The influence of insoluble spherical particles on the stability of a planar solidifying interface

The doping of a binary substance with a small volume fraction of second phase inclusions is used in the solidification processing of metal matrix composites to improve the material properties of the final cast. In this paper, we investigate the morphological stability of a planar solidifying front that is grown from a melt containing a small volume fraction of insoluble particles. For (phi/k) much less than 1, we demonstrate that the presence of the particles modifies the solutal distribution coefficient as follows: k(eff) = k + (3/2) (k - 1)phi where phi much less than 1 is the volume fraction of particles and k is the segregation coefficient in the absence of particles. The concentration far away from the interface, c(infinity), is chosen as the control parameter. A linear stability analysis of the planar interface reveals that the presence of the particles has a destabilizing influence. The threshold parameters for the onset of the Mullins-Sekerka instability are also altered. The dependence of the critical values of the concentration and corresponding wavenumber is calculated for a Pb-Sn alloy. For phi less than or equal to 0.01, it is found that c(infinity)* approximate to 0.005695-0.01906 phi and alpha* approximate to 14.69-11.81 phi. (C) 1998 Elsevier Science B.V. All rights reserved.