO(s)=CaO(R.S.)CaO(1)=CaO(R.S.)MgO(s)=MgO(R.S,)MgO(!)=MgO(R.S.)P205(1) =2P025(R.S.)

AG'= - 8540 +7. 142TAG'= +27150 -2.054TAG'= +27030 -1.983TAG'= +17450 +2,820TAG'= -32470 +26.143TAG'= -86860 +51.465TAG'=-185060 +22.866TAG'= +18 160 -23.309TAG'= - 40 880 - 4.703TAG'= +34350 -16.736TAG'= -23 300 + 1.833TAG'= +52720-230.706T

agreement would be able to be given to estimate theactivity value even if the effect of minor componentsless

than 5masso/o were ignored in quadratic formalism.

3. Determination of Interaction Energy and ConversionFactor of Activity

In order to apply the regular solution modelfor silicate

melts, one should knoiv the next three matters, (1) the

composition range in•which the regular nature is satis-

fied, (2) the value of the interaction energy, and (3) the

conversion factor for the reference states of the activities

between regular and real solution. These three mattershave been studied by the measurementsof Fe3+/Fe2+Fe2+/Fe equilibria and other sla~~metal reactionspreviously. They are listed in Tables 1, 2and 3.

This paper will describe howto determine above three

matters as one of the examples for the application of

3 C 1993 ISIJ

40

20~;i

oi~O~c:

Hcc

-20

H

ISIJ International, Vol.

2

:~:

~~Ieoo

oo.~

tr).

Lr)

onj o1600

d5

V F)

l O8 0•6Xsi02

04

40

O Kay &Tayior

c O Baird &Tay[oro" (

20~'L~)

1~~ l(E;

B/~~~ ~~'\O~~tn.. a

~(l *eo\--e o_

~~ A ulO6hocnj

~~o

o\ T\;\ -4(

- 20 tf]

1550'C

o 0.1 0.2 0.3

~ (1- XSi02)2

SiO -> CaO

o~u~o~

~O5~:~Hoc

-40

si02

Fig. 2. Acttvity coefficient or si02 in CaOSi02binary slag

at 1823K.

regular solution model. Baird and Talyorll) and Kayand Taylorl2) have studied the silica activity in moltenCaO-Si02binary melt by the next gas-slag reaction.

Si02(crist) +3C(s) =SiC(s) +2CO(g)..........

(4)

Ksi02("ist)= P~o/asi02(*ri*t) --"---"""'(5)

AGsio.(.,i,t) =675700- 365.7T (J).

..,.........(6)

The results of RTln ysio.(.,ist) obtained were plotted as

a function of (1 -Xsio.)2 in Fig. 213) according to the

relationship of binary regular solution. A good linear

relationship wasobserved for the values of RTln ysio.(.,i*t)

in the range of liquid state and the interaction energy of

ac*2' -si+ ' = ~ 133 900 (J) wasgiven from the slope of theline. Where, the reference state of silica activity is solid

pure cristobalite which is point A in Fig. 2. That is, the

base line of activity coefficient is the line AOfor the

measuredvalues. The conversion of the reference state

of activity from solid pure cristobalite to pure liquid

silica is given by the combination of Eq. (6) with thereaction,13) Si02(1) =Si02(crist), AG'= -9 580+4.80T

(J).

Si02(1) +3C(s) =SiC(s) +2CO(g) ............(7)

Ksi02(1) =P~o/asiO,(1) """--""""""'(8)

AGsi02(1)=666100-360.9T (J).

.............(9)

The reference state of silica activity in Eq. (9) is

supercooled pure silica, which is point B in Fig. 2. If

the molten CaO-Si02binary slag is really regular solu-

tion, the extrapolation of the experimental results to(1 -Xsi02)2 =0 should consist with the point Bin Fig. 2.

Namely, it is known that liqLrid the CaO-Si02 meltsatisfies the relationship of quadratic formalism but notregular solutlon. Since there is not any limitation for the

@1993 ISIJ 4

33 (1993). No. 1

reference state of the activity from the thermodynamicview-point, it is also possible to take hypothetical pureliquid silica of regular nature as the reference state ofsilica activity. The conversion factor of silica activity

from solid pure silica to hypothetical liquid silica ofregular nature wasalready determined as the reaction,13)

Si02(crist) =Si02(R.S.), AG'=27030- I.98T (J), by the

thermodynamicstudyl3) of FetO-Si02 binary melt. Thecombination of this equation with Eq. (6) gives us thefollowing equations:

Si02(R.S.) +3C(s) =SiC(s) +2CO(g) ......(lO)

Ksi02(R's.) =P~o/asio.(R,s.) ---""""(1 1)

AGsio,(R.s,) =648700- 363.7T (J).

