Oxidation State and Activities of Chromium Oxides
in CaO-SiO2-CrOx Slag System
Y. XIAO, L. HOLAPPA, and M.A. REUTER
The activities of chromium oxides in a CaO-SiO2-CrOx slag system were determined with the electromotive force (EMF) method by equilibrating with metallic chromium at 1873 K. The effect of slag
basicity on the activity coefficients of CrO and CrO1.5 was analyzed. The results showed that increasing
the slag basicity increased the activity coefficient of CrO; however, the effect on that of CrO1.5 was not
significant. The oxidation state of chromium in CaO-SiO2-CrOx slags was systematically investigated at
both 1873 and 1863 K. It was found that divalent and trivalent chromium coexists in the slags.
Divalent chromium oxide is favored, instead of trivalent chromium oxide, because of low slag basicity
and low oxygen potential. It was concluded that the oxidation state of chromium in the slag system
varied greatly from almost pure “CrO” to a composition corresponding to Cr3O4. In addition, the
thermodynamic data in the slag system were assessed based on the regular solution model to mathematically describe the activities of chromium oxides in the slags. A group of model parameters were
obtained. The calculated activities of chromium oxides were comparable to the measured data.
I. INTRODUCTION
KNOWLEDGE of the activities of chromium oxides
in slag melts is of great value for both theoretical evaluation
and practical applications in stainless steelmaking. Because
of the continuously increasing demand for stainless steel
production in recent years, there has been a persistent
research for effective and economic ways to raise the chromium recovery, which depends very much on the slag/metal
reactions. Because of the multivalence state of chromium
ions in slags, the behavior of chromium in metallurgical
slags is complicated. So far, little systematic attempts have
been made due to experimental difficulties, such as the high
melting point of chromium-oxide-containing slags as well
as crucible corrosion. Little literature was found concerning
activities of chromium oxides and the oxidation state of
chromium in slags,[1–10] but the data are still insufficient to
clarify the behavior of chromium in molten slags.
The purpose of this study is to determine quantitatively
the oxidation state of chromium and to measure the activities
of chromium oxides in the CaO-SiO2-CrOx slag system at
steelmaking temperatures. The slags were in equilibrium
with metallic crucible under argon atmosphere. The oxidation state of chromium was investigated at both 1873 and
1863 K and determined by wet-chemical analysis. Activities
of chromium oxides covering the isothermal liquidus section
in the CaO-SiO2-CrOx quasiternary system at 1873 K were
measured with the electromotive force (EMF) method and
mathematically evaluated based on the regular solution
model.
recording equipment, an oxygen probe, sampling tubes, and
a crucible assembly. The details of the experimental apparatus and procedure are illustrated in Figure 1.[11] A chromium
crucible with a 28 mm inner diameter, 32 mm outer diameter,
and 50 mm height was used as the working crucible. The
crucible was charged with 16 g of Cr-Ag alloy and 30 g
of slag. The working crucible was placed in a corundumprotecting crucible, lined with molybdenum sheet. The entire
crucible unit was fixed on a mullite supporting pedestal. The
solid electrolyte-oxygen probe, Ir/Cr ⫹ Cr2O3/ZrO2(MgO),
consisted of a 9 mol pct MgO-stabilized zirconia crucible
as an oxygen conductive electrolyte and a mixture of 4Cr ⫹
1Cr2O3 by weight as a reference electrode. An iridium wire
of 0.5 mm diameter was used as an electrical lead. The probe
was sealed with Al2O3 cement. The isostatically pressed,
zirconia solid electrolyte crucibles had dimensions of 5 mm
inner diameter, 8 mm outer diameter, and 50 mm height.
Electrical contact to the outer surface of the zirconia probe
was completed by a Cr-Ag alloy equilibrated with slag and
a ZrO2-Mo cermet rod welded to a Mo wire.
The reaction system was protected by purified argon gas
with a flow rate of 6 l/h. The vertical electrical-resistance
furnace was heated by LaCrO3 heating elements. The overall
error in the measurement and control of the temperature was
less than ⫾4 K.
Additional equilibrium experiments for determination of
oxidation state of chromium in slags were carried out in a
SiC electrical-resistance furnace under similar experimental
conditions.[12] The oxide mixtures were reacted and equilibrated with chromium crucible at 1863 K for about 20 hours
in the furnace.
II. EXPERIMENTAL
The experimental system consists of a high temperature
furnace, an argon purification line, EMF measuring and
A. Raw Materials
Y. XIAO, Research Scientist, and M.A. REUTER, Professor, are with
the Department of Applied Earth Science, Delft University of Technology,
2628 RX Delft, The Netherlands, Contact e-mail: [email protected]
L. HOLAPPA, Professor, is with the Laboratory of Metallurgy, Helsinki
University of Technology, FIN-02015 HUT, Espoo, Finland.
