Thermodynamic Studies of the Fe-Pt System and “Feo”-Containing Slags for Application Towards Ladle Refining

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

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

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.

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. 309- 320, 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 91- 7170-588-0.

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 4 3.2.1. Preparation of materials 4 3.2.2. Apparatus 6 3.2.3. Procedure 7

3.3. Calorimetric measurements 7 3.3.1. Preparation of materials 7 3.3.2. Apparatus and procedure 8 3.3.2.1. The NETZSCH calorimeter 8 3.3.2.2. The Setaram calorimeter 9

3.4. Gas equilibration measurements 10 3.4.1. Principle 10 3.4.2. Preparation of materials 10 3.4.3. Apparatus 11 3.4.4. Procedure 11

4. Thermodynamic modelling 13

4.1. Modelling of the Fe-Pt system 13 4.1.1 The pure elements 14 4.1.2. The liquid phase and the bcc phase 14 4.1.3. The fcc phases 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 Iron- Platinum 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

Thermodynamics of ternary Sulphide capacity to activities systems

Thermodynamics of binary systems Assessment

Fe-Pt experimental study Gas equlibration experiments Assessment

Figure 1. Structure of present study.

- 1 - 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, 4- binding them up in a SiO4 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 Mg F

CO S Cu A M F Mix

CO2 S M F

Exhaust O -probe Furnace 2

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 aFe(Pt) (1)  2F 

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 Supplier Air plus-grade AGA, Sweden α-alumina, single crystal 99.99% NETZSCH, Germany Alumina cement Haldewanger, Germany Alumina crucible 99.7% Haldewanger, Germany Alumina crucibles and caps 99.5% Setaram, France Alumina lining, 99.7% NETZSCH, Germany Aluminium Oxide anhydrous E. Merck, Germany Alumina tubes 99.7% Haldenwanger, Germany Ascarite II Thomas Scientific, USA Argon plus-grade AGA Gas, Sweden Argon-2% Hydrogen plus-grade AGA Gas, Sweden Calcia stabilised zirconia Yamari Industries, Japan Calcium Oxide Fischer Scientific, USA Carbon Monoxide plus-grade AGA Gas, Sweden Carbon Dioxide plus-grade AGA Gas, Sweden Carbonyl iron powder pro analysi E. Merck, Germany Cobalt powder 99.8 % Johnson Matthey Inc., UK Cobalt(II) nitrate hexahydrate 98 % Aldrich, USA Copper, turnings 99 % Johnson Matthey Inc., UK Gold 99.999% NETZSCH, Germany Helium plus-grade AGA Gas, Sweden Hematite powder anhydrous Fisher Scientific, USA Hydrogen plus-grade AGA Gas, Sweden Indium 99.999% NETZSCH, Germany Iron crucible 99.9 % Armco Iron, USA Iron foil 99.5% Goodfellow, UK Magnesium, turnings > 99 % E. Merck, Germany Magnesium Oxide pro analysi E. Merck, Germany Magnesium perchlorate (dehydrite) anhydrous GFS Chemicals, USA Magnetite 96.7% LKAB, Sweden Nickel foil 99.4% INCO Alloys, Canada Nitrogen plus-grade AGA Gas, Sweden di-Phosphorous penta oxide extra pure E. Merck, Germany Platinum crucibles and caps 99.99% NETZSCH, Germany Platinum powder 99.9 % Chempur, Germany Platinum wire 99.9 % Johnson Matthey Inc., UK Platinum/Rhodium wire 99.99% Johnson Matthey Inc., UK Platinum sheet 99.998 % Johnson Matthey Inc., UK Silica gel E. Merck, Germany Silicon Oxide pro analysi E. Merck, Germany Silver 99.99% NETZSCH, Germany Tin 99.99% NETZSCH, Germany Titanium foil 99.7 % Aldrich, USA Yttria stabilised zirconia Friatech, Germany Yttria stabilised zirconia K-Style Adv. Cer., China Zinc 99.999% NETZSCH, Germany

- 5 - 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.

