### Abstract

The formal theory of transformation kinetics describes the volume fraction of a phase transformed in a given time at a given temperature. The basic concepts are extended for isotropic crystal growth in a material having a known thermal history T(r, t). A crystal distribution function ψ(r, t, R) is defined such that the number of crystallites in a volume dυ at r having radii between R and R + dR at time t is ψ(r, t, R) dυ dR. The function ψ contains essentially complete statistical information about the state of crystallinity of a material. Formal expressions for ψ are obtained. Applications are discussed, including predictions of crystallinity when T(r, t) is known; predictions of glass-forming tendencies; experimental determination of nucleation rates; and the determination of the thermal history of a sample from post mortem crystallinity measurements. As an example, ψ(r, t, R) is calculated for a lunar glass composition subjected to a typical laboratory heat treatment.

Original language | English (US) |
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Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Journal of Non-Crystalline Solids |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - Apr 1974 |

Externally published | Yes |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Condensed Matter Physics
- Materials Chemistry

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## Cite this

*Journal of Non-Crystalline Solids*,

*15*(1), 45-62. https://doi.org/10.1016/0022-3093(74)90110-0