Thermochemical Modelling Of

THERMOCHEMICAL MODELLING OF

MULTICOMPONENT SLAGS

Du Sichen, J. Björkvall, R.E. Aune and S. Seetharaman

Division of Metallurgy

Royal Institute of Technology

SE-100 44 Stockholm, Sweden

ABSTRACT

This work summarises the recent studies carried out in the present laboratory on the development of a mathematical model to predict thermodynamic properties in multicomponent slag systems. The model pictures oxide melts including silicate solutions as an O2- matrix with different cations distributed in it. It avoids the difficulties in choosing the complex ionic species and the evaluation of their fractions. Only the next nearest neighbour interactions, viz. the interactions between different cations in the presence of oxygen are considered to be important in the solution thermodynamics. The model has the ability to describe high order systems using solely experimental information from the corresponding binary sub-systems. Thermodynamic calculations have been performed for molten slags in a number of multicomponent systems containing Al2O3, CaO, FeO, MgO, MnO and SiO2. The predicted oxide activities have been compared with the available literature experimental data. In general, the model predications have been found satisfactory when compared with the experimental values.

1. INTRODUCTION

Although great efforts have been put forward all over the world to determine the thermodynamic properties of slags, researchers and engineers very often find that there are still too few data available for the slag systems interesting to the industry. The industrial slags are always multicomponent in nature. In most of industrial practices, slag compositions vary with time. It is almost impossible to determine the thermodynamic properties for all the compositions. On the other hand, process simulation and control demand the activities of the slag components being described as functions of both temperature and composition. This demand was once more highlighted in the Panel Discussion in the Sixth International Conference on Molten Slags, Fluxes and Salts in Stockholm and Helsinki, June 2000.

A number of slag models are available in the literature with varying degrees of success. The development of structure based models has made considerable progress since the pioneering works of Toop and Samis (1) as well as Masson (2). These models have provided an insight into the relationship between the thermodynamic properties of the silicate melts and their structures. However, the use of these models is limited due to the lack of additional structural information especially in the case of high silica containing melts and complex slags. On the other hand, empirical or semi empirical models, that are based on the experimental information, have found their use in extrapolating and interpolating experimental data. Examples of this kind of models are regular solution model (3,4), Quasi-chemical approach (5), ionic "two-sublattice" model (6) and IRSID model (7). Good agreement between the results of model calculation and experimental data has been reported (4-7). Even in this kind of models, complex anionic species are used (6,7). However, difficulties have been encountered in choosing suitable species (8). The fractions of different species optimised in this way are somewhat arbitrary, as very little experimental evidence is available to support the same.

By assuming that two silicates of equal silica mole fraction mixed ideally, Richardson (9) was able to predict the thermodynamic properties of some ternary and quaternary silicate melts. However, disagreement was encountered in the case where the cationic radii were quite different. Despite the fact that Richardson's approach is simple and its applicability depends on the size difference of the cations involved, it shows the possibility of predicting thermodynamic properties of multicomponent solutions based on the information of corresponding binary systems. Richardson's approach also reveals that the next nearest neighbour interactions, viz. the cation interactions, play a dominant role in solution thermodynamics.

Inspired by Richardson's approach, a research program is currently being carried out in the present laboratory to develop a thermodynamic model for the estimation of thermodynamic properties of multicomponent ionic melts. The model is relatively simple so that it can be easily implemented into process models. This effort is in line with the demand on the flexibility of implementing thermodynamic models into process simulation, which was recently emphasised again in the Panel Discussion in the Sixth International Conference on Molten Slags, Fluxes and Salts held in Stockholm and Helsinki. The present paper intends to summarise the development of this model and the application of the same to multicomponent slags in the recent years.

