Thermodynamic Studies of the Fe-Pt
System and “FeO”-Containing
Slags for Application
Towards Ladle Refining
Patrik Fredriksson
Doctoral Dissertation
Stockholm 2003
Royal Institute of Technology
Department of Material Science and Engineering
Division of Metallurgy
Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i
Stockholm, framlägges för offentlig granskning för avläggande av Teknologie
doktorsexamen, fredagen den 7 November 2003, kl. 10.00 i Kollegiesalen,
Administrationsbyggnaden, Kungliga Tekniska Högskolan, Valhallavägen 79
Stockholm
ISRN KTH/MSE--03/36--SE+THMETU/AVH
ISBN 91-7283-592-3
To Anna
ii
Abstract
In the present work, the thermodynamic activites of iron oxide, denoted as “FeO” in
the slag systems Al2O3-“FeO”, CaO-“FeO”, “FeO”-SiO2, Al2O3-“FeO”-SiO2, CaO“FeO”-SiO2 and “FeO”-MgO-SiO2 were investigated by employing the gas
equilibration technique at steelmaking temperatures. The strategy was to expose the
molten slag mixtures kept in platinum crucibles for an oxygen potential, determined
by a CO/CO2-ratio. A part of the iron reduced from the “FeO” in the slag phase was
dissolved into the Pt crucible.
In order to obtain the activites of “FeO”, chemical analysis of the quenched slag
samples together with thermodynamic information of the binary metallic system Fe-Pt
is required. Careful experimental work was carried out by employing a solid-state
galvanic cell technique as well as calorimetric measurements in the temperature
ranges of 1073-1273 K and 300-1988 K respectively. The outcome of these
experiments was incorporated along with previous studies into a CALPHAD-type of
thermodynamic assessment performed with the Thermo-Calc™ software. The
proposed equilibrium diagram enabled extrapolation to higher temperatures.
The experimentally obtained activites of “FeO” in the present work, along with earlier
investigations were assessed with the KTH slag model, THERMOSLAG©. New
binary parameters were evolved and incorporated in THERMOSLAG©. The present
model calculations are compared with other commercially available software such as
F*A*C*T™ and Thermo-Calc™. The validity of the modified model was investigated
by measurements carried out in case of Al2O3-“FeO”-SiO2, CaO-“FeO”-SiO2 and
“FeO”-MgO-SiO2 ternary slags. The potential of the model to compute the activities
in the case of multicomponent slags was demonstrated.
A correlation between the activity of a metallic oxide in a ternary slag system and the
sulphide capacity of the slag was investigated by using the solubility of sulphur in the
binary systems CaO-SiO2 and Al2O3-CaO along with the sulphide capacity of the
Al2O3-CaO-SiO2 system. The estimated values of the activities were found to be in
good agreement with the measured values. This correlation also gives the possibility
to elucidate the applicability of Henry’s law to the activity of a metallic sulphide and
to determine the order in the affinity of a cation to sulphur between two metallic
oxides in a slag.
Model calculations were performed with THERMOSLAG©, by using plant data from
the ladle refining process at OVAKO Steel, Hofors, Sweden. It was found that oxygen
estimations in the metal from the “FeO” analyses of slags, obtained by conventional
sampling and analysis method were less reliable. Reliable estimation of the oxygen
levels utilising the sulphur partition between the slag and the metal were carried out
using THERMOSLAG® software.
Keywords: Thermodynamics, Activity, Galvanic cell, Calorimetry, Gas equilibration
technique, Iron-platinum alloys, FeO, Slags, Modelling, Ladle
iii
Acknowledgments
There is one man that urged me on by way of his untiring support and seemingly
unlimited belief in me, to that man, all else pales. This man, to whom I would like to
express my sincere gratitude and appreciation, is Professor Seshadri Seetharaman.
The author is grateful to Professor Du Sichen and Dr. Ragnhild E. Aune for valuable
suggestions and fruitful discussions.
Professor Bo Sundman, and Tech. Lic. Rosa Jerlerud, Division of Computational
Thermodynamics, the Royal Institute of Technology, Stockholm, Sweden, and Dr.
Alexandra Kusoffsky, the Swedish Institute of Metal Research, Stockholm, Sweden
are gratefully acknowledged for their support and guidance into the world of
modelling. Appreciation also goes to the CALPHAD:ians for giving an
experimentalist access to your hemisphere.
Dr. Johan Björkvall, MEFOS, Luleå, Sweden is gratefully acknowledged for
interesting discussions, valuable comments and his helpfulness in high temperature
thermochemistry issues, and other not so life-dependent matters.
The author also wants to thank all of the colleagues at the division of Metallurgy for
the support and encouragement during the years.
A special thanks to my dear friends and colleagues, Dr. Anders Tilliander, Dr. Robert
Eriksson and, Tech. Lic. Kristina Beskow respectively, for your friendship and
listening abilities during these years in our grotto.
Financial support for this work from The Swedish Board for Industrial and Technical
Development (former NUTEK) and The Gerhard von Hofstens Foundation for
Metallurgy and Research (Stiftelse för Metallurgi och Forskning) is gratefully
acknowledged.
Travelling grants from the Swedish Steel Producers´ Association and the Foundation
for Applied Thermodynamics are gratefully acknowledged.
The author would also like to express his appreciation to Mr. Peter Kling, the
department technician, for his superb service, clever solutions and king-size green
products.
Stockholm, October 2003
Patrik Fredriksson
iv
Supplements
The present thesis is based on the following papers:
1. On the Standard Gibbs Energy of Formation of CoO, P. Fredriksson and S.
Seetharaman, ISRN KTH/MSE--03/31--SE+THMETU/ART, Accepted for
publication in Scand. J. Metall.
2. Thermodynamic Studies of some Fe-Pt Alloys by the Solid Electrolyte Galvanic
Cell Method, P. Fredriksson and S. Seetharaman, Scand. J. Metall., 30, 4, pp.
258-264, 2001.
3. Differential Thermal Analysis (DTA) of the Iron-Platinum System, P.
Fredriksson, ISRN KTH/MSE--03/32--SE+THMETU/ART, Accepted for
publication in Scand. J. Metall.
4. A Thermodynamic Assessment of the Fe-Pt System, P. Fredriksson and B.
Sundman, CALPHAD, 25, 4, pp. 535-548, 2001.
5. Thermodynamic Activities of “FeO” in some Binary ”FeO”-Containing Slags, P.
Fredriksson and S. Seetharaman, ISRN KTH/MSE--03/33--SE+THMETU/ART,
Submitted to Steel Research International, September 2003.
6. Thermodynamic Activities of “FeO” in some Ternary “FeO”-Containing Slags, P.
Fredriksson and S. Seetharaman, ISRN KTH/MSE--03/34--SE+THMETU/ART,
Submitted to Steel Research International, October 2003.
7. Evaluation of Thermodynamic Activity of a Metallic Oxide in a Ternary Slag
from the Sulphide Capacity of the Slag, M. Hayashi, N. Sano and P. Fredriksson,
ISRN KTH/MSE--03/35--SE+THMETU/ART, Submitted to ISIJ International,
October 2003.
8. Thermodynamic Studies of “FeO”-Containing Slags and their Impact on the Ladle
Refining Process, P. Fredriksson and S. Seetharaman, ISRN KTH/MSE--03/37-SE+THMETU/ART, Accepted for presentation at the 7:th International
Conference on Molten Slags, Fluxes and Salts, Cape Town, South Africa, 25-28
January 2004.
Parts of this work were presented in the following conferences:
1. Activity Measurements in Slag Systems by Gas Equilibration Technique, P.
Fredriksson, M. M. Nzotta, R. E. Aune and S. Seetharaman, CALPHAD XXVIII,
Grenoble, France, May 2-7, 1999.
2. Reactions Between Steel and Slag in the Ladle Process, P. Fredriksson,
SCANMET, 1:st International Conference on Process Development in Iron and
Steelmaking, Luleå, Sweden, June 7-8, 1999.
v
3. Thermodynamic Investigation of the Fe-Pt System Coupled with some Gas
Equilibration Measurements, P. Fredriksson and B. Sundman, Thermodynamics
of Alloys, Stockholm, Sweden, May 8-11, 2000.
4. Activity Measurements in Slag Systems by Gas Equilibration Technique, P.
Fredriksson and S. Seetharaman, 6:th International Conference on Molten Slags,
Fluxes and Salts, Stockholm, Sweden-Helsinki, Finland, June 12-17, 2000.
5. A Thermodynamic Study of the Fe-Pt System, P. Fredriksson and B. Sundman,
CALPHAD XXX, York, England, May 27-June 1, 2001.
6. Impact of Experimentation in Thermodynamic Studies of some Metallic and
Oxidic Systems, R. E. Aune, P. Fredriksson and S. Seetharaman, Grafomed, Bor,
IOC 2002: 34th International October Conference on Mining and Metallurgy
Proceedings (Yugoslavia), pp. 570-575, 2002.
7. Experimentation and Modeling of FeO-Containing Slag Systems, P. Fredriksson
and S. Seetharaman, Minerals, Metals and Materials Society (TMS), Proceedings
of the EPD Congress 2003 held at the 2003 TMS Annual Meeting, March 2–6,
San Diego (USA), pp. 83-97, 2003.
Other contributions:
1. Solute Interactions with Dissolved Oxygen in Molten Copper Systems, R. E.
Aune, P. Fredriksson and S. Seetharaman, Minerals, Metals and Materials
Society (TMS), Yazawa International Symposium on Metallurgical and Materials
Processing: Principles and Technologies; Vol. 1, Materials Processing
Fundamentals and New Technologies (USA), pp. 119-130, 2003.
2. The Mysteries of Slags- Structure, Properties and Applications, M. Hayashi, R. E.
Aune, P. Fredriksson and S. Seetharaman, Iron and Steel Society/AIME,
ISSTech 2003 Conference Proceedings, Indianapolis, Indiana, (USA), pp. 309320, 2003.
3. Slags-Structure, Properties and Applications, M. Hayashi, R. E. Aune, P.
Fredriksson, D. Sichen and S. Seetharaman, the International Symposium on
Ionic Liquids in Honour of Professor Marcelle Gaune-Escard, Carry le Rouet,
France, June 26-28, 2003.
