ABSTRACT
In this chapter we shall briefly review crystalline growth and the MullinsSekerka instability. As a simplification, we shall assume that the interface is rough at the atomic scale and that there are no forbidden orientations (rendering the surface stiffness γ+γ" negative). We do not consider the case of faceted crystals, a few aspects of which will be discussed in chapter C.VI, dedicated to smectic B plastic crystals. Nevertheless, this chapter is very general in nature and applicable to all kinds of fronts and materials. For instance, it introduces the concepts necessary for understanding most of the solid-liquid interfaces in metals or plastic crystals, and also many of the liquidcrystal interfaces when the associated phase transition is first order. We shall generically term “solid” the most ordered phase and “liquid” the disordered one. In a pure substance, the rate of growth for the solid is given by the kinetics of molecular attachment to the interface and by diffusion of the latent heat rejected during crystallization. When the material is impure (which is generally difficult to avoid), impurity rejection from one phase to the other and its diffusion in the two phases must also be taken into account. The resulting inhomogeneous distribution of the impurity concentration field can destabilize the front in free or directional growth, just as the temperature field does. This is the Mullins and Sekerka instability [1, 2], whose nonlinear evolution can lead to very complex morphologies. The most studied is the dendritic morphology because of its importance in metallurgy. This microstructure, spontaneously appearing during solidification of metals and alloys, influences many of their properties, including mechanical, plastic, thermal, electrical, or chemical, such as corrosion resistance.
