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A formula for the minimal coordination number of a parallel bundle
1Centre for Nonlinear Dynamics, Department of Civil, Environmental and Geomatic Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom. e.starostin@ucl.ac.uk
The Journal of Chemical Physics
|December 3, 2008
Summary
This study provides an exact formula for minimal coordination numbers in parallel rod bundles. It considers optimal thickening in hexagonal and square lattice arrangements.
Area of Science:
- Materials Science
- Condensed Matter Physics
- Crystallography
Background:
- Understanding the packing density and coordination numbers of rod-like structures is crucial in materials science.
- Previous models often simplified the geometry or packing constraints of parallel rod bundles.
Purpose of the Study:
- To derive an exact mathematical formula for the minimal coordination numbers in parallel packed rod bundles.
- To analyze how lattice structure (hexagonal vs. square) influences these coordination numbers.
Main Methods:
- Development of an optimal thickening scenario to define minimal coordination.
- Analytical derivation of the formula based on geometric packing principles.
- Consideration of both hexagonal and square lattice arrangements.
Main Results:
- An exact formula for minimal coordination numbers is established.
- The formula quantifies the relationship between rod geometry and packing.
- Differences in minimal coordination for hexagonal and square lattices are highlighted.
Conclusions:
- The derived formula offers a precise tool for predicting coordination in ordered rod assemblies.
- This work advances the understanding of packing efficiency in anisotropic materials.
- The findings are applicable to fields involving ordered nanostructures and molecular self-assembly.
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