Oxide Solubility Minimum in Liquid Fe- M -O Alloy
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PRODUCTION of liquid metal including clean steel requires removal of impurities during the liquid metal processing. In particular, various kinds of gaseous impurities such as O, S, N, and H should be controlled as low as possible before casting of the metal. In a steelmaking process, N and H are removed as gas molecules under low pressure (RH process or vacuum degasser). On the other hand, O and S are removed by chemical reaction using metallic elements that form stable oxide and sulfide. As one of the typical reactions, a deoxidation reaction using Al in liquid Fe is written as: Al2 O3 (s) ¼ 2Al þ 3O;
energy change Dgð1Þ is: Dgð1Þ ¼2gAl þ 3gO gAl2 O3 ðsÞ ¼2ðgAl þ RT ln aAl Þ þ 3ðgO þ RT ln aO Þ
ðgAl2 O3 ðsÞ þ RT ln aAl2 O3 ðsÞ Þ
¼ð2gAl þ 3gO gAl2 O3 ðsÞ Þ þ RT ln
a2Al a3O aAl2 O3 ðsÞ
½2
½3
½4
Dgð1Þ ¼ Dgð1Þ þ RT ln Qð1Þ ½1
where Al and O are Al and O dissolved in the liquid Fe. Dgð1Þ , Dgð1Þ , and Qð1Þ are the Gibbs energy change, the standard Gibbs energy change, and the equilibrium quotient of Reaction [1], respectively. The Gibbs
YOUN-BAE KANG are with the Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, 77 Cheongamro, Namgu, Pohang, Kyungbuk 37673, Republic of Korea and also with the CRCT, Department of Chemical Engineering, E´cole Polytechnique de Montre´al, Montreal, QC, H3C 3A7, Canada. Contact e-mail: [email protected] Manuscript submitted February 18, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS B
¼Dgð1Þ þ RT ln Qð1Þ
½5
where gAl , gO , aAl , and aO are the partial Gibbs energies and the activities of Al and O dissolved in the liquid Fe, gAl and gO are the standard Gibbs energies of the Al and the O, gAl2 O3 ðsÞ and gAl2 O3 ðsÞ are the partial Gibbs energy of Al2 O3 in the deoxidation product and the standard Gibbs energy of Al2 O3 , respectively. If the deoxidation product is a pure solid Al2 O3 , gAl2 O3 ðsÞ ¼ gAl2 O3 ðsÞ and aAl2 O3 ðsÞ ¼ 1. At equilibrium, Dgð1Þ ¼ 0, then Qð1Þ becomes Kð1Þ , the equilibrium constant of Reaction [1]:
Kð1Þ ¼
a2Al a3O aAl2 O3 ðsÞ
ð2g þ 3g g O Al Al2 O3 ðsÞ Þ ½6 ¼ exp RT
The numerical value of each activity depends on the choice of the reference state (the standard Gibbs energy) of each component. Raoultian, Henrian, or 1 wt pct standard state has been widely used. The activities in Eq. [6] are further expressed: Kð1Þ ¼
a2Al a3O aAl2 O3 ðsÞ
¼
ðcAl XAl Þ2 ðcO XO Þ3 aAl2 O3 ðsÞ
½7
Activity coefficients of Al (cAl ) and O (cO ) are often described by Wagner’s interaction parameter formalism[1]: O Al 2 O 2 ln cAl ¼Al Al XAl þ Al XO þ qAl XAl þ qAl XO þ
Al O 2 Al 2 ln cO ¼O O XO þ O XAl þ qO XO þ qO XAl þ
½8
½9
where ji and qji are the first- and second-order interaction parameters, respectively. Under a condition of Al2 O3 saturation (equilibrium with the solid Al2 O3 ), Al and O contents in the liquid Fe can be obtained by solving a series of equations (Eqs. [6] through [9]) along with the known equilibrium constant and the interaction parameters. How much
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