Theoretical and numerical investigation of diffusive instabilities in multi-component alloys

TL;DR

This paper develops analytical models and phase-field simulations to understand diffusive instabilities in multicomponent alloys, revealing how microstructural length scales depend on diffusivities and growth velocities during solidification.

Contribution

It introduces new analytical expressions for instability behavior in multicomponent alloys and explores the influence of diffusivities and velocities on microstructural length scale selection.

Findings

Dispersion relations for multicomponent alloys derived analytically.

Microstructural length scales depend on diffusivities and growth velocities.

Validated models with phase-field simulations.

Abstract

Mechanical properties of engineering alloys are strongly correlated to their microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka type is one of the principal mechanisms through which the scale of the microstructural features are determined during solidification. In contrast to binary systems, in multicomponent alloys with arbitrary interdiffusivities, the growth rate as well as the maximally growing wavelengths characterizing these instabilities depend on the the dynamically selected equilibrium tie-lines and the steady state growth velocity. In this study, we derive analytical expressions to characterize the dispersion behavior in isothermally solidified multicomponent (quaternary) alloys for different choices of the inter-diffusivity matrices and confirm our calculations using phase-field simulations. Thereafter, we perform controlled studies to capture and isolate the dependence of instability length scales on solute diffusivities and steady state planar front velocities, which leads to an understanding of the process of length scale selection during the onset of instability for any alloy composition with arbitrary diffusivities, comprising of both independent and coupled diffusion of solutes.