ISIJ International, Vol. 33 (1993), No. 1, pp. 148 155

The Influence

Slags

of Structure on the Physico-chemical Properties of

Kenneth C. MILLS

Division of Materials Mettology.

(Received on Mayl8.

National Physical Laboratory. Teddington. Middx. TW111992, accepted in final form on September18. 1992)

OLW,UK.

The current knowledge of the structures of silicate slags is summarisedand the relationships betweenmeasuresof the depolymerisation of the melt and various physical properties are examined. It is shownthatthe optical basicity whencorrected for the cations required to charge-balance any AIO~tetrahedra present,provides a reasonable measureof the depolymerisation of the melt and has the advantage over the (NBO/T)ratio that it compensatesfor cation effects, It is shownthat the depolymerisation of the meit is the primaryfactor affecting most physical properties, the cations having only a secondary effect. The relationships

betweenstructure and the viscosity, electrical and thermal conductivity, diffusion coefficient, density, thermalexpansion coefficient, thermodynamicand optical properties of melts are discussed.

KEYWORDS:slags; structure; viscosity; electrical conductivity; thermal conductivity; diffusion coefficientthermal expansion coefficient; optical basicity; (NBO/T).

1. Introduction

In the last decadethe mathematical modelling of hightemperature processes has becomean established methodfor improving the performance and efficiency of these

processes. Mathematical modelling of the heat and fluid

fiow in these processes has resulted in a demandforphysical property data for the materials involved. Thedetermination of reliable physical property data at hightemperature is both difficult and time-consuming.Furthermore, the compositions of slag phases formed in

high temperature processes maydiffer significantly fromday-to-day and also plant engineers frequently wish to

know the effect that changing the concentrations ofcertain constituents of the slag would have on the

performance of the process. All of these factors have led

to a demandfor mathematical models to predict thephysical properties as a function of the chemicalcomposition.

Various models have been reported for the predictionof liquidus temperature, T]iql'2) viscosity,3 ~ 5) density6,7)

etc, of the slag phase. These models for the most partare based on numerlcal fits of experimental data and arerarely based on the structure of slag. However, the

dependenceof the physica] propertles upon the structureo.f silicate melts is demonstrated by the fact thatBockris8,9) and other workers were able to deduce the

structure from physical property measurements.Thusthe

demandfor more reliable estimates of the physicalproperties of slags wlil only be met by the developmentof models based on the structure of the slag.

Our knowledge of slag structure has improvedenormously in recent years with the introduction of new

techniques such as X-ray and neutron diffraction,10)

vibrational (especially Raman)spectroscopy and nuclearmagnetic resonance. Data from these sources combin-ed with information from structural thermodynamicmodels, molecular dynamics calculations and physical

property data has led to a rapid advancein our knowledgeof the structure of silicates. Manyof these advanceshave

comefrom the studies of the structures of magmasandrocks by the geological fraternity. The current status of

our knowledge of the silicate melts has been describedby Mysenl1) in two excellent reviews.

The structures of silicate melts are affected by (1) the

degree of polymerisation of the silicate melt (2) the fitting

of certain cations (eg. A13+, Ti4+) into the silicate

network and (3) the nature of the network-breakingcations (eg. Ca2+, Mg2+)present In the slag. The aimof the present study was to identify their effects on thephysical properties of the molten slag.

2. Structure of Silicates

Theprincipal features affecting the structure of moltensilicatesl 1)

are outlined below:(1) Silicate siags consist of 3-dimensional (3-D)

interconnected networks of Si0~4 tetrahedra in whichsilicons are joined by bonding oxygen atoms (O'). Th~gradual addition of cations (eg. Na+, Ca2+) results in

the progressive breaking of these oxygen bonds with the

formation of non-bridging oxygens (NBO), denoted O~andeventualiy the formation of free oxygen, 02~

,ions.