A part of this dissertation was presented as a licentiate thesis in 2000.
Thermodynamic Studies of Some Iron Oxide-Containing Slag Systems, ISBN 917170-588-0.
vi
Contributions by the author
Supplement 1.
Experimental work: 100 %
Literature survey: 100 %
Writing: 85 %
Supplement 2.
Experimental work: 100 %
Literature survey: 100 %
Writing: 55 %
Supplement 3.
Experimental work: 100 %
Literature survey: 100 %
Writing: 100 %
Supplement 4.
Experimental work: 100 %
Literature survey: 100 %
Modelling: 65 %
Writing: 90 %
Supplement 5.
Experimental work: 100 %
Literature survey: 100 %
Modelling: 100 %
Writing: 75 %
Supplement 6.
Experimental work: 100 %
Literature survey: 100 %
Modelling: 100 %
Writing: 85 %
Supplement 7.
Literature survey: 20 %
Writing: 40 %
Supplement 8.
Literature survey: 100 %
Modelling: 100 %
Writing: 70 %
vii
Contents
1. Introduction
1
2. Thermodynamics of liquid slags
2
3. Experimental work
3
3.1. The gas cleaning system
3
3.2. Galvanic cell measurements
3.2.1. Preparation of materials
3.2.2. Apparatus
3.2.3. Procedure
4
4
6
7
3.3. Calorimetric measurements
3.3.1. Preparation of materials
3.3.2. Apparatus and procedure
3.3.2.1. The NETZSCH calorimeter
3.3.2.2. The Setaram calorimeter
7
7
8
8
9
3.4. Gas equilibration measurements
3.4.1. Principle
3.4.2. Preparation of materials
3.4.3. Apparatus
3.4.4. Procedure
10
10
10
11
11
4. Thermodynamic modelling
13
4.1. Modelling of the Fe-Pt system
4.1.1 The pure elements
4.1.2. The liquid phase and the bcc phase
4.1.3. The fcc phases
13
14
14
14
4.2. Modelling of “FeO”-containing slag systems
17
5. Review of supplements
19
5.1. Supplement 1: On the Standard Gibbs Energy of Formation
of CoO
19
5.2. Supplement 2: Thermodynamic Studies of some Fe-Pt Alloys
by the Solid Electrolyte Galvanic Cell Method
20
5.3. Supplement 3: Differential Thermal Analysis (DTA) of the IronPlatinum System
21
5.4. Supplement 4: A Thermodynamic Assessment of the
Fe-Pt System
21
viii
5.5. Supplement 5: Thermodynamic Activities of “FeO” in some
Binary “FeO”-Containing Slags
22
5.6. Supplement 6: Thermodynamic Activities of “FeO” in some
Ternary “FeO”-Containing Slags
25
5.7. Supplement 7: Evaluation of Thermodynamic Activity of a
Metallic Oxide in a Ternary Slag from the
Sulphide Capacity of the Slag
27
5.8. Supplement 8: Thermodynamic Studies of “FeO”-Containing
Slags and their Impact on Ladle Refining
Process
28
6. General discussion
29
7. Summary and conclusions
30
8. Future work
32
Bibliography
ix
1. Introduction
1. Introduction
In order to meet the customer requirements for clean steels, the steel industry is forced
to keep the dissolved elements in the steel bath within specified intervals. Furthermore,
dissolved impurities as well as non-metallic inclusions have to be controlled to satisfy
the demands of the material. This is especially emphasised in the secondary
metallurgy process, where the reactions between the steel and slag play a significant
role on the resulting product. In steelmaking, final adjustments of the composition and
temperature take place in the ladle process before the molten metal is cast. In order to
optimise the ladle refining reactions, it is necessary to have a complete understanding
of the thermodynamics involved in slag-metal reactions. The present investigation is
part of an overall attempt to generate thermodynamic data with respect to ladle slags.
A thermodynamic slag model was developed at the Division of Metallurgy, which has
the feature to not only estimate the thermodynamic activities of slag systems, but also
sulphide capacities and viscosities of higher order systems based on the experimental
data for lower order systems as functions of composition and temperature. However,
the predictive capacity of this model is only as good as the input data for lower order
systems. In this connection, it was found that in the case of the systems Al2O3-“FeO”,
CaO-“FeO”, “FeO”-SiO2, further experimentation on the thermodynamic activities of
iron oxide was required at steelmaking temperatures. The present investigation was
started with a view to experimentally measure the thermodynamic activities of “FeO”
in these slag systems in the temperature range of 1823-1873 K and then on the basis
of these data, to modify the model parameters. In the case of the ternary systems,
Al2O3-“FeO”-SiO2, CaO-“FeO”-SiO2 and “FeO”-MgO-SiO2, it was considered
necessary to confirm the model predictions by experimental data for the slag
compositions at steelmaking temperatures. The measurements were performed by
equilibrating the slag kept in a platinum crucible with a CO/CO2 gas mixture. In order
to calculate the activities of iron oxide in the slag, the experimental data were coupled
with thermodynamic information of the Fe-Pt system. The present work was therefore
planned according to the scheme as illustrated in Figure 1.
Thermodynamics of
multicomponent systems
Plant studies
Sulphide capacity to activities
Thermodynamics of ternary
systems
Thermodynamics of binary
systems
Assessment
Gas equlibration experiments
Figure 1. Structure of present study.
-1-
Fe-Pt experimental study
Assessment
2. Thermodynamics of liquid slags
2. Thermodynamics of liquid slags
Slags are silicate melts which are ionic in nature have been extensively used in the
extraction and refining of metals. Due to the polymerisation of the silicate anions, the
structures of these melts are extremely complicated. When the content of the basic
oxides increases, these polymers are broken into smaller units. Amphoteric oxides like
Al2O3 enter into the silicate network contributing to the chain structure. As the
structure of slags has a serious impact on the thermophysical and thermodynamic
properties of these melts, the importance of an understanding of the properties and
structure of slags has received a great deal of attention during recent decades.
On the basis of mixing cations and anions in their respective subgroupings along with
the ionic nature of slags, Temkin [1] could explain the thermochemical properties of
salts and slags from a fundamental point of view. This was improved by Flood,
Førland and Grjotheim [2], who introduced equivalent ion fractions. The theory of
ideal mixing was suggested by Richardson [3, 4], where the silicates were considered
as a matrix of oxygen ions in which the cations are distributed in the “interstitials”.
This theory suggests that the Si4+ cation has the strongest attraction to O2- ions,
binding them up in a SiO44- tetrahedron and the other basic cations are likely to mix
randomly in the cationic subgrouping.
In order to describe the behaviour of silicate systems, several thermodynamic slag
models [5-13] based on different approaches have been developed over the years with
variable degrees of success. The different models can be classified into two major
groups: viz. structure-based models [5-7] and empirical or semi-empirical models [1,
8-13]. From the work of Toop and Samis [5] where free energies of mixing of binary
silicates were approximated, and the polymer theory, developed by Masson [6], the
development of structure-based models has made considerable progress in, for
example, the molecular dynamics simulation area.
Examples of experiment-based models are: the Quasi-chemical approach by Pelton
and Blander [9], the IRSID model by Gaye and Welfringer [10], developed from the
work of Kapoor and Frohberg [11], the ionic model by Hillert et al. [12] as well as the
regular solution model used by Ban-Ya and Shim [13] and Lumsden [8]. In an
investigation on the silica saturated liquidus in the “FeO”-SiO2 system, Lumsden [8]
described the silicate network being completely dissociated into Si4+ and O2- ions.
In order to study the thermodynamic and thermophysical properties of various slag
systems, the Division of Metallurgy has been developing a slag model that enables the
extrapolation of the properties of multicomponent slag systems as functions of
composition and temperature [14-18]. This model, referred to as the KTH model, is
based on Temkin´s description [1] of the entropy of ionic melts coupled with
Lumsden´s description [8] of silica melts. By using experimental information in lower
order systems, the model enables the estimation of the thermodynamic activities of
higher order systems.
The predictive capacity of the different types of models is only as good as the
structural information and experimental data available. Due to lack of experimental
information on silicate systems, empirical or semi-empirical models have often been
used when predicting thermodynamic properties.
-2-
3. Experimental work
3. Experimental work
3.1. The gas cleaning system
In order to lower the impurity levels in the various gases they were subjected to a
number of purification steps. The gas cleaning system used in the gas equilibrium
investigation is schematically presented in Figure 2. The cleaning train of Ar, without
the magnetic flow meter and the mixing device, is applicable to the calorimetric and
galvanic cell investigations. The moisture impurity in the argon gas was removed by
passing the gas successively through silica gel as well as Mg(ClO4)2. To remove
traces of CO2 in the gas, a column of ascarite was introduced in the system. The gas
was passed through columns of copper and magnesium turnings kept at 773 K in
order to bring down the oxygen impurity level. The final oxygen level in argon
cleaned in this way was found to be less than 10-18 atm.
Ar
S
Cu
A
M
CO
S
Cu
A
M
CO2
S
M
Exhaust
Mg
F
F
Mix
F
O2-probe
Furnace
Figure 2. The gas cleaning system: S = Silica Gel, Cu = Copper turnings at 773
K, A = Ascarite, M = Magnesium perchlorate, Mg = Magnesium turnings at
773 K, F = Magnetic flow meters, Mix = Gas mixing chamber.
The CO gas was purified in a similar way except for the last step involving Mg. The
oxygen impurity in the gas was allowed to react with CO over heated copper turnings
and the resulting CO2 was absorbed by ascarite. The moisture level in the CO2 gas
was brought down by passing the gas through silica gel as well as Mg(ClO4)2.
The flow rates of the different gases were controlled by a Bronkhorst High-Tech B.V.
Serie E-7000 system. After the purification step, the gases were mixed in a gas
chamber at room temperature and introduced into the alumina reaction tube. The
partial pressures of the different components in the gas mixture at the experimental
temperatures were calculated by using the Thermo-Calc™ software. The total flow rate
of the gases during the experiments was 0.2 dm3/min. The oxygen partial pressure of
the outgoing gas mixture was continuously monitored by a ZrO2-CaO galvanic cell
-3-
3. Experimental work
kept at 973 K. The data from the oxygen probe was found to be in agreement with the
calculated data.
