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
218
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+, O2and SiO44- (orthosilicate) ions. As the concentration of SiO2 increases, the SiO44tetrahedra 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
219
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:
C1
v1
, C 2v 2 , , Civi , , Cmvm p O2 q
(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:
y Ci 
N Ci
(2)
m
N
j 1
Cj
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- )
G2  35600  7.53  T
If
J
mole
(3)
(4)
X CiciOa i and GCi0 ciOai represent the mole fraction and the standard Gibbs energy of
oxide CiciOai , the integral Gibbs energy of a solution can be expressed as:
Gm   X CiciOai  GCi0 ciOai  R  T  p   yCi  ln  yCi   G E
220
(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:
m 1
 m

G E  f T , ySi4      yCi  yCj  Ci ,Cj ( 0) 
i 1  j i 1

(6)
Ci ,Cj ( 0) 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, f T , y Si4   is introduced. The term f T , y Si4   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
1

composition  ySi4   . Below this silica content, the silicate network would almost be
3

broken down completely into SiO44- tetrahedra, so that f T , y Si4   could be treated as
1

constant. This function has been assigned a value of zero when  ySi4   . On the basis
3

of the experimental information of a number of binary silicate systems including Al2O3SiO2, it has been found that f T , y Si4   can be expressed as:
f T , ySi4    A   ySi  ySi 
3
where
and
ySi 
A
y
1
3
G2
3
Si
ySi4  
with
1
3
(7)
(8)

1
(9)
3
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:
221
 GCiE vi  
ci
ai
ci







exp
(10)