2. THERMODYNAMIC MODEL

2.1 Description of Ionic Melts

It is well accepted that in a silicate melt, all Si atoms are tetrahedrally bonded to four oxygen atoms. For solutions rich in basic oxide, the melt consists essentially of M2+, O2- and SiO44- (orthosilicate) ions. As the concentration of SiO2 increases, the SiO44- tetrahedra start joining together forming dimers Si2O76-, trimers Si3O108-, cyclic polymers and even three dimensional network of bridged silica tetrahedra. On the other hand, a silicate melt can also be considered as an oxygen matrix with different cations including Si4+ distributed in it. This approach was originally suggested by Lumsden (3). The present model is in line with Lumsden's formulation. The presence of basic cations such as Ca2+, Fe2+, Mg2+ and Mn2+ along with Si4+ will distort the oxygen matrix and determine the configuration of the ionic melt and the bond energies between different ions. The configuration of the ions and the bond energies will be functions of composition and temperature. By picturing the oxide melts in this manner, the difficulties in choosing the anionic species and the fractions of the same are avoided. While there are mutual effects between the cations and oxygen ions, the thermodynamic properties of the solution can be formulated by the consideration of the next nearest neighbour interactions, namely the interactions between the cations when oxygen ions are present.

2.2 Mathematical Formulation

Based on the above considerations, a silicate melt containing m oxides, C1c1Oa1, C2c2Oa2,....CiciOai,....CcmOam can be expressed as:

(1)

where Cvi stands for cations, the superscript vi denotes the electrical charge. Even Si4+ ion is included in the cation group. p and q in Eqn. 1 are stoichiometric coefficients. Following the line of the above consideration, the thermodynamic properties of mixing can be formulated as functions of the interactions between different cations in the presence of O2-. It is logical to use ionic fractions to describe the composition of a melt. The ionic fraction of cation yi within the cation grouping is defined as:

(2)

where Ni is the number of Civi cations and the summation covers all the cations including Si4+.

The present description of silicate melts necessitates the assumption that the silicate network is completely dissociated into Si4+ and O2- ions and even any aluminate complex to Al3+ and O2- ions. As already mentioned, Lumsden (3) proposed the use of a hypothetical standard state for silica in his regular solution model. Based on the silica saturated liquidus line in the FeO-SiO2 system, Lumsden (3) deduced the Gibbs energy change for the fusion of silica:

SiO2 (solid) = SiO2 (liquid consisting of Si4+ and O2- ) (3)

(4)

If and represent the mole fraction and the standard Gibbs energy of oxide CiciOai , the integral Gibbs energy of a solution can be expressed as:

(5)

where R is the gas constant, T is the temperature, p is a stoichiometric number and yCi is the cation fraction. The second term in Eqn. 5 corresponds to Temkin's ideal mixing (10) and the GE, the excess Gibbs energy of the solution in Eqn. 5 is described as:

(6)

in Eqn. 6 represents the interaction between cations Civi and Cjvj when O2- ions are present. This interaction is a function of temperature and composition and is described as polynomials.

In order to compensate for the fact that the excess Gibbs energy is not zero due to the use of the hypothetical standard state for silica when the composition of the melt approaches pure SiO2, the function, is introduced. The term is expected to have strong dependency on the composition in the liquids of high silica content but to a lesser extent in liquids of low silica content. The dependency of this function on composition would only be negligible when the silica content is lower than the orthosilicate composition . Below this silica content, the silicate network would almost be broken down completely into SiO44- tetrahedra, so that could be treated as constant. This function has been assigned a value of zero when. On the basis of the experimental information of a number of binary silicate systems including Al2O3-SiO2, it has been found that can be expressed as:

(7)

where (8)

and (9)

The activity coefficient of CiciOai, according to Temkin's theory (10) , is related to the activity coefficient of the corresponding cation, CCi , which in turn, can be expressed by the partial excess Gibbs energy of the same species:

(10)

In the presentation of the results, the standard state for each component, unless specified, is the stable phase at the temperature in question.

3. MODEL CALCULATIONS

The model has been used to assess the experimental data for the Al2O3-CaO, Al2O3-FeO, Al2O3-MnO, CaO-FeO, CaO-SiO2, FeO-SiO2, MgO-SiO2, MnO-SiO2 and Al2O3-SiO2 systems. Model parameters have been optimised on the basis of these binaries. Calculations have been carried out for both binary and higher order systems. It should be pointed out that only binary interaction parameters obtained from above mentioned binaries have been used in all the model calculations.

