Mapping the Configuration Space of Half-Heusler Compounds via Subspace Identification for Thermoelectric Materials Discovery

Half-Heuslers are a promising family for thermoelectric (TE) applications, yet only a small fraction of their potential chemistries has been experimentally explored. In this work, we introduce a distinct computational high-throughput screening approach designed to identify underexplored yet promising material subspaces, and apply it to half-Heusler thermoelectrics. We analyze 1,126 half-Heuslers satisfying the $``$18 valence electron rule $''$, including 332 predicted to be semiconductors, using electronic structure calculations, semi-empirical transport models, and thermoelectric quality factor $\beta$. Unlike conventional filtering workflows, our approach employs statistical analysis of candidate material groups to uncover trends in their collective behavior, providing robust insights and minimizing reliance on uncertain predictions for individual compounds. Our findings link $n$-type performance to ultra-high mobility at conduction band edges and $p$-type performance to high band degeneracy. Statistical correlations reveal elemental subspaces associated with high $\beta$. We identify two primary (Y- and Zr-containing) and two secondary (Au- and Ir-containing) subspaces that reinforce key physical design principles, making them promising candidates for further exploration. These recommendations align with previous experimental results on yttrium pnictides. Inspired by these insights, we synthesize and characterize rare-earth gold stannides (REAuSn), finding Sc$_{0.5}$Lu$_{0.5}$AuSn to exhibit low thermal conductivity (0.9-2.3 Wm$^{-1}$K$^{-1}$ at 650 K). This work demonstrates alternative strategies for high throughput screening when using approximate but unbiased models, and offers predictive tools and design strategies for optimizing half-Heusler chemistries for TE performance.