### Abstract

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_{I} with respect to the concentration of Y, c_{Y} and the concentration of Z, c_{Z}: In the case of ∂^{2}f _{I}/∂c_{Y}∂c_{Z} > 0, the value of c _{Z} along the trajectory of the peak top of the Y decreases with time. When ∂^{2}f_{I}/∂c_{Z}∂c_{Y} < 0 at 0 ≤ t < ∞, peaks of c_{Z} formed at peak tops of Y. The amplitudes of these peaks increase with time. If ∂^{2}f _{I}/∂c_{Y}∂c_{Z} < 0 at 0 ≤ t < t_{0} and ∂^{2}f_{I}/∂c_{Y}∂ c_{Z} > 0 at t_{0} < t < ∞, bifurcation of peaks occurs at the later stage.

Original language | English |
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Pages (from-to) | 808-812 |

Number of pages | 5 |

Journal | Journal of the Physical Society of Japan |

Volume | 71 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 Mar |

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### Keywords

- Asymptotic behaviour
- Cahn-Hilliard equation
- Phase separation
- Ternary alloy system

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*71*(3), 808-812. https://doi.org/10.1143/JPSJ.71.808