### Abstract

In the present work the application of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory for the calculation of the volume fraction crystallized is discussed for several particular cases of isothermal transformations. In particular, the following three situations, for which the JMAK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and (3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle formation, finite size effects and non-uniform nucleation lead to a reduction of the crystallization rate. Furthermore, transformations which produce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK f^{4} law arising from time dependent nucleation must include size-dependent growth effects to obtain a logically consistent result.

Original language | English |
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Pages (from-to) | 89-99 |

Number of pages | 11 |

Journal | Journal of Non-Crystalline Solids |

Volume | 219 |

Publication status | Published - Oct 1 1997 |

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### ASJC Scopus subject areas

- Ceramics and Composites
- Electronic, Optical and Magnetic Materials

### Cite this

*Journal of Non-Crystalline Solids*,

*219*, 89-99.

**Crystallization kinetics and the JMAK equation.** / Weinberg, Michael C.; Birnie, Dunbar P; Shneidman, Vitaly A.

Research output: Contribution to journal › Article

*Journal of Non-Crystalline Solids*, vol. 219, pp. 89-99.

}

TY - JOUR

T1 - Crystallization kinetics and the JMAK equation

AU - Weinberg, Michael C.

AU - Birnie, Dunbar P

AU - Shneidman, Vitaly A.

PY - 1997/10/1

Y1 - 1997/10/1

N2 - In the present work the application of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory for the calculation of the volume fraction crystallized is discussed for several particular cases of isothermal transformations. In particular, the following three situations, for which the JMAK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and (3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle formation, finite size effects and non-uniform nucleation lead to a reduction of the crystallization rate. Furthermore, transformations which produce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK f4 law arising from time dependent nucleation must include size-dependent growth effects to obtain a logically consistent result.

AB - In the present work the application of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory for the calculation of the volume fraction crystallized is discussed for several particular cases of isothermal transformations. In particular, the following three situations, for which the JMAK theory requires extensions, are considered: (1) finite size effects and non-uniform nucleation, (2) anisotropic particle formation, and (3) transient nucleation. We present new equations which describe these three situations. In general, we find that anisotropic particle formation, finite size effects and non-uniform nucleation lead to a reduction of the crystallization rate. Furthermore, transformations which produce anisotropic particles are characterized by reduced values of the Avrami exponents. Finally, we demonstrate that corrections to the JMAK f4 law arising from time dependent nucleation must include size-dependent growth effects to obtain a logically consistent result.

UR - http://www.scopus.com/inward/record.url?scp=0031250005&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031250005&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031250005

VL - 219

SP - 89

EP - 99

JO - Journal of Non-Crystalline Solids

JF - Journal of Non-Crystalline Solids

SN - 0022-3093

ER -