Crystallization statistics, thermal history and glass formation

R. W. Hopper, G. Scherer, D. R. Uhlmann

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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 languageEnglish (US)
Pages (from-to)45-62
Number of pages18
JournalJournal of Non-Crystalline Solids
Issue number1
StatePublished - Apr 1974

All Science Journal Classification (ASJC) codes

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


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