(Ag,Cu)₂(S,Se,Te)-Based Auxetic Thermoelectric Metamaterials for Efficient and Durable Power Generation

Thermoelectric (TE) power generation, which converts waste heat into electricity, has gained significant attention as a solution to global challenges like fossil fuel depletion and the need for sustainable energy. The efficiency of thermoelectric generators (TEGs) depends on the performance of the TE material and the temperature gradient across the device. To enhance performance, research has focused on improving TE materials, measured by the figure of merit ZT=S2σT/κ where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity, and T is the absolute temperature. However, sustainable energy recovery in real-world conditions requires additional considerations, such as adaptability to dynamic heat source surfaces and durability under operational stress.
Many heat sources, like exhaust pipes and heat exchangers, feature curved surfaces and are subjected to mechanical vibrations. Conventional TE legs are produced through zone melting and hot pressing of ingots, followed by dicing, limiting TEGs to planar layouts. These layouts hinder heat transfer due to poor contact with irregular surfaces. Furthermore, brittle materials like Bi2Te3, PbTe, and SnSe are prone to failure from vibrations. A key challenge is improving the deformability of TE materials without sacrificing efficiency, allowing adaptation to complex surfaces and enhancing resistance to mechanical stress.
Mechanical metamaterials offer promising solutions with exceptional mechanical properties based on their designed topology rather than intrinsic material properties. These materials are applied in areas like strain sensing, vibration damping, and heat exchangers. Among them, auxetic metamaterials stand out with their negative Poisson’s ratio (NPR, ν<0), which allows them to expand laterally and perpendicularly under tension. This behavior enhances adaptability to dynamic surfaces and improves shear resistance, energy absorption, and fracture resistance.
Ag₂S-based compounds have emerged as promising ductile semiconductors, generating interest for flexible electronics and TE devices. High-entropy alloys, such as (Ag,Cu)₂(S,Se,Te), improve strength and ductility through solid solution strengthening while also enhancing TE efficiency. These materials offer excellent potential for deformable and efficient TE devices.
This study introduces a structural design strategy for auxetic metamaterials composed of high-entropy (Ag,Cu)₂(S,Se,Te) ductile TE materials. We employed 3D finite element method (FEM) simulations and experimentally validated the designs using extrusion-based 3D printing. Comparative FEM models included re-entrant auxetic, honeycomb, and lattice structures, allowing us to evaluate mechanical deformability. We conducted parametric studies to identify the best-performing auxetic structures.
The 3D-printed (Ag,Cu)₂(S,Se,Te) alloy achieved a ZT value of 1.15 at 950 K, with improved mechanical strength and ductility. These designs were further validated by testing their bending deformability on complex curved surfaces, such as monoclastic, synclastic, and monkey saddle geometries, along with vibrational stability. Among the tested designs, the auxetic structure demonstrated superior adaptability and stability.
Finally, an auxetic TEG was mounted on a synclastic curved heat source to evaluate its power generation capability. The device achieved a power density of 6.3 mW/cm² at a temperature difference of 155 K, confirming that our approach enhances the adaptability and durability of TEGs on irregular, dynamic heat sources.