Phase Field Modeling of Solidification in Single Component Systems

Using phase field modeling simulation approach we investigate the effect of various parameters on the primary and secondary dendrite arm spacing during directional solidification in a single component system. In previous studies the effect of temperature gradient was assumed to be negligible in the transversal directions with a temperature rate equal to the product of thermal gradient and solidification rate. In our study the temperature field is obtained from energy conservation equation by considering the balance of latent heat released in the regions where solidification occurs and energy dissipation due to directional temperature gradient as boundary condition. In our simulations, we implemented a numerical method that enables the investigation of solidification in larger domains. Specifically, the temperature and the order parameter equations are solved only in the domains close to the solidification front; approach that reduces the computational costs significantly. We investigate the interplay and the effect of thermal gradient, solidification rate, undercooling temperature, and the cooling heat flux on arm spacing. By using a well-established power law relation the primary and secondary arm spacing are calculated for various solidification parameters. We also show that, for large heat fluxes, the secondary arm spacing is almost constant for different undercooling temperatures; behavior that demonstrates the need for correction of the power law relation by including the effect of heat flux.