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Thermodynamic Model for Prediction of Slag-Steel-Inclusion
Reactions of 304 Stainless Steels
Ying REN and Lifeng ZHANG*
School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, No. 30, Xueyuan Road,
Haidian District, Beijing, 100083 China.
(Received on August 25, 2016; accepted on September 9, 2016; J-STAGE Advance published date:
November 1, 2016)
A thermodynamic model was developed to predict slag–steel–inclusion reactions of 304 stainless steels.
The dissolved aluminum in the steel, the sulfur distribution ratio and the composition of inclusions equilibrated with varying slags were predicted using the current model. The model can also be widely used to
predict the liquid fraction of inclusions. For Al-killed 304 stainless steels, the optimized composition of
CaO–Al2O3–SiO2–MgO slags is proposed to modify solid Al2O3 inclusions to liquid CaO–Al2O3–MgO at
1 873 K. For Si-Mn-killed 304 stainless steels, the optimized composition of CaO-SiO2-MgO-Al2O3-20%CaF2
slags is suggested to suppress the formation of Al2O3–MgO in SiO2–CaO–MnO–MgO–Al2O3 inclusions and
lower their melting temperatures.
KEY WORDS: thermodynamic model; slag; inclusions; 304 stainless steels.
1.
the models and optimized model parameters for low-order
(binary and ternary) sub-systems can be used to provide
good estimates for the lacking data for a multicomponent
system.43) Thus, the formation of inclusions at different
temperatures and varying steel compositions in a multicomponent system can be apace and accurately predicted
by means of thermodynamic software. Holappa et al.44)
developed a thermodynamic model using ChemSage to
calculate equilibrium oxide and sulfide inclusions in steel
and predict the “liquid window” for the formation of liquid
calcium aluminates. Jung et al. predicted the evolution of
liquid and solid inclusions during the ladle furnace process
using Factsage.45) Kang and Lee46) predicted the slag/steel
and steel/inclusions relationships in Si-Mn-killed steel using
Factsage. The sulfide capacity of Al2O3–CaO–FeO–Fe2O3–
MgO–MnO–SiO2–TiO2–Ti2O3 multicomponent slags can be
evaluated using Factsage.47)
Most of the reported models using thermodynamic software are used to predict the slag/steel reactions, or steel/
inclusion reactions. Whereas, there was few model developed to thermodynamically predict a large number of slag/
steel/inclusion reactions. In the current study, a thermodynamic model based on Factsage was developed to achieve
the control of steel chemistry and the composition of inclusions through optimizing the composition of refining slag of
304 stainless steels.
Introduction
As demand for high performance steels increases every
year, improving steel cleanliness is a main task of steelmakers.1,2) Non-metallic inclusions in steel have a detrimental
effect on the performance of steels, such as their strength,
toughness, fatigability, cleanliness, surface finishing, etc.3)
A wide range of operating approaches including deoxidation,4,5) calcium treatment,6–11) slag refining,12–17) and prevention against reoxidation18–21) are applied throughout the
steelmaking processes of stainless steels. Inclusion composition is greatly influenced by the composition of the top slag
and the refractory material.22) The precise control of the
composition of inclusions in stainless steels can be achieved
by choosing the proper top slag composition.12–17,23,24)
A large number of thermodynamic models based on thermodynamic and phase equilibrium data for a given system
has been developed,25) which can be used to predict the
relationship between compositions of slag, steel, and inclusions in relatively simple systems, such as Al–O,26–28) Al–
Mg–O,29–31) Al–Ca–O,32–34) Al–Ti–O,35–37) Al–Si–Ca–O,38,39)
Al–Si–Mn–O,40–42) etc. However, the thermodynamic models can hardly be applied to a multicomponent system due
to complicated calculations and lack of thermodynamic
data. With the application of the thermodynamic software,
all available thermodynamic and phase equilibrium data for
a system are critically evaluated simultaneously in order to
obtain one self-consistent set of model equations for the
Gibbs energies which best reproduce the data for all phases
as functions of temperature and composition. Meanwhile,
2. Thermodynamic Model
There are many reactions involved during the slag refining process, as shown in Fig. 1. In the schematic representation, each reaction represents the following: R1: Slag/Steel
reaction, R2: Steel/Inclusion reaction. To simplify the model
* Corresponding author: E-mail: zhanglifeng@ustb.edu.cn
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and calculation, the following assumptions are made in the
current thermodynamic model: (1) Slag/steel reaction and
steel/inclusion reaction are assumed to reach the equilibrium; (2) The temperature can be maintained at a curtained
fixed temperature; (3) The removal of inclusions to slag,
Refractory/Slag reaction and Refractory/Steel reaction are
Fig. 1.
not considered in the current model.