(2) The melt contains various 3-D interconnected,anionlc units, eg. Si02, Sl20~~, Si20~-, Si20~- andSiO~~ which coexist in the melt. These anionic units

C 1993 ISIJ 148

ISIJ International, Vo].

probably contain 3-6 atoms and can exrst in the formof chains, sheets and rmgs. The introduction of morenetwork-breaking cations, eg. Ca2+does not alter the

nature of the anionic units but does affect the amountsof the vanous umts, i.e. high concentrations of

moredepolymerrsed unrts are formed.(3) For a specific mole fraction (x) of oxide (eg.

x(CaO)) the nature of the cation does affect the

proportion of the various units, eg. Si20~- but not theoverall degree of polymensation. The cations wrthsmaller radii (r) and higher valence (z), eg. Mg2+

,favour

the formation of the more depolymerrsed (eg. SiO~-)and polymerised (eg. Si02) anionic units. The tendencyto form more extreme anionic units can be ranked in

terms of the parameter (z/r2) in the hierarchy Mg2+ >Ca2+ >Sr2 + >Pb2+ >Ba2+ >Li+ >Na+>K+

.

(4) Other cations such as A13+, Fe3+, B3+, Ti4+

and P5+ can form tetrahedra (eg. AIO~-) which usuallyfit into the 3-D silicate units and enhance the overall

polymerisation of the melt; thus it is customary to refer

to tetrahedrally-coordinated units by T rather than Si,

eg. T02, T205etc. However.AI0~~ ions havea different

charge to SiO~~tetrahedra, and thus cations are needed,

to provide electrical charge balance, eg. (NaAI04)4~and thus the Na+must be sited close to the Al atom.

(5) There is some evidence of ordering in meltscontaining divalent ions (eg. Ca2+) since these mustsatisfy two O~bondsor two AIO~- tetrahedra and this

task is particularly difficult for smaller cations, eg. Mg2+and hence the need for ordering of the melt.

(6) Ferric ions, Fe3+ can adopt both four-fold (IV)

or six-fold (VI) coordination, i.e. act as both networkformer and breaker, respectively. For slags containinglOo/o Fe203 rt has been reportedli,12) that Fe3+ (IV)

and (VI) coordination are favoured when the Fe3+/(Fe3+ +Fe2+) ratios are >0.5 and respectively.

In most steelmaking slags Fe3+ will act as a network-breaker (VI).

(7) In alumino-silicates the Al probably prefers the

morepolymerised units (eg. T02) of wrth a large T-O-Tangle.

(8) Ti can also adopt IV and VI coordination, rt is

reportedll) that for 1-7masso/o Ti02 the Ti acts asnetwork former but the substitution is not randomandtends to form titanates and alumino-titanates.

(9) P205 tends to form PO~- tetrahedra but al-

though someP-O-Si bonds are formed, the P205 tends

to form phosphate complexes which have a greateraffinity for cations, eg. Na+. A13+ than SiO~~ tetra-

hedra.

2.1. Measuresof the Degreeof Polymerisation

In recent years the (NBO/T) ratio, i,e. the nurnber ofnon-bridging oxygens per tetrahedrally-coordinated

atom, has been adopted by manyworkers to representthe degree of depolymerisation of the melt. It can be seenfrom Appendix I that the (NBO/T) ratio does allow for

the cations occupied on charge-balancing duties. The(NBO/T)ratio is probably the best measureof the degreeof polymerisation.

Considerable attention has been devoted recently to

149

33 (1993), No. 1

the optical basicity (A) which represents the powerof anoxide to donate a negative charge. Howeverthe opticalbasicity has been reported to provide a global measureof the concentrations of O', O~and 02~ present in themelt.13) Consequently, the optical basicity may beconsidered to provide an alternative measure of the

degree of polymerisation. Howeverthe optical basicity

(A) does not take into account the fact that someof thecations in alumino-silicates are required for chargebalancing duties; hence an adjustment was madeto A(outlined in Appendix 2) to compensatefor the cationsused for charge balancing. The principal advantage ofusing A is that it can beapplied to non-silicate slags.

..*'

2.2. Cation Effect

Various parameters have been used as a measureofthe effect of different cations on the structure andphysicalproperties; Mysenl1) preferred the parameter (z/r 2) where-• and r are the valence and radius of the cation,

respectively. It can be seen from Fig. I that (zlr2) is

inversely proportional to the optical basicity of the oxide.

