Exploration of Spinodal Decomposition in Multi-Principal Element Alloys (MPEAs) using CALPHAD Modeling

TL;DR

This paper develops a CALPHAD-based framework using the Hessian of free energy to analyze spinodal decomposition in multi-principal element alloys, providing insights into their phase stability and microstructure design.

Contribution

It introduces a novel CALPHAD modeling approach employing the Hessian and Gibbs simplex geometry to study spinodal decomposition in multicomponent alloys.

Findings

Identified specific concentration modulations leading to instability in MPEAs.

Applied the framework to various MPEAs, revealing their stability characteristics.

Provided a method to guide microstructure engineering in complex alloys.

Abstract

Researchers attributed the orderly arranged nanoscale phases observed in many multi-principal element alloys (MPEAs) to spinodal/spinodal-mediated phase transformation pathways. However, spinodal decomposition is not well understood in multicomponent systems. Although the theoretical background is available, CALPHAD databases were not used to explore the miscibility gap in MPEAs. In this work, we develop a CALPHAD framework utilizing the Hessian of free energy to study the stability of solid solutions in MPEAs. In particular, we utilize the geometry of higher dimensional Gibbs simplex in conjunction with the Hessian to calculate concentration modulations in early stages of spinodal decomposition. We apply this framework to a diverse set of multi-phase MPEAs that have been studied in the literature including TiZrNbTa (BCC/BCC), Fe15Co15Ni20Mn20Cu30 (FCC/FCC), Al0.5NbTa0.8Ti1.5V0.2Zr (BCC/B2), AlCo0.4Cr0.6FeNi (BCC/B2) and Al0.5Cr0.9FeNi2.5V0.2 (FCC/L12). We show that the MPEA systems are unstable only to certain concentration modulations which could be further explored to design microstructurally engineered alloys.