  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.