..........(12)

The reference state of silica activity in above equationsis hypothetical pure liquid silica of regular nature, whichis point Cin Fig. 2. Theexperimental results seen fromthe base line CO"strictly satisfy the regular nature. Fromresults mentioned above, the activity coefficients of silica

of different reference states are summarizedas follows:

RTlny = - 133 900(1 -Xsio.)2 (J)

si02(R's.)

RTlny = - 133 900(1 -Xsi02)2 +17450si02(1 )

+2.82T (J)

. = - 133900(1-Xsio.)2+27030RTIn ysio.(,.,*t)

-1.98T (J). ......

..........(13)

4. OxygenDistribution betweenSlag and Metal

The equilibrium relation of FeO-Fe203-MnO-Si02-MgO-CaOslag, which are major componentsin

steelmaking slag, with oxygen in metal can be written asfollows by the model, 5, 13, 14) using the interaction energies

given in our previous studies:

Fe(1) +O=FeO(R.S.) ....................(14)

RTlnK0=RTln(XF*o/ao)+RTlnyF*o """(15)

AG'=128 100-57.99T (J) ................(16)

RTlnyF.o = ~18660X~.o*=+7110XM2.0

- 41 840Xs2iO,+33 470XM2go~31380Xc2*o

+44930XF.o*='XM.0~93140XF.o*

=Xs,o

+ 17 740XF.o*.= ' XMgo+45 770XF,o,=

' Xc.o

+40580X ' X 21 340X ' XM*o sio ~. M*o Mgo+67780X 'X +58570Xs,o XMgoM*o c.o

+60 670Xsio, ' Xc.o + 102 510XMgo' Xc*o (J)

.(1 7)

Since the above equation is quadratic formalism, the

minor componentswhich are less than 5masso/o can beneglected for the approximate calculation.

In Fig. 3,13) the oxygencontents in iron calculated byaboveequation werecomparedwith the measuredvalues

for the typical measurementsof previous investigators.

Fromthe results, it is confirmed that the oxygencontentin liquid iron in equilibrium with slag can be estimated

within the accuracy of ~100/0 by the model.The reference state of FeOactivity in the model is

ISIJ International. Vol.

taken to the hypothetical stoichiometric FeO, in whichthe regular nature of the solution is satisfied. However,the reference state of conventional iron oxide activity is

the pure iron oxide in equilibrium with metallic iron. Theconversion of the reference state for both activities is

written as follows:6,1 5)

FetO(1) +(1 - t)Fe(s or /)= FeO(R.S.) ......(18)

AG'=-8540+7.142T(J) ...............(19)

RTlnaF, o(1) RTlnaF.o(R,s.)~8 540+7,142T(J).

.(20)

In Fig. 4,14) the activity of iron oxide, aF.,o, in

FetOCaOSi02ternary in equilibrium with liquid iron

estimated by the model is shownto comparewith the

experimental results of manyprevious investigators, who

1500FetO-Si02-cao-Mgo o A

cl Shim and Ban-yao Suito'Inoue and AA vcl ~b

eTakada

1' v T~tor arx:1 ChiPmAa~oA eo~ 1000 A wird([er and ~e

C:l

:' ChlPman ~Lu''u

l.•vcl

:loE

JL/~:~Ner///

e'r-loE 500~a

:/:::;:~~e ele el

LJ / FetO- Si02- cao:) JL Fetters and ChiPmand:L7A' G6r[ Oeters and

Schee[O

Fig. 3.

O 1500500 1OOO[ppm O] ca[culated

Estimated values for oxygen contents by regularsolution modeland the measuredvalues in liquid ironequilibrated with FetO-(CaO+MgO)-Si02slags.

33 (1993), No. 1

are referred in Fig. 3. Anagreement of both measuredand calculated values has been excellent over the widerange of slag composition from acid side to basic side

except for extremely FetO rich region of NF*,o >0.7.

5. Ferrous-Ferric lron Equilibrium in Slag

The ferrous-ferric iron equilibrium in slag is veryimportant concerning the slag basicity, but thequantitative treatment of A-ratio =Fe3+/Fe2+ has beenvery difficult due to the complicate variation by the slag

composition and temperature. The A-ratio can beobtained by the model as follows:5,13)

FeO1.5(R.S.) =FeO(R.S.) + l/4 02(g) .......(21)

RTlnKF*=RTln(XF*o/XF*o*=)+0.25RTln P02

+RTln(yF*o/ yF.o*.5 )"" - -""--(22)

AG'=126820-53.01T(J).

..............(23)

Thepast workers could not formulate quantitatively thevariation of A=Fe3+/Fe2+by the change of s]ag

composition. However,by the application of the regularsolution model, the values of A-ratio in slags areexpressed as follows from Eq, (22):

log(Fe3 +/Fe2+) =6625/T- 2.77 +0.25 Iog P02

+(RTlnyF.o~RTlnyF,oi.5)/(19,1 T).

