Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (fe-Cr (X=mo, Cu)) Based on Ternary Alloys

Abstract

In this paper, we investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (Fe-Cr-Mo) and (Fe-Cr-Cu) according to analytical and approximate simulation. We study the dynamic of the separation phase for the ternary alloys of iron. The dynamical process of this separation has been described in a mathematical model called the Cahn-Hilliard equation. The minor element behavior in the process has been described by the Cahn-Hilliard equation. It describes the process of phase separation for two components of a binary fluid in ternary alloys of (Fe-Cr-Mo) and (Fe-Cr-Cu). We implement a modified auxiliary equation method and the cubic B-spline scheme on this mathematical model to show the dynamical process of phase separation and the concentration of one of two components in a system. We try obtaining the solitary and approximate solutions of this model to show the relation between the components in this phase. We discuss our solutions in view of a Stefan, Thomas-Windle, and Navier-Stokes models. Whereas, these models describe the motion of viscous fluid substance. (C) 2019 Elsevier B.V. All rights reserved.