Simultaneous optimization of thermochemical data for liquid iron alloys containing C, N, Ti, Si, Mn, S, and P
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INTRODUCTION
THE fundamental role thermochemistry plays in the understanding and control of iron making and steelmaking processes has led researchers to carry out extensive studies of phase equilibria involving the iron-rich liquid phase. Most of these studies have involved either binary or ternary solutions from which interaction parameters of the solutes and standard Gibbs energies of formation of the precipitates were calculated. Each study produces its own set of data, which may agree or disagree with the others, the uncertainties in these hightemperature experiments sometimes producing significant discrepancies. This situation has led to critical reviews of the experimental results and to the publication of compilations of proposed data believed to be the best. Unfortunately, there are disagreements among some of the compilations. For example, the value of the carbon-carbon firstorder interaction parameter, ec.c, at 1873 K proposed by Lupis m is 6.9 whereas that from the Steelmaking Data Sourcebook (SDS) t2] is 12.8. Furthermore, inconsistencies can arise within the same publication. Two different values for the titanium activity coefficient at infinite dilution, 7~i, were cited by SDS tzl to calculate the standard Gibbs energy of formation of TiC and TiN in liquid iron. These two values, 0.017 and 0.050 respectively, yield a difference of approximately 17 kJ/mol at 1873 K for the change in standard states from pure liquid titanium to titanium at infinite dilution in liquid iron. Thermochemical data describing the properties of solutions can be obtained by the CALPHAD (CALculation of PHAse Diagrams) method. ~3~ From the modeling of Gibbs energy functions, a number of model parameters have been optimized by least-squares fitting of the experimental information to generate phase diagrams. To this effect, numerous unary, binary, ternary, and higherorder systems have been assessed and the results published in various journals. These systems have often DOMINIQUE BOUCHARD, formerly Graduate Student, l~cole Polytechnique de Montrral, is Postdoctoral Fellow, Institute for Materials Research, McMaster University, Hamilton, ON L8S 4L7, Canada. CHRISTOPHER W. BALE, Professor, Drpartement de Mrtallurgie et de Grnie des Mat6riaux, and Co-Director, Centre de Recherche en Calcul Thermochimique, is with l~cole Polytechnique de Montrral, C.P. 6079, Succ. A, Montrral, PQ H3C 3A7, Canada. Manuscript submitted June 7, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS B
been treated independently with the optimized parameters of lower-order systems used as input and held fixed to optimize parameters in higher-order systems. However, the uncertainties in the experimental measurements involving a binary system, for example Fe-C, are such that it is inappropriate to hold the binary parameters constant when optimizing ternary parameters in systems such as Fe-C-Ti, Fe-C-Mn, Fe-C-N, etc. One of the consequences of treating systems independently is that an accurate reproduction of experimental measurements of higher-order systems some
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