3.2. Galvanic cell measurements
The galvanic cell used in the present work is represented as:
(-) Pt, Fe(s), “FeO”(s) // ZrO2 (11 mol pct CaO) // “FeO”(s), Fe-Pt alloys, Pt(+)
(I)
The difference in chemical potential between the two electrodes in cell (I) is directly
related to the activity of Fe in the Fe-Pt alloy by the Nernst relationship
 RT 
E (V ) = − 
 ln a Fe ( Pt )
 2F 
(1)
For the Nernst equation to be applicable to cell (I), the electrolyte should be a total
ionic conductor at the experimental temperature and in the oxygen partial pressure
ranges. The establishment of proper functioning of the galvanic cell (I) and the
experimental arrangement were investigated by replacing the working electrode, i.e.,
the “FeO” and Fe-Pt alloy with a Co-CoO mixture:
(-) Pt, Fe(s), “FeO”(s) // ZrO2 (partially stabilised // CoO(s), Co, Pt(+)
with CaO or Y2O3)
(II)
3.2.1. Preparation of materials
The materials used in the present work along with their purity and their suppliers are
presented in Table I. “FeO” was prepared by mixing the required amounts of
electrolytic iron powder and Fe2O3 (dried previously at approximately 400 K in air) so
that the final composition corresponded to that of “FeO” in equilibrium with iron at
1273 K. The mixture was sintered in a sealed iron crucible kept in an argon
atmosphere at 1273 K over a period of 12 hours, after which the crucible was
quenched. The “FeO” thus produced was examined by X-ray diffraction and the
absence of both metallic iron and magnetite was confirmed. From the diffraction
pattern, the lattice parameter of the “FeO” produced was computed to be 4.30 Å,
which is in agreement with the literature value of 4.3088 Å [19].
The CoO used for the calibration experiment was prepared by the decomposition of
Co(NO3)2·6H2O, placed in a platinum dish, in a stream of nitrogen at 1073 K for six
hours. The purity of the CoO produced was confirmed by X-ray diffraction analysis.
The alloys of Fe and Pt were prepared by careful mixing of the required proportions
of the powders of the pure metals and sintered in situ in the galvanic cell for over 12
hours at 1473 K. Some alloys were also prepared by premelting in an induction
furnace in highly purified Ar atmosphere. The stability of the cell EMF values
ensured the completion of the alloy formation. Further, the alloys were examined by
X-ray diffraction after the experiments, and the diffraction patterns corresponded to
the alloys.
-4-
3. Experimental work
Table I. Materials used in the present work.
Material
Purity
Air
plus-grade
α-alumina, single crystal
99.99%
Alumina cement
Alumina crucible
99.7%
Alumina crucibles and caps
99.5%
Alumina lining,
99.7%
Aluminium Oxide
anhydrous
Alumina tubes
99.7%
Ascarite II
Argon
plus-grade
Argon-2% Hydrogen
plus-grade
Calcia stabilised zirconia
Calcium Oxide
Carbon Monoxide
plus-grade
Carbon Dioxide
plus-grade
Carbonyl iron powder
pro analysi
Cobalt powder
99.8 %
Cobalt(II) nitrate hexahydrate
98 %
Copper, turnings
99 %
Gold
99.999%
Helium
plus-grade
Hematite powder
anhydrous
Hydrogen
plus-grade
Indium
99.999%
Iron crucible
99.9 %
Iron foil
99.5%
Magnesium, turnings
> 99 %
Magnesium Oxide
pro analysi
Magnesium perchlorate (dehydrite) anhydrous
Magnetite
96.7%
Nickel foil
99.4%
Nitrogen
plus-grade
di-Phosphorous penta oxide
extra pure
Platinum crucibles and caps
99.99%
Platinum powder
99.9 %
Platinum wire
99.9 %
Platinum/Rhodium wire
99.99%
Platinum sheet
99.998 %
Silica gel
Silicon Oxide
pro analysi
Silver
99.99%
Tin
99.99%
Titanium foil
99.7 %
Yttria stabilised zirconia
Yttria stabilised zirconia
Zinc
99.999%
-5-
Supplier
AGA, Sweden
NETZSCH, Germany
Haldewanger, Germany
Haldewanger, Germany
Setaram, France
NETZSCH, Germany
E. Merck, Germany
Haldenwanger, Germany
Thomas Scientific, USA
AGA Gas, Sweden
AGA Gas, Sweden
Yamari Industries, Japan
Fischer Scientific, USA
AGA Gas, Sweden
AGA Gas, Sweden
E. Merck, Germany
Johnson Matthey Inc., UK
Aldrich, USA
Johnson Matthey Inc., UK
NETZSCH, Germany
AGA Gas, Sweden
Fisher Scientific, USA
AGA Gas, Sweden
NETZSCH, Germany
Armco Iron, USA
Goodfellow, UK
E. Merck, Germany
E. Merck, Germany
GFS Chemicals, USA
LKAB, Sweden
INCO Alloys, Canada
AGA Gas, Sweden
E. Merck, Germany
NETZSCH, Germany
Chempur, Germany
Johnson Matthey Inc., UK
Johnson Matthey Inc., UK
Johnson Matthey Inc., UK
E. Merck, Germany
E. Merck, Germany
NETZSCH, Germany
NETZSCH, Germany
Aldrich, USA
Friatech, Germany
K-Style Adv. Cer., China
NETZSCH, Germany
3. Experimental work
3.2.2. Apparatus
The cell assembly used in the present work is shown in Figure 3. The working
electrode was packed inside the solid electrolyte tube with a Pt wire embedded in the
same. The reference electrode was packed in an alumina crucible with the electrolyte
tube in the middle and a lead of Pt in contact with the electrode.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Figure 3. The experimental assembly: (1) Gas inlet, (2) Silica stopper, (3) Cooling
coils, (4) Refractory, (5) Alumina reaction tube, (6) Pt wire, (7) Alumina cement,
(8) Heating coil, (9) Thermocouple, (10) Alumina crucible, (11) Solid electrolyte,
(12) Working electrode, (13) Reference electrode, (14) Iron foil, (15)
Thermocouple, (16) Nickel foil, (17) Gas outlet.
The cell assembly was positioned in the constant temperature zone (±1 K) of a
vertical tube furnace with KANTHAL A1 heating elements, which was controlled by
a Eurotherm 902 programmable temperature regulator with a thermocouple of Type S
-6-
3. Experimental work
(Pt-10pctRh/Pt) as the sensor. A separate thermocouple in contact with the cell
arrangement at the bottom enabled accurate measurements of the cell temperature.
The thermocouple wires were calibrated against the melting points of pure gold and
palladium prior to use.
3.2.3. Procedure
Before the furnace was started, the reaction tube with the cell assembly was evacuated
and filled repeatedly with argon. When the oxygen partial pressure of the outgoing
gas stream was less than 10-13 atm, the furnace temperature was raised to 1473 K in
one step. The cell was maintained at this temperature for a minimum of 6 hours until
the cell EMF value was steady for at least 1 hour within ± 0.5 mV. The EMF values
were monitored by a KEITHLY 199 System DMM/Scanner with an input impedance
of 1 GΩ. All the EMF and temperature data were recorded by EASY VIEW PC
software. The cell was taken through temperature cycles and the values were found to
be reversible within ± 0.4 mV. The reversibility of the cell was confirmed by
polarising the cell repeatedly and confirming that the EMF returned to the original
value. At the end of the experiment, the contents of the working electrode were
subjected to chemical analysis and X-ray diffraction. Iron was analysed by redox
titration while Pt was analysed by atomic absorption spectroscopy. The EMF
measurements with one high Pt alloy were carried out using Fe3O4 as the equilibrating
oxide.
3.3. Calorimetric measurements
3.3.1. Preparation of materials
The alloys were synthesized by carefully mixing iron and dried platinum in an agate
mortar. The powder mixture was then pressed (500 MPa) into a tablet and placed in
an alumina boat made indigenously from alumina. The boat was wrapped in a
titanium foil which acted as an internal oxygen getter during sintering of the powder
mixture. The alumina boat was placed in the even-temperature zone of an Elsund
horizontal furnace and the mixture of the metal powders was sintered for 14 days in
an Ar-2% H2 atmosphere at 1273 K. In order to release any dissolved hydrogen, the
temperature was maintained at 773 K for 24 hours in the final stage of the heat
treatment and then brought to room temperature. In an alternative procedure, 3 alloys
were prepared by induction melting in a highly purified Ar atmosphere. Dissolution of
Al into the alloys was previously found to be negligible [20], which also was
confirmed in the present work. No oxidation of the samples was observed. X-ray
diffraction and Electron Microprobe Analysis were used for phase identification and
composition determination for the different alloys respectively.
-7-
3. Experimental work
3.3.2. Apparatus and procedure
3.3.2.1 The NETZSCH calorimeter
An illustration of the NETZSCH STA 449C Jupiter© unit used in the present work is
presented in Figure 4. The apparatus was calibrated against In, Sn, Zn, Ag and Au.
Fusion temperatures and heats of fusion were in agreement with literature [21] and the
recommended values from NETZSCH Instruments [22]. The experiment was initiated
by placing a polished piece of the metal alloy into a platinum crucible provided with
an Al2O3 lining. The crucible was sealed with a Pt-lid and positioned, along with a
reference crucible with similar size specifications, on the platinum sample holder
provided with a previously calibrated type S (Pt-10%Rh/Pt) thermocouple. Both
crucibles were weighed before and after each experiment and placed in exactly the
same position throughout the measurement series.
Sample and
reference crucible
Sample carrier
Figure 4. The NETZSCH STA 449C Jupiter© apparatus with the sample carrier.
Before each experiment was started, the furnace chamber was repeatedly evacuated
and flushed with Ar and finally with the measurement gas, H2 or He. The outgoing
gas composition was continuously monitored by a Balzer “Thermo Star” Quadrupole
Gas Mass Spectrometer (Model QMS 200). The experiment was started whenever the
fraction of H2 or He was greater than ~99.6 %.