3.1 Model Calculations for Binary Systems

Comparison between the results of model calculations and the experimental data has shown satisfactory agreement in the case of most of the systems. The agreement between the results of model calculation and experimental studies is exemplified by the comparisons for the systems FeO-SiO2, Al2O3-MnO and Al2O3-SiO2 shown in Fig. 1-3.

3.2 Model Predications for Multicomponent Systems

Model predications have been made for a number of ternary systems, namely, FeO-MgO- SiO2, FeO-MnO-SiO2, CaO-FeO-SiO2, CaO-MnO-SiO2, Al2O3-FeO-MnO, Al2O3-CaO-MnO, Al2O3-CaO-SiO2, Al2O3-FeO-SiO2 and Al2O3-MnO-SiO2. Because of its importance in ladle refining processes, the Al2O3-CaO-SiO2 system has been investigated by a great number of researchers (11-23). Hence, the results of this system are taken as examples in this presentation. In Fig. 4, the calculated iso-activity lines of SiO2 at 1873 K are compared with the experimental results at 1823 K from Cho and Suito (20) as well as Baird and Taylor (23) at 1873 K. For the sake of clarity, the results of Sanbongi and Omori (13, 17) as well as Kay and Taylor (15), which agree well with the results of Baird and Taylor (23) as well as Cho and Suito (20) are not included in this figure.

The results from Zhang et al. (21) are plotted in Fig. 5 together with the calculated iso- activity lines of CaO at 1873 K. The agreement between the experimental points and the model calculation are satisfactory except in the region close to the Al2O3-CaO binary. The silica activity acquired by Stolyarova et al. (22) are in excellent accordance with the model calculations, as shown in Fig. 6.

As another example, Fig. 7 illustrates the good agreement between the predicted FeO activity values and the experimental data by Yamanka et al. (24) in the Al2O3-FeO-SiO2 system at 1673 K.

Only limited thermodynamic data can be found in the literature for silicate systems having more than three components, presumably due to the experimental difficulties associated with the measurements. As a literature survey revealed that the experimental data regarding the oxide activities were available for the systems CaO - FeO - MgO-SiO2, Al2O3 - CaO - MgO - SiO2, Al2O3 - FeO - MnO - SiO2 and Al2O3 - CaO - FeO - MgO - MnO - SiO2, model calculations were carried out in these systems in order to examine the reliability of the model in predicting the activities in higher order systems.

Sommerville et al. (25) and Ivanchev et al. (26) studied the equilibrium between liquid iron and Al2O3-FeO-MnO-SiO2 slags in an Al2O3 crucible at 1823 K. The activities of FeO and MnO were calculated based on the composition of the slag and the chemical analysis of the liquid iron. The calculated MnO and FeO activities are compared with the experimental results (25-26) in Fig. 8a and 8b, respectively. While the calculated FeO activities are slightly lower than the experimental data, the calculated MnO activities show an opposite trend. Nevertheless, the agreement between the model predictions and the experimental values could be considered reasonable except for the point having highest aMnO value in Fig. 8a.

Bishop et. al. (27) summarized the experimental results of the thermodynamic studies on the CaO-FeO-MgO-SiO2 melts (28-31). In all these experimental investigations (28-31), the technique of equilibration between liquid iron and slag was employed. The investigated slags (28-31) contained small amount of Al2O3, MnO and P2O5. From these works, Bishop et. al. (27) selected the slags, in which, the contents of Al2O3, MnO or P2O5 were all less that 2 mass pct. Since the authors (27-31) believed that CaO and MgO had similar effect on the FeO activities, for the sake of convenience, they did not specify the ratio of the contents of the two basic oxides when they presented their activity data (27-31). Instead, the sum of the mole fractions of MgO and CaO was employed in their presentation for the FeO activities.