3. Physical Properties

Mostphysical properties are strongly dependent'upon

temperature, thus whencomparing slags with different

liquidus temperatures. Tuq, it is necessary to compareproperty values at some reference temperature. Thevalue at Tliq Wasselected since the structures of the meltwould be unaffected by temperature effects and wouldallow the physical properties to be comparedon an equalbasis.

The temperature dependence of most transportproperties can be represented by the Arrhenius re-lationship (Eq. (1)) where P is the property, E the ac-tivation energy, R the gas constant and T the ther-

modynamictemperature.

P=Aexp(-EpIRT)=Aexp(-Bp/T) ..........(1)

The_activation energy for viscous flow is considered to

be the energy required to break the bonds necessary for

viscous flow, consequently the activation energy couldalso be used to determine the effect of structure onphysical properties.

3.1. Viscosity (n)

Viscosity (n) data are prone to appreciable errors, arecent interlaboratory comparison prograrnme indicatedthat someof the reported viscosities for a referencematerial varied by more than ~500/0 from the

~5

~ I'~ 1'O t~ lo oo(~ 8~ L's'o oooc'ccD

0'5 x z v)JU LLN~1 2 43

(Zlr2 )Fig. l. The parameters (z/,'2) as a function of the optical

basicity. A.

C 1993 ISIJ

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

(a)

20

18

16

(D 14ul

OCL 12o~10

~ 8*

64

OXx

2O

-2

o

l Si02o Siiicates

e FeO(MnO)-Si02x MO-Ai 203 - Si02

O OO

qsO

o 1 2 3(N801T)

4

EFC

20

18

,6

14

12

10

8S42O

-2

(b)

~X

x

X

o

oo

~xx

~x~xx

xoxoex

Axo9*:oo *~~o

0.4 O6O. 5Acorr

07 0.8

Fig. 2.

Theviscosity at the liquidus temperature (In n~)

as a function of (a) (NBO/T) ratio and (b)

corrected optical basicity A , O, O, silicates, ..*' ,

x ,alumino-silicates. *: calcium aluminates, A:

Si02-A1203, V: Si02-B203

60(a)

50

40X

30~Fco

x xo20~ O

x

10

c?'

Xooo ,~

o

o

oe

,

o 1 2 3(NBO/T)

4

F

60

50

40

30

20

10

(b)

X

)~c

o

B~ = exp( 177 (2 881Acorr)

x~(~c

.o% x;r C~

O0+

o

o

c

O4 0.5 06Acorr

0,7 o~

Fig. 3.

The parameters. B,, (=E,,/R) as a function of(a) the (NBO/T) ratio and (b) the correctedoptical basicity. A..**; O. O; silicates, x , +:alumino-silicates. ~:systemscontaining Fe203,A: Si02Al203.

recommendedvalues.*i4) In order to eliminate thesystematic differences in the viscosity associated withdifferences in experimental procedure used by different

laboratories, it wasdecided to use only the data reportedby Urbain et al,15~18) since these data should be self

consistent and should reveal any trends due to de-polymerization, cation effects etc. It wasalso noted thatviscosity values recorded by Urbain et al:i5-18) forvarious reference materials for high temperature viscosi-

ty measurementswere in good agreement with the

recommendedvalues.

Therelationships betweenIn n~ and the (NBO/T)ratio

and A.~,, are shownin Figs. 2(a) and 2(b) respectively.

The following observations were made:(1) The two divergent points in Figs. 2(a) and 2(b)

were for two Na20Si02slags with very low Tnq, thedeviations could be due to the long extrapolationsrequired

.

(2) It can be seen from Fig. 2(a) that there areappreciable differences in the Inn~ values for thealumino-silicates with (NBO/T)=Oand the deviation wasfound to increase with increasing Al content. Inspection

F

60

40

20

o

+ LI20

++BaO

CaO SrOMgO

Fig. 4.

SI02 O2 OA 0.6 O8 A{203(x /x +xsi)Al Al

The effect of Al substitution of Si in the silicat~ net-

work upon the activation energy p~r~ngeter. B,,.

of Fig. 2(b) indicates the A..** provides somecompensation for the effect of Al203 on Inn~.

