Concentration Micro-Field for Lamellar Eutectic Growth
A possibility of a modification of the Jackson-Hunt theory of an oriented structure formation is analysed. A new model for the formation of a concentration field ahead of growing regular lamellae with respect to the solid / liquid interface shape is presented. A coordinate system applied in the model is attached to the solid / liquid interface to be advancing in the z - direction, identically with interface moving at a constant velocity, v . The solution to a diffusion equation is given for the improved formulation of the boundary conditions. The boundary conditions are related to the interplay between the diffusion required for phase separation and the formation of the interphase between both lamellae. The boundary conditions are formulated to establish the stability of lamellar structure formation under steady-state conditions. It is assumed that stable growth of the lamellae is ensured by the separation of concentration fields within a boundary layer ahead of the solid / liquid interfaces of both the α and β " phases. Coupled lamellar growth with the presence of a leading phase protrusion is defined. The general mass balance is analysed for a solute concentration in the liquid, taking into account a planar solid / liquid interface. A local mass balance is also ensured but it requires envisaging a protrusion of the minor eutectic phase. The existence of a lead distance is confirmed experimentally for the (Pb)-(Cd) eutectic system. The difference in undercooling is also considered as a phenomenon associated with the separation of concentration fields and the existence of a protrusion to relax the assumption of an isothermal interface (ideally coupled growth) given by the Hunt and Jackson theory.
D. J. Fisher
W. Wołczyński "Concentration Micro-Field for Lamellar Eutectic Growth", Defect and Diffusion Forum, Vol. 272, pp. 123-138, 2007