In the FactSage software, the Equilib program can be
called by the embedded coding called ‘‘Macro Processing.’’
All the input conditions and output can be stored and passed
to the different equilibrium calculations or externally to a
simple text file or Microsoft ExcelTM worksheets using this
macro processing code. A small program can be written
using this macro processing code for equilibrium calculations.45) Thus, the calculation process of the current model
is as following: (1) The initial conditions (compositions and
amounts of slag, steel and inclusions, and temperature) are
set up using the Microsoft ExcelTM as an interface. (2) The
initial slag reacts with the initial steel; (3) The reacted steel
reacts with the initial inclusions; (4) The equilibrated conditions are output to the Microsoft ExcelTM. In the calculation, the reactions are calculated one by one in the order of
reaction number and the outputs of the previous equilibrium
reaction can be added as stream inputs to further calculations
to keep track of reaction heats. The thermodynamic phase
equilibria of all reactions were calculated adiabatically using
FactSage with FactPS, FToxid and FTmisc databases.43)
Schematic diagram of reactions during the slag refining
process. (Online version in color.)
Fig. 2. Comparison of predicted and measured data of 304 stainless steels.
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steels are given in Fig. 3. Figure 3(a) shows the predicted
[Al]s in 304 stainless steels equilibrated with various slags.
With the requirement of the liquid slag during the refining
process, the liquidus of the slags at 1 873 K is illustrated as
the outer contour line of colour zone in the ternary phase
diagram. Different colours mean various [Al]s in stainless
steels. The [Al]s in stainless steels dramatically declines
with decreasing slag basicity since [Al]s in stainless steels is
expected to react with the unstable SiO2 in the low basicity
(CaO/SiO2) slag as given in Eq. (1). With the slag basicity lower than 2.0, the addition of Al2O3 in slag enhances
[Al]s. With the slag basicity higher than 2.0, there is lower
[Al]s in steel equilibrated with the high Al2O3 slag. It can
be inferred that low [Al]s in 304 stainless steels can be
achieved by using the low basicity CaO-SiO2-based slag.
The high basicity CaO-Al2O3-based slag can increase [Al]s
in 304 stainless steels.
3. Verification of Thermodynamic Model
To verify the accuracy of the developed model, experimental data reported in the previous studies is referenced
and compared with the calculated results, as shown in Fig.
2. Reported data of the initial slag, steel, and inclusions of
304 stainless is given in Table 1.4,12,23) Figure 2(a) shows
the comparison of the predicted dissolved aluminum ([Al]s)
and measured [Al]s in 304 stainless steels. The predicted
result shows a good agreement with the measured result in
the range of [Al]s from several ppm to above 200 ppm. The
calculated sulfur distribution ratio (Ls) roughly agrees with
the measured results, as shown in Fig. 2(b). The agreement
between the calculated and measured concentrations of [Al]s
and S in stainless steels demonstrates that the current thermodynamic model can be used to predict the effect of slags
on steel chemistry. In Figs. 2(c) and 2(d), the calculated
Al2O3 and MgO in inclusions are basically in accordance
with experimental values, indicating that the composition of
inclusions influenced by slags and steels can be successfully
predicted using the current thermodynamic model.
4.
4[ Al ] + 3(SiO2 )slag = 3[ Si ] + 2( Al2O3 )slag ........... (1)
The calculated sulfur distribution ratio, (S)/[S], of 304
stainless steels equilibrated with various slags are given in
Fig. 3(b). The desulfurization reaction is given in Eq. (2).
Increasing the slag basicity in slag can significantly enhance
the (S)/[S] of 304 stainless steels. The (S)/[S] increases with
decreasing SiO2 in slag. Therefore, the CaO-Al2O3-based
slag is recommended to promote the desulfurization of 304
stainless steels.