Manuscript submitted October 15, 2001.
Laboratory reagent-grade oxides were used as raw materials in the experiments. The SiO2 and Cr2O3 powders were
heated at 873 K for 8 hours and CaO at 1673 K for 24
hours. Then, they were crushed and ground into powder and
kept in a desiccator ready for use. Chromium powder with
99.99 pct purity and silver powder with 99.99 pct purity
METALLURGICAL AND MATERIALS TRANSACTIONS B
VOLUME 33B, AUGUST 2002—595
Fig. 1—Schematic diagram of the experimental apparatus.
Fig. 2—Isothermal section through CaO-SiO2-CrOx quasiternary system at
1873 K in equilibrium with metallic chromium.
were used for preparing the Cr-Ag alloy. The purity of the
chromium crucible was 99.7 pct.
B. Experimental Procedure
The compositions of the oxide mixtures were chosen
within the liquid region of the system in Figure 2, which is
596—VOLUME 33B, AUGUST 2002
drawn based on the results from de Villiers and Muan.[13]
To reduce the equilibrating time of the reaction system, CrO
was added to the slag systems with a stoichiometric mixture
of Cr2O3 and a chromium metal powder based on proper
divalent chromium fractions.
The required oxides powders were homogeneously mixed
and pressed into tablets and, then, packed in the chromium
working crucible. When the system had reached equilibrium
state at the required temperature, the oxygen probe was
slowly moved downwards until its lower end was close to
the slag melt. After the thermodynamic equilibration, the
probe was immersed slowly into the melt so as to contact
the slag as well as the metal phase but above the bottom of
the crucible. The oxygen probe was inserted through a rubber
stopper for sealing the furnace tube on the top of the watercooled brass flange. The stable EMF value was achieved
within a few seconds after immersion. After a stable EMF
was obtained, the probe was removed from the melt. Subsequently, a slag sample was taken with an alumina tube under
controlled suction and was quickly quenched in cold water.
Next, a subslag was added from the top of the reaction tube
through a guiding pipe to change the slag composition that
had about the same weight compared to the previous slag
sample. The subslag was made up by stoichiometric calculation including all the slag components and metallic chromium powder. The next measurement could be made after
2 to 3 hours equilibration at 1873 K.
The color of the slag samples varied from deep blue to
METALLURGICAL AND MATERIALS TRANSACTIONS B
bluish green with increasing the total amount of the chromium oxides and slag basicity. The slag was carefully
removed from the sampling tubes, ground, and screened to
a particle size less than 122 ␮m for slag analysis. The weight
percentage of divalent chromium in slags was analyzed with
the wet-chemical method of indirect chemical-redox titration. The total chromium and other slag components, CaO
and SiO2, were determined by X-ray fluorescence. In addition, the slag samples from the experiments at 1863 K were
examined by a scanning electron microprobe and X-ray
diffraction.
C. Experimental Principles
In view of the volatility of CrOx-containing slags, the
electrochemical oxygen probes were used for the activity
measurements in the present study. The galvanic cell in the
present experiment was constructed as follows:
When pure liquid CrO and pure solid Cr are chosen as
the standard states of activities of CrO and Cr, respectively,
the standard Gibbs energy of formation for liquid CrO is
⌬G⬚1 ⫽ ⫺333,898 ⫹ 63.74T(J)[16]
where ⌬G⬚1 was given only in the temperature range of 1938
to 2023 K.[16] Because this was the only data available, it
was adopted and extrapolated to the present experimental
temperatures. In the present calculation, an error of ⫾1 kJ
from ⌬G⬚1 would lead to an error of ⫾6.5 pct in the activity
of CrO. Therefore, one has to be aware that the activity data
can only be referred to when one uses the same free energy
of CrO formation.