.........(24)

The Fe203contents in FetO-CaOand FetO•--CaO-Si02slags estimated by aboveequation are shownin Fi~• 5,1 3)

to confirm the validity of the mode] at the rang~ ofaF**o O.7.

Theexperimental data by Taylor andChipmanshowedthe higher values for the estimated data by the model,but the points of data by the other investigators of four

groups agree well each other within the accuracy of

~IOo/o. Thesimilar agreementfor the ferrous and ferric

iron equilibrium was observed in FetO-Na20-(Si02+

Si02

oeC]

IAA

IF

vv

CaO

aFetO0'9 - 1O'S - 0190'7 - 0'8

0180'20'6 - O' 7Ot5 - 0'60'4 - O' 50'3 - 0'40'2 - 013 Si02

sat~vO'I - 0'2' 0'6

O -'0'1 O014 v '~i\S)":I

1~~:VllF~ 'r(Jer

v

0~)l~: v\ l 'Q~~(/

)1 ~/

/b~A~)~/r'~~

~:~piv"'4~,

$1'1b:~1\'~'vl(~'I):'J'b

0'6 ~~ I

t

A

A-(t7:~/:;;J:~~ A Iha

.

A/ It;i

,.

/ ~ I~ l:1L~Clej)Q~S)~b ~3Cc~Q~SI

';~F i~1;~ J!t,1~

~( cl'\"p

lbp~~ '$Oi8

's:ej!/

/ "_'1" 012'

A

JL

,t ." \IF

: 'ol q)l~tAA o(~ o)'

ejlO~t~ ,lJbA

(,:~

\ \ cS!Lei

I~l~"~:l]clcllt~"e~D.o J2)0.2 0.4 0,6 0.8 FetO

Fig. 4.

Estimated values for aF** o(1 ) by regular solution modeland the measured values in Fe,O-CaO•-Si02 slags

equilibrated with liquid iron at 1873K.

NFetO

5 C 1993 ISIJ

ISIJ International, Vol. 33 (1993), No. 1

o(u 008(~)'

Nou)

o 0.06LLO

.E

- 0.04u,'1'

Q,

E~o"~0.02

LLa,

z

o

oNFe203 (ca[.) in FetO-CaOO.1 0.2 0.40.3

FetO- CaOl Gurry and DarkenFetO - Si 02- CaOA Fetters and Chipman .o Tay[or and Chipman

ee

e0~Sl ee t.

.o c: e. t.

eo ' FetO- Si02 -CaOo o Bodsworth

o . G6rt, Oeterso~)and Schee[

o. 4

0.3

o. 2

o.1

O

O'1'

uO~

co,1'

oEoLL(P

Z

Fig. 5.

O O.O2 0.0 4 O.06 0.0 8NFe203(cal.) in FetO - Si02 -CaO

Estimated values for NF*,o, by regular solution modeland the measuredvalues in Fe*O-CaOslags equili-

brated with Pco, = Iatm and in FetO-CaO-Si02slags

equilibrated with iron,

P205)'6) (Fe,0+MnO)-(Ca0+MgO)-Si02ls)FetO-(CaO+MgO)- (Si02 +p205)16) slags.

and

6. Equilibrium of ManganeseDistribution

The equilibrium relation of manganesedistribution

between FeO-Fe203-MnO-Si02-MgO-CaOslag andliquid iron can be written as follows:8)

FeO(R.S.) +Mn=Fe(1) +MnO(R.S.) .......(25)

RTln KM*=RTln[XM*o/(aF.o(R.s.) ' aM*)]

+RTlnyM~o(R.s.) """""""-"""(26)

AG'= - 141 400+66.28T(J) ..............(27)

RTlnyM.o(R,s.) =71lOXF2.0~56480XF2.0,

s

- 75 31OXs2i02+61 920XM2go~ IOO420Xc2*o

- 30710X ' X , =- 26 360X ' XF.o F.o F.o si02

+35560XF,o XMg0~53560X 'XF,o c*o

- 164430XF.o,s

' Xsi02 +8370XF.o,j

' XMgo

- 52 720XF,o,5

' Xc.o +53 550Xsi02 ' XMgo

- 33 470Xsi02 ' Xc*o+70 290XMgo' Xc*o (J).

.(28)

In Fig. 6,8) the equilibrium constant of manganesedistribution in FetO-MnO-CaO-MgO-Si02Slag areplotted against the silica content to examine the validity

of model. Thecomposition of four groups of manganesesilicate calculated in Fig. 6 was within the range ofNF*,o and Nsi02 As seen in Fig. 6, the valuesof log KM*evaluated by the modelwerealmost a constantvalue within experimental error over the wide range ofslag composition.