Values of B~ (=Eu/R) are plotted as functions of(NBO/T)and A in Figs. 3(a) and 3(b) respectively. It

*~''

can be seen that in Fig. 3(a) that Bn values foralumino-silicates with (NBO/T)=Oshowedconsiderablescatter. Theeffects of A1 substitution of the Si on Bn areshownin Fig. 4. This behaviour results mainly from the

* Basedon the meanof five determinations lying within a scatterband of ~100/..

@1993 ISIJ 150

ISIJ International, Vol. 33

fact that the bond length of A1-0 is longer than that ofSi-O (1.715cf. 1.58 A).11)

It can be seen from Fig. 3(b) that A*~** allows somecompensation for the effect of A1203on Bn' It can also

be observed in Fig. 4 that the effect of Al203 on Bnincreases as (zlr2) for the cation increases (or A for theoxide decreases). This maybe aconsequenceof increasedordering produced when small, divalent cations areneededto charge balance two AIO~- tetrahedra.

The pre-exponential term An is shownas function ofA*~** in Fig. 5. Oneof the attractions of the optical basicity

concept is that it could be applied to other forms of slags

and it can be seen from Fig. 6that the relationships for

borates and phosphates have a similar form to that ofsilicates but the curves are moved to lower opticalbasicities since A(B203) and A(P205) are lower thanA(Si02)' Recent workl9) has shownthat viscosities ofglasses for temperatures between Tnq and the glass

transition temperature (Tg) can be reliably estimatedusing A."''.

-5

o

(F

0~G oooo oo

oo ox,~/+

l xe

ee

(1993), No. 1

(1, -10V1

5~F

-1 5

f~~.~~.

f-!*

X

0,4 0.5 0.7 0.80,6

Acorr

Fig. 5. TheArrhenius pre-exponential term, A,i, as a functionof the corrected optical basicity; O, O; silicates, x ,

+ :alumino-silicates, ,~,

~~;systemscontaining Fe203.

3.2. Electrical Conductivity (1c)

Specific electrical conductivity (1c) data reported byBockris et al.20,21) for 8 binary silicate systems wereextrapolated to Tliq andvalues for alumino-silicates werethose reported by Winterhager et al.22) Bockris et al.

noted that the activation energy E~ (unlike En) did notvary muchwith Si02 content and suggested that themobility of the cations (e.g. Ca2+) was the most im-portant mechanismaffecting electrical conduction. Thushigher electrical conductivities might be expected for

systems with (1) cations with high values of (z/r2) orlow A values and (2) more depolymerised melts, i.e.

hiQh fNBOlT\ and A values'~ ~ / ) *.** '

Plots of In lc~ as a function of (NBO/T) and A*.** areshown in Figs. 7(a) and 7(b), respectively, and thefollowing observations were made:

(1) The values of In ,(~ increases markedly withincreasing depolymerisation, i.e. increasing NBO/TandA values and thus it appears that the hinderance of

*~'' ,cationic mobility by the silicate network is the primaryfactor affecting electrical conductivity, especially in theacidic region.

(2) The In ,(~ values for GroupI oxides were higher

20

18

16

14

ou, 12

oC~ 10

F8c:

64

2O

-2

X

D I CaO-Si02-Ti02A CaF2- A1203-CaO

**I I Borate,phosphaie

Boro-Si [icat eSi [icate

\x\

x \. \\\

.\\\ '\\1 \\A o'~'l"~

+0.4 0.7 O805 0.6

Acorr

Fig. 6. The Inn* for borates and phosphates as function ofA,~,,, x ,

borates, *: borosilicates. O, phosphates, +:CaO-A12O3-

2

o

-2

E -4~(

c

-6

-8

-1 O

(a)

oeooo

e,

o

e

o

e

o GroupIe GroupIE

o NnOx CaO-A[ 203 - SiO

o 1 2 3(NBOIT)

4

,2

o

-2

-4

Ey,

~ -6

-8

-10

(b)

/

.5e

"Ix7

e

e/ e

'Fl~o~E

/

0.4 0.5 0.70.6

Acorr

Fig. 7.

The electrical conductivity at Tl~q (In K~) asfunctions of (a) (NBO/T)and (b) the correctedoptical basicity.

