Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm

Abstract

It is often of interest, for a multicomponent system, to identify the low melting compositions at which local minima of the liquidus surface occur. The experimental determination of these minima can be very time-consuming. An alternative is to employ the CALPHAD approach using evaluated thermodynamic databases containing optimized model parameters giving the thermodynamic properties of all phases as functions of composition and temperature. Liquidus temperatures are then calculated by Gibbs free energy minimization algorithms which access the databases. Several such large databases for many multicomponent systems have been developed over the last 40 years, and calculated liquidus temperatures are generally quite accurate. In principle, one could then search for local liquidus minima by simply calculating liquidus temperatures over a compositional grid. In practice, such an approach is prohibitively time-consuming for all but the simplest systems since the required number of grid points is extremely large. In the present article, the FactSage database computing system is coupled with the powerful Mesh Adaptive Direct Search (MADS) algorithm in order to search for and calculate automatically all liquidus minima in a multicomponent system. Sample calculations for a 4-component oxide system, a 7-component chloride system, and a 9-component ferrous alloy system are presented. It is shown that the algorithm is robust and rapid.