Hyperuniformity order metric of Barlow packings

Area of Science:

• Physics
• Materials Science
• Mathematical Sciences

Background:

• Hyperuniformity is key for studying density fluctuations in diverse systems.
• The hyperuniformity order metric (Λ) ranks systems by their ability to suppress these fluctuations.
• Barlow packings, densest sphere packings, are known to be stealthy hyperuniform.

Purpose of the Study:

• To apply the hyperuniformity order metric (Λ) to Barlow packings.
• To investigate the relationship between packing geometry and hyperuniformity.
• To understand the role of local cluster geometry in density fluctuation suppression.

Main Methods:

• Geometric analysis of three classes of Barlow packings (two disordered, one small-period).
• Computation of a lower bound for the scattering wave vector K.
• Calculation of the hyperuniformity order metric (Λ) for each packing class.

Main Results:

• Barlow packings exhibit stealthy hyperuniformity, suppressing scattering up to wave vector K.
• The hyperuniformity order metric (Λ) is approximately linear with the fraction of fcc-like clusters.
• Λ values range between those of hcp and fcc packings, primarily dictated by local cluster geometry.

Conclusions:

• Local cluster geometry is the primary determinant of the hyperuniformity order metric (Λ) in Barlow packings.
• Anisotropic stacking disorder in these packings is a significant factor.
• Future research should focus on anisotropic order metrics and hyperuniformity properties.