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Abstract
Modeling free dendritic growth in supercooled alloys is a critical requirement in controlling the microstructure of materials during rapid solidification processing of materials. Recent models developed to predict the growth of a dendrite in a highly supercooled melt adopt modifications that account for the interface kinetics and thermodynamics at high interface velocities, but the assumptions necessary to simplify the mathematical problem impose inherent restrictions. The assumption of straight phase boundaries adopted in early models often loses validity at high supercoolings, where phase boundaries are often curved. The use of equations with Henrian restrictions, such as the Baker-Cahn equation for the interfacial driving force and the Aziz equation for solute trapping confine these models to dilute solutions. Turnbull's collision-limited linear kinetic equation for interface growth may not apply to large interfacial driving forces. Therefore, a useful application and modification of free dendritic growth models require a thorough understanding of their limitations in producing consistent results.
One of the objectives of this research is to numerically compare the free dendritic growth models derived from the earlier LGK model developed by Lipton et al. The subsequent LKT model by Lipton et al., the TLK model by Trivedi et al., and the BCT model by Boettinger et al., together with a modification of the TLK model, and the DA model by DiVenuti and Ando are compared through application to an Ag-15 mass % Cu alloy. In addition, a new model to extend the DA model is developed by incorporating a thermodynamic solution model for the calculation of the interfacial driving force, thereby eliminating the Baker-Cahn equation that limits the use of the correct BCT and DA models to dilute solutions. Direct computation of the interfacial driving force by calculating a metastable phase diagram for the Ag-Cu system using a temperature dependent subregular solution model is carried out. Comparison of the results of the new model with the DA model confirms that the Baker-Cahn equation is applicable at low solute concentrations. As a future research direction, the new model can be extended to apply to higher concentration alloys by using a new solute trapping equation to further eliminate the dilute solution limitations.