Theeffect of temperature on the log KM*evaluated bythe sameprocedure is shown in Fig. 7,8) in which thedata, reported by other eight groups of Maurer andBischof, Krings and Schackmann,K6rber and Oelsen,Bell et al., Bell, Fischer and Bardenheuer, Suito and

~~th.C'

CCl~+~Oc:UIOt

:~~)Cl~

(,

o)o

6

4

2

o

-2

-4

FetO- lvlnOsat ~Si02 ~823KC] Ban-ya. Hino & Kikuchi FetO-MnO-Si02sat.

V FiScher &Bardenheuer I X6rber &oel5en(18a3t 2a~)

_e(tD aa,:l]

l]

FetO-lvlnO-MgOsat~Si02

e Bell

O Be[1, Murad&Carter

Fet O-MnO-CaO-NgOsat~Si 02

A Xrings &Schackmann(] Winkler & Chipman

A Suito & Inoue

~ 600.2 0•4 0•6

NSi02

Fig. 6. Relation between equilibrium constant calculated byregular solution model and Nsio, at 1823K.

Temp., K2000 1900 1800

~2t/ioOi;~~~uo,ca:;~:-0~

QQ1a

3

2

1

o

-1

-2

-3

FeLO MnOsat~Si02

OFischer ~Bardenheuere Ban-ya, Hino &Kikuchi

FetO-lvlnO-Si02sat

O~brber &Oeisen

ai ~'. ~~~-~

~'!

FejO- MnO-CaOsat.- SiO2Ban-ya.Hlno &Fujisawa

FetO h4nO CaO-Si02O Mavrer &Bischof

logKMn=7386/T 34S2

Feta -MnO-h4gO- Si02

ABel[ lylurad &Carter

FeIO-MnO-h4gOsat.~ SiO2A Be[i

V8an-ya, Hino &Fujisawa

l

~

9c] o

o

FetO -lylnO- CaO-lvlgOsat.-Si02C] Krings &Schackmannl Winkler &Chipmanx suito & Inoue

5,0

Fig. 7.

5.1 5•4 5552 5.3104!T

Temperature dependence of equilibriumcalculated by regular solution model.

56 5.7

constant

Inoue and Winkler and Chipman, are also shownbyrecalculation. The results obtained by different kind ofslags and by manydifferent investigators are in fairly

goodagreementeach other, and the results obtained areexpressed by Eq. (27).

As similar to the case of the activities of FetO(!) andFeO(R.S.) in slag, the conversion factor between theactivities of conventional liquid MnO(/) and thehypothetical liquid MnO(R.S.) in slag is necessary. Theconversion factor can be derived in our previous workas follows:8)

MnO(1)=MnO(R.S.) ....................(29)

AG'=-86860+51.465T(J) ..........,...(30)

RTlnaM.o(1)=RTlnaM~o(R.s,) ~86 860+51.465T (J).

.(3 1)From above relation, the activity coefficients of eachcomponentin FetO-Si02-MnOslags can be given bythe following equations: 15)

RTlnaM.o(*) =7113XF2.0~56490XF2,0*

=~75 320Xs2io,

- 30710X • X * * - 26 360X • XF,o F.o.

F,o sio,

164440XF,o*=

Xsio, ~32470+25.04T(J)

.(32)

C 1993 ISIJ 6

1,0NlnSi03 Mn2Si04

ISIJ lnternational, Vol.

\j i\1

l;!

\ /f!

aMno(s)a -Si02(o cr )

\Ifil'! lil'tL 1773K

~ !i,/:

/!\ Ift l'

~ ' Abraham'

- - Davies'/'

~

Richardson7= / Mehta'~~ / ~ Richardson/

'(~ \,---- Rao'Gaskett

f~J' ' ~

_ Regu[arsotution/ \ri~ f \'

mode[_/ \

~/r/ \~~~'~~

~~

33 (1 993),

o. 8

o~O.6

O

o 0.4Lr)

O

Fig. 8.

o. 2

o

l

0.4 0.6

NM~o

Comparison of the activities

MnO-Si02slags at 1773K,

Si02

o. 8

of the

8

6

~2CL:(

ol oo~ -2

-6

-8

No. 1

•1~~~~~D_~J~~~_OOlaS~.~.O_ _ ~ _ ~ _

_t3__(f~

_ _

OC:I

Present

Trdrnel

~nUppel

D~! 6>•-o

' ~ ~~~~d~~

worket al

et al.

1.0

components in

aFeto

A 0.10o 0.30I O50A 0.70

1

Fig.

(XcaO+XFeO)/ Xp025

lO. Relation between logKpl and (Xc*0+XF.o)/Xpo,, m

FeO-FeOls~P02,5CaOslags equilibrated withliquid iron and solid CaOat 1873K.

