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and Mn1 1 (1/4) O2 5 (3/4) M(n 1 1)1 1 (1/4)MO2 (3
n)


I. INTRODUCTION

and

IT has been suggested that the oxidation-reduction equilibrium for the Cu21/Cu1 couple within glasses and slags can be expressed by either of the following reactions: [1–7]

Cu1 1 (1/4) O2 5 Cu2 1 1 (1/2)O2


[1]

K(1) 5 (Cu21) aO2
1/2 /(Cu1 )PO2 1/4

[2]

log f(Cu21 )/(Cu1 )PO2 1/ 4 g51(3/2) log aO2
1log K(3) [6] In the case of the Fe31/Fe21 couple, corresponding reactions for the oxidation-reduction equilibrium can be written as

or Cu1 1 (1/4) O2 1 (3/2) O2
5 CuO2 2


[3]

K(3) 5 (Cu21)/(Cu1)PO2 1/4 aO2
3/2

[4]

where (Cu1) and (Cu21) are the concentrations of Cu1 and Cu21, respectively, in wt pct, and aO2- is the activity of the oxygen anion. Equations [1] and [3] are for acidic and relatively basic melts, respectively. It should be noted here at this point that conventional wet chemical analysis does not distinguish between CuO22
and Cu21. From Eqs. [2] and [4], one obtains log f(Cu21 )/(Cu1 )PO2 1/ 4 g5
(1/2) log aO2
1 log K(1) [5]

M. NAKASAKI, Graduate Student, M. HASEGAWA, Assistant Professor, and M. IWASE, Professor, are with the Ferrous Metallurgy Research Group, Department of Energy Science and Technology, Kyoto University Kyoto, 606-8501, Japan. Contact e-mail: [email protected] Manuscript submitted June 15, 2006. METALLURGICAL AND MATERIALS TRANSACTIONS B

Fe2 1 1 (1/4) O2 5 Fe31 1 (1/2) O2


[7]

K(7) 5 (Fe31 ) aO2
1/2 /(Fe2 1 ) PO2 1/ 4

[8]

Fe21 1 (1/4) O2 1 (3/2) O2
5 FeO2


[9]

K(9) 5 (Fe31)=(Fe21 ) PO2 1/ 4 aO2
3/2

[10]

or

where (Fe31) and (Fe21) are the concentrations of Fe31 and Fe21, respectively. It should be noted again that conventional wet chemical analysis does not distinguish between FeO2
and Fe31. From Eqs. [8] and [10], one obtains log f(Fe31 )/(Fe21 )PO2 1/ 4 g5
(1/2) log aO2
1 log K(7) [11] and log f(Fe3 1 )/(Fe2 1 )PO2 1=4 g 5 1 (3/2) log aO2
1 log K(9) [12] VOLUME 37B, DECEMBER 2006—949

Although the absolute values of K(1), K(3), K(7), and K(9) are not measurable, a schematic representation can be constructed, as shown in Figure 1, corresponding to Eqs. [5] and [6] and Eqs. [11] and [12]. In this figure, the relationships are based upon the following general reactions: Mn 1 1 (1=4)O2 5 M(n 1 1) 1 1 (1=2)O2


[13]

and Mn 1 1 (1=4)O2 1 (3=2) O2
5 MO2 ð3
nÞ


[14]

where Mn1 corresponds to either Fe21 or Cu1. For acidic melts, Reaction [13] would be predominant; hence, {(Cu21)/(Cu1)PO21/4} and {(Fe31)/(Fe21)PO21/4} should decrease with an increase in basicity or oxygen anion activity (region I of Figure 1). For relatively basic melts, the reverse should hold true, because the oxidation-reduction equilibrium would be prevailed by Reaction [14] (region II of Figure 1). In the previous study,[8] the authors have shown such anticipated variations in {(Cu21)/(Cu1)PO21/4} and {(Fe31)/(Fe21)PO21/4} with melt basicities. For oxide melts with relatively large proportions of amphoteric components, however, one would anticipate region III between regions I and II, as shown in Figure