151 C 1993 ISIJ

ISIJ Internationa[, Vol. 33 (1993), No, 1

~:(E

;1'

coul

u)Q,

15

Ea,J:

H

4

14

x 10E~.

4(E

o

06

02

(b)x

o

Ox

()

xo() xo

()

I

~+

IX

IE

~,

E,

(c)X

C!

•;o

(~

~\Xo(.)

*~~

o ()()'~o.

A

Fig. 8.

1 2 3 o. 7O.6(NBo/T) (NBo/T) kcorr

The effect of (NBO/T) on the (a) thermal resistance and (b) thermal conductivity and (c) shows the latter

as a function of A

08

-93 2

(NBOIT)1

E 10d~o

-1 1

1600'C

~~X\\~~~x.\X_~

Si o

O4 0705 C6~(Si02)

Fig. 9. The self diffusion coefficients, D of Ca, Si and Oat

i 600"C as a function of mole fraction Si02 and21-29](NBO/T),

than those for Group11 oxides; this maybe due to order-ing of the melt to accommodatethe need for M2+jons

to be sited near two O~.(3) Although In K,~ values decreased in the hierarchy

Li20>Na20>K20and MgO>Ca0>(SrO, BaO), i.e.

increasing cationic radius, however the differences weresmall.

(4) Since In K,~ values for the alumino-silicates are in

agreementwith those for silicates with similar (NBO/T)or A it was concluded that the cations involved in

.~'*'charge balancing duties do not contribute to the electrical

conductivity of the melt.

Onthe basis of these observations it was concludedthat degree of depolymerisation was the primary factoraffecting the electrical conductivity of the melt, especially

for Si02-rich compositions.

3.3. Thermal Conductivity (A)

Accurate values of the thermal conductivities of melts

are notoriously difficult to obtain since the measuredvalues can contain large contributions from bothconvection and radiation conductlon. In order to

30

' 2015

EE"o

~~

l> 10

l///

///

//

//

l;

l;

O 0.5

x(Si02)

Fig. lO. Theparameter, xV(Si02), as a function of both molerraction Si02 and (NBO/T).

minimise these contributions transient techniques havebeenused, the values at Tliq obtained using these methodshave been employedhere.23 ~27)

It has been suggested28) that the thermal resistance

(1/~) associated with the movementof phonons alongthe silicate chain or ring is relatively small whencomparedwith that associated with the movementof phononsfromchain to chain. Thus the thermal resistance (1/~) wouldbe expected to increase as the melt becomesprogressively

depolymerised. It can be seen from Fig. 8 that the

experimental data are in agreementwith this proposition.

Consequently it might be expected that melts with large

cations would have higher conductivities, unfortunately,there are insufficient data to deducewhether the size ofthe cation has any effect on the thermal conductivity ofthe melt.

3.4. Self Diffusion Coefficients (D)

Experimental data for self diffusion coefficients, D, in

liquid slags are prone to large experimental uncertainties.

Nevertheless, the effect of the degree of depolymerisationof the melt on the diffusion coefficient can be clearly seenin the results obtained for the CaO-Si02system29~31)

C 1993 ISIJ 152

ISIJ International, Vol.

shownin Fig. 9.

Theexperimental uncertainties in the D(Ca) values for

the CaO-A1203-Si02system were considered to be toolarge to determine whether the cations on charge-balancing duties play a part in the diffusion processes.

3.5. Molar Volume(V) Density (p)

Molar volumes (V) for mixed oxides can usually beestimated accurately using Eq. (2) where x is the molefraction and Vis the partial molar volume of the oxideand usually has a fixed value.7)

V=xl V1+x2V2+x3V3+ ' ' '..........(2)

The values for xlVl for Si02 can be obtained fromexperimental molar volumedata for slags (using Eq. (3))

xlVl V x2V2-x3V3 ...............(3)

It can be seen from Fig. 10 that there is a small departurefrom linearity which presumably is a result of structural

effects.

3.6. Thermal Expansion Coefficients (~)

Thermal expansion coefficients (~) data for theliquids21,32,33) have been shown to be functions of(NBO/T)andA in Figs. Il(a) and 11(b). The thermal

..'*

33 (1993), No. 1

expansion coefficients can be seen to increase as:(1) the melt becornes more depolymerised, i.e.

