Solidification modeling in ternary alloys using the bismuth-lead-tin system as an example

A generalized solidification model used to simulate microsegregation and phase fraction in binary and ternary alloys has been constructed. Unlike other models, the model developed in this work considers diffusion and moving boundaries in each phase present in the microstructure. Additionally, the model developed in this work uses a thermodynamic database to determine the relevant phase equilibria of the system being simulated. For the first time, thermodynamic calculations have been incorporated into ternary solidification calculations that include provisions for multiple moving boundaries and diffusion in multiple phases. The Bi-Pb-Sn system was picked as the model system because it contained eutectic and quasi-peritectic invariant reactions. Due to the limited amount of information available on the microstructures of quasi-peritectic alloys, an experimental study was also completed where microstructures and thermal analysis of alloys in this system were investigated. Specifically, alloys near the high-temperature transitional reaction in the bismuth-lead-tin system have been investigated. The thermal and microstructural analyses of these alloys throughout the bismuth-lead-tin system were found to agree with the published phase diagram. Modeling results have been compared to Lever and Scheil calculations in an attempt to set boundaries for the model presented here by two limiting cases.