For CrO1.5 in the slag, it can be written as
Cr(s) ⫹
Po2(ref)1/4 ⫹ Pe1/4
RT
ln
F
Po2(slag)1/4 ⫹ Pe1/4
[1]
where, E is the EMF measured with calibration, volt; R is
the gas constant, 8.314 J/K/mol; F is the Faraday constant,
96,500 J/V/mol; T is the temperature, K; Po2(slag) is the
oxygen-partial pressure referring to the slag system to be
measured, atm; and Po2(ref) is the oxygen-partial pressure
referring to the Cr/Cr2O3 reference electrode, atm:
log Po2(ref) ⫽ 8.613 ⫺ 3.87 ⫻ 104 /T [14]
Pe is the characteristic oxygen-partial pressure at which the
ionic and n-type electronic conductivities are equal. For a
corresponding electrolyte material from the same producer,
it was given[15]
log Pe ⫽ 20.40 ⫺ 6.45 ⫻ 10 /T
4
[15]
The use of dissimilar electrical connections requires a
correction in the thermal EMF of the (⫹) Ir/ZrO2 ⫹ Mo/
Mo (⫺) couple. The relation of the thermoelectromotive
force with temperature was formulated into the following
equation through a separate experiment (1773 to 1873 K):
E⬘(mv) ⫽ 6.65 ⫺ 1.83 ⫻ 10⫺2T(K)
[2]
The real EMF values should be equal to the measured
values, Em , minus the thermal EMF, E⬘:
E ⫽ Em ⫺ E⬘
[3]
In the equilibrium system, CrO and CrO1.5 coexist. The
equilibrium relations of chromium in the measuring system
can be represented as follows:
Cr(s) ⫹
[7]
aCrO1.5
[8]
aCr ⭈ Po 23/4
Because
Considering the influence of electronic conduction in the
electrolyte at high temperatures, the open-circuit EMF of
the cell is given by the following equation according to the
Nernst equation:
E⫽
3
O2 ⫽ CrO1.5(slag)
4
⌬G⬚2 ⫽ ⫺RT ln
(⫹)Ir, (Cr ⫹ Cr2O3)㥋ZrO2(9MgO)㥋(CrOx)slag,
(Cr-Ag), (ZrO2-Mo), Mo(⫺)
[6]
1
O ⫽ CrO(slag)
2 2
aCrO
⌬G⬚1 ⫽ ⫺RT ln
aCr ⭈ Po21/2
METALLURGICAL AND MATERIALS TRANSACTIONS B
1
⌬G⬚CrO1.5 ⫽ ⌬G⬚Cr2O3
2
[9]
⌬G⬚2 ⫽ ⫺554,540 ⫹ 123.54T(J)[14]
[10]
it follows that
where a pure solid was chosen as the standard state both
for Cr and CrO1.5.
Since the melt was saturated with the Cr crucible, the
activity of chromium (aCr) is unity in the present work.
According to Eq. [1], if the EMF is measured, the oxygenpartial pressure, Po2, in the slag system can be calculated.
Consequently, the activities of CrO and CrO1.5 in the slags
can be obtained as follows:
⌬G⬚1
aCrO ⫽ Po21/2 ⭈ exp ⫺
RT
冢
冣
[11]
⌬G⬚2
aCrO1.5 ⫽ Po23/4 ⭈ exp ⫺
RT
[12]
冢
冣
III. RESULTS AND DISCUSSION
The experimental results and calculated activity coefficients at different standard states are listed in Tables I and II.
A. Oxidation State of Chromium in Slags
The slags containing chromium oxides have a similar
problem as the iron-containing slags: the nonstoichiometry
of CrOx varies with temperature, slag basicity, and total
chromium-oxide content in the system equilibrated with
metallic chromium. When Cr2O3 is mixed with other slagging oxide components at high temperatures in contact with
chromium metal, the following equilibrium of chromium
oxides is expected:
[4]
2CrO1.5(slag) ⫹ Cr ⫽ 3CrO(slag)
[5]
Chromium is, therefore, distributed in slag both as divalent
