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August 18, 2025Open Access

Hyper–Micro/NanoStructures and SuperHyper–Micro/NanoStructures: A Unified Framework for Multi-Scale Structural Modeling

Key Points

Hyperstructures enable modeling complexities across multiple scales, enhancing material understanding.
NanoStructures, confined to 0.1–100 nm, influence properties, showcasing their critical role in material science.
Theoretical properties of extended microstructures and nanostructures are examined through hyperstructure frameworks.
Understanding these structures may lead to advancements in nanomaterials and their applications.

Abstract

Hyperstructures and their hierarchical extensions 1—SuperHyperStructures—provide a versatile formalism for modeling multi-layered and complex phenomena 2, 3. A MicroStructure is a measurable mapping that assigns to each material point a single local state, representing attributes such as phase, crystal orientation, chemical composition, and porosity at the microscale 4–8. A NanoStructure is a physical feature in which one or more dimensions are confined to the nanoscale range (0.1–100 nm), a constraint that significantly influences the material’s properties and functionality 9–12. Related concepts include Nanofoam 13, 14, Nanomaterials 15–17, Nanohole 18, 19, Nanomesh 20–22, and Nanoparticle 23–25. In this paper, we define extended concepts of both MicroStructure and NanoStructure using the frameworks of HyperStructure and SuperHyperStructure, and examine their theoretical properties.

Hyper–Micro/NanoStructures and SuperHyper–Micro/NanoStructures: A Unified Framework for Multi-Scale Structural Modeling

Key Points

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