Examination of the Zener relationship between grain size and particle dispersion

Taiji Nishizawa, Ikuo Ohnuma, Kiyohito Ishida

Research output: Contribution to journalArticlepeer-review

126 Citations (Scopus)


Zener-Smith proposed the original relation R=4r/3fv in 1948, where R and r are the mean radii of the matrix grains and dispersed particles, and fv is the volume fraction of dispersed particles. They derived the relation under the assumption that the configuration of the grain boundary was independent of particle distribution. In the present work a modified relation R=4r/3fv2/3 has been obtained by assuming that (1) the grain boundary is roughened by particle pinning, and (2) the amplitude of the roughness is λ/2, where λ is the inter-particle distance. Experimental data on the radii of austenite grains and the dispersed cementite particles in high C high Mn steels are shown to agree well with the modified relation.

Original languageEnglish
Pages (from-to)950-956
Number of pages7
JournalMaterials Transactions, JIM
Issue number11
Publication statusPublished - 1997 Nov
Externally publishedYes


  • Computer simulation
  • Correlation model
  • Grain boundary
  • Pinning by particles
  • Zener relation

ASJC Scopus subject areas

  • Engineering(all)


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