Kinetics of phase separation in ternary alloys

The asymptotic behavior of the minor element, Z, in a X-Y-Z ternary alloy associated with decomposition of the major element, Y, is classified into three groups according to the sign of the second derivative of the chemical free energy f(1), with respect to the concentration of Y, c(Y) and the concentration of Z, c(Z): In the case of partial derivative(2)f(1)/partial derivativec(Y)partial derivativec(Z) > 0, the value of c(Z) along the trajectory of the peak top of the Y decreases with time. When partial derivative(2)f(1)/partial derivativec(Z)partial derivativec(Y) < 0 at 0 less than or equal to t < infinity, peaks of c(Z) formed at peak tops of Y. The amplitudes of these peaks increase with time. If partial derivative(2)f(1)/partial derivativec(Y)partial derivativec(Z) < 0 at 0 less than or equal to t < t(0) and partial derivative(2)f(1)/partial derivativec(Y)partial derivativec(Z) > 0 at t(0) < t < infinity, bifurcation of peaks occurs at the later stage.