Prediction of Slag–Steel–Inclusion Reactions of 304
Stainless Steels
To optimize the composition of refining slag and improve
the cleanliness of 304 stainless steels, a large number of
calculations were apace carried out using FactSage macro
processing. Based on the analysis of a typical slab of 304
stainless steels, the initial compositions of steel and inclusions in Si-Mn-killed 304 stainless steels are listed in
Tables 2 and 3. Since CaO–SiO2–Al2O3–MgO–CaF2 slag is
widely used during the slag refining process of Si-Mn-killed
304 stainless steels, the composition of the initial slag is
given in Table 4. The contents of CaF2 and MgO are fixed
to 20% and 5%, respectively. The CaO, SiO2, and Al2O3 in
slags were in a wide range from 0 to 75%. Four hundred calculations were carried out with a 3.75% increment of each
component in the CaO–SiO2–Al2O3 ternary phase diagram.
The mass ratio of slag/steel is fixed at 1/50.
The predicted effects of the initial slag composition on
inclusion characteristics and steel chemistry of 304 stainless
Table 3.
Composition of the initial inclusions (wt%).
Deoxidation
Al2O3
MgO
SiO2
CaO
MnO
TiO2
Si–Mn
20.04
1.65
39.10
8.37
26.04
4.79
Al
100
0
0
0
0
0
Table 4. Composition of the initial slag (wt%).
CaF2
MgO
CaO
SiO2
Al2O3
20
5
0–75
0–75
0–75
Table 1. Reported data of the initial slag, steel and inclusions of 304 stainless steels.
Slag
Steel
Inclusions
Basicity
Al2O3
(%)
MgO
(%)
[Al]s
(%)
Mass
ratio of
slag/steel
Mizuno et al.
1.7–5.0
2.8–8.5
6.7–8.7
0.001–0.24
1/5
Cr2O3
The previous work
1.0–2.3
0.7–20
2.2–20
0.0018
2/25
CaO–SiO2–Al2O3–
MnO–MgO–TiO2
Authors
Table 2.
Deoxidation
Si–Mn
Al
Temperature
(K)
Ref.
35
1 823 K
4, 23)
50
1 873 K
12)
Type
T.O.
(ppm)
Composition of the initial stainless steel (wt%).
C
Si
Mn
S
P
Cr
Ni
N
Ti
Ca
0.048
0.48
1.06
0.003
0.024
18.11
8.00
0.037
0.003
0.00033
3
T.O.
[Al]s
0.0050
0.0018
0.0020
0.0500
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Fig. 3. Effects of the initial slag composition on inclusion characteristic and steel chemistry of 304 stainless steels. (a)
[Al]s in 304 stainless steels, (b) (S)/[S] of 304 stainless steels, (c) Al 2O3 in inclusions in 304 stainless steels, (d)
MgO in inclusions in 304 stainless steels, (e) Liquid fraction of inclusions. (Online version in color.)
Al2O3 in inclusions.
[O] + (S 2 − )slag = [ S ] + (O 2 − )slag ................... (2)
4[ Al ] + 3(SiO2 )inclusion = 3[ Si ] + 2( Al2O3 )inclusion ...... (3)
The Al2O3-rich inclusions are harmful to both the quality
of steel products and the castability of stainless steels due
to the high melting point and hardness.12) The effect of slag
composition on Al2O3 in inclusions in 304 stainless steels
is shown in Fig. 3(c). The unstable oxides in inclusions are
reduced by [Al]s in 304 stainless steels. The main reactions
of the formation of Al2O3 in inclusions are given in Eqs.
(3) and (4). The Al2O3 in inclusions distinctly rises up with
increasing slag basicity. It is mainly because high basicity
slag increases [Al]s in 304 stainless steels, promoting the
formation of Al2O3 in inclusions. It can be deduced that
the low basicity CaO-SiO2-based slag is beneficial to lower
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2[ Al ] + 3( MnO)inclusion = 3[ Mn] + ( Al2O3 )inclusion ...... (4)
Figure 3(d) shows the relationship between slag composition and MgO in inclusions in 304 stainless steels. It
can be seen that MgO in inclusions obviously goes up with
increasing slag basicity. It should be noted that the evolution
of MgO in inclusions has a similar tendency with that of the
predicted [Al]s in 304 stainless steels in Fig. 3(a) due to the
reduction of MgO in slag by [Al]s in 304 stainless steels.48)
With the main reduction reactions between inclusions and
the [Mg] in Eqs. (5) and (6), MgO in inclusions can be
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lowered by using the low basicity CaO-SiO2-based slag.
