1. 1 MODELING OF SURFACE PROPERTIES OF METALLURGICAL SOLUTIONS: STEELS, SLAGS AND STEEL-SLAG SYSTEMS Jerzy Iwanciw, Krzysztof Pytel, Elżbieta Kawecka-Cebula, Magdalena Kostołowska Faculty of Metals Engineering & Industrial Comp. Science, AGH University of Science and Technology at Krakow

2. 2 Importance of Surface Properties in Iron Metallurgy Phenomena Removal of inclusions from molten metal Slag spreading on metal (work of adhesion) Filtration of metals (work of adhesion) Slag penetration into refractory (capillary effect) Welding pool shape (Marangoni effect) CCS mould meniscus shape (Marangoni effect)...

3. 3 Scattering of the base data – pure Fe effect of neglecting the small amount of surface active elements: Ref.: T. Utigard: ISIJ International, Vol. 34 (1994), No. 12, pp. 951-959, Surface and Interfacial Tensions of Iron Based Systems The surface tension of pure Fe seems to rise from year to year

4. 4 The Aim of the Study Elaboration of a models for prediction of the surface properties of metallurgical solutions like : - steels, - slags, - steel/slag interfaces for broad range of chemical compositions of the phases and temperatures Model representations for metallurgical calculations as a function: = f(X1... Xi, T) or = f(%1... %i, T)

5. 5 Liquid-Gas Surface Tension Models Linear and polynomial models Excess models for surface non-active components: Calphad and Redlich-Kister model (excess property expansion) Thermodynamic Szyszkowskis (Peltons) models for surface active components: Butlers model:

6. 6 Liquid-Liquid Interfacial Tension Models Linear and polynomial models Calphad and Redlich-Kistler model Excess model Szyszkowskis model Butlers model Girifalco-Goods model where: = f(X1...Xi, T) Similar to the surface tension

7. 7 Elaborated tools Databases with browsing and sorting facilities based on MS Excel 2000 worksheets Program for multi-variable correlations (up to 600 variables), easy creating of new complex variables and eliminating the uneffective ones Program for simulation of the equilibrium between melt and slag Program for visualisation of surface properties

8. 8 Program for multi-variable correlation Adding (creating) new variables (x1x2,...) Variable elimination Data import from *.csv file Start of correlation Reading data from database Model coefficients Model comparison

9. 9 Program for metal-slag equlibrium simulation (using M-S-G simulator)

10. 10 Configuration of Program for Visualisation of Steel Surface Tension

11. 11 Formulae for the iron solutions confining ferritic steels, austenitic steels and cast irons Model sensitive to all components (influence on S, O, C activity coefficients) - st. dev = 55 mN/m : Simplified model for practical use - st. dev = 55 mN/m :

12. 12 Simplified Surface Tension Model for ferritic steels, austenitic steels and cast irons Database rangeModel fitting

13. 13 Visualisation of Liquid Steel Surface Tension Surface tension of RSt37 grade at 1510 °C d /dT dependence of RSt37 grade at 1510 °C

14. 14 Optimal Slag Surface Tension Model where: – the surface tension of the slag, mN/m, i 0 – the extrapolated surface tension of i component at 0 0 K, d i /dT – the temperature coefficient of the surface tension of i component, i,j – the interaction parameters, T – temperature in K, X i, X j – the mole f ra c tio n s of the slag components. A fragment of the model coefficients matrix ( 10 main components, st. dev. = 33mN/m)

15. 15 Visualisation of Slag Surface Tension CaO-Al2O3-SiO2 systemCCS mould slag

16. 16 Metal-Slag Interfacial Tension Models (I) Linear model (31 variables): st. dev. = 13 4 mN/m Girifalco-Good type: st. dev. = 170 mN/m 2 s 1/2 = 585.06 0.30335 T[K] + 0.2122 %FeO + 143.0415 %Fe 2 O 3 + 53.6515 %Cr 2 O 3 3.8361 %TiO 2 For slags without Fe 2 O 3, Cr 2 O 3 and TiO 2 : = 0.7167+0.003927 %FeO = ~ 0.7167 + 0.3537 X FeO

17. 17 Metal-Slag Interfacial Tension Models (II) Excess model (755 exp. points, 243 variables): st. dev. = 84 mN/m (after equilibration of metal-slag data)

18. 18 Conclusions The surface tension of the iron solutions (steels) and metal-slag interfacial tension is affected mainly and non-linearly by such intensive surfactants like oxygen and sulphur. When the oxygen content is below 5 ppm, the sulphur dominantly determines the surface tension quantity. As to the slag solutions it was found that - for pure oxides - the highest surface tension levels exhibit the alkali oxides like CaO, MgO, MnO, FeO and Cr 2 O 3. The interfacial tension for metal/slag systems is predominantly set by the metal phase while the effect of the slag phase is secondary. Further progress in modeling of the surface properties for metallurgical systems depends to much extent on a supply of new, more precise experimental surface and interfacial tensions data to fill the lacking gaps.

19. 19 Thank you for your attention The study was sponsored by KBN Grant No 3 T08B 023 28