Linear morphological stability analysis of the solid-liquid interface in rapid solidification of a binary system

TL;DR

This paper extends classical morphological stability analysis to include local nonequilibrium effects in rapid solidification, providing analytical insights into interface stability under different thermal gradients and comparing predictions with experimental data.

Contribution

It introduces a local nonequilibrium model for solute diffusion in rapid solidification, enhancing the understanding of interface stability beyond classical theories.

Findings

The model predicts conditions for neutral and absolute stability of the interface.

Stability analysis varies with thermal gradient direction.

Quantitative agreement with experimental critical solute concentrations.

Abstract

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz (Trivedi R, Kurz W. Acta Metall 1986;34:1663), which is advancing the original treatment of morphological stability by Mullins and Sekerka (Mullins WW, Sekerka RF. J Appl Phys 1964;35:444) to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the perturbed interface is given in the presence of the local nonequilibrium solute diffusion. Using the developing local nonequilibrium model of solidification, the self-consistent analysis of linear morphological stability is presented with the attribution to the marginal (neutral) and absolute morphological stability of a rapidly moving interface. Special consideration of the interface stability for the cases of solidification in negative and positive thermal gradients is given. A quantitative comparison of the model predictions for the absolute morphological stability is presented with regard to experimental results of Hoglund and Aziz (Hoglund DE, Aziz MJ. Mat Res Soc Symp Proc 1992;205:325) on critical solute concentration for the interface breakdown during rapid solidification of Si--Sn alloys.