General concept for a stability analysis of a planar interface under rapid solidification conditions in multi-component alloy systems

Stability analysis of a growing planar solid/liquid interface is not only important for predicting the limit of constitutional supercooling, VC, or the limit of absolute stability, Vabs, but also for the formulation of the so-called marginal stability criterion. This criterion is widely used as an approximate theory for dendritic growth. In this paper, a general concept is introduced which allows analysis of the stability of a planar solid/liquid interface in technical, i.e. multi-component alloys. Capillarity and kinetic effects, and off-equilibrium thermodynamics are taken into account by solving an adequate non-linear system of equations. It is shown that dendrite tip radii and dendrite tip temperatures can be estimated as a function of growth rate and temperature gradient for multi-component alloys. For this the solution of a second linear system of equations coming from the general stability analysis is necessary.