2[ Mg ] + (SiO2 )inclusion = [ Si ] + 2( MgO)inclusion ........ (5)
[ Mg ] + ( MnO)inclusion = [ Mn] + ( MgO)inclusion ........ (6)
Since the mass of the formed species in inclusions can
be output, the liquid fraction of inclusions at 1 873 K can
be calculated, as shown in Fig. 3(e). It can be seen that the
generated inclusions are almost fully liquid with slag basicity below 1.0. There is more solid phase formed in inclusions with increasing basicity and Al2O3 in slag. The change
of the liquid fraction of inclusions has a similar tendency
with that of Al2O3 in inclusions, indicating that the melting temperature of inclusions is significantly influenced by
Al2O3 in inclusions.
5.
Optimization of Slag Composition to Control Inclusions in 304 Stainless Steels
5.1.
Optimization of the CaO–Al2O3–SiO2–MgO Slag
for Al-killed 304 Stainless Steels
There are two typical process routes to control inclusions
in 304 stainless steels. The first route is to lower the amount
of oxide inclusions by Al deoxidation. Meanwhile, the slag
refining or calcium treatment is commonly used to modify
solid alumina inclusions to the liquid calcium aluminate and
avoid the nozzle clogging during the continuous casting process. It has been reported that the CaO–Al2O3–SiO2–MgO
slag has excellent refining properties, such as low oxidation
potential, low melting temperature and low viscosity at
steelmaking temperature.15,16) Therefore, the compositions
of CaO–Al2O3–SiO2–MgO slags were optimized using the
current thermodynamic model to increase the CaO/Al2O3 in
inclusions at 1 873 K and lower the melting temperature of
inclusions in Al-killed 304 stainless steels. The compositions of the initial Al-killed 304 stainless steel and inclusions in the calculations are listed in Tables 2 and 3. The
mass ratio of slag and steel is 1/50.
Figure 4 shows the predicted effect of the CaO–Al2O3–
SiO2–MgO slag on the CaO/Al2O3 in inclusions in Al-killed
304 stainless steels. It can be seen from Fig. 4(a), with the
CaO/Al2O3 in the CaO–Al2O3–SiO2 slag increasing from
0.5 to 1.5, the CaO/Al2O3 in inclusions obviously goes up.
It should be noted that the CaO/Al2O3 in inclusions remains
unchanged with the CaO/Al2O3 in slag reaching roughly
1.5–2.0 since CaO in the molten slag is oversaturated and
the solid CaO phase is generated in the molten slag at 1 873
K. To increase the CaO/Al2O3 in inclusions and avoid the
formation of solid phases in the molten slag, the CaO/Al2O3
in slag at inflection points of the curves are recommended. It
can be seen that the addition of SiO2 in slag can dramatically
decrease the CaO/Al2O3 in inclusions. Figure 4(b) shows the
relationship between the CaO/Al2O3 in inclusions and the
CaO/Al2O3 in slags with varying MgO contents. Increasing
MgO in slag from 0 to 10% can slightly enhance the CaO/
Al2O3 in inclusions.
Since Si is alloyed in the molten steel, there is a small
amount of SiO2 formed in slag. Typically, the predicted
effect of a CaO-Al2O3-4%SiO2-2%MgO slag on the composition of inclusions at 1 873 K is shown in Fig. 5(a).
The decrease of CaO/Al2O3 in the CaO-Al2O3-4%SiO2-
Fig. 4. Effect of the CaO–Al2O3–SiO2–MgO slag on the CaO/
Al2O3 in inclusions in Al-killed 304 stainless steels.
(Online version in color.)
