Application of the quasi-subsubregular solution model: The iron-carbon system
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I.
INTRODUCTION
MOST of the previously published reports
on the modeling of the thermodynamic properties of interstitial alloys have used solution models based on the presence of a "sublattice" of the interstitial component within the lattice structure of the base element. Such an example is the Fe-C system, as recently illustrated by Gustafson m and Ohtani et al.[21 among others. However, increasing interest in modeling the phase diagrams and thermodynamic properties of multicomponent solutions (which may contain one or more interstitial elements) suggests some value in attempting to use, instead, one of the many models proposed for substitutional solutions in order to avoid dealing with multiple formalisms and to limit the number of needed data bases. One of the more recent substitutional solution models is the quasi-subsubregular solution model developed by Chuang et al.,[3~ which has been successfully used to generate equilibrium phase diagrams in the Cu-Fe, Ga-Sb, and In-Sb systems, t4J However, the model has not yet been used to generate dilute-solution phase diagrams or to assess interstitialsolution thermodynamics. The presence of a considerable body of experimental data on the thermodynamic properties of various phases of the iron-carbon system offers an opportunity to perform such an assessment and, thus, to further test the applicability of this model.
II.
THE
QUASI-SUBSUBREGULAR
MODEL
The .quasi-subsubregular solution model is related to the subsubregular model originally illustrated by Sharkey et al. is] This latter formalism generates integral solution excess free energies of mixing in a binary solution through a three-parameter polynomial expression: A G ~ = XIX2(XIA21 q- X2A12 q- XIX2BI2 )
[1]
M A R K E. SCHLESINGER, Assistant Professor, is with the Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112. Manuscript submitted February 16, 1989. METALLURGICAL TRANSACTIONS A
where X1 and X2 are the component mole fractions and A2], AI2, and BL2 are composition- and temperatureindependent parameters determined by the choice of components. Chuang et al. t31 have developed a similar expression for binary systems: A G ~ = RTX1X2(XlW21 + X2Wl2 -- 4X1X2Vl2 )
[2]
Equation [2] can be reassessed to yield expressions for partial molar excess free energies of mixing: - E = RTX~[2X1w21 + (1 AGM, -
-
2Xl)W12
4(2 - 3X0vl2]
[3]
Ad~t: = RTX~[2X2w,2 + (1 - 2X2)w2~
- 4(2 - 3X2)v12 ]
[4]
The addition of the RT term to the right-hand side of Eqs. [2] through [4] results in the advantage of w21, w12, and v12 becoming dimensionless parameters. The use of three parameters in this type of expression rather than the single constant proposed in the regular solution model has been shown to deal adequately with compositional nonregularity in a solution at a given temperature tSl but does not deal with temperature-related anomalies. Chuang et al.[31 have included a temperature dependence for their subsubregular solution model parameters: W21 = A 1 / T + A2
[51
B2
[6]
YI2 = C1
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