A sole-material hierarchical lattice structure with simultaneous tunable thermal expansion and low-frequency bandgap properties

Hierarchical lattice structures (HLSs) characterized by multiscale and self-similar geometries have attracted increasing attention due to their exceptional mechanical and functional performance. However, almost HLSs focus on bi-material systems, which often suffer from interfacial mismatches. Herein, we propose an HLS composed of a sole-material system of Ti₅Si₃ with an anisotropic characteristic. This design eliminates interfacial mismatches inherent in bi-material systems and leverages geometry-anisotropy coupling to achieve tunable behavior with reliable and predictable performance. A theoretical framework is established to derive the expressions of thermal expansion coefficient (α). Bloch wave theory and eigenfrequency simulations are employed to evaluate bandgap characteristics and wave propagation behavior. Our results demonstrate that the α is significantly reduced at a small internal angle of 30° and high aspect ratio of 15, achieving a minimum value of 2.56 ppm K⁻¹ at the third hierarchical level. Accompanied by the decrease in α values, low-frequency bandgaps below 1000 Hz occur. It is also demonstrated that with the increase in hierarchical level, multiple narrower bandgaps are observed due to altered vibration mode patterns. In contrast with previous bi-material HLSs, our sole-material HLS exhibits not only simple manufacturability but also multi-functionalization.