Nonlinear Interface Stability Analysis of Alloy Solidification Including Effects of Surface Energy

The morphologoical stability of the solid-liquid interface in the solidification of a dilute binary alloy is analyzed using linear and nonlinear perturbation analyses. The energy-balance condition at the interface is modified to incorporate the effects of surface excess energy. The Landau coefficient, which represents the nonlinear growth rate, is calculated using the direct method of undetermined coefficients. The results are applied to practical metallic and nonmetallic systems. The proposed surface energy correction is found to be significant at large growth velocities and low frequencies of interface perturbation. Linear stability is obtained over a larger range of frequencies and velocities; while the correction restricts the frequency range of nonlinear stability, the Landau coefficients obtained are larger and indicate greater stability over this range