Model of banding in diffusive and convective regimes during directional solidification of peritectic systems

Abstract

The formation of banded microstructure in peritectic systems is examined theoretically in both diffusive and convective regimes. A rigorous model is developed in the diffusive regime that describes the non-steady-state growth of alternate solid α and β phase bands with a planar solid-liquid interface. The model is extended to incorporate the effect of convection by assuming that solute diffusion takes place within a boundary layer of constant thickness, with a uniform composition in the mixed liquid zone outside this layer. The model predicts that convection effects in a semi-infinite sample narrow the composition range over which extended banding can occur, and the spacing of bands is reduced compared to the diffusive growth model. In a finite length sample, convection is shown to lead only to the transient formation of bands. In this transient banding regime, only a few bands with a variable width are formed, and this transient banding process can occur over a wide range of compositions inside the two-phase peritectic region. Directional solidification studies in the Pb-Bi system show transient bands and agree qualitatively with these predictions. However, the basic mechanisms of band formation observed in this system is found to be significantly different from the one assumed in the model. A new mechanisms of banding is proposed in which continuous growth of both phases is present instead of nucleation at the boundary of the pre-existing phase. This mechanism yields an oscillatory structure with a shorter spatial periodicity than the band spacing predicted by the purely diffusive or boundary layer convective models.