Kinetics of phase separation in iron-based ternary alloys. I. Theoretical analysis of phase separation behavior in iron-based ternary alloys

Phase sepation behavior in an Fe-based ternary system was investigated by using a model based on the Cahn–Hilliard equation. The asymptotic behavior of the minor element, Y, in an Fe–X–Y ternary alloy along a trajectory of a peak top of the major element, X, is classified into three groups according to the sign of the second derivative of the chemical free energy f1 with respect to the concentration of X, cX and the concentration of Y, cY, f′XY≡∂2f1∂CX∂CY. If f′XY>0,, the value of cY along the trajectory of the peak top of Y decreases with time. When f′XY<0 at 0⩽t<∞, peaks of cY formed at the peak tops of Y. The amplitute of the peak increases with time. In the case that f′XY<0 at 0⩽t<t0and f′XY>0 at t0<t<∞, peaks of cY formed at the peak tops of Y at the initial stage. Bifurcation of peaks occurs. The concentration of the major element, cX, along the trajectory of its peak increases with time regardless of the sign of f′XY.