08

oo. 4

'E:s

~,':

o. 6 AA

02

O. I O. 2

l

o

08

03

l

o. 6

O~O. 5

O. 5

A0.7

08

~U).

~~,

o. 4

02

h,InO

Fig.

o2 0.4 FetOo, 6 o.o

NFeto

9. Comparisonof calculated ap.*o(1) with the measured

one in FetO-Si02-MnOslags in equilibrium with solid

iron at 1723K.

RTlnaFe,o(1) =18660XF2eol5~41842Xs2i02

~7113XM2no

- 93 140XFeol5

' Xsi02 +44940XFeol,5 ' XMno+40590Xslo XMno~8540+7.172T (J) ........(33)

RTlnasi02(crist) = ~26 360XM2.0~41 842XF2eo

+32040XF2eoi5~ 124270XM.o' XFeo

+13 510X 'X1 5

+9456X 'Xi 5Mno Feo

,Feo Feo

.

+27030- 1.983T (J). ...............,................,.

(34)

Theactivities of the componentsin MnO-Si02binaryi 5)

and FetO-MnO-Si02ternaryl5) slags are shownin Figs.

8 and 9 respectively. The values of activity estimated

7

from the modelshowedgoodagreementwith other data.

7. Equilibrium of PhosphorusDistribution

The equilibrium relation of phosphorus with FeO-Fe203-P20s~Si02-CaO-MgOslag can be written asfollows:7,17)

P+2.50=(P02.5)(R.S.) .................(35)

RTlnKpi RTln[Xpo, =/(ap 'ag•5)] +RTlnypo,.=(R S):(~6)

AG'= - 326520+ 162.88T (a= 13 810) (J) ...(37)

RTlnypo. =(R,s.) = 31 380XF2.0+ 14 640XF2.0*.=

251040Xc2*o~37 660XM2go+83 680Xs2io,

+1920XF.o XF.o,=~251 040X • XF.o c*o

- 102510X • X +94 140X • XF*o MgO F*o siO,

140590XF.o*=

Xc.o 20090XF.o*.='XMgo

+65680XF.o*.

Xsio ~ 188280X •X, c*o Mgo

- 33 470Xc.o ' XsiO, + I12 960XMgO• XsiO, (J).

.(38)

In order to showthe validity of the model, the value~of equilibrium constant of Eq, (36), Kpi, calculated fromthe data obtained in FetO-P205-CaOslag were plotted

as a function of (Xc*o +XF.o)/Xp0==

at 1873K in Fig.

10. As seen in Fig, l0,7) the values of log Kpl evaluatedby the model were truly a constant within experimental

error over the wide range of slag composition. Thesimilarresults were given in the other slag systems studied at

present work.The effect of temperature on the log Kpl evaluated by

the sameprocedure is shownin Fig. Il,7) in which the

data reported by other five groups of Winkler andChipman,Kntippel et al., Trdmel et al., Suito et a/, andKor are also shownby recalculation. Theresults obtained

by different kinds of slags and by many different

investigators were in fairly good agreement each other,

and Eq, (37) wasgiven.

The equilibrium relation of phosphorus in iron withiron oxide in slag can be derived as follows by the

combination of Eqs. (16) and (37):

C 1993 ISIJ

8

e

4

2

o

-2

-4

-6

-8

ISIJ International, Vol. 33 (1 993),

No. 1

~(alo

~ ~Feo- Feot s ~ P02'5 - Cao sat. Feo- Feol 5~ p02'5 - Si 02 - cao(2CaoSi02sat.)

~ ~ -Feo-Feol s~ P025-hJ490sat, Feo Feo],5-p02 5- Cao-N90sat

~Feo-Feols~P02s~Si02sat f3CF_

D~-~I~~~;~'~o~~~~~:~~~~~~/C]

______i8

D ~'----

~Trdmel et al

~HnUppel et al,

~Winkler et al

~Suito et al

~

iog ~pl = 17060l T- 8.

(~=0.4 )~or

51 o

Prese n twork

D

o. 50 0.55T~1 / 1ri~3 L/~1

v r\

o 60 o 65

8~~Feo-Feol 5-p02 5-cao sat. Feo-Feol 5-p02.5- Si02-c ao

6 (2cao,si02sat ) present~~ • Feo- FeoL5- Pol s~ cao -Mgosat '

wor kFeo- Feol 5- p02,s~N90sat

4~ Feo- Feol 5~ poi.!~Si02 sat

2 iog Kp2=3281T-O936(\'

_ _____~_Cf = O~,_4__)_

_______t_

_

3cf'~

~( OJD~,0:~;{~~o ~~~~~~

c]

oo-~_~~~if-Itr~~~~

D____i______{_______~_(7)

-2 -- ~~~i5~cr~~

~-4 ~Trdmel et al xor~suito et al

_6 ~Knuppel et al. ~Ba[aiiva et al

~winkler et al ~shirota et al

~8O 50 O60O 55

T~1 / 10 3K 1

E+2.5(FeO) (in slag) = (P02, s) (R.S.) +2.5Fe(1)...(39)

AGp2=6280+17.908T ((T= 13 810) (J).