2%MgO slag dramatically promotes the formation of solid
Ca2Mg2Al28O45, CaMg2Al16O27, CaAl4O7, CaAl12O19 and
Al2O3 inclusions. The inclusions can be fully modified to
liquid inclusions by increasing the CaO/Al2O3 in slag to
above 1.4 at 1 873 K. The calculated liquidus and solidus
of formed oxide inclusions are shown in Fig. 5(b). The
solidus of inclusions is roughly unchanged with the CaO/
Al2O3 in the CaO-Al2O3-4%SiO2-2%MgO slag higher than
1.3. The liquidus of inclusions significantly declines with
the increase of the CaO/Al2O3 in slag. The liquidus of
inclusions can be lowered to 1 479 K with a CaO/Al2O3
ratio of 1.6 in the CaO-Al2O3-4%SiO2-2%MgO slag, which
agrees with the recommended ratios of the CaO/Al2O3 in
the CaO–Al2O3–SiO2–MgO slag to increase the CaO/Al2O3
in inclusions.
To optimize the composition of CaO–Al2O3–SiO2–MgO
slag for Al-killed 304 stainless steels, a large number of
calculations were apace carried out using FactSage macro
processing. The ratios of CaO/Al2O3 in slags with varying
SiO2 and MgO are recommended to increase the CaO/Al2O3
in inclusions, lower the melting temperature of inclusions
and avoid the formation of solid phases in the molten slag,
as shown in Fig. 6. It can be seen that the proposed CaO/
Al2O3 in slags distinctly goes up from 1.5 to 2.0 with an
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Fig. 5. Effect of the CaO-Al2O3-4%SiO2-2%MgO slag on the
composition and melting temperature of inclusions in Alkilled 304 stainless steels. (Online version in color.)
Fig. 7.
ity, causing defects on the surface of stainless steel products
due to their poor deformability.3) It has been reported that
lowering the Al2O3–MgO in Al2O3–SiO2–CaO–MnO inclusions can significantly decrease the melting temperature and
improve deformability of inclusions.49) In order to avoid the
generation of the nondeformable Al2O3-MgO-rich inclusions, the Si–Mn deoxidation was introduced. However, the
aluminum in the added ferrosilicon alloy can significantly
promote the formation of spinel inclusions in Si-Mn-killed
stainless steels.5) Typically, the CaO–SiO2–Al2O3–MgO–
CaF2 slag is used to lower [Al]s in steel and suppress the
formation of the Al2O3–MgO in inclusions.12,17) In the
current study, the CaO–SiO2–Al2O3–MgO–CaF2 slag was
optimized using the current thermodynamic model to lower
the Al2O3–MgO in inclusions at 1 873 K and decrease the
melting temperature of inclusions in Si-Mn-killed 304 stainless steels. The compositions of the initial Si-Mn-killed 304
stainless steel and inclusions in the calculations are given in
Tables 2 and 3. The CaF2 in the initial slag is fixed at 20%.
The mass ratio of slag and steel is 1/50.
Figure 7 shows the predicted the effect of the CaO–
SiO2–Al2O3–MgO–CaF2 slag on Al2O3–MgO in inclusions
in Si-Mn-killed 304 stainless steels. It can be seen from Fig.
7(a), the Al2O3–MgO in inclusions rises up with an increase
Fig. 6. Proposed CaO/Al2O3 in the CaO–Al2O3–SiO2–MgO slag
for Al-killed 304 stainless steels. (Online version in color.)
increase of SiO2 in slag from 2% to 10% since the addition of SiO2 in slag decreases CaO/Al2O3 in inclusions in
Fig. 5(a). Meanwhile, the proposed CaO/Al2O3 in slags can
hardly be influenced by MgO in slag in the range from 4% to
10%, which is in accord with the results given in Fig. 5(b).
5.2.
Optimization of the CaO–SiO2–Al2O3–MgO–CaF2
Slag for Si-Mn-killed 304 Stainless Steels
The Al2O3-MgO-rich inclusions have a poor deformabil-
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Effect of the CaO–SiO2–MgO–Al2O3–CaF2 slag on the
Al2O3–MgO in inclusions in Si-Mn-killed 304 stainless
steels. (Online version in color.)
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Fig. 9.
Proposed CaO/SiO2 in the CaO-SiO2-Al2O3-MgO-20%
CaF2 slag for Si-Mn-killed 304 stainless steels. (Online
version in color.)
roughly 1.4 is proposed to lower the melting temperature of
inclusions in Si-Mn-killed stainless steels.