The measurements were conducted in the temperature range of 300-1673 K with a
rate of 10 K/min in two heating and cooling cycles respectively. An initiating
stabilising level at 313 K was used before the commencement of the temperature
program. All experimental data were recorded by NETZSCH thermal measurement
-8-
3. Experimental work
software and Balzer Quadstar 422 measurement program with a time-step of 1.5 sec.
and 6.0 sec. respectively. For a standard reference, α-alumina was employed.
Enthalpies of transformation and transition temperatures were calculated with the
NETZSCH Proteus® thermal analysis software [22] and by numerical integration with
the Origin graphical software respectively.
3.3.2.2. The Setaram calorimeter
The differential thermal analysis investigation was performed from room temperature
to 1988 K by employing a Setaram high temperature calorimeter, HTC 1800 K- DSC
2000 K. Figure 5 shows this apparatus along with the sample holder. The apparatus
was calibrated with Au and the melting point, 1337.3 K, was in agreement with
literature [21].
Sample carrier
Sample and
reference crucible
Figure 5. The Setaram high temperature calorimeter.
The experiment was initiated by mounting the alloy in the Al2O3 sample crucible
along with an empty reference crucible on the sample holder. The holder was
equipped with a type B (Pt-30 pct Rh/Pt-6 pct Rh) thermocouple which was calibrated
prior to use. The crucibles were closed with Al2O3-caps. After lowering the sample
holder into the alumina reaction chamber, evacuation and flushing of highly purified
Ar was performed. The oxygen partial pressure of the outgoing gas was continuously
monitored by a solid-state oxygen probe kept at 973 K. When a satisfactory partial
-9-
3. Experimental work
pressure of oxygen was established in the sample chamber, i.e., less than 10-15 atm,
the furnace was heated up using the predetermined temperature program, operated by
a Setaram G 11 controller. All data were recorded on an IBM personal computer and
exported to the Origin graphical software for evaluation. To enhance the accuracy of
the measurements, key operational parameters such as sample size and weight,
crucible and cap weights, and gas flow were kept as constant as possible throughout
the measurement series. Selected experiments were repeated to confirm the
reproducibility of the results.
3.4. Gas equilibration measurements
3.4.1. Principle
The principle employed is based upon the equilibria between the molten slag in a
platinum crucible and the partial pressure of oxygen well-defined by an Ar-CO-CO2
gas mixture. After the required equilibration time at different temperatures, the
crucibles with the slags of different composition were quenched. During the
equilibration, iron from a part of the “FeO”-component in the slag had dissolved in
the Pt crucible. The reaction at equilibrium can be represented as
1
Fe (Pt ) + O2 ( g ) = " FeO " (slag )
2
(2)
Assuming that the dissolution of Fe in Pt had reached equilibrium under the
experimental duration, the activity of “FeO” in the slag can be calculated with
knowledge of the thermodynamic data for the binary alloy system Fe-Pt as follows:
a FeO = a Fe ( Pt ) ⋅ pO1 /22 ⋅ C 2
(3)
where aFe(Pt) is the activity of iron in platinum, pO2 is the partial pressure of oxygen
and, C2 is the equilibrium constant for Eq. (2). In these calculations, the value of the
standard Gibbs energy for reaction (2) was taken from JANAF [23] where the
reference state for iron is pure solid Fe at 298 K and 1 atm.
3.4.2. Preparation of materials
The oxides of aluminium, calcium, magnesium and silicon were heated to 1273 K for
12 hours and transferred at 373 K to a desiccator with P2O5 desiccant. Wüstite was
synthesized according to the method described in section 3.2.1. The different oxides
were carefully mixed in an agate mortar, placed in glass containers and stored in a
desiccator. Platinum crucibles were made from platinum sheets with a thickness of
0.12 mm. Great care was taken in shaping the crucibles in order to avoid creeping of
the samples along the walls. Precautions were also taken to avoid contamination
between the different slag samples due to the foaming of the slag by placing a Ptspiral inside each crucible.
- 10 -
3. Experimental work
3.4.3. Apparatus
The experimental set-up used in this study is illustrated in Figure 6. An alumina tube
(60 mm o.d. and 50 mm i.d.) placed in a horizontal resistance furnace served as the
reaction tube. The furnace was equipped with KANTHAL SUPER 1800 molybdenum
disilicide heating elements and had a maximum working temperature of 1973 K. An
alumina crucible holder with provision for four platinum crucibles was designed and
cast from pure alumina cement so that it could fit in the constant temperature zone of
40 mm in the reaction tube. The zone was enhanced by alumina radiation shields. The
sample temperature in the furnace was monitored by a Type B (Pt-30pctRh/Pt-6pctRh)
thermocouple which was calibrated prior to experiments. In order to protect the
reaction tube from cracking during the quenching of the samples, alumina runners
were provided inside the reaction tube. The reaction tube was closed with silica
stoppers and cooled at the ends by water-cooling. The gas-mixture was led into the
reaction zone by an alumina tube of 5 mm i.d. and the gas was delivered in the hot
zone of the furnace just above the samples. This arrangement enabled the
minimisation of concentration gradients in the gas mixture due to thermal diffusion.
The temperature in the furnace was controlled by a programmable Eurotherm 2408 P4
regulator with a Pt-30 pct Rh/Pt-6 pct Rh thermocouple as the sensor with an accuracy
of ± 3 K.
1
2
3
4 5
6
7
8
Figure 6. The furnace assembly: 1. Gas inlet, 2. Silicon rubber stopper, 3.
Alumina reaction tube, 4. Gas inlet, 5. Thermocouple, 6. Alumina crucible
holder, 7. Platinum crucible, 8. Gas outlet.
3.4.4. Procedure
The experiments were started by heating the furnace to the required temperature under
constant argon flow. When the experimental temperature was reached, the sample
holder with the slag samples packed in the platinum crucibles was introduced into the
even temperature zone of the furnace. The CO-CO2-Ar gas mixture was then
introduced into the system and the slags were equilibrated with the gas mixture for 8
- 11 -
3. Experimental work
hours. This time interval was found to be sufficient for the attainment of equilibrium
between the gas and the slag phases as found from earlier studies carried out in the
present laboratory. Further, trials with an equilibration time of 15 and 24 hrs indicated
similar results. The experiments were performed in the temperature range of 18231973 K. After the equilibration, the samples were quenched by quickly withdrawing
the sample holder to the cold part of the furnace. The cold samples were taken out and
preserved in desiccators and subsequently were subjected to chemical analysis. Cross
sections of pieces of Pt crucibles from different experiments were examined by SEMEDS analysis. No concentration gradient was found across the thickness of the
crucible thereby confirming that the entire crucible was in equilibrium with the slag
and gas phases. The platinum crucibles were analysed for dissolved iron as well as for
aluminium, calcium, magnesium and silicon in appropriate cases using atomic
absorption spectroscopy. The aluminium, calcium and magnesium contents were less
than 0.1-wt% in all cases and, hence, were not included in the calculations. Maximum
silicon content was found to be 0.12-wt%. Contamination of the crucibles from the
sample holder was checked by a blank run and was found to be negligible. The oxides
were investigated by X-ray fluorescence spectroscopy and some analyses were also
reconfirmed by employing Mössbauer analysis. The contents of the di- and trivalent
iron in the slag samples were determined by redox titration. The overall experimental
uncertainty, when all errors are considered, was +/- 3-5 % of the calculated value of
the activity.
- 12 -
4. Thermodynamic modelling
4. Thermodynamic Modelling
4.1. Modelling of the Fe-Pt system
All calculations in this thermodynamic assessment were performed by using the
Thermo-Calc™ software which has been developed at the Department of Materials
Science and Engineering at the Royal Institute of Technology [24]. This software
contains several modules which are displayed in Figure 7. During the optimisation
work, the “POLY-3 Module” was used to calculate Gibbs energies of the involved
phases at equilibrium. Tabulation and plotting were performed in the “Tabulation
Module” and “POST Processor”. Assessment of experimental information and
evaluation of model parameters was carried out in the “Parrot Module” using least
square fitting.
User
Database Module
Tabulation Module
POLY-3 Module
Post Processor
GES Model Module
Parrot Module
Edit Experiments
User Written Applications
Binary Module
Potential Module
Scheil Module
Pourbaix Module
System Utility Module
User Written Applications
Figure 7. Module structure of Thermo-Calc™ from [25].
In order to describe the thermodynamic properties of a given system from both
thermodynamic as well as phase diagram data, the feature to obtain a consistent set of
parameters, from the assessment of model parameters is enabled by using the
CALPHAD (CALculation of PHAse Diagram) approach. This assessment method
also provides the possibility to obtain information in multicomponent systems by
extrapolating data from lower order systems.
- 13 -
4. Thermodynamic modelling
4.1.1 The pure elements
The pure solid elements in their stable state at 298.15 K were chosen as a reference
state for the system (standard element reference SER). The Gibbs energies as a
function of temperature for stable and metastable states of pure iron and platinum
were taken from the SGTE databank [26].
4.1.2. The liquid phase and the bcc phase
The liquid and the bcc phase were modelled as a substitutional solution
Gm = ∑ xi oGi + RT ∑ xi ln ( xi ) + E Gm
i
(4)
i
where xi is the mole fraction of element i and °Gi is the Gibbs energy of element i in
the liquid phase and the bcc phase relative to its reference state. The second term is
the ideal entropy of mixing and the last term is the excess Gibbs energy, which is:
E
Gm = x Fe x Pt LFePt
(5)
with the composition dependent interaction parameter LFePt . This is in the form of a
Redlich-Kister (RK) series:
LFePt = ∑ ( x Fe − x Pt ) υ LFePt
υ
(6)
υ =0
where the RK coefficients υ LFePt can be temperature dependent.
