A hybrid topological and shape-matching approach for structure analysis

Area of Science:

• Materials Science
• Crystallography
• Condensed Matter Physics

Background:

• Crystalline and amorphous materials possess distinct long-range and local order.
• Deformations and defects are crucial in processes like plasticity, ice formation, and crystal growth.
• Topological network partitioning is a common method for classifying crystal structures, but fails for non-convex blocks.

Purpose of the Study:

• To introduce a novel framework, Topological Unit Matching (TUM), for efficient shape-matching and structural analysis.
• To develop a general algorithm capable of quantifying deformations and identifying crystal grains in various ice polymorphs.
• To improve the identification of complex ice structures, including quasi-one-dimensional ice and topological defects.

Main Methods:

• Development of the Topological Unit Matching (TUM) framework, leveraging topological criteria for shape matching.
• Application of TUM to quantify deformations and determine grains in bulk and confined ice polymorphs.
• Analysis of supercooled water nanoparticles, amorphous ice, and phase transitions in ice nanotubes.

Main Results:

• TUM provides an efficient shape-matching procedure, overcoming limitations of convex hull-based methods.
• The framework accurately quantifies deformations and identifies ice polymorphs, including quasi-one-dimensional ice with deformed prism blocks.
• TUM demonstrates superiority in resolving topological defect structures with minimal parameterization.

Conclusions:

• Topological Unit Matching (TUM) offers a robust and generalizable method for analyzing crystalline and amorphous materials.
• TUM significantly enhances the identification and characterization of complex ice structures and their defects.
• This framework has broad applicability in studying phase transitions and material properties under various conditions.