Quantum mechanics

Separation (statistics)

Phase (matter)

Statistics

Metallurgy

Materials science

Chromatography

Differential equation

Separation process

Computer science

Ternary alloy

Ternary operation

Thermodynamics

Physics

Organic chemistry

Alloy

Mathematics

Phase diagram

Mathematical analysis

Spinodal decomposition

Kinetics

Chemistry

Programming language

Partial differential equation

Cahn–Hilliard equation

Binary number

Arithmetic

Physica A Statistical Mechanics and its Applications

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.

Analytical and numerical simulations for the kinetics of phase separation in iron (Fe–Cr–X (X=Mo, Cu)) based on ternary alloys