To optimize the composition of CaO-SiO2-MgO-Al2O320%CaF2 slag for Si-Mn-killed 304 stainless steels, a large
number of calculations were apace carried out using FactSage macro processing. The ratios of CaO/SiO2 in slags
with varying Al2O3 and MgO are recommended to reduce
the Al2O3–MgO in inclusions to below 35%, lower the melting temperature of inclusions, and decrease the erosion of
MgO refractory, as shown in Fig. 9. It can be seen that the
proposed CaO/SiO2 in slags significantly declined from 1.6
to 0.6 with the increases of Al2O3 and MgO in slag from
2% to 10% since the addition of Al2O3 and MgO in slag
can promote the formation of Al2O3–MgO in inclusions as
shown in Fig. 7.
Fig. 8. Effect of the CaO-SiO2-5%MgO-2%Al2O3-20% CaF2 slag
on the composition and melting temperature of inclusions
in Si-Mn-killed 304 stainless steels. (Online version in
color.)
of the CaO/SiO2 in the CaO–SiO2–Al2O3–MgO–CaF2 slag
from 0.8 to 1.8. Meanwhile, adding Al2O3 in slag can promote the formation of the Al2O3–MgO in inclusions. As
shown in Fig. 7(b), the addition of MgO in slag can increase
the Al2O3–MgO in inclusions. It should be noted that the
breakpoints of the relationship curves are mainly caused by
the saturation of MgO in the molten slag at 1 873 K. Since
low basicity slag increases the erosion of MgO refractory,12)
the slag can lower the Al2O3–MgO in inclusions to below
35%, which is suggested for Si-Mn-killed 304 stainless
steels.
The Al2O3 and MgO in the CaO–SiO2–Al2O3–MgO–CaF2
slag can hardly be completely avoided due to the oxidation
of [Al]s in the molten steel, the removal of Al2O3-rich inclusions, and the erosion of MgO refractory. Typically, the predicted effect of a CaO-SiO2-5%MgO-2%Al2O3-20% CaF2
slag on the composition of inclusions at 1 873 K is shown
in Fig. 8(a). The formed inclusions are fully liquid with the
CaO/SiO2 in slag ranging from 0.8 to 1.8 at 1 873 K. It can
be seen that the increasing rate of Al2O3–MgO in inclusions
apparently rises up with the CaO/SiO2 in slag exceeding
1.4. In Fig. 8(b), the calculated liquidus and solidus of
formed oxide inclusions show an increasing trend with the
CaO/SiO2 in CaO-SiO2-5%MgO-2%Al2O3-20%CaF2 slag
rising up from 0.8 to 1.8. Since the low basicity slag can
increase the erosion of the MgO refractory,12) the CaO-SiO25%MgO-2%Al2O3-20%CaF2 slag with a CaO/SiO2 ratio of
6.
Conclusions
(1) A thermodynamic model was developed using
Factsage macro processing to investigate the effect of slag
composition on the cleanliness of 304 stainless steels. The
calculated results show a good agreement with the experimental data from the literature.
(2) The CaO-Al2O3-based slag can modify inclusions
to CaO–Al2O3–MgO inclusions in Al-killed 304 stainless
steels. The addition of SiO2 in the CaO–Al2O3–SiO2–MgO
slag decreases the CaO/Al2O3 in inclusions. The CaO/
Al2O3 in inclusions can hardly be influenced by MgO in
the CaO–Al2O3–SiO2–MgO slag. The composition of the
CaO–Al2O3–SiO2–MgO slag is optimized to increase the
CaO/Al2O3 in inclusions and lower the melting temperature
of inclusions.
(3) The CaO-SiO2-CaF2-based can modify inclusions to
Al2O3-MgO-poor inclusions in Si-Mn-killed 304 stainless
steels. The addition of Al2O3 and MgO in the CaO-SiO2MgO-Al2O3-20%CaF2 slag can promote the formation of
the Al2O3–MgO in inclusions. The CaO/SiO2 in slags with
varying Al2O3 and MgO in slag is proposed to lower the
Al2O3–MgO in inclusions and the melting temperature of
inclusions.
7
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Acknowledgements
The authors are grateful for support from the National Science Foundation China (Grant No. 51274034, No. 51334002,
and No. 51404019), Beijing Key Laboratory of Green Recycling and Extraction of Metals (GREM), the Laboratory of
Green Process Metallurgy and Modeling (GPM2) and the
High Quality steel Consortium (HQSC) at the School of
Metallurgical and Ecological Engineering at University of
Science and Technology Beijing (USTB), China.
19)
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