Numerical simulation of phase separation in Fe-Cr binary and Fe-Cr-Mo ternary alloys with use of the Cahn-Hilliard equation

Abstract

The Cahn-Hilliard nonlinear diffusion equation for a binary alloy system was extended to a ternary system. Numerical model based on the Cahn-Hilliard equation for multicomponent system was applied to the prediction of microstructural evolutions in Fe-Cr binary and Fe-Cr-Mo ternary alloys. The free energy of the system was approximated by the regular solution model. In an Fe-40at%Cr binary alloy, the Cr composition profile at 800 K shows a modulated structure with the wave length of about 4 nm. This result is consistent with those of reported Atom-probe FIM analyses. In an Fe-40at%Cr-3at%Mo ternary alloys, the wave lengths of Cr and Mo composition profiles were similar to that for the binary alloy. However, the decrease in the Mo composition was observed at the peak position of Cr composition because of the repulsive interaction of Cr and Mo atoms.