Computer Modeling of the Evolution of Dendrite Microstructure in Binary Alloys During Non-isothermal Solidification

Two-dimensional simulations of the evolution of dendrite microstructure during isothermal and non-isothermal solidifications of a Ni-0.41Cu binary alloy are carried out using the phase-field method. The governing evolution equation for the phase field variable, the solute mole fraction and the temperature are formulated and numerically solved using an explicit finite difference scheme. To make the computations tractable, parallel computing is employed. The results obtained show that under lower cooling rates, the solidification process is controlled by partitioning of the solute between the solid and the liquid at the solid/liquid interface. At high cooling rates, on the other hand, solute trapping takes place and solidification is controlled by the heat extraction rate. An increase in the cooling rate is also found to have a pronounced effect on the dendrite microstructure causing it to change from poorly developed dendrites consisting of only primary stalks, via fully developed dendrites containing secondary and tertiary arms to the diamond-shaped grains with cellular surfaces. These findings are in excellent agreement with experimental observations.