and trivalent states in different fractions. For the calculation
of slag composition, the total content of chromium oxides
[13]
VOLUME 33B, AUGUST 2002—597
Table I. Equilibrium Slag Compositions and Measured Activities in Equilibrium with Metallic Chromium in Argon
Atmosphere at 1873 K
Slag Compositions (Mol
Pct)
Number CaO
SiO2
CrO
CrO1.5
Cr2+/TCr
x
B
CSC1
CSC2
CSC3
CSC4
CSC5
CSC6
CSC7
CSC8
CSC9
CSC10
CSC11
CSC12
CSC13
CSC14
CSC15
CSC16
CSC17
CSC18
CSC19
CSC20
CSC21
CSC22
CSC23
CSC24
CSC25
CSC26
CSC27
CSC28
CSC29
CSC30
CSC31
CSC32
CSC33
CSC34
CSC35
CSC36
CSC37
CSC38
CSC39
CSC40
CSC41
CSC42
CSC43
CSC44
CSC45
CSC46
CSC47
CSC48
36.9
33.8
29.9
26.1
20.4
21.7
50.9
48.0
47.9
44.7
40.3
37.6
33.6
27.4
44.3
43.9
43.2
42.2
40.5
38.3
35.6
40.6
37.4
35.7
32.9
31.3
60.0
56.2
52.5
48.2
44.8
41.3
37.5
31.1
28.0
24.9
46.8
51.0
29.5
25.5
23.2
25.4
20.6
27.1
22.6
23.8
31.9
31.7
6.2
11.8
14.3
16.9
21.8
21.7
4.9
10.1
10.1
11.5
14.7
16.3
17.5
23.6
6.6
7.3
9.2
10.2
14.4
16.8
23.4
9.4
18.2
18.6
20.4
22.4
8.5
14.4
15.6
22.9
27.1
21.2
23.7
20.8
23.2
23.2
30.8
19.5
25.1
27.6
32.2
27.3
33.9
23.2
25.4
32.6
21.8
18.8
2.6
5.8
13.1
19.9
29.4
27.5
0.7
0.9
0.8
2.0
6.7
11.0
17.0
23.3
0.1
0.6
0.8
2.2
2.2
5.3
8.6
6.8
14.7
18.1
21.5
22.5
0.1
0.7
5.1
4.3
5.5
16.9
20.3
33.1
35.5
40.2
3.0
3.6
41.1
46.2
44.6
42.5
42.0
40.5
42.4
39.4
44.2
48.0
0.70
0.67
0.52
0.46
0.42
0.44
0.88
0.92
0.92
0.85
0.69
0.60
0.51
0.50
0.98
0.92
0.92
0.82
0.87
0.76
0.73
0.58
0.55
0.51
0.49
0.50
0.98
0.95
0.75
0.84
0.83
0.56
0.54
0.38
0.40
0.36
0.91
0.84
0.38
0.37
0.42
0.39
0.45
0.36
0.38
0.45
0.33
0.28
1.15
1.16
1.23
1.27
1.29
1.28
1.06
1.04
1.04
1.07
1.16
1.20
1.25
1.25
1.01
1.04
1.04
1.08
1.07
1.12
1.13
1.21
1.22
1.25
1.26
1.25
1.01
1.02
1.12
1.08
1.08
1.22
1.23
1.31
1.30
1.32
1.04
1.08
1.31
1.31
1.29
1.30
1.28
1.32
1.31
1.27
1.33
1.36
1.47
1.43
1.43
1.42
1.39
1.34
0.85
0.85
0.86
0.94
0.95
0.93
0.95
0.94
1.11
1.10
1.08
1.08
1.06
1.03
0.91
1.06
0.80
0.78
0.76
0.76
0.52
0.51
0.51
0.51
0.50
0.50
0.49
0.48
0.47
0.47
0.41
0.51
0.15
0.02
0.00
0.19
0.17
0.34
0.42
0.18
0.06
0.05
54.3
48.5
42.7
37.1
28.4
29.1
43.5
41.0
41.2
41.8
38.3
35.1
31.9
25.7
49.0
48.1
46.8
45.4
42.9
39.6
32.5
43.2
29.8
27.7
25.1
23.8
31.4
28.7
26.8
24.6
22.6
20.5
18.4
15.0
13.2
11.8
19.3
25.8
4.3
0.6
0.0
4.7
3.6
9.2
9.6
4.2
2.0
1.5
EMF
(⫺mv)
51.2
35.1
14.8
0.0
0.0
0.0
114
87.7
84.7
65.7
34.7
30.1
16.4
0.0
99.8
85.4
96.7
77.7
59.0
41.2
16.5
40.6
25.6
22.7
12.6
9.5
104.2
85.2
64.3
44.5
36.6
30.7
21.7
14.5
3.8
0.0
40.1
60.3
11.6
6.9
9.1
6.5
3.6
9.7
3.7
4.2
12.5
13.7
was expressed with CrOx and calculated with the following formula:
mol pct CrOx ⫽ mol pct CrO ⫹ mol pct CrO1.5 [14]
The effects of the slag basicity and total chromium-oxide
content on the oxidation state of chromium in the slag are
represented in Figure 3. It is clear that higher slag basicity
and higher concentration of the total chromium oxide will
lead to a lower divalent-chromium fraction in the slag. The
oxidation state of chromium in the CaO-SiO2-CrOx slags
598—VOLUME 33B, AUGUST 2002