7 8 9 10 11 12 13 14

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 + O ()g =" FeO" (slag ) (2) 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:

1/ 2 a = a ⋅ p ⋅ C (3) FeO Fe(Pt) O2 2 where aFe(Pt) is the activity of iron in platinum, p is the partial pressure of oxygen O2 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 Pt- spiral 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 1823- 1973 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 SEM- EDS 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

o E Gm = ∑ xi Gi + RT ∑ xi ln()xi + Gm (4) i 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 = xFe xPt LFePt (5)

with the composition dependent interaction parameter LFePt . This is in the form of a Redlich-Kister (RK) series:

υ υ LFePt = ∑()xFe − xPt LFePt (6) υ=0

υ where the RK coefficients 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:

dis ord Gm = Gm ()xi + ∆Gm ()yi (8) where the relation between the mole fraction, xi, and the site fractions, yi, is

4 ()s xi = 0.25∑ yi (9) s=1

ord 4sl 4sl ∆Gm = Gm ()yi − Gm ()xi (10)

(s) The mole fraction xi is calculated from Eq. (9) where yi 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 ord order to make ∆Gm zero when the phase is disordered. Hence, all parameters that dis describe the disordered state are described by a substitutional model, Gm ()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

4sl (1) (2) (3) (4) o (s) (i) E Gm = ∑∑∑∑yi y j yk yl Gi: j:k:l + 0.25RT ∑∑ yi ln yi + Gm (11) ijkl si

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.

oG = oG = ... = G FeFeFePt FeFePtFe Fe3Pt o o GFeFePtPt = GFePtFePt = ... = GFePt (12) oG = oG = ... = G FePtPtPt PtFePtPt FePt3

CEF assumes random mixing on each sublattice. In the present work, the excess E Gibbs energy Gm includes the first two interaction terms according to CEF for a binary system as shown below

EG = y (r) y (r) y (s) y (t) y (u) L + ...... + m ∑∑∑∑∑ i1 i2 j k l i1 ,i2: j:k:l iii > jkl 112 (13) y (r) y (r) y (s) y (s) y (t) y (u) L + ...... ∑∑∑∑∑∑ i1 i2 j1 j2 k l i1 ,i2: j1 , j2:k:l ii11i2 >>jj11j2 kl

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, L which i1 ,i2 : j:k:l 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”, L . These represent interactions in two sublattices, s i1 ,i2: j1, j2:k:l 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

EG = y (s) y (s) L + y (s) y (s) y (t) y (t) L (14) m ∑∑ i1 i2 i1 ,i2:∗:∗:∗ ∑∑∑∑ i1 j2 j1 j2 i1 ,i2: j1 , j2:∗:∗ ii12 ii12jj12 where the sublattice with interaction of the L parameters have been permuted cyclically.

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

v1 v2 vi vm 2− (C1 , C2 ,...Ci ,...,Cm )p (O )q (15) 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 O2- ions 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

NCi yCi = (16) ∑ NCj j =1to m

vi where Ni is the number of moles of cation Ci and the summation includes all the cations. The integral molar Gibbs energy of a solution can be expressed as:

o E (17) Gm = ∑ xCi ci O ai GCi ci O ai + RTp∑ yci ln(yci ) + G i i

o where xCici Oai and GCi 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  CiCj(O)  G = f T, y 4+ +  y y Ω  (18) ()Si ∑∑ Ci Cj  im=+11to m−1 j = i to 

The interaction, ΩCiCj(O) , is a function of temperature and composition as shown below

Ci,Cj(O) Ci,Cj(O) Ci,Cj(O) Ci,Cj(O) Ci,Cj(O) Ω = Ω1 + Ω 2 T + (yCi − yCj )(Ω3 + Ω 4 T ) + (19) 2 Ci,Cj(O) Ci,Cj(O) ()yCi − yCj ()Ω5 + Ω6 T + ....

The function f T, y 4 in equation (18) compensates for the adopted hypothetical ( Si + ) 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 (+) (III) with AxOy )

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 o I CoO, ∆ GCoO is

o I ∆ 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 -120 Kiukkola and Wagner [41] Tretjakow and Schmalzried [42] Moriyama et al. [43] Vasileva et al. [44] -130 Jacobsson and Rosén [45] Suggested Eq. -140

G (kJ/mol) ˚ ∆ -150

-160 Co(s) + 0.5O (g) = CoO(s) 2

-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.

