### Abstract

It has been shown that when higher derivative tenns of the diffuse interface expansion are included in the theory of spinodal decomposition, exceptional results are obtained. Within a mean field pair interaction (MFPI) interpretation, the coefficients of terms ▽^{2n}c in the extended diffuse interface expansion eventually become infinite in magnitude. These anomalies are discussed and circumvented in a new analysis of spinodal decomposition. Within the MFPI interpretation a Fourier analysis of the composition is made at an earlier stage in the analysis. The result is a diffusion equation which can be related to the usual diffusion equation of spinodal decomposition. In the early stages, the only change encountered is that the factor κβ^{2} in the amplification factor is replaced by a function K(β). When κ is defined, K(β) approaches κβ^{2} in the limit of small β. When, because of long-range intermolecular potentials, the standard definition of κ does not converge, K(β) remains well defined but no longer increases as β^{2} in the small β limit. This can result in amplification factors which are qualitatively different from those predicted by the standard theory.

Original language | English (US) |
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Pages (from-to) | 35-42 |

Number of pages | 8 |

Journal | Acta Metallurgica |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1973 |

Externally published | Yes |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Acta Metallurgica*,

*21*(1), 35-42. https://doi.org/10.1016/0001-6160(73)90216-2