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
⫾
0.2
0.7
0.5
0.8
1.5
2.0
1.0
0.8
1.0
0.4
0.2
0.2
0.7
2.4
0.7
0.7
0.5
0.8
0.5
0.7
0.3
0.4
0.5
0.4
0.1
0.3
2.5
0.7
1.2
0.2
0.1
0.5
0.5
0.3
0.5
1.2
0.4
0.7
0.3
0.8
0.4
0.3
0.2
0.4
0.2
0.7
0.5
0.4
a(CrO)
(liquid state)
a(CrO1.5)
(solid state)
␥ (CrO)
(liquid state)
␥ (CrO1.5)
(solid state)
0.39
0.52
0.74
0.95
0.95
0.95
0.11
0.19
0.20
0.30
0.53
0.57
0.72
0.95
0.15
0.20
0.16
0.23
0.34
0.47
0.72
0.47
0.62
0.65
0.77
0.81
0.13
0.20
0.31
0.44
0.51
0.56
0.66
0.75
0.89
0.95
0.48
0.33
0.78
0.85
0.82
0.85
0.89
0.81
0.89
0.88
0.77
0.76
0.27
0.41
0.70
1.00
1.00
1.00
0.03
0.09
0.10
0.18
0.42
0.47
0.67
1.00
0.06
0.10
0.07
0.12
0.21
0.35
0.67
0.36
0.53
0.57
0.74
0.80
0.05
0.10
0.18
0.32
0.40
0.46
0.59
0.70
0.92
1.00
0.36
0.21
0.76
0.85
0.80
0.86
0.92
0.91
0.92
0.91
0.74
0.72
6.31
4.42
5.18
5.60
4.34
4.36
2.16
1.89
2.01
2.58
3.58
3.50
4.12
4.01
2.23
2.74
1.71
2.29
2.35
2.79
3.08
5.04
3.39
3.48
3.77
3.61
1.56
1.40
1.96
1.93
1.88
2.66
2.78
3.58
3.83
4.08
1.55
1.69
3.12
3.06
2.53
3.12
2.63
3.48
3.51
2.71
3.53
4.02
10.2
7.13
5.33
5.03
3.40
3.64
4.52
9.94
12.5
8.80
6.23
4.28
3.94
4.29
63.2
16.7
8.84
5.57
9.75
6.62
7.77
5.24
3.61
3.15
3.43
3.54
54.8
14.3
3.62
7.46
7.23
2.74
2.89
2.12
2.58
2.49
12.1
5.76
1.84
1.84
1.80
2.02
2.20
2.25
2.17
2.31
1.67
1.50
changed from almost stoichiometric CrO to a composition
corresponding to Cr3O4 (divalent to trivalent ratio 1:2).
For the slags of the CrOx-SiO2 system and the slags with
lower chromium-oxide contents (about ⬍20 wt pct) in the
CaO-SiO2-CrOx system, the slag samples have a deep-blue
glassy nature after quenching. Inhomogeneity in microscale
exists possibly because of the different interaction forces of
the ions and different ratio of divalent to trivalent chromium,
as shown in Figures 4 and 5. For the Cr-Si-O system, chromium oxide exists mainly in combination with silica as
METALLURGICAL AND MATERIALS TRANSACTIONS B
Table II. Slag Compositions of CaO-SiO2-CrO-CrO1.5
Oxide System in Equilibrium with Metallic Chromium in
Argon Atmosphere at 1863 K
Slag Compositions
(Mol Pct)
Samples
CaO
SiO2
CrO
CrO1.5
Cr2+/TCr
x
B
A1
A2
A3
A4
A5
A6
A7
A8
A9
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
C1
C2
0.3
0.0
0.1
0.6
0.6
1.0
1.1
0.7
0.8
46.1
46.0
46.0
43.7
35.4
34.6
36.9
41.5
41.1
40.7
42.4
44.5
39.7
36.8
37.3
17.7
15.0
25.8
25.8
37.6
28.1
43.6
43.4
42.9
41.0
34.5
34.1
34.5
41.1
41.2
41.8
31.3
32.5
45.7
29.1
45.4
41.6
35.9
34.3
34.3
31.1
40.0
8.7
9.4
10.1
13.5
19.7
21.9
23.8
14.9
13.6
15.0
13.7
13.1
14.4
34.1
17.2
40.1
48.5
38.9
38.8
30.6
31.1
1.6
1.2
1.0
1.8
10.4
9.4
4.8
2.5
4.1
2.5
12.5
9.9
0.76
0.46
0.73
0.51
0.43
0.47
0.47
0.50
0.56
0.84
0.89
0.91
0.88
0.65
0.70
0.83
0.85
0.77
0.86
0.52
0.57
1.12
1.27
1.14
1.25
1.29
1.27
1.27
1.25
1.22
1.08
1.06
1.04
1.06
1.17
1.15
1.08
1.07
1.12
1.07
1.24
1.21
0.01
0.00
0.00
0.04
0.04
0.04
0.04
0.02
0.03
1.06
1.06
1.07
1.07
1.02
1.02
1.07
1.01
1.00
0.97
1.35
1.37
Fig. 3—Oxidation state of chromium in CaO-SiO2-CrOx slag.
