Thermodynamic Optimization Under Topological Constraints - Balakumar, Thevika (My University, 2008)
Computational thermodynamics is a powerful tool for solving practically important problems including the design of new materials and the analysis of their internal and external stability. This thesis contributes to computational thermodynamics by proposing several practical solutions to eliminate the so-called thermodynamic artifacts rather frequently found in thermodynamic assessments. First, a method is developed to eliminate the artifacts such as inverted miscibility gaps in the liquid phase at high-temperatures and reappearance of the liquid phase at low-temperatures or reappearance of a solid phase at elevated temperatures. This method is based on introducing a sufficiently dense mesh of knots (not related to experimental points utilized in the optimization) and ensuring that specific inequality conditions (topological constraints) governing the appearance of the phase diagram are satisfied in these knots. A feasibility of the approach proposed is exemplified by carrying out a re-optimization of the Mg-Sb system. Generally re-optimization of a system would take months to get the optimized results. Hence, to minimize time needed to get rid of artifacts, two different quick correction methods are developed to eliminate the unrealistic inverted miscibility gap in the liquid phase at elevated temperatures. Both methods employ optimization under topological constraints via controlling the sign of the second derivative of the Gibbs energy. Their applicability is exemplified on the Sn-Zr system. Also, a theoretical study was done on undulate phase boundaries. Usually, an inflection point on a phase boundary is considered as an unambiguous indication that one of the phases participating in the equilibrium is internally unstable, i.e., that it is prone to phase separation. It has been generally assumed that an inflection point may occur only if the thermodynamic model of this phase contains an excess Gibbs energy term. It is shown that in contrast to this assumption, inflection points on a phase boundary may appear when a pure solid component or a stoichiometric binary phase is in equilibrium with the ideal binary solution, which is internally stable. Finally, in addition to the theoretical analysis on undulate phase boundaries, a thermodynamic optimization is done on an imaginary A-B binary system subjected to topological constraints. Since, Thermo-Calc does not have the necessary tools to implement such topological constraints as d^2T/dx^2 >0 or d^2T/dx^2 <0. A Fortran 90 program was developed to make use of these constraints.
Keywords: Computational thermodynamics, materials, temperatures, liquid, solid