4.1.3. The fcc phases
The ordered phases, Fe3Pt (L12), FePt (L10), and FePt3 (L12) and the disordered phase,
fcc (A1), were modelled with a Gibbs energy expression in the Compound Energy
Formalism (CEF). It can describe phases using two or more sublattices depending on
the structure of the phase. For a fcc phase that can order as L12 and L10, the Gibbs
energy can be described as
( A, B )0.25 ( A, B )0.25 ( A, B )0.25 ( A, B )0.25
(7)
The four different sublattices describe the four corners of a tetrahedron in a unit cell
and due to symmetry, they must be identical. This is illustrated in Figure 8. This also
implies that all nearest neighbours of an atom are on a different sublattice. The
number of sites is 0.25 for each sublattice and thus 1 mole of atoms is in the model.
When the phase is disordered, all sublattices are equivalent and have the same fraction
of the components. This is known as the A1 structure, which can be described with a
substitutional model (A, B). If three sublattices have the same fractions and one is
different, this is called an L12 structure. If two sublattices have the same fractions but
- 14 -
4. Thermodynamic modelling
are different from the other two which also have the same fractions, it is called an L10
structure. The Gibbs energy equation for this ordered fcc model is divided in two parts:
Gm = Gmdis ( xi ) + ∆Gmord ( yi )
(8)
where the relation between the mole fraction, xi, and the site fractions, yi, is
4
xi = 0.25∑ yi(s )
(9)
∆Gmord = Gm4 sl ( yi ) − Gm4 sl ( xi )
(10)
s =1
The mole fraction xi is calculated from Eq. (9) where yi( s ) represent the site fractions
of constituent i on sublattice s. When the phase is disordered, the site fractions in all
sublattices are equal and hence equal to the mole fraction. This is used in Eq. (10) in
order to make ∆Gmord zero when the phase is disordered. Hence, all parameters that
describe the disordered state are described by a substitutional model, Gmdis ( xi ) like Eqs.
(4)-(6). The expression for the ordered term in a four-sublattice model with an
arbitrary number of components and where all components are present on all
sublattices is
Gm4 sl = ∑∑∑∑ yi(1) y (j2 ) y k( 3) yl( 4 ) oGi: j:k:l + 0.25RT ∑∑ yi( s ) ln yi(i ) + E Gm
i
j
k
l
s
(11)
i
In the “compound energies”, °Gi:j:k:l, the colon is used to separate the constituents on
different sublattices. In the four-sublattice model used in the present work, the size
ratios are equal for all sublattices, as the four sublattices are equivalent. The
parameters for the different “end members” of the phase must be equal, independent
of the distribution of the elements on the sublattices.
o
GFeFeFePt = oGFeFePtFe = ... = GFe3Pt
o
GFeFePtPt = oGFePtFePt = ... = GFePt
o
GFePtPtPt = oGPtFePtPt = ... = GFePt3
(12)
CEF assumes random mixing on each sublattice. In the present work, the excess
Gibbs energy EGm includes the first two interaction terms according to CEF for a
binary system as shown below
E
Gm = ∑ ∑∑∑∑ yi(1r ) yi(2r ) y (js ) y k( t ) yl( u ) Li1 ,i2 : j:k:l + ........ +
i1 i2 >i1
j
k
l
∑ ∑∑ ∑∑∑ yi(1r ) yi(2r ) y (j1s ) y (j2s ) yk(t ) yl(u ) Li1 ,i2: j1 , j2:k:l + .......
i1 i2 >i1 j1 j2 > j1 k
(13)
l
The “,” is used to separate the constituents interacting on the same sublattice. The first
summation is for the interaction in sublattice r and the second is for both sublattice r
and s. As all sublattices are equivalent, these interactions must be permuted cyclically.
- 15 -
4. Thermodynamic modelling
The first summation is for the “regular interaction” parameters, Li1 ,i2 : j :k :l which
represent interactions between constituents i1 and i2 in sublattice r, when the other
sublattices, s, t and u are occupied by constituents j, k and l respectively. These
interactions represent next-nearest neighbour interactions. The second summation is
the “reciprocal parameter”, Li1 ,i2 : j1 , j2 :k:l . These represent interactions in two sublattices, s
and t, simultaneously, when the two other sublattices, u and v, are occupied by k and l
respectively. In sublattice r, the interaction is between constituents i1 and i2 and in
sublattice s between constituents j1 and j2. As all sublattices are equivalent, a number
of symmetry relations can be applied and this will reduce the number of independent
parameters.
This “reciprocal parameter” is necessary to get the correct topology of the ordered fcc
phase diagram as shown by Sundman [27]. This parameter represents the first
approximation to the short range order (sro) in a fcc lattice.
In some cases, one may reduce the number of interaction parameters by ignoring the
constituent on the sublattice without interaction. Thus Eq. (13) can be simplified to
E
Gm = ∑∑ yi(1s ) yi(2s ) Li1 ,i2 :∗:∗:∗ + ∑∑∑∑ yi(1s ) y (j2s ) y (j1t ) y (jt2) Li1 ,i2 : j1 , j2 :∗:∗
i1
i2
i1
i2
j1
(14)
j2
where the sublattice with interaction of the L parameters have been permuted
cyclically.
3
1
2
4
Figure 8. Face-centred cubic structure. The numbers indicate the four
sublattices for ordering.
- 16 -
4. Thermodynamic modelling
4.2. Modelling of “FeO”-containing slag systems
The software used in the present work for determination of activites of iron oxide
THERMOSLAG©, has been developed on the basis of a unified description of the slag
in order to extrapolate the thermophysical and thermochemical properties of slags as
functions of temperature and composition. An over view of the running software,
showing the point calculation mode of activites in the Al2O3-CaO-MgO-SiO2 system
at different temperatures, is shown in Figure 9.
Figure 9. The calculated activities in the Al2O3-CaO-MgO-SiO2 system.
Presently, the software is capable of estimating the thermodynamic activities of slag
components [14-18], sulphide capacities [28-35] and viscosities [36-38]. The
computation module is complemented by a databank containing the experimental data
available in literature used for optimisation along with data sources and model
parameters. A substantial part of the experimental data in the databank was generated
in the laboratory at the Division of Metallurgy. The reliability and reproducibility of
this data, generated under identical conditions has been tested and confirmed.
According to this model, a system containing m different oxides, C1c1Oa1, C2c2Oa2,....
CiciOai,.... CcmOam can be represented as
(C1
v1
, C 2 v 2 ,...Ci vi ,..., Cm vm
) (O )
2−
p
(15)
q
where p and q are stoichiometric numbers, Ci%i stands for cations, and the superscript
%i represents the electrical charge. The presence of basic cations such as Ca2+, Fe2+,
Mg2+ and Mn2+ along with Si4+ will distort the oxygen matrix and determine the
- 17 -
4. Thermodynamic modelling
configuration of the ionic melt as well as the bond energies between different ions.
The configuration of the ions and the bond energies will be functions of composition
and temperature. 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. The present description of silicate melts necessitates
the assumption that the silicate network is completely dissociated into Si4+ and O2ions and even any aluminate complex to Al3+ and O2- ions. Engaging the next-nearest
neighbour interactions entails the use of the cation fractions defined as
N Ci
∑ NCj
yCi =
(16)
j = 1 to m
where Ni is the number of moles of cation Civi and the summation includes all the
cations. The integral molar Gibbs energy of a solution can be expressed as:
Gm = ∑ xCi ci O ai o GCi ci O ai + RTp ∑ yci ln ( yci ) + E G
i
(17)
i
where xCi ci O ai and oGCi ci O ai is the mole fraction and the Gibbs energy formation of
oxide i respectively. R is the universal gas constant, T is the temperature in Kelvin
and p is a stoichiometric number. The second term corresponds to Temkin´s [1] ideal
entropy of mixing and the last term is the excess Gibbs energy that considers the
interaction between different cations in the presence of oxygen ions. This is
E
G = f (T , ySi 4+ ) +


 ∑ yCi yCj ΩCiCj ( O ) 


i = 1 to m−1  j = i + 1 to m

∑
(18)
The interaction, ΩCiCj (O ) , is a function of temperature and composition as shown
below
(
T ) + ....
)
, Cj ( O )
, Cj ( O )
Ω Ci , Cj ( O ) = Ω1Ci , Cj (O ) + Ω Ci
T + ( y Ci − y Cj ) Ω 3Ci , Cj ( O ) + Ω Ci
T +
2
4
(y
2
Ci
(
, Cj ( O )
− y Cj ) Ω 5Ci , Cj ( O ) + Ω Ci
6
(19)
The function f (T , ySi 4+ ) in equation (18) compensates for the adopted hypothetical
standard state of silica, as the Gibbs excess energy is not zero when the composition
of the solution is nearly pure silica. The model calculations were carried out assuming
that “FeO” is stoichiometric. The model along with the database is commercially
available under the trade name “THERMOSLAG©”
- 18 -
5. Review of supplements
5. Review of supplements
5.1. Supplement 1: On the Standard Gibbs Energy of Formation of CoO
This investigation was carried out in order to study the standard Gibbs energy of
formation of CoO by employing the galvanic cell technique in the temperature range
of 1052-1488 K. The galvanic cell used in the present study can be represented as:
(-) Pt, Fe(s), “FeO”(s) // ZrO2 (partially stabilised // CoO(s), Co(s), Pt (+)
with AxOy )
(III)
where AxOy represents Y2O3 (cell I) and CaO (cell II) respectively. By using
thermodynamic information of the reference electrode obtained from [39-40] along
with the created potential difference, the standard Gibbs energy of formation for solid
I
CoO, ∆ oGCoO
is
I
∆ o GCoO
= -233996 + 69.28T (1052-1488 K) ±450 J/mol
(20)
which was found to be in agreement with previous investigations as presented in
Figure 10.
-110
Cell I Present work
Cell II
Kiukkola and Wagner [41]
Tretjakow and Schmalzried [42]
Moriyama et al. [43]
Vasileva et al. [44]
Jacobsson and Rosén [45]
Suggested Eq.
∆˚G (kJ/mol)
-120
-130
-140
-150
Co(s) + 0.5O2(g) = CoO(s)
-160
-170
900
1000
1100
1200
1300
1400
1500
1600
Temperature (K)
Figure 10. Gibbs energy of formation for cobaltous oxide; results from the
present work compared with earlier trials.