Ci
O
Ci
ci Oai
R

T


In the presentation of the results, the standard state for each component, unless specified,
is the stable phase at the temperature in question.
 Ci
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-MgOSiO2, FeO-MnO-SiO2, CaO-FeO-SiO2, CaO-MnO-SiO2, Al2O3-FeO-MnO, Al2O3-CaOMnO, 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 isoactivity 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
222
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).
223
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.
224
4. MODEL CALCULATIONS FOR SOME TYPICAL SLAG COMPOSITIONS
RELEVANT TO THE STEEL INDUSTRY
The above comparisons of the calculated activities of the oxide components in the CaOFeO- MgO-SiO2, Al2O3-CaO-MgO-SiO2, Al2O3-FeO-MnO-SiO2 and Al2O3-CaO-FeOMgO-MnO- SiO2 systems with the available literature data show that the model could be
employed to make reliable predictions of the thermodynamic properties of the
multicomponent slags. Using the model, the oxide activities of different iron-making and
steel-making slags could be predicted. The slag compositions for different industrial
processes differ greatly. In Table I, some typical slag compositions, relevant to the
Swedish steel industry, used in the blast furnace (BF), electric arc furnace (EAF) and
ladle furnace (LF) are presented. As an example of the model calculations, the effect of
the replacement of SiO2 by CaO on the activities of alumina in the case of BF, EAF and
LF slags is illustrated in Fig. 13. In the calculation for each type of slag, the contents of
the other components given in Table I were kept constant. It is seen in Fig. 13 that the
activity of alumina is lower in EAF slag than in BF slag at the same mass pct CaO/mass
pct SiO2 ratio. It is also seen that an increase of the mass pct CaO/mass pct SiO2 ratio
leads to a considerable decrease of the alumina activity, irrespective of the type of the
slag. However, the decrease in alumina activity with the increasing mass pct CaO/mass
pct SiO2 ratio is more profound in the case of BF and EAF slags. Thus, the model
calculations would provide the researchers and the engineers a useful tool for gaining an
insight into the processes. For example, in the case of LF slags, the increase of the mass
pct CaO/mass pct SiO2 ratio from 4 to 7 would decrease the alumina activity from about
0.08 to about 0.03. This decrease would be beneficial for deoxidation process. Further
increase of the mass pct CaO/mass pct SiO2 ratio would have less effect on the decrease
the alumina activity.
5. SUMMARY
A thermodynamic model for ionic solutions was developed as a part of a long term
research program. In line with Lumsden’s approach, the model considers a silicate melts
as an oxygen matrix with different cations included Si4+ distributed in it. Model
calculations were carried out for both binary and higher order systems using only the
binary model parameters based on the thermodynamic information of corresponding
binary systems. The predicted oxide activities were compared with the available literature
experimental data. In general, the model predications were found satisfactory when
compared with the experimental values. Examples of model predications for some typical
Table I Some typical slag compositions of the blast furnace (BF), electric arc furnace
(EAF) and ladel furnace (LF) processs used in Sweden.
225
Oxide
Al2O3
CaO
FeO
MgO
MnO
SiO2
Compositions in mass pct
BF
EAF
13
10
32
40
2
15
17
9
2
5
34
21
LF
33.5
53.5
0.6
6
0.4
6
slag compositions, relevant to the Swedish steel industry, used in the blast furnace (BF),
electrical arc furnace (EAF) and ladle furnace (LF) were also presented.
226
1.0
a MnO
0.7
0.6
1.0
0.8
0.8
0.6
0.6
0.4
0.5
a
MnO Sharma&Richardson,
a
MnO
a
MnO Jacob ,
T=1933 K
Jacob, T=1873 K
2 3
a
0.8
1.0
aAl O
aFeOcalculated
0.9
Schumann and Ensio
Bodsworth
Ban-Ya et al.
Wijngaarden and Dippenaar
Wanibe et al.
Fujita and Maru hashi
Distin et al.
0.4
T=1933 K
calculated, T=1873 K
calculated, T=1933 K
0.2
0.2
0.4
0.3
0.3
0.4
0.5
a
0.6
a
0.7
0.8
0.9
0.0
0.15
1.0
(Experimental)
0.20
experimental
FeO
Fig. 1. Comparison between calculated
activities of FeO with experimental data
in the FeO-SiO2 system.
0.9
0.8
SiO
0.7
2
0.6
0.5
0.4
0.3
and a SiO
2
1.0
0.8
Activity, a
Al O
2 3
0.6
at 2150K
calculated aAlAl2O3
O
3
2
0.4
calculated aSiO
SiO2
at 2150K
experimentalSiO
a SiO2 at 2150K
2
Klug et al.
0.2
Aksay and Pask
Shindo
0.0
0.0
0.1
0.2
0.30
0.0
0.35
Al 2 O
3
Fig.
2
Comparison
between
experimentally determined and calculated
activities of MnO together with