.....(40)

Theeffect of temperature on the equilibrium constantof Eq. (39) is shownin Fig. 12. in which the results bypresent authors and other investigators of Winkler andChipman, Balajiva et al., Kntppel et al., Tr6mel et al.,

Suito et al., Kor, and Shirota et al. are plotted for

comparison. The results shown in Fig. 12 are a little

scattered in comparison with those in Fig. I l, but it will

be seen that they fairly agree with each other within theexperimental error. In Fig. 13, the phosphorus dis-

tribution ratio L~ calculated from the model is plottedagainst the measuredL~ for the data by present authorsand other investigators. The agreement between bothcalculated andmeasuredvalues wasalso goodwithin theexperimental error.

As similar to the case of the activities of FetO(1) andFeO(R.S.) in slags, the conversion factor between theactivities of conventional liquid P205and hypotheticalliquid P02.5 in slag is necessary. Turkdogan andPearsonl8) have derived the standard free energy of

C 1993 ISIJ 8

o 65

Fig. Il.

Temperature dependenceof log Kpl,

Fig. 12.

Temperature dependenceof log Kp2'

formation of liquid P205from solutes in liquid iron asfollows:

2P(1 o/o)+50(1 o/o)=P205 (pure liquid) .....(41)

AG41= -705 420+556.472T(J).

..........(42)

The conversion factor can be derived as follows by the

combination of Eq. (40) with Eq. (42):

P205(1)=2P02.5(R.S.).......

..........(43)

RTlnap,0=(1 )=2RTlnapo, =(R.s.) +52720

-230.706T (J). ......

.........,,(44)

In the past, the slag models, proposed by Flood andGrjeftheim,19) and Turkdogan and Pearsonl8) wereenough accurate to predict the phosphorus content in

metal and the phosphorusdistribution ratio betweenslag

and metal for basic slag, but the modelsof the sameidea

werenot successful to predict the oxygencontent in metal

and the oxygen distribution between slag and metal.

However, in the approximate application of the regular

solution model, the both oxygen and phosphoruscontents in metal and the distribution ratios of oxygenand phosphorus can be estimated within the error of

ISIJ International, Vol. 33 (1993), No. 1

4

3-CL

JOIO 2

1:~QJ 1re

l~iOU

-1

~Al5/V1

dl

Vl

li

oooo

40

~~:(:c

L~ 20o:

~og:o

o

AGH02p=~19800• 26.32 T(J)

cl~l_/:Ae

e

A_/o

.~/~]_lO

O CaO-Si02

~ KO0.5-Si02

e NaO0.5-Si02

[] LiOo.5-Si02

- 221 2- O 1 43

Measured logL~

FetO P205- CaOsat. FetO-P205- CaO-~lgOsat.o ~nUppei et ai. A present worko Tr~mel et al. FetO-P205-Si02-CaOe Present work (2CaO•Si02 sat )

FetO-P205-CaO v Present worko Shirota et al. FetO-P205-Si02- CaO-hdgOsat.

FetO-P205-~lgOsat. Winkler et al.

x present work VBaiajiva et al.

FetO-P:205 -Si02sat. ASuito et ai.

DTrdmel et a[.

I Present work

Fig. 13. Relation between calculated and measured phos-

phorus distribution.

~10 o/o over the wide range from basic slag to acid slag.

8. Estimation of Hydroxyl Capacity

An attempt has been madeto estimate the hydroxylcapacity by the regular solution model. Theequilibriumrelation of water vapor solubility in silicate melts is

written as follows:

l /2 H20(g)=HO0.5(R.S.). .. . .... . ..... ...

(45)

RTlnKH20=RTlnXHo.=~ 1/2 Iog PH,o

+RTlnyHo...(R.s.) """""""""'(46)

AG~,o= ~ 19 800+26.32T (J) (1 430-1 873K)..(47)

Therefore, hydroxyl capacity is expressed as follows:

RTln CbH=RTlnKH,o~RTlnyHo..=(R.s.)

=RTlnKH=0~~0cH,X,

-~~(oe _, •.......(48)

H ,+c(H_j-oeiJ)X,XJ

ijThe values of free energy of Eq. (45) are shownin Fig.

