On secondary dendrite arm coarsening in peritectic solidification

A model for isothermal coarsening of secondary dendrite arms in peritectic reaction and transformation (liquid + primary-phase → peritectic-phase) is proposed to evaluate the secondary dendrite arm spacing (λ₂) of the primary phase in directional solidification of peritectic alloys. The model defines three stages for thin-arm dissolution (or thick-arm coarsening), i.e. the initial, intermediate and final stages: The initial thin-arm dissolution through the primary phase is sustained solely by the Gibbs-Thomson effect; the intermediate thin-arm dissolution through the peritectic phase is driven by Gibbs-Thomson effect but retarded by the peritectic reaction and transformation; the final dissolution through the primary and peritectic phases is enhanced by the Gibbs-Thomson effect and the phase transformation. The kinetics of peritectic reaction and transformation were found to be crucial to determine the thin-arm dissolution, which were characterized by the reaction constant (f) and the diffusion coefficient of solute in solid peritectic-phase (D_S), respectively. The present model shows that λ₂ V^m is constant for a given Pb-Bi peritectic alloy, where V is growth velocity, and the factor, m, ranges from 1/3 to 1/2, rather than that normally observed (e.g. 1/3) for single-phase solidification. It is also notable that the calculated λ₂ for a Zn-7.37 wt.% Cu peritectic alloy was reasonably consistent with our earlier experiments for various growth velocities.