In Fig. 9, the calculated FeO activities at 1873 K are compared with the values suggested by Bishop et. al. (27) based on the experimental results (28-31) for constant mole fractions of FeO, XFeO=0.60. While the solid line is reproduced from the publication of Bishop et. al. (27), the dotted lines corresponding to different concentrations of MgO are calculated using the present model. It is seen that the calculated curves show very similar trends as the curves based on experimental data. On the other hand, the activities reported by Bishop et. al. (27) are generally higher than the activities calculated by the model. The difference between the experimental and calculated activities of FeO decreases when the basicity increases. It is noted that one of the curves (XMgO=0) corresponds to the slags in the CaO-FeO-SiO2 ternary system. Model predictions for this ternary show good agreement with the available experimental data. In this connection, it is felt that although the model calculation in this quaternary might be affected by the uncertainty involved with the Ca2+-Mg2+ interaction parameters, the high impurity level in the studied slags (28-31) is more likely to cause the discrepancy between the model predictions and the curves suggested by Bishop et. al. (27).

Rein and Chipman (32-33) investigated the SiO2 activities in this system at 1873 K by equilibrating slags with liquid Fe-Si-C alloys in graphite or SiC crucibles. These authors (32-33) investigated the Al2O3-CaO-MgO-SiO2 system for the 10 mass pct MgO, 20 mass pct MgO and 30 mass pct MgO planes. The iso-activity contours of SiO2 were constructed by the authors based on the measurements of four compositions in each plane. Their results are reproduced in Fig. 10 for the planes of 10 mass pct MgO. The compositions of the experimentally studied slags are also presented in this figure. Unfortunately, raw data for the activities of these slags were not provided in the original publications (32-33). The calculated iso-activity lines using the present model are incorporated in this figure for comparison. The calculated activities of silica in the regions close to the experimental points agree very well with the results of Rein and Chipman (32-33). It is only in the regions away from the experimental compositions that the model predications show deviation from the suggested activity contours. Comparisons in the case of 20 mass pct MgO and 30 mass pct MgO show the same trends. It should admitted that the uncertainties possibly involved with the Ca2+- Mg2+ interaction parameters might introduce some uncertainties in the model predictions, especially at higher MgO contents.

Ohita and Suito (34-35) as well as Seo and Suito (36) investigated the Al2O3, FeO, MnO and SiO2 activities in the Al2O3-CaO-FeO-MgO-MnO-SiO2 system with low concentrations of both FeO and MnO (below 2 mass pct). Slag-metal equilibration technique was employed. The experiments were conducted in either CaO or MgO crucibles at 1873 K. Figures 11a and 11b present the comparisons between the calculated and experimental activities of alumina and silica respectively at 1873 K for the plane with 20 mass pct Al2O3 in the pseudo quaternary Al2O3-CaO-MgO-SiO2 system.

It should be mentioned that in view of the small amounts of FeO (0.07 to 1.2 mass pct) and MnO (0.2 to 1.9 mass pct) present in these slags, for the sake of convenience, the contents of FeO and MnO were neglected in the comparisons of silica and alumina activities. It is seen in these figures that the scatter in the results of these experimental studies (34-36) is considerable. In general, the calculated results agree with the experimental data within the uncertainty limits. However, the calculated alumina activities in the plane of 20 mass pct Al2O3 (Fig. 11a) are lower than the experimental values.

Comparisons between experimentally reported and predicted activities of FeO and MnO are presented in Fig. 12a and 12b, respectively. The error bars associated with the experimental data, which were reported by Ohita and Suito (35) are also included in the same figures. As shown by the error bars, the experimental uncertainties are, in many cases larger than the activity values themselves. While the calculated FeO activities generally agree with the experimental data within the uncertainty limits, there is no clear trend in the case of MnO activities. However, both model predictions and experimental results indicate that the manganese oxide activities in the slags are all below 0.025.

4. MODEL CALCULATIONS FOR SOME TYPICAL SLAG COMPOSITIONS