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MODELINGMODELING OFOF SURFACE PROPERTIES SURFACE PROPERTIES

OFOF METALLURGICAL METALLURGICAL SOLUTIONS:SOLUTIONS: STEELS, STEELS,

SLAGS SLAGS ANDAND STEEL-SLAG STEEL-SLAG SYSTEMS SYSTEMS

Jerzy Iwanciw, Krzysztof Pytel, Elżbieta Kawecka-Cebula, Magdalena Kostołowska Faculty of Metals Faculty of Metals EngEngineeringineering & Industrial Comp& Industrial Comp.. Science,Science,

AGH University of AGH University of Science and Technology Science and Technology at Krakowat Krakow

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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)• ...

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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

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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)

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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 Szyszkowski’s (Pelton’s) models for surface active components:

• Butler’s model:

]1ln[)( iiii

mFe aKRTTTA

bk

sk

kbk

sk

kk S

RT

x

x

S

RT

lnln

)()lnln(0

00BAi

n

iBABBAABBAA

Ex xxLxxxxxxRTxx

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Liquid-Liquid Interfacial Tension Models

• Linear and polynomial models

• Calphad and Redlich-Kistler model

• Excess model

• Szyszkowski’s model

• Butler’s model

• Girifalco-Good’s model

where: = f(X1...Xi, T)

Similar to the surface tension

2/1/ )(2 smsmsm

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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

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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

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

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Configuration of Program for Visualisation of Steel Surface Tension

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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 :

])[%)5.731000

exp(1ln(0007096.0])[%)4.1949500

exp(1ln(011306.0

])[%)2.726300

exp(1ln(])[%006035.005918.0(43.07.2674]/[

CT

TOT

T

ST

TCTmmN

])1046000

exp(1ln[0121.0])1950000

exp(1ln[0165.0

])25.719800

exp(1ln[])[%004895.007236.0(43.02699)/(

CO

S

aT

TaT

T

aT

TCTmmN

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Simplified Surface Tension Model for ferritic steels, austenitic steels

and cast irons• Database range

Model fitting the data over all database

600

800

1000

1200

1400

1600

1800

2000

600 800 1000 1200 1400 1600 1800 2000

Experimental surface tension, mN/m

Mo

de

l su

rfa

ce t

en

sio

n,

mN

/mreference line

cast irons (0-0.5%S)

Fe-C (0.06%S)

Fe-C (1.1%Si)

cast iron (0.02-0.2%S)

ferritic & austenitic steels

Fe pure

Number of points = 351 St. Dev. = 54.9 mN/mr^2 = 0.9672

Database for Fe-base melts

600

800

1000

1200

1400

1600

1800

2000

1500 1700 1900 2100 2300

Temperature, K

Su

rfa

ce t

en

sio

n,

mN

/m

experimental

model

austenitic & ferrituic steels

Fe-C (0.06%S)cast irons

Fe pure

• Model fitting

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Visualisation of Liquid Steel Surface Tension

• Surface tension of RSt37 grade at 1510 °C

• d /dT dependence of RSt37 grade at 1510 °C

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Optimal Slag Surface Tension Model

i Al2O3 CaO FeO MgO MnO Na2O P2O5 SiO2 TiO2 CaF2Sigma0 768.4 614.9 -199.2 298 1147.9 433.3 80.8 446.9 482.3 -883.7dSig/dT -0.056 0.012 0.457 0.1158 -0.2777 -0.0814 -0.038 -0.0944 -0.0546 0.691

j \ i Al2O3 CaO FeO MgO MnO Na2O P2O5 SiO2 TiO2 CaF2Al2O3 -619.2 332.7 -726.7 -784.68 -1211.33 3.25E+10 63.246 -1495.46 -665.545CaO -243.1 784.07 -2500.9 -191.407 -25899.6 4.081 -869838 -569.458FeO -868 -170.15 -2029.73 -3233.78 -166.89 -152.46 -523.607MgO -4142.2 -30.9893 1.09E+10 481.56 -5.60E+08 913.82MnO -17214.5 208476.5 -288.022 -272.456 10977.1Na2O 1.29E+11 1694.93 1.23E+09 -3834.77P2O5 17040.95 6.80E+08SiO2 -65.7082 -961.592TiO2 -6.80E+08CaF2

Parameters ai,j

i ij

jijiiii

oi XXXdTTd ,)/(

where: – the surface tension of the slag, mN/m, i

0 – the extrapolated surface tension of “i” component at 00K, di/dT – the temperature coefficient of the surface tension of „i” component, i,j

– the interaction parameters, T – temperature in K, Xi, Xj – the mole fractions of the slag components.

A fragment of the model coefficients

matrix

( 10 main components,

st. dev. = 33mN/m)

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Visualisation of Slag Surface Tension

• CaO-Al2O3-SiO2 system • CCS mould slag

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Metal-Slag Interfacial Tension Models (I)

• Linear model (31 variables):st. dev. = 134 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 %Fe2O3 + 53.6515 %Cr2O3 ‑ 3.8361 %TiO2

For slags without Fe2O3, Cr2O3 and

TiO2 :

= 0.7167+0.003927 %FeO

= ~ 0.7167 + 0.3537 XFeO

Interfacial tension between metal and slag

y = 0.7402x + 228.13

R2 = 0.7402st.dev = 134 mN/m

y = 0.595x + 357.92

R2 = 0.559st.dev = 170 mN/m

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 400 800 1200 1600 2000

Experimental interfacial tension, mN/m

Mod

el in

terfa

cial

tens

ion,

mN/

msig_MS model: lin-31v

sig_MS model = sig_M-sig_M 0̂.5

Linear (sig_MS model: lin-31v)

Linear (sig_M-sig_M 0̂.5)

Database: 755 exp. points, variables: - 13 metal comp., - 17 slag comp., - temperature.

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Metal-Slag Interfacial Tension Models (II)

• Excess model (755 exp. points, 243 variables):st. dev. = 84 mN/m

(after equilibration of metal-slag data)

y = 0.9276x + 68.056

R2 = 0.9276

0

300

600

900

1200

1500

1800

0 300 600 900 1200 1500 1800

Experimental interfacial tension, mN/m

Mo

del

inte

rfac

ial t

ensi

on

, mN

/m

model 243 variables

trend line

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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 Cr2O3 .

• 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.

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Thank you for

your attention

The study was sponsored by KBN Grant No 3 T08B 023 28