Cr2SiO4, according to the X-ray diffraction analysis of the
solidified samples. The liquid matrix may be depleted of
chromium oxides and becomes richer in SiO2. Based on the
electron microprobe analysis, the Cr/Si ratio in the darker
phase is slightly lower than that in the lighter phase. Because
of the amorphous structure, the existing form of chromium
in sample B1 is difficult to establish from the analysis of
X-ray diffraction. The quantitative analysis showed that, in
Figure 5, the amount of chromium and calcium in the light
phase is a little higher than that in the dark matrix.
For the CaO-SiO2-CrOx slag system with higher CrOx
content, the disproportion of CrO in the slag seems to occur,
as demonstrated in Figure 6. With the reaction of 3CrO ⫽
2CrO1.5 ⫹ Cr, the precipitated Cr2O3 is in the needle shape
and the metallic chromium inclusions are normally associated with these precipitates. For the same slag compositions,
the microstructure is quite different if the slag was cooled
naturally in the furnace under the argon gas protection; the
METALLURGICAL AND MATERIALS TRANSACTIONS B
Fig. 4—Microstructure of sample A1 quenched from 1863 K with compositions of 0.3 mol pct CaO ⫺ 39.7 mol pct SiO2 ⫺ 45.7 mol pct
CrO ⫺ 14.4 mol pct CrO1.5.
Fig. 5—Microstructure of sample B1 quenched from 1863 K with compositions of 46.1 mol pct CaO ⫺ 43.6 mol pct SiO2 ⫺ 8.7 mol pct
CrO ⫺ 1.6 mol pct CrO1.5.
Cr2O3 and chromium-metal phase were normally concomitant and dispersed in the silicate phase, as observed in Figure
7. The disproportionation of CrO to Cr2O3 and chromium
proceeded to a greater or lesser extent, depending upon the
slag compositions. This phenomenon was also reported by
Körber and Oelsen[17] as well as Healy and Schottmiller.[18]
As it is known, the structure of the silicate is very complicated. For the slags with low chromium-oxide concentration
and high SiO2 content, the nuclei formation and growth of
the new phase during cooling may be slow; the solidified
silicate slag may still keep its characteristics of the structure
in the molten state. Therefore, no disproportion of CrO was
found in the quenched slags. For the slag with high concentration of chromium oxide, it is not appropriate to conclude
and extend the results to the molten slag because of the
precipitation of quenched crystals and the presence of metal
droplets in the slag. However, in the wet-chemical analysis,
oxidation of 1 mol Cr consumes the same amount of Fe3+
as the oxidation of 3 mol Cr2+, which is just equivalent
VOLUME 33B, AUGUST 2002—599
Fig. 6—Microstructure of sample B6 quenched from 1863 K with compositions of 34.65 mol pct CaO ⫺ 34.09 mol pct SiO2 ⫺ 21.90 mol pct
CrO ⫺ 9.36 mol pct CrO1.5.
Fig. 7—Microstructure of sample B6 naturally cooled in the furnace from
1863 K.
to the consumption of CrO and the formation of metallic
chromium during the disproportionation reaction.[11] Therefore, it can be concluded that the disproportionation may
have complicated the divalent chromium analysis of the
slags, but its effect on the determination of divalent chromium in molten slags can be compensated in the wet-chemical analysis.
The disproportionation reaction would have introduced
certain random error for the analyzed results of divalent
chromium oxides. In addition, the difficulties encountered
in the wet-chemical analysis may also add uncertainties in
the divalent chromium determination. A complete reaction
and dissolution of chromium containing slags without oxidizing the divalent chromium ion by atmosphere and/or by
any other undesirable factors are very important for less
scattered results, for which the sample preparation and the
ground-slag powder size should be well controlled.
B. Activities of Chromium Oxides
In the CaO-SiO2-CrOx-based slag system, equilibrium is
reached between CrO and CrO1.5 at a constant temperature
600—VOLUME 33B, AUGUST 2002
Fig. 8—Activity coefficients of CrO at 1873 K, standard state ⫺ pure
liquid CrO.
Fig. 9—Activity coefficients of CrO1.5 at 1873 K, standard state ⫺ pure
solid CrO1.5.
under the conditions of contact with metallic chromium. The
activities of CrO and CrO1.5 can be determined according
to the system equilibrium oxygen-partial pressure. In the
present work, the activities of CrO and CrO1.5 are influenced
by the following parameters: oxygen-partial pressure, Po2,
via the total CrOx content and slag basicity via the effect on
the oxidation state of chromium in the slag or on the oxygenpartial pressure. In addition, the free energy of CrO and
CrO1.5 formation will also influence the calculated activity
coefficients, which should be considered when referring to
the results. The activity coefficients of CrO and CrO1.5 at
1873 K are shown in Figures 8 and 9. The activity of CrO
shows a positive deviation from the ideal solution. Higher
slag basicity leads to higher activity coefficients of CrO, but
the effect of slag basicity on the activity coefficients of
CrO1.5 is not so significant. Some high values of activity
coefficients of CrO1.5 in Table I are due to relative high
uncertainty in oxidation state analysis, when the tested chromium oxide content is low.
