### Abstract

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 f_{1} with respect to the concentration of X, c_{X} and the concentration of Y, c_{Y}, f′_{XY}≡∂^{2}f _{1}/∂_{CX}∂_{CY}. If f′_{XY} > 0 the value of c_{Y} along the trajectory of the peak top of Y decreases with time. When f′_{XY} < 0 at 0 ≤ t < t _{0} and f′_{XY} > 0 at t_{0} < t < ∞, peaks of c_{Y} 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 < t_{0} and f′_{XY}0 at t_{0} < t < ∞, peaks of c_{Y} formed at the peak tops of Y at the initial stage. Bifurcation of peaks occurs. The concentration of the major element, c_{X}, along the trajectory of its peak increases with time regardless of the sign of f′_{XY}.

Original language | English |
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Pages (from-to) | 1273-1277 |

Number of pages | 5 |

Journal | Intermetallics |

Volume | 11 |

Issue number | 11-12 SPEC. ISS |

DOIs | |

Publication status | Published - 2003 Nov |

### Fingerprint

### Keywords

- A. Ternary alloy systems
- B. Phase transformations

### ASJC Scopus subject areas

- Metals and Alloys

### Cite this

*Intermetallics*,

*11*(11-12 SPEC. ISS), 1273-1277. https://doi.org/10.1016/S0966-9795(03)00168-7

**Kinetics of phase separation in iron-based ternary alloys. I. Theoretical analysis of phase separation behavior in iron-based ternary alloys.** / Aoki, T.; Saito, Y.; Suwa, Y.

Research output: Contribution to journal › Article

*Intermetallics*, vol. 11, no. 11-12 SPEC. ISS, pp. 1273-1277. https://doi.org/10.1016/S0966-9795(03)00168-7

}

TY - JOUR

T1 - Kinetics of phase separation in iron-based ternary alloys. I. Theoretical analysis of phase separation behavior in iron-based ternary alloys

AU - Aoki, T.

AU - Saito, Y.

AU - Suwa, Y.

PY - 2003/11

Y1 - 2003/11

N2 - 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≡∂2f 1/∂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 < t 0 and f′XY > 0 at t0 < 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 < t0 and f′XY0 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.

AB - 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≡∂2f 1/∂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 < t 0 and f′XY > 0 at t0 < 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 < t0 and f′XY0 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.

KW - A. Ternary alloy systems

KW - B. Phase transformations

UR - http://www.scopus.com/inward/record.url?scp=0142153853&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142153853&partnerID=8YFLogxK

U2 - 10.1016/S0966-9795(03)00168-7

DO - 10.1016/S0966-9795(03)00168-7

M3 - Article

VL - 11

SP - 1273

EP - 1277

JO - Intermetallics

JF - Intermetallics

SN - 0966-9795

IS - 11-12 SPEC. ISS

ER -