### 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) |
---|---|

Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Journal of Non-Crystalline Solids |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Ceramics and Composites
- Electronic, Optical and Magnetic Materials

### Cite this

*Journal of Non-Crystalline Solids*,

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

**Crystallization statistics, thermal history and glass formation.** / Hopper, R. W.; Scherer, G.; Uhlmann, Donald R.

Research output: Contribution to journal › Article

*Journal of Non-Crystalline Solids*, vol. 15, no. 1, pp. 45-62. https://doi.org/10.1016/0022-3093(74)90110-0

}

TY - JOUR

T1 - Crystallization statistics, thermal history and glass formation

AU - Hopper, R. W.

AU - Scherer, G.

AU - Uhlmann, Donald R

PY - 1974

Y1 - 1974

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0016047248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016047248&partnerID=8YFLogxK

U2 - 10.1016/0022-3093(74)90110-0

DO - 10.1016/0022-3093(74)90110-0

M3 - Article

AN - SCOPUS:0016047248

VL - 15

SP - 45

EP - 62

JO - Journal of Non-Crystalline Solids

JF - Journal of Non-Crystalline Solids

SN - 0022-3093

IS - 1

ER -