5 Present study Sundaresen et al. [47] Alcock et al. [48] 0

-5

-10 (kJ/mol) (kJ/mol)

M H

∆ -15

-20

-25 0.0 0.2 0.4 0.6 0.8 1.0 X Fe

Figure 11. Enthalpies of mixing at 1123 K.

- 20 - 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 2 Alloy 3 - 9 Liquidus 2000 2042

1811 1800

1600 1667 γ

FePt 1400 3

Unit A 1200 FePt Unit A with He (K) Temperature Unit B Rellinghaus et al. [50] 1000 Isaac Fe Pt and Tamman [51] 3 Buckley 800 α(Fe) and Hume Rothery [52]

0 102030405060708090100 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

L1 2

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] 0.8 Distin at 2058-2233 K [56] Wanibe at 1502-1615 K [57] Ban-Ya at 1673 K [58] Wijngaarden at 1673 K [59] 0.6 Dhima at 1673 K [60] Present study 1823-1873 K

Calculated 0.4 "FeO" a

0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 a Experimental "FeO" 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

0.9

0.8

Calculated "FeO"

a 0.7

0.6 0.6 0.7 0.8 0.9 1.0 a Experimental "FeO"

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] 0.8 Takeda at 1473 and 1573 K [62] Iwase at 1673 K [63] Present study at 1823 and 1873 K 0.6

Calculated 0.4

"FeO"

a 0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 a Experimental "FeO"

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.

0.0 1.0 Present work at 1873 K 0-0.1 0.1-0.2 0.2 0.8 0.2-0.3 0.1 0.3-0.4 0.4-0.5

0.4 0.6 0.1 " x O e S F iO x " 0.2 2 0.3 0.6 0.4

0.4

0.5 0.8 0.6 0.2 0.7 0.8

0.9 1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 x Al O 2 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 1.0 Present work at 1873 K 0-0.1 0.1-0.2

0.2-0.3 0.2 0.8 0.3-0.4

0.4 0.1 0.6 O 0.2 x a S C x iO 0.3 2

0.6 0.4 0.4 0.5 0.6 0.7 0.8 0.8 0.2

0.9 0.4 0.9 0.5 0.7 0.8 1.0 0.3 0.6 0.0

0.00.20.40.60.81.0 x "FeO"

Figure 18. Activities of “FeO” in the CaO-“FeO”-SiO2 system at 1873 K obtained from experiments and calculations.

Filled: Present work Ban-Ya and Shim [13] Half filled: Kojima et al. [64] 0.0 1.0 0.25-0.45 0.45-0.525 0.0-0.1 0.525-0.575 0.2-0.3 0.575-0.625 0.3-0.4 0.2 0.8 0.625-0.675 0.4-0.5 0.675-0.725 0.5-0.6 0.725-0.775 0.6-0.7 0.775-0.825 0.7-0.8 0.4 0.6 0.825-0.875 x 0.875-1.0 O S 0.2 i Mg 0.1 0.3 O x 2 0.4 0.6 0.5 0.4

0.6 0.7 0.8 0.2 0.8

0.9 1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 x "FeO"

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: SiO - 32: 2: 17: 2: 34 2 0.4 EAF: CaO: "FeO": MgO: MnO: SiO - 40: 15: 9: 5: 21 2 0.012 LF: CaO: "FeO": MgO: MnO: SiO - 53.5: 0.6: 6: 0.4: 6.0 2 T=1873 K 0.010 0.3 in LF in 3 0.008 O 2

EAF and BF in 3

O 2 0.2 0.006

0.004 Al of Activity 0.1

Al of Activity 0.002

0.0 0.000 0 5 10 15 20 25 30 wt% Al O 2 3

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.

(ppm) 4 O

0 0 2 4 6 8 1012141618202224

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. 790- 790. 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. 353- 376. 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. 153- 190. 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. 1170- 1179. 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. 212- 227. 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. 472- 476. 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. 359- 370. 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.