By using information from the latest assessment of the Co-O system as carried out by
Chen et al. [46], the standard Gibbs energy of formation for oxygen dissolution in
solid cobalt, the reaction
- 19 -
5. Review of supplements
Co(s) + O(Co, fcc) = CoO(s)
(21)
was evaluated to
∆˚G21 = -29385 + 5.756T J/mol (1050-1450 K)
(22)
The experimental set-up as well as the satisfactory performance of the galvanic cell
and the mutual consistency with previous studies were validated by this work.
5.2. Supplement 2: Thermodynamic Studies of some Fe-Pt Alloys by the Solid
Electrolyte Galvanic Cell Method
In the present investigation, the thermodynamic activities of iron in iron-platinum
solid alloys were measured by the solid electrolyte galvanic cell method in the
temperature range of 1073-1273 K. The galvanic cell employed can be represented as:
(-) Pt, Fe(s), “FeO”(s)// ZrO2 (11 mol pct CaO) //
“FeO”(s), Fe-Pt alloys, Pt (+)
(IV)
Six different Fe-Pt alloys covering the entire composition range were studied and the
cell EMF values were found to be linear functions of composition. The activities
showed a strong negative deviation from Raoult’s law. The activity coefficients from
the present results showed general agreement with earlier measurements. The
thermodynamics of this system were fitted into a Hildebrand regular solution model
and, correspondingly, the enthalpies were estimated as illustrated in Figure 11. The
results of the present work enable the estimation of the activities of “FeO” in
metallurgical slags contained in thin Pt crucibles and equilibrated with gas mixtures of
known oxygen partial pressures.
Present study
Sundaresen et al. [47]
Alcock et al. [48]
5
∆HM (kJ/mol)
0
-5
-10
-15
-20
-25
0.0
0.2
0.4
0.6
XFe
Figure 11. Enthalpies of mixing at 1123 K.
- 20 -
0.8
1.0
5. Review of supplements
5.3. Supplement 3: Differential Thermal Analysis (DTA) of the Iron-Platinum
System
In order to further investigate the binary metallic system Fe-Pt, DTA measurements
were carried out aiming at confirming some liquidus temperatures and to measure
transition temperatures. Twelve different alloys were prepared and investigated with a
NETZSCH calorimeter in the temperature range from 300 to 1673 K and also 3 alloys
with a Setaram high temperature calorimeter in the temperature range of 300-1988 K.
The measurements were carried out in Ar as well as H2 atmospheres where the effect
of H2 was checked by using He.
The results obtained show a good agreement with previous investigations and bring
new information for order/disorder phase transitions for FePt and FePt3 alloys
respectively in the temperature range of 1420-1610 K. This can bring clarifications to
some uncertainties in the suggested equilibrium diagram by [49] as shown in Figure
12. Use of He instead of H2 in some of the trials showed that the impact of hydrogen
on the measurements was insignificant.
2200
Alloy 1
Alloy 3 - 9
Alloy 2
Liquidus
2042
2000
1811
Temperature (K)
1800
1667
1600
γ
1400
FePt3
1200
Unit A
Unit A with He
Unit B
Rellinghaus et al. [50]
Isaac
and Tamman [51]
Buckley
and Hume Rothery [52]
FePt
1000
Fe3Pt
800
α(Fe)
0
10
20
30
40
50
60
70
80
90
100
At% Platinum
Figure 12. Result from the present measurements along with previous
investigations. (A = The NETZSCH unit, B = The Setaram unit). The phase
diagram is reproduced from [49].
5.4. Supplement 4: A Thermodynamic Assessment of the Fe-Pt System
A good understanding of the thermodynamic properties of the binary metallic system
Fe-Pt is essential in extrapolating data to higher temperatures. In view of the
discrepancies in the thermodynamical experimental data available in literature, the
first attempt of performing a CALPHAD investigation of the binary iron-platinum
system was initiated.
- 21 -
5. Review of supplements
This work presents a complete assessment of the binary metallic Fe-Pt system by
means of the CALPHAD method. The liquid and the bcc phase have been modelled as
substitutional solutions where the interaction parameter is composition-dependent in
the form of a Redlich-Kister series. The ordered phases and the disordered fcc phases
were modelled in CEF formalism with a single Gibbs energy function.
The obtained phase equilibria, illustrated in Figure 13, and activities of iron and
platinum agree reasonably well with the literature data. Validation of the liquidus
maxima around 50 at% Pt, found in the optimisation work, was performed by a
quenching experiment followed by SEM analysis.
Liquid
fcc
L12
L10
L12
Figure 13. The assessed Fe-Pt phase diagram.
5.5. Supplement 5: Thermodynamic Activities of “FeO” in some Binary ”FeO”Containing Slags
The Division of Metallurgy has developed a slag model that enables the extrapolation
of the thermodynamic data of multicomponent slags as functions of composition and
temperature. This model, referred to as the KTH model enables the estimation of the
thermodynamic activities of higher order systems from the experimental data for
lower order systems. The predictive capacity of the model is only as good as the input
data for lower order systems. In this connection, the thermodynamic activities of
“FeO” in the case of the binary systems Al2O3-“FeO”, CaO-“FeO” and “FeO”-SiO2
were determined by employing the gas equilibration method in the temperature range
of 1823-1873 K.
The molten slag, kept in a Pt-crucible was brought to equilibrium with a gas mixture
of known oxygen partial pressure. A part of the Fe from the “FeO” was reduced
- 22 -
5. Review of supplements
during the equilibration and got dissolved in the Pt phase. The samples were quenched
after the required equilibration time and the slag phase as well as the platinum
crucible were subjected to chemical analysis. The activities of “FeO” in the slag were
calculated from the experimental data using thermodynamic information on the Fe-Pt
binary metallic system generated and assessed earlier in supplements 1-4.
The experimental results are compared with earlier thermodynamic studies of the slag
systems. Reassessment with the KTH slag model is performed and the results are
compared with other thermodynamic models, viz. F*A*C*T™ and Thermo-Calc™. A
comparison between experimentally determined and calculated activities of “FeO” in
the “FeO”-SiO2 and Al2O3-“FeO” systems are presented in Figures 14 and 15
respectively. The result from the present measurements along with literature
information on the activities of “FeO” in the CaO-“FeO” system is illustrated in
Figure 16. The experimental activities predicted by the KTH slag model are in good
agreement with the experimental data available in the literature. A general agreement
between the various models is also observed.
1.0
Schuhmann at 1531-1680 K [53]
Bodsworth at 1530-1641 K [54]
Fujita at 1833 K [55]
Distin at 2058-2233 K [56]
Wanibe at 1502-1615 K [57]
Ban-Ya at 1673 K [58]
Wijngaarden at 1673 K [59]
Dhima at 1673 K [60]
Present study 1823-1873 K
a"FeO" Calculated
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
a"FeO" Experimental
Figure 14. Comparison between experimentally determined and calculated
activities of “FeO” in the “FeO”-SiO2 system.
- 23 -
5. Review of supplements
1.0
Ban-Ya at 1673 [58]
Present study at 1823-1873 K
a"FeO" Calculated
0.9
0.8
0.7
0.6
0.6
0.7
0.8
0.9
1.0
a"FeO" Experimental
Figure 15. Comparison between experimentally determined and calculated
activities of “FeO” in the Al2O3-“FeO”-system.
1.0
Ban-Ya at 1673 K [58]
Wijngaarden at 1673 K [59]
Fujita at 1833 K [61]
Takeda at 1473 and 1573 K [62]
Iwase at 1673 K [63]
Present study at 1823 and 1873 K
a"FeO" Calculated
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
a"FeO" Experimental
Figure 16. Comparison between experimentally determined and calculated
activities of “FeO” in the CaO-“FeO”-system.
- 24 -
5. Review of supplements
5.6. Supplement 6: Thermodynamic Activities of “FeO” in some Ternary “FeO”Containing Slags
Thermodynamic data concerning “FeO”-containing slags is of importance in ladle
refining of steel. With a view to generate a set of reliable and self-consistent
thermodynamic data for these slags, experimental determination of the activities of
iron oxide in the Al2O3-“FeO”-SiO2, CaO-“FeO”-SiO2 and “FeO”-MgO-SiO2 systems
was carried out using the gas equilibration method involving CO-CO2-Ar gas
mixtures in the temperature range of 1823-1923 K. The slag samples kept in Pt
crucibles were quenched after the equilibration and subjected to chemical analysis.
The thermodynamic activities of “FeO” in the slags were calculated from the
experimental data. The results are incorporated into the KTH model in order to
compute the thermodynamics of higher order systems from lower order ones.
Model calculations of the iso-activity, along with experimentally determined activities
of “FeO” in the Al2O3-“FeO”-SiO2, CaO-“FeO”-SiO2 and “FeO”-MgO-SiO2 systems
at 1873 K are presented in Figures 17-19 respectively. The capacity of the model to
predict the thermodynamic activites in four, five, and six component slags is
demonstrated in the case of steelmaking slags. This is illustrated in the case of six
component slags in Figure 20.
1.0
0.0
Present work at 1873 K
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.2
0.8
0.1
0.4
0.6
x
0.6
0.2
2
0.3
x SiO
"F
eO
"
0.1
0.4
0.4
0.5
0.6
0.8
0.8
1.0
0.0
0.2
0.7
0.9
0.0
0.2
0.4
xAl O
2
0.6
0.8
1.0
3
Figure 17. Activities of “FeO” in the Al2O3-“FeO”-SiO2 system at 1873 K obtained
from experiments and calculations.
- 25 -
5. Review of supplements
0.0
Present work at 1873 K
0-0.1
0.1-0.2
0.2-0.3
0.2
0.3-0.4
0.4
1.0
0.8
0.1
0.6
Ca
O
x
x SiO
0.2
2
0.3
0.6
0.4
0.4
0.5
0.6
0.7
0.8
0.2
0.8
0.9
0.4 0.5
0.3
1.0
0.0
0.2
0.4
0.6
0.7
0.6
0.8 0.9
0.0
0.8
1.0
x"FeO"
Figure 18. Activities of “FeO” in the CaO-“FeO”-SiO2 system at 1873 K obtained
from experiments and calculations.
