On the equivalence of two spinodal decomposition criteria with a case study of Fe${}_{15}$Co${}_{15}$Ni${}_{35}$Cu${}_{35}$ multicomponent alloy

TL;DR

This paper proves the mathematical equivalence of two main methods for predicting spinodal decomposition in multicomponent alloys and validates the findings with experimental results on a specific alloy, enhancing understanding and future research.

Contribution

It demonstrates the equivalence of the REM and PMM methods for spinodal decomposition prediction, enabling cross-application of results and advancing alloy design.

Findings

Mathematically proven the equivalence of REM and PMM methods.

Experimental validation of spinodal decomposition in Fe15Co15Ni35Cu35 alloy.

Enhanced strength and ductility observed in the heat-treated alloy.

Abstract

Spinodal decomposition in multicomponent alloys has attracted increasing attention due to its beneficial effect on their mechanical and functional properties and potential applications. Both based on the Cahn-Hillard equation, the reference element method (REM) and the projection matrix method (PMM) are the two main methods to predict the occurrence of spinodal decomposition in multicomponent alloys. In this work, it is mathematically proven that the two methods are equivalent, and therefore the advanced results based on one method can be applied to the other. Based on these methods, the $Fe{}_{15}$Co${}_{15}$Ni${}_{35}$Cu${}_{35}$ multicomponent alloy is designed as a case study. Experimental results confirm the spinodal decomposition in the heat-treated alloy, and its strength and ductility are simultaneously enhanced. This work can be the pavement for further theoretical and experimental studies on the spinodal decomposition in multicomponent alloys.