### Abstract

A recent mean field pair interaction (MFPI) formulation of the theory of spinodal decomposition is extended with quantitative calculations based on representative pair potentials. These include a nearneighbor potential, a screened impurity potential, and various inverse power law potentials. For the nearneighbor potential, as well as for power law potentials with exponents n ≥ 5, results in accord with the standard theory are obtained. For power law exponents n < 5 (for systems in which long-range intermolecular potentials are important), the amplification factor, R(β), is expected to decrease less rapidly with increasing wavenumber at large β than predicted by the standard theory, and R(β) should not be quadratic in β for small β. The predictions of the MFPI formulation are compared with experimental data on the kinetics of phase separation. A qualitative preference for the MFPI formulation seems indicated: but in quantitative detail, the agreement between theory and experiment still leaves much to be desired. The needs for further extensions of the theory, and most importantly for reliable experimental data on initially homogeneous specimens, are emphasized.

Original language | English (US) |
---|---|

Pages (from-to) | 377-384 |

Number of pages | 8 |

Journal | Acta Metallurgica |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - 1973 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Acta Metallurgica*,

*21*(4), 377-384. https://doi.org/10.1016/0001-6160(73)90193-4

**Spinodal decomposition without diffuse interface theory, II : K(β) and comparisons.** / Hopper, R. W.; Uhlmann, Donald R.

Research output: Contribution to journal › Article

*Acta Metallurgica*, vol. 21, no. 4, pp. 377-384. https://doi.org/10.1016/0001-6160(73)90193-4

}

TY - JOUR

T1 - Spinodal decomposition without diffuse interface theory, II

T2 - K(β) and comparisons

AU - Hopper, R. W.

AU - Uhlmann, Donald R

PY - 1973

Y1 - 1973

N2 - A recent mean field pair interaction (MFPI) formulation of the theory of spinodal decomposition is extended with quantitative calculations based on representative pair potentials. These include a nearneighbor potential, a screened impurity potential, and various inverse power law potentials. For the nearneighbor potential, as well as for power law potentials with exponents n ≥ 5, results in accord with the standard theory are obtained. For power law exponents n < 5 (for systems in which long-range intermolecular potentials are important), the amplification factor, R(β), is expected to decrease less rapidly with increasing wavenumber at large β than predicted by the standard theory, and R(β) should not be quadratic in β for small β. The predictions of the MFPI formulation are compared with experimental data on the kinetics of phase separation. A qualitative preference for the MFPI formulation seems indicated: but in quantitative detail, the agreement between theory and experiment still leaves much to be desired. The needs for further extensions of the theory, and most importantly for reliable experimental data on initially homogeneous specimens, are emphasized.

AB - A recent mean field pair interaction (MFPI) formulation of the theory of spinodal decomposition is extended with quantitative calculations based on representative pair potentials. These include a nearneighbor potential, a screened impurity potential, and various inverse power law potentials. For the nearneighbor potential, as well as for power law potentials with exponents n ≥ 5, results in accord with the standard theory are obtained. For power law exponents n < 5 (for systems in which long-range intermolecular potentials are important), the amplification factor, R(β), is expected to decrease less rapidly with increasing wavenumber at large β than predicted by the standard theory, and R(β) should not be quadratic in β for small β. The predictions of the MFPI formulation are compared with experimental data on the kinetics of phase separation. A qualitative preference for the MFPI formulation seems indicated: but in quantitative detail, the agreement between theory and experiment still leaves much to be desired. The needs for further extensions of the theory, and most importantly for reliable experimental data on initially homogeneous specimens, are emphasized.

UR - http://www.scopus.com/inward/record.url?scp=0015617351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0015617351&partnerID=8YFLogxK

U2 - 10.1016/0001-6160(73)90193-4

DO - 10.1016/0001-6160(73)90193-4

M3 - Article

VL - 21

SP - 377

EP - 384

JO - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

IS - 4

ER -