Any determination of oxygen-partial pressure with the
solid electrolyte-cell method will have some errors because
the polarization of the electrochemical cell is unavoidable
METALLURGICAL AND MATERIALS TRANSACTIONS B
multicomponent solutions based on the regular solution
model are listed as follows:
RT ln (␥i)(RS) ⫽ 兺 ␣ijX 2j ⫹ 兺兺 (␣ij ⫹ ␣ik ⫺ ␣jk)XjXk
j
j
[15]
k
RT ln (␥i)(s/liq) ⫽ RT ln (␥i)(RS) ⫹ ⌬Gconv
[16]
here, i ⫽ j or k, ␣ij ⫽ ␣ji , ␣ii ⫽ ␣jj ⫽ ␣kk ⫽ 0, and ⌬Gconv
is the conversion factor associated with the change in the
standard states. These parameters can be assessed by the
experimental data.
B. Equilibrium Relations of Cr 2+ and Cr 3+ in SlagConstraint of the Assessment
Fig. 10—Effect of Pe on the activity of CrO1.5 , standard state ⫺ pure
solid CrO1.5.
for the measurement, particularly at high temperatures and
low oxygen-partial pressures. Therefore, the cell design and
experimental method should be adopted to minimize the
polarization. Although many types of polarization may occur
in principle, here, the focus will mainly be put on the electronic-conduction polarization, which can result in significant errors for measured EMFs. The effect of electronic
conduction on the results is calculated and shown in Figure
10. The Pe value was measured for the solid electrolytes
with the same compositions and produced by the same manufacturer.[15] It is noted that when considering the electronicconduction influence, quite different results will be obtained,
especially under the condition of lower oxygen-partial
pressures.
Considering the eventual dissolution of the solid electrolyte material into the slag, no considerable reaction was
observed. Thus, its influence on the slag composition was
negligible. Further, polarization effects due to diffusion and
thermal or concentration gradients were minimized by
contacting the electrolyte probe with a bottom metal alloy
(Cr-Ag) having the same oxygen activity as the slag.
IV. MATHEMATICAL EXPRESSION OF
CHROMIUM OXIDE ACTIVITIES
A. Regular Solution Model
The original regular solution model was proposed in 1961
by Lumsden.[19] In the melts with regular solution behavior,
the molecular/ionic species, such as SiO2 or SiO44⫺, were
taken as “dissociated” ionic species consisting of Si4+ cations
and O2⫺ anions. It was assumed that the cations are almost
randomly distributed among a three-dimensional matrix of
oxygen anions (O2⫺). The mixing energy of the system can
be expressed in terms of the binary interaction energies
between the cations and the mole fractions of the cations.
Because of the fact that there is not any restriction for choosing the standard state of the activity, in order to calculate
the activities of species, the hypothetical pure-liquid oxides
with regular nature were taken as the standard states of
chromium oxides. The conversion energy from this hypothetical regular solution standard state (RS) to the conventional standard states (pure solid or liquid) is necessary. The
general relations expressing the excess Gibbs energy of the
METALLURGICAL AND MATERIALS TRANSACTIONS B
The distribution of divalent and trivalent chromium in the
slags equilibrated with metallic chromium is very important
in order to clarify the activities of chromium oxides in slags.
The distributions of divalent chromium and trivalent chromium can be obtained as follows:
CrO1.5(s) ⫽ CrO(liq) ⫹
⌬G⬚ ⫽ ⫺RT ln
1
O2
4
[17]
aCrO ⭈ Po 21/4
⫽ 220641 ⫺ 59.82T(J)
aCrO1.5
[18]
The quantitative relation between the oxidation state of
chromium and the activity coefficient, a constraint in the
assessment, can be derived from the preceding relation:
ln
␥CrO
冢 X 冣 ⫽ ln 冢␥ 冣 ⫹ 4 ln Po ⫹
XCrO1.5
1
2
CrO
CrO1.5
26565
⫺ 7.199
T
[19]
C. Assessment of the Model Parameters
The applicability of the regular solution model in various
slag systems has been investigated for over 30 years by
different researchers. The investigated slag systems with
respect to the regular solution model contain the following
components: Al2O3, CaO, CoO, Cu2O, FeO, Fe2O3, MgO,
MnO, NiO, P2O5, PbO, SiO2, TiO2, and ZnO. However, for
the slags containing chromium oxides, there is not yet any
publication found to describe the thermodynamic properties
with the regular solution model. In the present assessment
work, multiple linear-regression analysis has been used as
a quick and convenient method for determining the model
parameters. The assessment was processed from binary CaOSiO2 to CaO-SiO2-CrO-CrO1.5 systems. The experimental
data in CaO-SiO2 system were taken from the literature.[20–23]
The activity data for chromium oxides were based on the
present research, including the results at different temperatures.[11] A group of interaction energy parameters were
optimized mathematically and are given in Table III.
