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Ring correlations in random networks.

Mahdi Sadjadi1, M F Thorpe2

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Correlations between rings in 2D random network glasses were studied. Geometric distance, not topological, accurately reveals generalized Aboav-Weaire law, showing correlations decay beyond three rings apart.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Computational Materials Science

Background:

  • Random network glasses exhibit complex topological structures.
  • Understanding ring correlations is crucial for material properties.
  • Previous studies faced limitations with topological separation metrics.

Purpose of the Study:

  • To investigate correlations between rings in 2D random network glasses.
  • To determine the appropriate metric for ring separation (topological vs. geometrical).
  • To generalize the Aboav-Weaire law for random networks.

Main Methods:

  • Simulating 2D random network glasses.
  • Analyzing ring structures and their spatial arrangements.
  • Calculating correlations using both topological and geometrical separation.

Main Results:

  • Topological separation yields pseudo-long-range correlations due to charge neutrality issues.
  • Noncircular shells complicate topological distance measurements.
  • Geometrical distance provides accurate correlations, generalizing the Aboav-Weaire law.
  • Ring correlations decay significantly when separated by more than three rings.

Conclusions:

  • Geometric distance is the correct metric for analyzing ring correlations in these systems.
  • The generalized Aboav-Weaire law holds for larger distances in 2D random networks.
  • Ring interactions are short-range, diminishing rapidly with separation.