Oscillatory Morphological Instabilities During Rapid Solidification A The Role of Diffusion In The Solid

Abstract

ABSTRACTRecent results by Coriell and Sekerka [J. Crystal Growth, 61, 499(1983)] on the oscillatory instability of a planar rapidly solidifying binary melt are extended to include diffusion in the solid phase. Under assumptions equivalent to those made by Coriell and Sekerka, it is shown that no matter how small the diffusion coefficient is in the solid, the system is stable to all oscillatory and non-oscillatory disturbance modes if the modified constitutional supercooling criterion is satisfied and if the nonriequilibrium segregation coefficient is zero. Thus, a range of the non-equilibrium segregation parameter exists where these results allow the possibility of instability, whereas Coriell and Sekerka predict that the system will be stable.System stability is increased for both oscillatory and non-oscillatory modes. It is necessary for the diffusivity ratio Ds/D1 to be nearly 0.1 before oscillatory modes are affected. Both the critical wavelength of the disturbance as well as the oscillation frequency are reduced slightly from the case where diffusion in the solid is ignored.