14 for the four kinds of binary silicates of Si02-MO(M0=CaO,Na20, K20, Li20)20-22) systems. Theresults obtained in Fig. 14 is expressed with Eq. (47). In

Fig. 15, the estimated hydroxyl capacity of binary silicate

melt is shownwith the experimental data of Kurkjian &Russell20) to confirm the validity of the model. There areminimumvalues of hydroxyl capacity for three kinds ofsilicate melts at the composition of NMOO

s=0.4, and a

good agreement is observed for both ~;:easured andcalculated values. Figure 16 showsapproximate validity

of the model for the hydroxyl capacity for CaO-

Fig. 14.

Fig. 15.

1400 1600 1800

T (K)

Temperature dependenceof free energy of solution

of hydrogen in silicate melts.

0,02

Iuo 0.01

o

Kurkjian &Russell

AKO0.5-Si02(1 573K)

e NaO0.5-Si02(1 590X)

[] LiO0.5-Si02 (1573X)

calcuiated

A eeA Al(//

e-e'~eD/

l:)

fO

I*OV

Fig. 16

O O4 O.6 0.8O.2XMO0.5

Comparisonof CbHcalculated by regular solution

model with CbHmeasuredin alkaline metal silicate

melts.

0.016

0,008

lrO /llo

/nlF/vQ)/1F //1~ O~)V/V

VIZe~~F:~tl~flrl(DV

/

/1(D:S~~~)~~/

//1'F

//

//

l o

OO 0.008 0.016

C' (measured)OH

CaO-Si02 CaO-SiO-AI O2 23e lguchi et a[ O Iguchi et a[.

Na20-Si02 e sachdev et a[.

Q) Russet[ I Ban-ya et al.

1) Kurkjian & Russell CaO-Si02-MgOK20-SI02 v lguchi &Fuwav Kurkjian & Russe[1 A Sosinsky et al.

L 20-Si02 A Ban-ya et al.

l Kurkjian & Russe[[ CaO-Si02-MnOc Iguchi & Fuwa

Comparisonof estimated values of Cb}1 by regular

solution model and the measuredvalues in moltensilicate slags.

9 C 1993 ISIJ

ISIJ International, Vol.

cao FeoCao' Mgo

'tvl~g.O. 4 Fe203

~:,~f

22~~g ~je0203J~•S~/0/2~~~'IFeo Fe o.

'

2/ .23

~2F~OS~02cMago?F~;g:I~~g2L/~i~/'~Q

'

~,Feo 'Ti02\FeO'Si02

3Cao' SiO'--~0 2Mgo'Si02I Na20'Fe203

~(/02Cad.Si02

' acao SiO// 2 l

33 (1993), No. 1

o

-2 5

oE -5 O

-7 5

o(~I~

-1 oo

-125

.Na20 2Si020

l Ferrite

OSi[icate Oe phosphateL~ Others

cao'p205 ee 4cao'p205/e 3lcao'p205

e ~cao p205

OA[2 03 ' Si02

JFe203' P205

02Na20!sej

02Na20•S i02

e 3lvlgO P20

e 3NaO•PO2 25

40

_2O

O~:

~;1_2O

q,LL

~S

-40

,5

\ +4

p5' e\\e

e lv'lg2'*1

A[3+0

"Mn2tIP3* \Na e\

Fe e

o Fe3\\\

Si L

\

Ti4* e

e Ban-ya et

o Others

Ca2

ai.

-75 -50 -25 oo(jj xj Xj(kJ )

Fig. 17. Correlation between interaction energies and the

heats of formation of complex oxides at 298K.

S02,2i 22) NaOS02,20) K20-Si02,20) Li20-Si02,20)CaO-Si02-A12203,23.24)

CaOSi02Mg025,26)andCaO-Si02Mn027) systems.

9. Correction of the Interaction Energy with OtherPhysico-chemical Properties

The interaction energy betweencations can be written

as follows in the regular solution:

c(ij=(ZN012)(2Uij- Uii- Ujj), .

..........(49)

where Uij is the bond energy of (i cation)-O-(j cation)ion pair, and Z and No are coordination numberofcation and Avogadro's numberrespectively. The valueof ceij should have close correlation with otherphysico-chemical properties of oxides.

Theheat of mixing of multicomponent regular,solution

can be expressed as follows:

AHM=V~ cc..X.X.. ...

..........(50)LL. *J * JiJAs a rough approximation of Eq. (50), the heat offormation of binary complex oxide. AH298, can bewritten as follows:

AH298~c(,,X.X.....

......,...(51)* 'J ' J

Figure 176) shows the relationship between the heat offormation of binary complex oxides, AH298, and theinteraction energy related to these complex oxides. Agoodcorrelation is found betweenthem, especially in the

range lower than AH298= - 41 .8 kJ.It is said that the bondenergy of (i cation)-O-(j cation)

consists of the coulombic force, polarization of oxygen

C 1993 ISIJ 10

O25

Fig. 18. Relationradii.