Filled: Present work
Half filled: Kojima et al. [64]
0.0-0.1
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.0
1.0
0.8
0.2
0.6
x
x SiO
Mg
O
0.4
0.1 0.2 0.3
Ban-Ya and Shim [13]
0.25-0.45
0.45-0.525
0.525-0.575
0.575-0.625
0.625-0.675
0.675-0.725
0.725-0.775
0.775-0.825
0.825-0.875
0.875-1.0
2
0.4
0.6
0.4
0.5
0.6
0.7
0.8
0.8
0.9
1.0
0.0
0.2
0.2
0.4
x"FeO"
0.6
0.8
0.0
1.0
Figure 19. Activities of “FeO” in the “FeO”-MgO-SiO2 system at 1873 K obtained from
the experiments and calculations.
- 26 -
5. Review of supplements
0.014
BF: CaO: "FeO": MgO: MnO: SiO2 - 32: 2: 17: 2: 34
EAF: CaO: "FeO": MgO: MnO: SiO2 - 40: 15: 9: 5: 21
LF: CaO: "FeO": MgO: MnO: SiO2 - 53.5: 0.6: 6: 0.4: 6.0
T=1873 K
0.012
0.010
0.3
0.008
0.2
0.006
0.004
Activity of Al2O3 in LF
Activity of Al2O3 in BF and EAF
0.4
0.1
0.002
0.0
0.000
0
5
10
15
20
25
30
wt% Al2O3
Figure 20. The activity of Al2O3 in the Al2O3-CaO-“FeO”-MgO-MnO-SiO2
system at 1873 K for the BF, EAF and LF process.
5.7. Supplement 7: Evaluation of Thermodynamic Activity of a Metallic Oxide in
a Ternary Slag from the Sulphide Capacity of the Slag
In the refining of steel, activities of slag components and sulphide capacities of slag
systems are both important thermodynamic concepts. In view of the great importance
of these properties, considerable efforts have been made to obtain reliable
experimental data regarding these properties as well as to extrapolate the data using
suitable theoretical models. It has earlier been shown by Nilsson et al. [65] for a
number of binary oxide systems that the sulphide capacities are linear functions of the
activities of the basic oxides. Similar correlations are extremely desirable for higher
order systems. Development of such correlations is difficult due to the non-adherence
of the sulphide activities in the complex slags according to Henry’s law and the
uncertainty regarding the relative effects of the various metal oxides with respect to
their affinities to sulphur.
Hence, this study was initiated where the correlation between the activity of a metallic
oxide in a ternary slag system and the sulphide capacity of the slag was investigated.
The solubility of sulphur in the binary systems: CaO-SiO2 and Al2O3-CaO along with
its sulphide capacity of the Al2O3-CaO-SiO2 system has been used to estimate the
activities of CaO at the compositions of some Al2O3-CaO-SiO2 intermediate
compounds.
The estimated values of the activities were found to be in good agreement with the
measured values. This correlation is not only used to evaluate the activity, but also to
elucidate the applicability of Henry’s law to the activity of a metallic sulphide and to
- 27 -
5. Review of supplements
determine the order in the affinity of a cation to sulphur between two metallic oxides
in a slag.
5.8. Supplement 8: Thermodynamic Studies of “FeO”-Containing Slags and their
Impact on the Ladle Refining Process
An optimisation of unit processes in steel production and quality control of the
products presupposes a fundamental understanding of the thermodynamics of the
metallic and slag systems. Further, during plant operations, it is necessary to have the
chemical compositions of these phases by well-planned sampling and quick chemical
analysis. However, due to the uncertainties involved in sampling and analysis,
contradictory information of the process status could be created. In order to sort this
out, it is necessary to have a complete understanding of the thermodynamics involving
slag-metal reactions. This, however, requires access to reliable and accurate
estimations of the thermodynamic properties of the metallic and slag systems.
Model calculations were performed with the KTH slag software, THERMOSLAG©,
by using plant data from OVAKO Steel, Hofors, Sweden. It was found that oxygen
estimations in the metal from the “FeO” analyses of slags, obtained by conventional
sampling and analysis method were less reliable. Estimations of the oxygen levels
utilising the sulphur partition between the slag and the metal were carried out using
the THERMOSLAG© software. This is graphically presented in Figure 21.
10
Oxygen content in:
©
Liquid steel, THERMOSLAG calculations
Finished product (total)
8
O (ppm)
6
4
2
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Heat no.
Figure 21. Dissolved oxygen in the liquid steel based on chemical analysis
and present calculations for the various heats.
- 28 -
6. General discussion
6. General discussion
Today steel producers are striving towards a beneficial usage of the processes for the
company itself as well as the society, viz. in terms of energy consumption,
optimisation and environmental aspects. Simultaneously, several researchers are, and
have been trying for decades, to optimise the reactions occurring between the molten
metal and the slag phase.
Due to the limited success of extracting the properties of slags from their structure, it
may be necessary to reverse the order and extract structural information from the slag
properties. This would mean a convergence of the thermochemical and
thermophysical properties aiming towards a common structural factor. Thus, it is
strongly suggested that the thermochemical and thermophysical properties of slags are
modelled on a common basis. This will also enable establishment of correlations
between the various properties so that the mutual compatibilities between the
properties is established. Since the thermochemical and thermophysical properties of
slags are dependent on the slag structure, it is logical to expect mutual correlations
between the different properties.
The thermodynamics of silicates would strongly depend upon the next-nearest
neighbour interactions, viz. the interactions between the cations. The integral molar
enthalpies of mixing of silicates would be dependent on these interactions, as also the
densities (molar volumes). Exothermic enthalpies are indicative of attractive forces
which would even manifest in volume shrinkage. Molar volume and molar volume of
mixing data of molten slags can be obtained from the experimental densities of the
same. A relationship between the integral molar enthalpy and the molar volume of
mixing has been developed in the present laboratory. Hence it is possible to estimate
the slag volume as a function of temperature and composition from slag
thermodynamics and, thereby linking thermophysical properties with thermochemical
properties.
However, in order to obtain reliable model predictions, it is of the greatest importance
to have accurately determined thermodynamic information. Unfortunately, the
experimental thermodynamics has become a rare discipline within the academia as
well as the R & D departments.
- 29 -
7. Summary and conclusions
7. Summary and conclusions
In the present work, the thermodynamic activites of iron oxide in the slag systems
Al2O3-“FeO”, CaO-“FeO”, “FeO”-SiO2, Al2O3-“FeO”-SiO2, CaO-“FeO”-SiO2 and
“FeO”-MgO-SiO2 respectively were investigated by employing the gas equilibration
technique in the temperature range of 1823-1923 K. The molten slag, kept in a
platinum crucible was brought to equilibrium with a gas mixture of defined oxygen
partial pressure. A part of the iron from the “FeO” was reduced during the
equilibration and got dissolved in the Pt phase. In order to compute “FeO” activities,
knowledge of the thermodynamics of the Fe-Pt system were needed.
The Fe-Pt system was investigated by employing solid-state galvanic cell and
calorimetric technique in the temperature ranges, 1073-1273 K and 300-1988 K,
respectively. The proper functioning of the galvanic cell apparatus used in the present
work was verified by studying the Gibbs energy of formation of CoO. The results are
in good agreement with earlier investigations of the cobalt-oxygen system. The cell
EMF values from the Fe-Pt investigation were found to be linear functions of
composition and the activities showed a strong negative deviation from Raoult’s law.
The activity coefficients from the present results showed general agreement with
earlier measurements.
The results obtained from the calorimetric work show a good agreement with previous
investigations and bring new information for order/disorder phase transitions for FePt
and FePt3 alloys in the temperature range of 1420-1610 K, respectively. It was also
concluded that the use of He instead of H2 showed that the impact of hydrogen on the
measurements was insignificant.
The results of these experimental investigations were incorporated along with
previous studies into a CALPHAD-type of thermodynamic assessment performed
with the Thermo-Calc™ software. The obtained phase equilibria and activities of iron
and platinum agree reasonably well with the literature data. Validation of the liquidus
maxima around 50 at% Pt, found in the optimisation work, was performed by a
quenching experiment followed by SEM analysis.
The activites of “FeO” in the slag were calculated by using the chemical analysis of
the furnace quenched slag samples together with thermodynamic information of the
Fe-Pt system. The results obtained from the gas equilibration investigations show that
activities of liquid “FeO” are in general agreement with previous investigations
performed in the different systems. It could also be concluded that the temperature
coefficient was negligible for the activities of “FeO”.
Reassessment with the KTH slag model was performed and it was also observed that
the agreement between the model calculation and most of the experimental results is
satisfactory. The presence of trivalent iron in the systems CaO-“FeO” and “FeO”MgO-SiO2 respectively does not seem to affect the activity of “FeO” significantly as
seen from the point of the model estimations. A comparison has been made between
commercially available software, F*A*C*T, Thermo-Calc and the KTH slag
model, THERMOSLAG©. A general agreement between the various models was also
observed.
- 30 -
7. Summary and conclusions
Model calculations of oxygen in steel were performed with THERMOSLAG© by
using plant data from the ladle refining process at OVAKO Steel, Hofors, Sweden.
During the calculations it was found that oxygen estimations in the metal from the
slag analysis obtained by conventional sampling and analysis method were less
reliable. Estimation of the oxygen levels utilising the sulphur partition between the
slag and the metal were carried out using THERMOSLAG® software. Reasonable
estimations of the oxygen contents in the metal as well as the activities of all slag
components as functions of temperature and composition confirmed that this could be
a powerful tool for process modellers and plant operators.
A correlation between the activity of a metallic oxide in a ternary slag system and the
sulphide capacity of the slag was investigated by using the solubility of sulphur in the
binary systems Al2O3-CaO and CaO-SiO2 together with the sulphide capacity of the
Al2O3-CaO-SiO2 system. The activities of CaO for some Al2O3-CaO-SiO2 compounds
were successfully evaluated from the sulphide capacity data and the activity
coefficient of CaS in the CaO-SiO2 and CaO-Al2O3 binary systems.