(NBO/T) and A Increase'*.'' ,

(2) the parameter (zlr2) decreases for the cation orA(MO)increases.

It can also be seen that ~ values for the alumino-silicates agree well with the values for silicates withe"uivalent fNBO/TI or A and that the use of A* \ / ) *~** ..'*

compensatesfor the effect of cation size and charge.

3.7. Surface Tension (y)

Although the surface tension (y) of a slag is not a bulkproperty like those discussed above, there are indicationsthat the surface properties may be affected by the

structure of the liquid. Positive temperature coefficients

(dyldT) has been reported34,35) in slags with high Si02contents and this behaviour maybe associated with the

presence of BO's on the surface.

3.8. ThermodynamicProperties

Our current knowledge of the structure of silicates

has been assisted by the development of mathematicalmodels to calculate thermodynamicproperties of silicate

systemsI '2, 37) andsomeof these modelsprovide estimatesof the numberof tetrahedrally coordinated Si atoms in

a 16Li

~ 12

c 8a~~;

E 4

o

(a)

o

oe

X20

BaOeMgO

Na20

Li20

CoO

o 1 2 3(NBO/T)

4

L,1

Ot,

COUa,

OvCOtl,

CCCL,,a,

~;

E1,!:H

'OL

16

12

8

4

o

(b)

/

o

o

o //

elCf

/'x'l

Xlx

/

eel

O

0.4 0.5 0.6 0.7 0.8

Acorr

Fig. Il.

Thermal expansion coefficients (~) as afunction of (a) (NBO/T) and (b) the cor-rected optical basicity; O, O, silicates,

x ,alumino-silicates.

2 1(NBO/T)

o

1900

1700Xos 1500~(bCl

E1300H'u

1100

900

(a)

~/7;;~"".

CaOSrO BaO

Li20

Na20eK20

0,5 O6Metal oxide

oi~?-

2-o~3

-o 6

-o 4

-o 2

o

02

04

~(NBO/T)

o2 1

(NBOIT)(b)

MgO~~~o

--CaOCf~ \~\SrO + \

BaOLi20

Na20K20

\\\\~:~\~\

8

XL6OE

U)4

2

Fig.

o(*)

Li20

Na20

K20

0,7 O8 O9 o8 0.907O.8 09 0,5 O6 0.5 06 07Si02 Metal oxide Si02

,

x (Sf 02) x (Si 02) x (Si 02)12. (a) Liquidus temperature, (b) activity coefficient of Si02 and (c) entropy of fusion as a function of mole

fraction Si02 and (NBO/T) ratio.

Si02

153 C 1993 ISIJ

ISIJ International, Vol.

the chain or ring.36,37) Howeverthe effect of the degreeof polymerisation on thermodynamicproperties can beclearly be seen in Fig. 12, i.e, that (1) the Tnq Valuesincrease with decreasing (NBO/T) ratios in the range Oto 2, (2) the depression in T]iq is greater for Group Ioxides than for Group11 oxides and (3) within any oneGroupthe depression increases with decreasing (zlr2) for

the cation (or increasing A for the oxide).

Thesesametrends are shownin Figs. 12(b) and 12(c)

where the activity coefficient of Si02 and the entropy offusion are shownas function of x(Si02) and NBO/T.Thecation effects maybe due to the ordering of the meltrequired to enable divalent cations to be sited near twoO~ ions.

3.9. Optical Properties

Theaddition of network-breaking cations to the Si02network results in the destruction of O' bonds and theformation of O~and 02~. Under these circumstancesthe electron polarisability of the oxygen is increased andthis results in an increase in refractive index.38) In fact

refractive index measurements have been used bylwamoto et al.38) to determine the relative amountsofO', O~and 02-. There is also evidence to show thatthe absorption edge in visible/ultra-violet region(associated with the charge transfer band) is movedtohigher wavelengths as a result of increased electronpolarisation.39)

3.10. Sulphur and PhosphorusCapacities

Optical basicities have been used by several investi-

gators to calculate the sulphur and phosphoruscapacities of slags. Recently the corrected optical basicity

has been correlated with sulphur capacity data derivedfrom many sources.39) It was found that there wasconsiderably less scatter in these plots than with thoseobtained using the uncorrected optical basicity. Howeverthe use of A had little effect on the P capacity

..*'correlation which could only be improved by using amuchsmaller value of A(FeO).40)

4. Future WorkTherelationships of individual physical properties with

global measures of the degree of polymerisation, i.e.

