Quantifying microstructural evolution via time-dependent reduced-dimension metrics based on hierarchical n-point...

Area of Science:

• Materials Science
• Computational Materials Science
• Statistical Mechanics

Background:

• Characterizing microstructural evolution is crucial for understanding material properties.
• Traditional methods often struggle to capture complex, evolving symmetries.
• Hierarchical n-point polytope functions (P_n) offer a novel approach to structural decomposition.

Purpose of the Study:

• To develop reduced-dimension metrics (Ω_n) for quantifying microstructure distance and evolution pathways.
• To utilize P_n functions to capture evolving polyhedral symmetries during material transformations.
• To demonstrate the utility of Ω_n metrics in analyzing phase separation and thin-film deposition dynamics.

Main Methods:

• Defined nth order metric Ω_n as the L1 norm of P_n functions between two microstructures.
• Applied Ω_n metrics to a 2D binary system undergoing spinodal decomposition.
• Analyzed pattern evolution in phase-separating alloy films using Ω_n(t) metrics.

Main Results:

• Ω_n metrics effectively quantify microstructural evolution and reveal temporal scaling behavior.
• Demonstrated the ability of Ω_n metrics to capture emerging polyhedral symmetries.
• Successfully analyzed complex dynamics in spinodal decomposition and vapor deposition systems.

Conclusions:

• The developed Ω_n metrics provide a powerful tool for analyzing complex microstructural evolution.
• These metrics can establish quantitative processing-structure-property relationships.
• Potential applications include real-time processing control and optimization of heterogeneous materials.