A local orientational order parameter for systems of interacting particles.

Area of Science:

• Materials Science
• Statistical Mechanics
• Information Theory

Background:

• Physical systems are often modeled as interacting particles.
• Quantifying local particle order is crucial but lacks a general method.
• Existing methods like Steinhardt order parameter (Q6) and polyhedral template matching (PTM) have limitations.

Purpose of the Study:

• Introduce a novel quantity, E, to measure the absolute degree of local order around a particle.
• Develop a computationally efficient and informative metric for structural characterization.
• Compare the performance of E against established order parameters.

Main Methods:

• Defined E based on pairwise informational redundancy among particle bonds.
• Analyzed mathematical properties of E, including monotonicity with coordination number.
• Developed an algorithm to compute E for various material structures.
• Applied E to characterize crystalline and glassy systems.

Main Results:

• E increases with bond angle diversity, indicating simpler neighborhoods for higher E.
• E demonstrates intuitive properties, such as monotonicity in Platonic solids.
• E can distinguish a wide range of structures and is conjectured to be maximized by icosahedral geometry.
• E shows comparable resolution to Q6 and robustness to PTM, while being simpler and more informative.

Conclusions:

• The quantity E provides a simple yet powerful tool for quantifying local particle order.
• E offers a valuable alternative to existing order parameters for analyzing material structures.
• The findings support E's utility in distinguishing and characterizing complex systems like crystals and glasses.