The correlation of the thermodynamic properties of wustite by a gaussian based formalism
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I.
INTRODUCTION
EARLIER work on a Gaussian-based model by Esdaile2 was concerned with liquid alloys or those possessing substantially complete solid solubility. For most of these simple systems, it was shown that the precise representation of the isothermal free energy as a function of composition required the addition of a Gaussian term to either of the conventional subregular or Krupkowski equations. For strong compound behavior, however, and particularly over the narrow range of existence of compounds such as wustite, it was anticipated that the Gaussian term could form the major component of the thermodynamic behavior, and in the present case it is shown that no ideal, subregular, or Krupkowski terms are required. The wustite compound phase, as indicated by the phase diagram of Figure 1, was chosen as a test of the Gaussian formalism because of the availability of the meticulous data of Darken and Gurry ~ and the importance of this system to the metallurgy of iron and steel making. As will be seen, the correlation lies in satisfactory agreement with the data of these authors, thus reflecting the applicability of the present model. While wustite exists over a range of composition excluding the formula FeO, it conforms closely to this simple stoichiometry when present in reduced silicate slags. It thus has importance in relation to reactions exchanging metals and oxides during smelting, e.g., the following reaction for tin smelting: Fe (Metal) + SnO (Slag) = Sn (Metal) + FeO (Slag) For this reason, the free energy of formation of metastable FeO is given as a function of temperature from 3,-Fe and oxygen at 1 atm. The equations obtained from the Correlation are first presented, the nature of the Gaussian curve is briefly discussed, the method of correlation is outlined, the model requirements are compared with the data of Darken and Gurry I and, finally, equations representing the free energies and heats of formation of the iron oxides are derived.
II.
THE EQUATIONS USED
It is convenient at this stage to present the equations finally obtained by the present correlation prior to discussing J.D. ESDAILE is Senior Principal Research Scientist, C.S.I.R.O. Division of Mineral Engineering, P.O. Box 312, Clayton, Victoria, 3168, Australia. Manuscript submitted August 31, 1982. METALLURGICAL TRANSACTIONS A
their derivation and application. The standard states chosen for the components are oxygen at 1 atm and 3, iron since most of Darken and Gurry's t work was done in the temperature region in which this form of iron is stable, i.e., 1183 to 1663 K. The activity of 3,-Fe saturated by wustite is taken as unity since Dunwald and Wagner 3 report an oxygen solubility less than 0.01 pct between 800 and 1000 ~ The subscripts Fe, O, and G represent 7-Fe, oxygen, and the Gaussian term, respectively, No is taken as the atomic fraction of oxygen in wustite, AFG is in J/g mol of Fe + O, AffG is in J/g mol, T in Kelvin degrees, and R is 8.3143 J/g mol. A FG = C ( e -h2( 4~-1/2)2 - e -h2/4) [1] A-fiG.o = 1/2RT lnpo2 /
= C ~e -h2
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