calculated alumina activities in the
Al2O3-MnO system at 1873 K and 1923
K.
X
1.0
0.25
X
0.3
0.4
0.5
0.6
0.7
X Al O
2 3
Fig. 3. Experimental activities of
SiO2 together with phase boundary
infor-mation from Klug et al.,
Aksay and Pask and Shindo.
227
Baird and Taylor
SiO 2
Cho and Suito
0
SiO
2
0 1.0
1.0
0.1
0.9
0.2
0.1
0.8
0.823
0.4
0.9
3. 10-5
1.0
CaO
0
0.1
0.2
0.4
0.2
0.107
0.6
0.5
0.5
0.6
0.003
0.2
0.8
0.1
10 -4
0.9
1.0
0
0.4
0.5
0.3
0.005
0.08
0.011 0.05
10 -3
0.3
0.4
0.0015
0.7
0.3
0.01
4. 10-4
0.8
0.5
2
0.1
0.7
0.7
SiO
0.041
0.6
0.5
0.4
0.3
3
0.502
0.544
0.332
0.256
0.21
0.178
0.108 0.082
0.8
0.3
0.4
0.6
O
2
0.6
0.8
0.7
Al
0.5
0.7
0.9
Ca
O
Ca
O
0.3
0.9
0.2
0.794
0.0029-0.0032
0.0048-0.0050
0.0080-0.0086
0.0130-0.0150
0.0190-0.0200
0.0770-0.083
0.091-0.14
0.23-0.24
0.28-0.34
0.39-41
0.49-0.50
0.6
0.7
0.8
0.9
1.0
Al O3
Al O
2 3
2
CaO
CaO
0.1
0.3
0.2
0.008
0.5
0.02
0.05
0.8
0.08
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
AlO3
2
Al O
2 3
Fig. 4. Calculated iso-activity lines of
SiO2 at 1873 K together with experimentally obtained SiO2 activities from
Baird and Taylor at 1823 K and Cho
and Suito at 1873 K.
Fig. 5. Calculated iso-activity lines of
CaO at 1873 K together with
experimental points from Zhang et al. at
1873 K.
1.0
0.6
Stolyarova et al.
Yamanka et al.
0.5
0.8
a calculated
0.6
2
0.3
0.4
FeO
0.2
a
SiO
calculated
0.4
0.2
0.1
0.0
0.0
0.0
0.1
0.2
a
0.3
0.4
0.5
0.0
0.6
experimental
SiO
0.2
0.4
a
0.6
0.8
1.0
experimental
FeO
2
Fig. 6.
Comparison between
calculated and experimentally
obtained SiO2 activies.
Fig. 7.
Comparison between
calculated and experimental activities
of FeO in the Al2O3 - FeO - SiO2
system at 1673 K.
228
1 .0
1.0
Sommerville et al.
and Ivanchev et al.
0.8
0 .8
0 .7
0.6
0 .6
a calculated
0.7
0.5
FeO
0.4
MnO
a calculated
0 .9
Sommerville et al
0.9
0.3
0 .5
0 .4
0 .3
0.2
0 .2
0.1
0 .1
0.0
and Ivanchev et al.
0 .0
0.0
0.1
0.2 0.3
0.4
0.5
0.6
0.7 0.8
0.9
1.0
0 .0
0 .1
0.2
0. 3
a experimental
0 .4
0 .5
0 .6
0 .7
0. 8
0 .9
1 .0
a F eOexperimental
MnO
Fig. 8a. Calculated and experim-ental
activities of MnO in the Al2O3-FeOMnO-SiO2 system
Fig. 8b.
Calculated and
experime-ntal activities of FeO in
the
Al2O3-FeO-MnO-SiO2
system.
1.0
Rein and Chipman
Experimental compositions
Calculated
0.8
10% MgO
90% SiO2
10
80
(0.9 )
20
70
0.9
(0 .8 )
Ca
O
0.6
FeO
60
0.8
0.7
40
50
50
0. 5
0.4
0. 3
0. 2
0.1
60
x = 0,calculated
40
2
Bishop et al.
0.6
S iO
a
(0 .6 )
(0 .3 )
xFeO= 0.60
0.4
(0. 7)
30
30
MgO
70
x = 0.05,calculated
MgO
0.2
20
80
x = 0.1,calculated
10
MgO
0.0
0
1
2
(x
3
4
5
10
90% CaO
10% MgO
6
20
30
40
50
Al O
2
3
60
70
80 90% Al O
2
10% MgO
+x
)/x
CaO
MgO
SiO2
Fig. 9. Reported activity of FeO
compared with calculated FeO
activity as a function of the molar
basicity at XFeO = 0.6 for constant
MgO concentrations, XMgO = 0,
XMgO = 0.05, XMgO = 0.10.
Fig. 10. Comparison between
iso-activity lines of SiO2
suggested by Rein and Chipman
and calculated by the present
model at 1873 K in the Al2O3CaO-MgO-SiO2 system in the
10 mass pct MgO plane
229
3
Ohita and Suito
Ohita and Suito
Seo and Suito
Seo and Suito
30
30
50
50
Ca
O
pc
t
O
Ca
sp
ct
ma
s
ma
ss
(0.0037)
60 (0.0038)
(0.034)
20
(0.02)
(0.003)
(0.024)
70
10
(0.025)
30
20
(0.0078)
20
0.003
40
50
70
70
60
10
0
30
40
mass pct MgO
20
mass pct MgO
Fig. 11a. Calculated iso-actvity lines of
Al2O3 by the present model and
experimental values at 1873 K in the
pseudo quaternary Al2O3-CaO-MgOSiO2 system for the 20 mass pct Al2O3
plane.
0.03
10
70
0.01
0.01
0.00
0.00
0.00
0.03
0.02
MnO
a experimental
0.03
0.02
FeO
a experimental
0.04
0.02
60
Ohita and Suito
Ohita and Suito
0.01
50
Fig. 11b. Calculated iso-actvity lines of
SiO2 by the present model and
experimental values at 1873 K in the
pseudo quaternary Al2O3-CaO-MgOSiO2 system for the 20 mass pct Al2O3
plane.
0.04
0.00
30
0.008
10^3
(0.00087)
(0.00074)
(0.015)
0
0.06
50
0.02
(0.068)
40
2
30
(0.017)
60
0.2
0.1
SiO
(0.068)
0.002
40
2
SiO
50
0.06
t
pc
40
0.006
ct
sp
0.01
40
0.3
s
ma
0.1
ss
ma
0.04
0.02
0.04
0.01
0.02
0.03
0.04
a calculated
a calculated
MnO
FeO
Fig. 12a.
Comparison between
calculated and experimentally obtained
FeO activities in the Al2O3-FeO-MgOMnO-SiO2 system.
230
Fig. 12b.
Comparison between
calculated and experimentally obtained
MnO activities in the Al2O3-FeO-MgOMnO-SiO2 system
0.10
0.09
0.08
0.07
a Al O
2 3
0.06
BF
0.05
LF
0.04
0.03
0.02
EAF
0.01
0.00
2
4
6
8
10
12
pct CaO / pct SiO 2
Fig. 13. The activities of Al2O3 for
some typical slag compositions in
BF, EAF and LF slags as a functions
of the ratio mass pct CaO/mass pct
SiO2 .
231
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