(NBO/T)andA will lead to developmentof improved..*''

mathematical models for the estimation of physicalproperties of slags. However, Mysenll) has shownthatit is possible to calculate the relative concentrations ofvarious anionic units. Correlations between physicalproperties and the concentration of anionic units, eg.

T205 could be used to develop predictive models andthese could lead to improved accuracy in the predictedvalues. However, before this approach can be appliedrigorously to multicomponent industrial slags further

information will be neededon the waythat elements such

as P, and Ti influence the relative concentrations of theanionic units like T02, T205 etc.

5. Conclusions

(1) Thedegree ofdepolymerisation of the melt is the

C 1993 ISIJ 154

33 (1993), No. 1

primary factor affecting most physical properties; theeffect of different cations tends to be "second order" for

most of the properti~s studied.(2) Although the (NBO/T)ratio is probably superior

to A..,, as a measureof the depolymerisation of silicate

melts, the latter has the advantages that it is capable ofapplication to non-silicate systems and makes somecompensation for the effect of the cations.

(3) For alumino-silicates, it would appear thatcations involved in charge-balancing duties do notcontribute to the depolymerisation of the melt.

(4) The(NBO/T) ratio can not account for the effect

of the longer A1-0 bondlengths on the activation energyfor viscous flow in alumino-silicates, whereas A*.''provides somecompensation.

(5) There is someevidence of "ordering" in meltscontaining small, divalent cations such as Mg2+

.This

ordering mayresult from the need for the Mg2+ cationsto be sited near two O~or two A]O~~ tetrahedra.

Acknowledgements

The useful discussions held with Brian Keene PaulGrieveson, Ake Bergman, Bob Young (British Steel)

and Masahiro Susa are gratefully acknowledged. Thiswork was carried out for the "Materials MeasurmentProgramme"financed by the UK, Departmentof Tradeand Industry.

1)

2)

3)

4)

5)

6)

7)

8)

9)

lO)

ll)

l2)

l3)

14)

l5)

l6)

l7)

18)

l9)

20)

21)

22)

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(NBO/T) =(YNBIXT)

where x=mole fraction,

f =Fe3+ (IV)/(Fe 3+ (IV) +Fe3+ (VI)),

i.e. fraction of Fe3+ with IV coordination.

Appendix 2Calculation of Optical Basicity

A- ~xlnlAi +x2n2A2+x3n3A3+~ ~xlnl +x2n2+x3n3+ ' ' '

where n is the numberof oxygens in the oxide, eg. 3for

A1203, 2for Si02'

Values of Ath used in the calculation of A

K.O Na20 BaO SrO Li20 CaO MgO Al203

l .4 0.78 0.60l.15 l.15 l,lO I O l .O

Ti02 Si02 B203 P20s FeO Fe203 MnO CaF

0.61 0.48 O.42 0.40 l.O 0.75 1O 0,43

Appendix lCalculation of NBO/T

YNB =~2[x(CaO)+x(MgO)+x(FeO)

+x(MnO)+x(Na20) +x(K20)]

+6(1 - f)x(Fe203) - 2x(Al203)

- 2fx(Fe203)

XT =~x(Si02) +2x(Al203) +2fx(Fe203)

+x(Ti02) +2x(P205)

Calculation of A*.**

Take a slag of composition, (0.5Si02+0.15Al203+0.2Ca0+0.lMg0+0.05K20), the AIO~- are chargebalanced by cations with higher A values: thus K20>CaO>MgO.ThusO. 15(oxide) will be required to chargebalance O.15(A1203)-thus 0.05 K20+0.1CaO.Thesecations play no part in the depolymerization of themelt, thus A*.** would be derived for the composition(0.5Si02 +O. 15A1203+O. ICaO+O. IMgO)using the val-

ues tabulated above.

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