- 31 -
8. Future work
8. Future work
Further experimental work has to be carried out in the binary metallic Fe-Pt system in
order to amend the description of the involved phases. Heat capacities along with
enthalpies of fusion are highly desirable during the optimising procedure. Similar
approach is suggested for the Pt-Si system along with verification of earlier work in
the Mn-Pt system. This would enable the possibility to calculate the MnO and SiO2
activities of the multicomponent slag system Al2O3-CaO-“FeO”-MgO-MnO-SiO2
with its subsystems at steelmaking temperatures.
Due to the large amount of sulphide capacity data, the method of relating the
thermodynamic activity of a metal oxide from the solubility of a metal sulphide in a
liquid oxide, it is recommended to further penetrate this area by carrying out solubility
measurements in selected systems.
Incorporation of metal oxides relevant to stainless steel as well as high speed steel
production into the present thermodynamic description of silicate melts is suggested.
Thermochemical and thermophysical properties of slags depend directly on the
structure of slags. These properties have shown to have serious impacts on the
applications of slags and fluxes in steelmaking and casting. Further, the various
physical and chemical properties should exhibit mutual consistencies if they are all
based on slag structure. Therefore, it is strongly suggested to investigate the
correlation of a common structural factor for these properties. Hence, a total
optimization of the refining process can be carried out by incorporating these
correlations along with kinetic information into micro models in CFD (Computational
Fluid Dynamics) calculations.
- 32 -
Bibliography
Bibliography
1. M. Temkin, Acta Phys. Chim. U.R.S.S., (1945), 4, pp. 411-420.
2. H. Flood, T. Førland and K. Grjotheim Acta Chem. Scand., (1947), 1, 9, pp. 790790.
3. F. D. Richardson, “Physical Chemistry of Melts in Metallurgy”, (1974), 1,
Academic Press, London, pp. 92-99.
4. F. D. Richardson, Trans. Faraday Soc., (1956), 52, pp. 1312-1324.
5. G. W. Toop and C. S. Samis, Trans. Soc. AIME, (1962), 224, pp. 878-887.
6. C. R. Masson, J. Iron Steel Inst., (1972), 210, pp. 89-96.
7. P. L. Lin and A. D. Pelton, Metall. Trans., (1979), 10B, pp. 667-674.
8. J. Lumsden, Physical Chemistry of Process Metallurgy, Part 1, New York,
Interscience, (1961), pp. 165-205.
9. A. D. Pelton and M. Blander, Metall. Trans., 17B, (1986), pp. 805-815.
10. H. Gaye and J. Welfringer, 2:nd Int. Symposium on Metallurgical Slags and
Fluxes, editors: H. A. Fine and D. R. Gaskell, Lake Tahoe, Nevada, USA, AIME,
Nov. (1984), pp. 357-375.
11. M. L. Kapoor and M. G. Frohberg, Int. Metallurgical Chemistry-Applications in
Ferrous Metallurgy, Sheffield, UK, July (1971), Iron Steel Inst., pp. 17-23.
12. M. Hillert, B. Jansson, B. Sundman and J. Ågren, Metall Trans., (1985), 16A, pp.
261-266.
13. S. Ban-Ya and J. D. Shim, Canadian Met. Quart., 21, (1982), pp. 319-328.
14. J. Bygdén, D. Sichen and S. Seetharaman, Steel Research, (1994), 10, pp. 421-428.
15. J. Björkvall and V. L. Stolyarova, TRITA-MET 066, Dep. of Met., Royal Inst. of
Tech., Stockholm, Sweden, (1999).
16. J. Björkvall, D. Sichen and S. Seetharaman, High Temperature Materials and
Processes (UK), (2000), 19, 1, pp. 49-59.
17. J. Björkvall, D. Sichen and S. Seetharaman, CALPHAD, (2000), 24, 3, pp. 353376.
18. J. Björkvall, D. Sichen and S. Seetharaman, Ironmaking and Steelmaking (UK),
(2001), 28, 3, pp. 250-257.
19. Handbook of Chemistry and Physics, 60:th ed., CRC Press, Cleveland, Ohio,
1974-1979, pp. B-196.
20. P. Fredriksson and S. Seetharaman, Submitted to Steel Research International,
October 2003.
21. Handbook of Chemistry and Physics, Ed: D. R. Lide, 78:th ed., CRC Press,
Cleveland, Ohio, 1997-1998, pp. 4-122.
22. NETZSCH Instruments, Thermal analysis software, Proteus®, for MS® Windows,
ver. 4.2, Aldridge, West Midlands UK, (2003).
23. JANAF, Thermochemical Tables, 3:rd ed., (1985), 14, 1, pp. 1190.
24. B. Sundman, B. Jansson, and J-O Andersson, CALPHAD, (1985), 9, 2, pp. 153190.
25. B. Sundman, Thermo-Calc Users´ Guide, Version M, Dept. Mat. Sci. and Eng.,
The Royal Institute of Technology, Stockholm, Sweden (1999).
26. A. Dinsdale, CALPHAD, (1991), 15, pp. 317-425.
27. B. Sundman, CALPHAD, (1998), 22, pp. 335-354.
28. M. M. Nzotta, R. Nilsson, D. Sichen, and S. Seetharaman, Ironmaking and
Steelmaking, (1997), 24, 4, pp. 300-305.
29. M. M. Nzotta, Scand. J. Metall., (1997), 26, 4, pp. 169-177.
30. M. M. Nzotta, High Temp. Mat. Proc., (1997), 16, 4, pp. 261-271
Bibliography
31. M. M. Nzotta, D. Sichen and S. Seetharaman, ISIJ Int., (1998), 38, 11, pp. 11701179.
32. M. M. Nzotta, D. Sichen and S. Seetharaman, Metall. Mat. Trans. (1999), 30B, 5,
pp. 909-920.
33. M. M. Nzotta, D. Sichen and S. Seetharaman, ISIJ Int., (1999), 39, 7, pp. 657-663.
34. M. A. T. Andersson, P. Jönsson and M. M. Nzotta, ISIJ Int., (1999), 39, 11, pp.
1140-1149
35. M. M. Nzotta, M. Andreasson, P. Jönsson and S. Seetharaman, Scand. J. Metall.
(2000), 29, 4, pp. 177-184.
36. S. Seetharaman, D. Sichen and Y. Zhang, J. Met., (1999), 51, pp. 38-40.
37. S. Seetharaman, D. Sichen and F.Z. Ji, Metall. Mat. Trans., (2000), 31B, 1, pp.
105-109.
38. F. Z. Ji, Metall. Mat. Trans. (2001), 32B, 1, pp. 181-186.
39. O. Sjödén, S. Seetharaman and L-I Staffansson, Metall. Trans. (1986), 17B, pp.
179-184.
40. Thermochemical Data of Pure Substances, 2:nd ed., I. Barin (ed), (1993), pp. 560.
41. K. Kiukkola and C. Wagner, J. Electrochem. Soc. (1957), 104, pp. 379-390.
42. J. D. Tretjakow and H. Schmalzried, Ber. Bunsenges Phys. Chem., (1965), 65, pp.
396-402.
43. J. Moriyama, N. Sato, H. Asao and Z. Kozuka, Memoirs of the Faculty of
Engineering, Kyoto University, (1969), 31, pp. 253-267.
44. I. A. Vasileva, I. S. Sukhushina, Z. V. Granovskaya, R. F. Balabaeva and A. F.
Maiorova, Russ. J. Phys. Chem., (1975), 49, pp. 1275-1278
45. E. Jacobsson and E. Rosén, Scand. J. Metall., (1981), 10, pp. 39-43.
46. M. Chen, B. Hallstedt and J. J. Gauckler, J. Phase Equilib., (2003), 24, pp. 212227.
47. M. Sundaresen, Ya. I. Gerasimov, V. A. Geiderikh and I. A. Vasil’eva, Russ. J.
Phys. Chem., (1963), 37, pp.1330-1330.
48. C. B. Alcock and A. Kubik, Acta Metall. (1969), 17, pp. 437-42.
49. H. Okamoto, Binary Alloy Phase Diagrams, ASM Int. 3: ed. (1993), pp. 330-336.
50. B. Rellinghaus, J. Kastner, T, Schneider, E. F. Wassermann and P. Mohn, Phys.
Rev. B Condens. Matter., (1995), 51, pp. 2983-2993.
51. E. Isaac and G. Tamman, Z. Anorg. Chem., (1907), 55, pp. 63-71.
52. R. A. Buckley and W. Hume-Rothery, J. Iron Steel Inst. (London), (1959), 193, pp.
61-32.
53. R. Schuman and P. J. Ensio, Trans. AIME, (1951), pp. 401-411.
54. C. Bodsworth, J. Iron Steel Inst., 193, (1959), pp. 13-24.
55. H. Fuijita and S. Maruhashi, Tetsu-to-Hagane, (1969), 55, 4, pp. 249-260.
56. P. A. Distin, S. G. Whiteway and C. R. Masson, Can. Met. Quart., (1971), 10, 2,
pp. 73-78.
57. Y. Wanibe, Y. Yamauchi, K. Kawai and H. Sako, ISIJ Int., (1972), 12, pp. 472476.
58. S. Ban-Ya, A. Chiba, and A. Hikosaka, Tetsu-to-Hagane, (1980), 66, 10, pp.
1484-1493.
59. M. J. U. T. Van Wijngaarden and R. J. Dippenaar, J. South Afr. Inst. Min. Metall,
(1986), 86, 11, pp. 443-453.
60. A. Dhima, B. Stafa and M. Allibert, High Temperature Science, (1986), 21, 3, pp.
143-159.
61. H. Fujita, Y. Iritani and S. Maruhashi, Tetsu-to-Hagane, (1968), 54, 4, pp. 359370.
Bibliography
62. Y. Takeda and A. Yazawa, Nippon Kogyokashi, (1980), 96, pp. 901-905.
63. M. Iwase, N. Yamada, K. Nishida and E. Ichise, Trans. ISS, (1984), 4, pp. 69-75.
64. Y. Kojima, M. Inouye and K. Sano, Arch. Eisenhüttenw., (1969), 40, 1, pp. 37-40.
65. R. Nilsson, S. Seetharaman and K. T. Jacob: ISIJ Int., (1994), 34, 11, pp. 876-882.