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The Journal of Chemical Thermodynamics, Volume 60, May 2013, Pages 19-24.
Youn-Bae Kang, Arthur D. Pelton
Graduate Institute of Ferrous Technology (GIFT), Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang, Kyungbuk 790784, South Korea
Centre de Calcul Thermochimique, Département de génie chimique, École Polytechnique de Montréal, C.P. 6079, succursale Centre-ville, Montréal, Québec, Canada
Abstract
The observed “flattened” shape of liquid miscibility gaps in binary alloys is not easily reproduced by a simple Gibbs energy equation involving a random-mixing Bragg–Williams (BW) expression for the configurational entropy and a polynomial expansion of the excess Gibbs energy since short-range-ordering (SRO) is not taken into account. It is shown that accounting for the SRO through a simple application of the modified quasi-chemical model (MQM) in the nearest-neighbour pair approximation is sufficient to provide a good representation of miscibility gaps using only a very few temperature-independent coefficients. For the many systems in which the only data available are the miscibility gap boundaries at lower temperatures, the MQM can therefore provide a good prediction of the gap boundaries at higher temperatures, as well as of the excess enthalpy. Furthermore, the MQM provides a significantly better prediction of the miscibility gap in a ternary system based only upon optimized model parameters of its three binary sub-systems than does the BW polynomial model. For binary systems in which deviations from ideal behaviour are not too large, it is shown that the MQM can be approximated by one additional term in the polynomial BW expression involving no additional empirical coefficients.
