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Correlated grain-boundary distributions in two-dimensional networks.

Jeremy K Mason1, Christopher A Schuh

  • 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|June 16, 2007
PubMed
Summary

Crystallographic consistency creates spatial correlations in grain boundaries, even with random grain orientations. This study rigorously analyzes these correlations in polycrystals, providing general analytical solutions for boundary properties.

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Area of Science:

  • Materials Science
  • Crystallography
  • Condensed Matter Physics

Background:

  • Polycrystals exhibit spatial correlations in grain boundary species, influenced by crystallographic consistency requirements.
  • These correlations impact grain boundary network connectivity but are often understood empirically.
  • A rigorous theoretical framework is needed to fully characterize these relationships.

Purpose of the Study:

  • To rigorously analyze spatial correlations in grain boundary species within a model polycrystal.
  • To derive general analytical solutions for grain boundary properties and triple junction distributions.
  • To provide a theoretical foundation for understanding structure-property relationships in polycrystals.

Main Methods:

  • Developed a model for a two-dimensional polycrystal with uncorrelated grain orientations.
  • Derived distributions for misorientations (theta), boundary inclinations (phi), and triple junction misorientations.
  • Utilized arbitrary crystal symmetry and orientation distribution functions for comprehensive analysis.

Main Results:

  • Derived general analytical solutions for the fraction of low-angle boundaries.
  • Obtained general analytical solutions for triple junction distributions.
  • Results align with specific literature cases while offering significant generalization.

Conclusions:

  • Crystallographic consistency fundamentally dictates grain boundary correlations, independent of orientation correlations.
  • The derived analytical solutions provide a powerful tool for predicting polycrystal properties.
  • This work advances the fundamental understanding of grain boundary networks and their impact on material behavior.