The solubility of alumina in liquid iron
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I.
A1203 ~,~ 2AI + 30
[1]
been neglected, as is the usual case in the epsilon formalism, which results in a two-parameter quadratic. The two-parameter quadratic of Eq. [3] results in an inappropriate and unrealistic upward curvature for aluminum contents greater than 1.2 pct. It will be shown that this upward curvature predicts an oxygen solubility that decreases with increasing aluminum contents (pct AI > 1.2 pct) much faster than the observed slope of - 2 / 3 . The addition of higher-order interaction coefficients in the "truncated" equation would be expected to correct this upward curvature; however, they are not known. Therefore, an exponential function is proposed, namely,
K = [A112[O]3
[2]
logfo = (logf*) (1 - e-" pet A~)
INTRODUCTION
THE saturation of iron with A1203 can be represented by pct O v s pet A1 solubility curves. Solubility minima t~-41 and maxima t3'4J of oxygen as a function of aluminum content in iron have been established by several researchers, as well as in many other Fe-M-O systems.t4'5'6] The slope of the log pet O v s log pet AI solubility curve prior to the minimum is approximately - 2 / 3 , as established by the equilibrium constant, K, of the dissolution of alumina:
At the minimum, clustering of aluminum around the oxygen interstitials allows the solubility to increase. At the maximum, the oxygen interstitials have all been screened, so that the solubility product drops off again. The slope of log pet O v s log pct AI is approximately - 2 / 3 after the maximum. In this article, it is shown that a two-parameter exponential form of the activity coefficient of oxygen, log fo, as a function of pct A1 represents the A1-O clustering in iron and the solubility of A1203 in iron better than using the first- and second-order interaction coefficients based on the epsilon formalism. II.
ACTIVITY C O E F F I C I E N T F O R M A L I S M S
Activity coefficients of oxygen, fo, and aluminum, fA~, are used to calculate the solubility of alumina in iron. The activity coefficient of oxygen, fo, can be expressed in terms of the epsilon formalism interaction coefficients, e~ l and r Al, in accord with Eq. [3]. logfo = e A~(pct AI) + r~ ~(pct A1)2 + (higher-order terms)
[3]
Equation [3], using interaction coefficients compiled by Sigworth and Elliott, t71 as well as the data of Fruehan, t~l is presented in Figure 1. The higher-order terms have
which uses the two parameters f * and K. Figure 1 compares the quadratic epsilon formalism and the exponential function. The exponential function better describes high aluminum content behavior than the two-parameter quadratic epsilon formalism. There is no physical reason for the increase in log fo shown by the quadratic form of log fo. In Eq. [4], log fo decreases to a saturation value of log f * as pct A1 increases. As oxygen interstitials become screened by aluminum atoms, additional aluminum has less effect on the oxygen activity. This type of saturation behavior is consistent with the clustering and central atom solvation models of St. Pierre and Sh
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