Correlations in randomly stacked solids.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• Sphere packing is a fundamental problem with historical roots, leading to dense structures like face-centered-cubic (FCC) and hexagonal-close-packed (HCP).
• Barlow stackings represent maximal-density structures, while Torquato-Stillinger stackings are proposed for minimal density while maintaining stability.
• Understanding layer correlations is crucial for predicting the properties and formation of stacked solids.

Purpose of the Study:

• To characterize layer correlations in random Barlow and Torquato-Stillinger stacking families.
• To investigate the effect of chirality bias on layer correlations in Barlow stackings.
• To relate stacking structures to models in statistical mechanics for analytical insights.

Main Methods:

• Utilizing the Hägg code to map Barlow stackings to a one-dimensional Ising magnet model.
• Relating layer correlation functions to moment-generating functions of the Ising model.
• Analyzing Torquato-Stillinger stackings by mapping them to a combined Ising and three-state Potts model.

Main Results:

• Random Barlow stackings exhibit exponentially decaying layer correlations.
• Introducing a chirality bias, favoring FCC ordering, still results in exponential decay, indicating no long-ranged order.
• Random Torquato-Stillinger stackings also show exponentially decaying correlations, similar in form to Barlow stackings.

Conclusions:

• Layer correlations in both maximal (Barlow) and minimal (Torquato-Stillinger) density stacking families decay exponentially under random conditions.
• Even with a bias towards specific structures like FCC, long-range order is not achieved in these stacking models.
• The findings have implications for the ordering of clusters in stacked solids and for layer-deposition synthesis techniques.