fig2

Figure 2. (A) Schematic of hierarchical (panoscopic) nanostructuring, where atomic defects, nanoinclusions, and grain boundaries - spanning atomic to macro scales - act as phonon scattering centers across different mean-free-paths (mfps), reducing lattice thermal conductivity^[35]. The lower color plot illustrates typical frequency and mfp contributions to thermal conductivity. Combining various defect types and sizes is essential to target the full phonon spectrum. (B) Nanostructured material schematic showing optimal placement of: (1) Atomistic defects (e.g., vacancies, dopants) for high-frequency phonon scattering, with controlled concentrations to minimize electron scattering; (2) Nanoinclusions of varied sizes and interface types to scatter a wide mfp range while preserving electron transport; and (3) Grain boundaries in nanocrystalline materials for mid- to long-mfp phonon scattering^[36], with secondary phases at boundaries to enhance phonon blocking without significantly impeding electron flow.