Thermodynamic modeling of the solid-liquid interaction in oxides and silicates

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Thermodynamic modeling of the solid-liquid interaction in

oxides and silicates

Citation for published version (APA):

Michels, M. A. J., & Wesker, E. (1985). Thermodynamic modeling of the solid-liquid interaction in oxides and

silicates. Solid State Ionics, 16, 33-38. https://doi.org/10.1016/0167-2738(85)90021-9

DOI:

10.1016/0167-2738(85)90021-9

Document status and date:

Published: 01/01/1985

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34 M.A.J. Michels, E. Wesker / The solid-liquid interaction in oxides arid .silicates

c. The enthalpy and entropy of mixing are given -

by: %iix =i) (8)

yiiix = 3n(O-)E Smix = kGlo9"mix

(2) (3

ap

wwvn5i02

(3) _{After back-substitution of the resulting equili-} Here E is the reaction enthalpy of the bond-

breaking reaction (I) ana f:mix is the combinato- rial factor for interchanging species M and Si in the mixture.

brium value

d. At given composition and temperature the -

state of the mixture is cnaracterized by the mole number of broken bonds $n(O-), or equi- valently, by tne degree of polymerization p:

n(O-)/4n(SiUz) = l-p (4)

It is easily verified that the value of p lies between 0 and 1.

p = P(nM0,nSiU2) (9)

into (7), the model for the mixture thermodyna- mics is fully defined, apart from the adjustable parameters in (6). In particular, the tnermo- dynamic activities of the individual components in the mixture are given by:

I %nix aMU = exp - - [O I RT

ant40

nsiuz

10)

e. Obviously, the combinatorial factor "mix is -

not only a function of overall composition, but also of the state of the network, i.e. of p:

aSiU2 = exp

(11)

"mix =

Rmix(nMo,nsio2,P)

In addition, we propose that the enthalpy E will vary with p:

E = E(P) (6)

This expresses that the depolymerization reac- tion (1) may be influenced energetically or ste- rically by the extent of network formation. The precise functional dependence of "mix on mole numbers and on p is derived from statistical mechanics; details will be left out here. Any dependence of the (metal-oxide-specific) enthal- py E on p is found by fitting the final model to experimental thermodynamic data for the binary mixture MO-Si02; in other words, the coeffi- cients in the function (6) are the adjustable parameters of the model.

(Note that in view of the equilibrium condi- tion (8) the differentiations of Gmix (Eq. (7) with (9)) occurring here can simply be performed at constant p, which greatly facilitates the calculation.)

3. ADJUSTMENT OF THE MODEL PAKAMETEKS TO BINAKY MIXTURES

f. The Gibbs free energy of mixing follows from E)-(6) as:

C,ix =

Gmix(nMolnsio2,P)

=

Hmix-T$nix (7) So far, the actual value of the degree of poly- merization p has not been specified. It is ob- tained by minimizing the Gibbs free energy at constant composition:

In order to obtain values for the adjustable parameters in the metal-oxide-specific enthalpy of bond-breaking E(p), Eq. (6), we have fitted the model to experimental data for a number of binary mixtures MO-Si02. By way of example we show in Figure 1 the experimental and fitted component activities for the highly non-ideal system MgO-SiUZ at 1973 K (hypothetical liquid reference states). Note that the model is flexible enough to simulate such strong devia- tions from ideal mixing. It even predicts liquid-liquid demixing at the silica-rich end. At the temperature considered here the silica- rich liquid is actually undercooled, but at higher temperatures this demixing has indeed been observed experimentally.

Once the adjustable enthalpy E(p), Eq. (b), has been established, the variation of the

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M.A.J. Michels, E. Wesker / The solid-liquid interaction in oxides and silicates

0.20 0.40 0.60 1.00

SILICA CONCENTRATION XSi02

FItiURE 1 FIGURE 2

Experimental (m) and calculated (-) activities in MgO-Si02 at 1973 K. The model predictions have been made to fit the data by adjusting the enthalpy of bond breaking (see Fig. 3). Data from: S. Kambayashi and E. Kato; J. Chem. Ther- modynamics 16 (1984) 241. _-

Degree of polymerization p (Equation (4)) in MgO-Si02 at 1973 K, as calculated from the fit of Fig. 1. Beyond the orthosilicate composition (XSiO2=1/3) the network grows rapidly.

degree of polymerization p with composition, Eq. (9), is also fixed. For the system of Figure 1 this variation is draw in Figure 2. One clearly recognizes the rapid growth of the silica network beyond the orthosilicate compo- sition (XSi02 = l/3). Substitution of p(xSi02)

in the adjusted bond-breaking enthalpy E(p) gives the latter as a function of overall compo- sition. This function is shown in Figure 3. It stays remarkably constant in the MgO-rich region, where only finite silicate anions are expected, but increases drastically in the silica-rich region, where the infinite network starts to form.

0.6 -

I

0.00

0.20 0.40 0.60 0.80 1.00

SILICA CONCENTRATION XSi02

The bond-breaking enthalpy turns out to have not only a physically understandable variation with composition, but also a logical trend with the type of basic oxide considered. This is il- lustrated in Table I, which gives the values of E(p=O) for a number of such oxides. The rough correlation with oxide basicity strength is ob- vious.

