A thermodynamic model for deoxidation equilibria in steel
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A Thermodynamic Model for Deoxidation Equilibria in Steel IN-HO JUNG, SERGEI A. DECTEROV, and ARTHUR D. PELTON For relatively dilute solutions of oxygen and a deoxidizer M (M ⫽ Al, Cr, Ca, Mg, . . .) in molten Fe, a thermodynamic model is proposed wherein the dissolved species are M*O associates as well as unassociated M and O atoms. At higher metal concentrations, a small amount of M2*O associates also form. Experimental deoxidation equilibria for 15 deoxidizers M are quantitatively reproduced at all temperatures, with only a constant, temperature-independent and composition-independent empirical parameter for the Gibbs energy of formation of each associate. The deoxidation behavior of Mg, Ca, and Ba is elucidated for the first time. The parameters are stored in a database, which can be used to predict complex deoxidation equilibria in multicomponent steels.
I.
INTRODUCTION
THERMODYNAMIC equilibria during the deoxidation of steel are usually treated by the well-known interaction parameter formalism of Wagner.[1] In Al deoxidation, for example, for the equilibrium among dissolved Al and O and pure solid Al2O3, 2Al ⫹ 3O ⫽ Al2O3 (solid)
[1]
the equilibrium constant is written as KAl2O3 ⫽
1 2 # 3 f O) (X 2Al # X O3 )( f Al
[2]
where XAl and XO are the mole fractions of dissolved aluminum and oxygen, and fAl and fO are activity coefficients (relative to the infinite dilution standard state) given by O Al 2 O 2 Al,O ln fAl ⫽Al Al XAl ⫹rAl XAl ⫹AlXO ⫹rAlXO ⫹rAl XAl XO ⫹ p
[3] ln
O 2 Al Al 2 fO ⫽O O XO ⫹rO XO ⫹O XAl ⫹rO XAl
⫹rO,Al O XO XAl ⫹ p [4]
where the and coefficients are called first- and secondorder interaction parameters. Note that OAl ⫽ OAl . Other interaction parameters may be included in the expansion to account for interactions with other alloying elements. In order to reproduce the measured data, it is necessary for O O , Al , and Al the cross-interaction parameters Al O to be very negative in order to account for the very strong attractive interaction between dissolved Al and O atoms. Furthermore, in order to reproduce the measured data over a range of temperatures, the interaction parameters must generally have a strong empirical temperature dependence, usually expressed as ⫽ a ⫹ b/T
[5]
(and ⫽ c ⫹ d/T). By using many empirical parameters, it is often possible to reproduce the measured equilibria over
IN-HO JUNG, Senior Researcher, is with the New Metals Research Team, Research Institute of Industrial Science & Technology (RIST), Pohang, South Korea 790-600. SERGEI A. DECTEROV, Research Professor, and ARTHUR D. PELTON, Professor, are with the CRCT, Ecole Polytechnique de Montreal, Montreal, PQ, Canada H3C 3A7. Contact e-mail: [email protected] Manuscript submitted July 26, 2002. METALLURGICAL AND MATERIALS TRANSACTIONS B
a limited range of temperature and composition. However, the resultant equations extrapolate very poorly outside this range. In the case of very strong deoxidants such as Ca and Mg, the interaction parameter formalism has proven
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