Because the chromium-containing slags are not strictly
regular solutions, the conversion energies for changing the
standard state of activity coefficients from the hypothetical
regular solution to the traditional pure solid or pure liquid
were also optimized simultaneously by the experimental
VOLUME 33B, AUGUST 2002—601
Table III. Optimized Interaction Energy Parameters,
␣i j (J), between Cations in CaO-SiO2-CrO-CrO1.5 Slags
i\j
Ca2+
Si4+
Cr2+
Cr3+
Ca2+
Si4+
Cr2+
Cr3+
—
⫺139,100
⫺6,140
44,235
⫺139,100
—
⫺60,540
⫺ 48,975
⫺6,140
⫺60,540
—
32,710
44,235
⫺48,975
32,710
—
Table IV. Conversion Gibbs Energy of CrO, CrO1.5, and
SiO2 in Slags from the Hypothetical Pure Liquid with
the Regular Solution Nature to the Traditional Pure Solid
or Liquid Standard State
Reactions
Gibbs Energy Change
CrO(liq) ⫽ CrO(RS)
CrO1.5(s) ⫽ CrO1.5(RS)
CrO1.5(liq) ⫽ CrO1.5(RS)
CrO1.5(s) ⫽ CrO1.5(liq)
SiO2(s) ⫽ SiO2(RS)
⌬G⬚ ⫽ 77,150-33.5T (J)
⌬G⬚ ⫽ 74,967-37.5T (J)
⌬G⬚ ⫽ 10,152-12.6T (J)
⌬G⬚ ⫽ 64,815-24.9T (J)
⌬G⬚ ⫽ 51,346-13.88T (J)
Fig. 12—Comparison between calculated and measured activities of CrO
in CaO-SiO2-CrO-CrO1.5 slag system in equilibrium with Cr at 1873 K,
standard state ⫺ pure liquid CrO.
Fig. 13—Comparison between calculated and measured activities of CrO1.5
in CaO-SiO2-CrO-CrO1.5 slag system in equilibrium with Cr at 1873 K,
standard state ⫺ pure solid CrO1.5.
V. CONCLUSIONS
Fig. 11—Measured and calculated activities.
data. The obtained conversion Gibbs energies for CrO,
CrO1.5, and SiO2 are listed in Table IV.
D. Comparison between Calculated and Measured
Activities of Chromium Oxides in the Slags
The comparison between calculated activities and those
experimentally measured in the chromium-containing slag
systems is shown in Figures 11 through 13. According to
these comparison results, considering the existence of a
certain degree of scatter in the experimental data, the
results give an acceptable agreement. In Figures 12 and
13, the dashed lines are the isothermal liquidus section of
the slag system in contact with metallic chromium at 1873
K. In general, the results show that the mathematical formalism based on the regular solution model can describe
the CaO-SiO2-CrOx slag system reasonably well in the
liquidus area under the present experimental conditions.
602—VOLUME 33B, AUGUST 2002
The activities of CrO and CrO1.5 in the CaO-SiO2-CrOx
slag system were measured by means of solid electrolyteoxygen probes at 1873 K in equilibrium with metallic chromium. The oxidation state of chromium was analyzed in the
slags. It can be concluded that at low oxygen-partial pressures divalent and trivalent chromium are the major existing
forms. Low slag basicity favors the presence of divalent
chromium in the slags. The activities of both CrO and CrO1.5
have positive deviation from the ideal, when pure liquid
CrO and pure solid CrO1.5 are taken as the standard states,
respectively. The activity values increase with increasing
CrOx content and slag basicity.
The validity of the regular slag model in chromium-oxidecontaining slags has been investigated by applying the present experimental results. It was shown that the activities in
the slag system under the present experimental conditions
could be approximately described by mathematical quadratic
formalism based on the regular slag model.
ACKNOWLEDGMENTS
The authors thank AvestaPolarit Stainless Oy (Tornio,
Finland) and the analytical group in Raw Materials Technology, Delft University of Technology, The Netherlands, for
the analysis of the slag samples.
METALLURGICAL AND MATERIALS TRANSACTIONS B
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