4. APPLICATION OF THE MODEL TO THE SOLID-LIQUID INTERACTION IN THE PERICLASE REGION OF THE SYSTEM CaO-MgO-Si02

In order to enable the calculation of solid- liquid equilibria in the system CaO-MgO-Si02 we have taken the following steps.

a. The adjustable parameters ECaO(p) and EMgO -

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36 M.A.J. Michels, E. Wesker / The solid-liquid interaction in oxides and silicates - 6.t - 8.C -10.1 -12.1 -14.1

ENTHALPY OF BOND BREAKING

KCAL/MOL)

0.00 0.20 0.40 0.60 0.80 1 .oo

SILICA CONCENTRATION Xsi02

FIGURE 3 FIGURE 4

Enthalpy of bond breaking E in MgO-Si02 at 1973 K, as found from the fit of Fig. 1. The re- sults shows a drastic increase of the enthalpy in the silica-rich region where the network for- mation takes place.

Crystallization paths (P-P', Q-Q' and R-R', with absolute temperatures in brackets) in the periclase region of the ternary system CaO-MgO- -SiO2. The free-energy model for the liquid phase has been adjusted only to the two under- lying binary silicate systems. Solid free-energy data have been incorporated by modelling the bi- nary solid solution CaO-MgO and by fitting inva- riant points around the stoichiometric compounds C3S, C2S, C3MS2, CMS and M2S.

of the liquid-silicate model have been deter- mined from the two binary silicate systems. b. The interaction of CaO and MgO in the liquid -

has been assumed to be negligible.

c. The free-energy of the (Ca,Mg)O solid solu- -

tion has been modelled with a sub-regular solu- tion model.

TABLE

I

Basic oxide (MO)

Na20 CaO mg0 ZnO MnO PbO Fe0 NiO GO (p=O) at 1873

I

(kcal/mol) N- -52.5 -24.9 -14.0 12.3 8.0 3.0 1.0 1.0

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M.A.J. Michels, E. Wesker / The solid-liquid interaction in oxides and silicates 31 TEMPERATURE, K 2J/-yj;; 1800 - M+CMS+L M+CMS _C3MSz - M+M2S+CMS +C3MS2 +C2S M+C2S+C3S M+C3S+C I I I I I 1.0 2.0 3.0 OVERALL COMPOSITION XCaO/XSi02 AT CONSTANT XMgOiXSi02=2

FIGURE 5

Phase-stability diagram showing the melting be- haviour in the ternary system CaO-MgO-Si02 along the line Of Overall COInpOSitiOn XMgO/XSi02 =

2 (P-Q-R in Fig. 4). The liquidus (onset of solid formation) and solidus (onset of liquid formation) are indicated by heavy lines.

d. The free-energy differences between the solid -

and liquid phases of CaO, MgO and Si02 have been taken from the literature. As similar and equal- ly reliable data for the binary and ternary stoichiometric intermediates C3S, C2S, C3MS2, CMS and M2S (C=CaO, M=MgO, S=SiO2) are lacking, the free-energy differences of these compounds have been chosen so as to give proper locations of the invariant.points in the ternary phase diagram.

The results of the phase-equilibrium calcula- tions are drawn in Figures 4-6. In Figure 4 three

initial liquid compositions are chosen, each

with an MgO-Si02 mole ratio of 2.0, but with

10-l CaO IMPURITY DISSOLVED IN SOLID MgO

5.10-4[ I I I I I I i 1.0 2.0 3.0 OVERALL COMPOSITION XCaO/XSi02 AT CONSTANT _{X MgO’XSi02=2}

FIGURE 6

CaO impurity dissolved out the liquid slag into the solid HgO, for varying overall composition

varying CaO/Si02 ratio: 3.0 (P), 2.0 (Q) and 1.0 (R). The dotted lines over the liquidus sur- face, and the end points P', Q', R' in the eutectic valley indicate the crystallization paths on cooling. The same information on the solidification behaviour can be found from the calculated phase-stability diagram in Figure 5. (Note that this is not a phase diagram: the crystallization pat.rP-P', Q-Q' and R-R' are strictly vertical lines between the liquidus and the solidus).

In

Figure 6 we have plotted the equilibrium amount of CaO that dissolves out of the liquid slag into periclase, for three different temperatures. Because of this small CaO impurity in solid MgO, the three dotted lines in Figure 4 do not extrapolate exactly in- to the MgO point; for the same reason the verti- cal phase boundaries in Figure 5 do not end pre- cisely at stoichiometric compositions.

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38 M.A.J. Michels, E. Wesker 1 The solid-liquid interactiorz 01 oxides arid si1icutc.s

5. CONCLUSIONS

From what has been presented in the paper, and in particular from the results shown in Sections 3 and 4, we may conclude the following.

a. The large deviations from ideal mixing in -

multicomponent melts containing silica and basic metal oxides can adequately be simulated with a new and fundamental free-energy model (Figure 1). b. Trends in tne model parameters allow a phy- -

sical interpretation, in particular in terms of oxide basicity (Table I) and of the silicate netwrok structure (Figures 2 and 3).

c.

When combined with free-energy data on stoi-

-

chiometric solid compounds and with a standard free-energy model for oxide solid solutions the new model enables the calculation of solid-

liquid equilibria in oxides and silicates. Example: MgO(solid) in contact with CaO-Si02(liquid) (Figures 4-6).

In addition to these conclusions we have to mention that, for wide application of the model,

it should be generalized towards amphoteric oxides, notably alumina. Extensions in this di- rection are underway.

REFERENCE

1. 1vl.A.J. lvlichels and E. Wesker, A network [model

for the thermodynamics of multicomponent silicate melts, Paper to be presented at the CALPHAD XIV Conference, Cambridge, Mass., June 1985; idem, to be published.

Thermodynamic modeling of the solid-liquid interaction in oxides and silicates