Average Atomic Size Mismatch Engineering Achieving High Sulfur Solubility in Bi₂Te₃ for Thermoelectric Power Generation

Doping and alloying are pivotal methods for tailoring the properties of materials. Yet, the Hume-Rothery rule indicates that a significant atomic radius difference between the dopant and matrix atoms leads to low solubility, which limits the enhancement of material performance. Here, we propose a strategy to reduce the average atomic size mismatch ((Formula presented.)), thereby enhancing the solubility of insoluble elements. This strategy is demonstrated in sulfur-alloyed Bi₂Te₃, where co-alloying with Sb and Se reduces (Formula presented.), boosting the solubility of S from 3% to over 16% and effectively widening the bandgap. Meanwhile, configurational entropy enhancement via alloying induces lattice distortion, which significantly strengthens phonon scattering. Directional solidification is employed to form a near-single-crystal texture that boosts carrier mobility. As a result, an ultralow lattice thermal conductivity of 0.49 W m⁻¹ K⁻¹ at 423 K and a remarkable ZT of 0.92 at 450 K are achieved in n-type (Bi₂Te₃)_0.8(Sb₂Se₂S)_0.2. A segmented module realizes an exceptional conversion efficiency of 8.27% at a temperature difference of 290 K, surpassing that of the state-of-the-art Bi₂Te₃-based power generators. This work provides an effective strategy for enhancing the solubility of dopants, offering a pathway for the design of advanced material properties.