O50

between

O.75rMz' (~)

interaction energies

1.00

and cation

ion and London's force, but their theoretical treatmentis not knowneven in present day. However, they areaffected by the valence and radius of cation. Therefore,Fig. 1814) shows the relationship of ionic radius andvalence for the oeF... _M.. as one of the exampleof manyinteraction pararneter. Agood correlation is also found

amongthe ionic radius, valence and interaction pa-rameter except for Ti4+. From these results, it is con-firmed that the values of interaction energy obtainedis not only parameter for curve fitting.

10. Conclusion

The application of regular solution model for silicate

melts was studied to espimate the activities of slagconstituents, the capacity of slag andslag-metal reactionsconcerning steelmaking process. it was confirmed thatthe model was satisfied over the wide range of slag

composition from basic to acidic sides. The content ofthe elements dissolved in iron in equilibrium with theslag can be estimated within the accuracy of ~: 100/0.

Acknowledgments

Theauthor wishes to thank Drs. M. Hino and F. Ishii,

and manycolleagues in our laboratory for their effective

assistance in completing this paper.

REFERENCESl) SlagAtlas, VDEh,VerlagStahleisen M. B. H. Dtisseldorf, (1981).2)

3)

4)

5)

6)

7)

8)

9)

lO)

l l)

12)

Chemical Properties of Molten Slags, ed. by S. Ban-ya and M.Hino. ISIJ, Tokyo, (1991).J. Lumsden:Physical Chemistry of Process Metallurgy, Part I,

Interscience, NewYork, (1961).I. D. Sommerville, I. Ivanchev and H. B. Bell: ChemicalMetallurgy of lron and Steel, Iron Steel Inst., London, (1973).S. Ban-ya and J.-D, Shim: Can. Metall. Q., 23 (1983), 319,

Tetsu-to-Hagan~, 67 (1981), 1735, 1745.S. Ban-ya, M. Hino and H. Takezoe: Trans. Iron Steel Inst. Jpn.,

25 (1985), I122.

R. Nagabayashi, M. Hino andS. Ban-ya: ISIJlnt., 29 (1989), 140.

M. Hino, I. Kikuchi, A, Fujisawa and S. Ban-ya: Proc. 5th Int.

lron and Steel Cong., ISIJ, Tokyo, (1990), 264,

Y. Waseda.Y. Shiraishi and J. M. Toguri: J. Jpn. Inst, Met., 43(1979), 1009.

L, S, Darken: Trans. Metal!. Soc., AIME, 239 (1967), 80, 90.

J. D. Baird and J. Taylor: T,'ans. Fa,'aday Soc., 54 (1958), 527.

D. A. R. KayandJ. Taylor: Trans. FaradaySoc., 56 (1960), 1372.

ISIJ International, Vol. 33 (1993). No. 1

13)

l4)

l5)

l6)

l7)

l8)

l9)

20)

21)

S. Ban-ya and M. Hino: Tetsu-to-Hagan~, 74 (1988), 1701.S. Ban-ya and M. Hino: Tetsu-to-Haganb, 73 (1987), 476.S. Ban-ya, M.Hino andN. Yuge: Tetsu-to-Hagan~, 71 (1 985), 853.

R. Nagabayashi, M. Hino and S. Ban-ya: Tetsu-to-Hagan~, 74(1988), 1577.

R. Nagabayashi. M. Hino and S. Ban-ya: Tetsu-to-Hagan~, 74(1988), 1585.

E, T. TurkdoganandJ. Pearson: J. Iron Steel Inst,, 175 (1953), 398.

H. Flood and K. Grjotheim: J. Iron Steel Inst., 171 (1952), 64.

C. R. Kurkjian and L. E. Russell: J. Soc. Glass Tech., 42 (1958),

130T.

T. Fuwa, S. Ban-ya, T. Fukushima and Y. Iguchi: Tetsu-to-

22)

23)

24)

25)

26)

27)

Hagan~,53 (1967), 91.

Y. Iguchi, S. Ban-ya and T. Fuwa: Trans. Iron Steel Inst. Jpn.,

9(1969), 189.

S. Ban-ya, Y, Iguchi and S. Nagata: Tetsu-to-Hagan~, 71 (1985),55.

D. J. Sosinsky, M. MaedaandA. McLean:Metall, Trans. B, 16B(1985), 61.

S. Ban-ya, Y. Iguchi and S. Yamamoto:Tetsu-to-Hagan~, 72(1986), 2210.

Y. Iguchi andT. Fuwa: Trans. Iron Steel Inst. Jpn., 10 (1970), 29.

Y. Iguchi and T. Fuwa:L' HydrogeneDansLes Metaux, 2(1 972),

424.

11 C 1993 ISIJ