The sections' fractal dimension of grain boundary

Miki Takahashi, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


The fractal dimensional increment of the experimentally dynamic recrystallized grain boundary is proportional to logarithm of Zener-Hollomon parameter. The fractal dimensional increment is defined as the fractal dimension of the grain shape minus the Euclidean dimension of certain transection. To draw the geometrical image of the fractal dimensional increment, the basic rule of the sections' fractal dimension is introduced. The geometrical implication of the fractal dimensional increment is concluded as the fractal dimension of the crossing point distribution on the grain boundary transected by the circumscribing circle or ellipse with the equivalent-area of the grain, and a power law relationship between the Zener-Hollomon parameter and the number of crossing points is found. Therefore, summarizing power laws among the Zener-Hollomon parameter, the differential stress and the number of the crossing points on the grain boundary, the number of crossing points could respond to the differential stress.

Original languageEnglish
Pages (from-to)297-301
Number of pages5
JournalApplied Surface Science
Issue number3-4
Publication statusPublished - 2001 Oct 22


  • Fractal dimensional increment
  • Recrystallized grain boundary
  • The sections' fractal dimension
  • Zener-Hollomon parameter

ASJC Scopus subject areas

  • Chemistry(all)
  • Condensed Matter Physics
  • Physics and Astronomy(all)
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films


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