Isothermal solidification in peritectic systems

The peritectic reaction consists in the growth of the peritectic solid phase along the metastable interface between the primary solid phase and the liquid phase. We study theoretically the two-dimensional isothermal peritectic reaction in the limit of small undercoolings using the boundary-integral technique. First, we focus on the case where the liquid phase occupies a semi-infinite space and the peritectic phase presents a finger-like shape. Secondly, we investigate the case where the growth takes place in a channel of liquid phase and the peritectic phase fills the whole channel as a product of the transformation. It is found that for a critical channel width, the velocities of the channel filling and the finger-like solutions are equal. For smaller (larger) widths, the channel filling (finger-like) solution has a larger velocity and is likely to be predominant. This confirms some previously reported qualitative results of time-dependent phase-field calculations (Boussinot et al., 2010) [5]. We also discuss the relevance of our study to directional solidification experiments.