Solid–liquid interface stability in the rapid solidification of a binary mixture

A concept of morphological instability of the solid–liquid interface introduced by W. W. Mullins and R. F. Sekerka [J. Appl. Phys. 35, 444 (1964)] is the basis for the evolution of phase interfaces and the formation of solid phase microstructures. We recently re-examined Mullins–Sekerka theory [D. V. Alexandrov and P. K. Galenko, J. Appl. Phys. 136, 055103 (2024); Alexandrov et al., J. Appl. Phys. 137, 125110 (2025)] and showed that the steady-state solutions and range of morphological instability essentially depend on the distance h between the cooling unit and solid–liquid interface. In addition, we showed that temperature perturbations appearing at the cooling unit and propagating through the solid–liquid interface into the liquid phase substantially increase the instability domain. Taking these aspects into account, we re-examine the morphological stability analysis of the planar solid–liquid interface in rapid nonequilibrium solidification of a binary melt. We derived a new dispersion relation that connects the amplification rate of perturbations and their wavenumber. A nonlinear system of equations defining the maximum amplification rate and the corresponding critical wavenumber of perturbations is found too. Numerical analysis of the dispersion relation shows the possibility of either (i) real and positive amplification rate or (ii) complex amplification rate with positive real part. Case (i) describes the morphological perturbations in the range of cellular/dendritic/eutectic microstructures, and case (ii) describes oscillatory perturbations in the range of band structures. Their mixing (morphological and oscillatory modes) corresponds to mixed-type microstructures. We analytically show that the solid–liquid interface is stable when the solidification velocity is larger than the diffusion speed.