Lattice-to-total thermal conductivity ratio: a phonon-glass electron-crystal descriptor for data-driven thermoelectric design

TL;DR

This work addresses the challenge of identifying high-$ZT$ thermoelectrics by quantifying the PGEC design principle through the lattice-to-total thermal conductivity ratio $\kappa_\mathrm{L}/\kappa$, identifying a near-0.5 cluster for optimized materials. It builds two composition- and temperature-aware predictors for $\kappa_\mathrm{L}$ and $\kappa_\mathrm{e}$ from 108 features (Magpie descriptors + temperature), enabling simultaneous prediction of $\kappa$ and $\kappa_\mathrm{L}/\kappa$. Applying these models to over $10^5$ inorganic compounds yields 2{,}522 ultralow-$\kappa$ candidates and demonstrates generalization to unseen materials, while SHAP analysis provides chemical insights into decoupling phonon and carrier transport. The study also offers practical dopant/alloying strategies to move pristine materials toward $\kappa_\mathrm{L}/\kappa \approx 0.5$, effectively bridging materials discovery and performance optimization within a data-driven PGEC framework.

Abstract

Thermoelectrics (TEs) are promising candidates for energy harvesting with performance quantified by figure of merit, $ZT$. To accelerate the discovery of high-$ZT$ materials, efforts have focused on identifying compounds with low thermal conductivity $κ$. Using a curated dataset of 71,913 entries, we show that high-$ZT$ materials reside not only in the low-$κ$ regime but also cluster near a lattice-to-total thermal conductivity ratio ($κ_\mathrm{L}/κ$) of approximately 0.5, consistent with the phonon-glass electron-crystal design concept. Building on this insight, we construct a framework consisting of two machine learning models for the lattice and electronic components of thermal conductivity that jointly provide both $κ$ and $κ_\mathrm{L}/κ$ for screening and guiding the optimization of TE materials. Among 104,567 compounds screened, our models identify 2,522 ultralow-$κ$ candidates. Follow-up case studies demonstrate that this framework can reliably provide optimization strategies by suggesting new dopants and alloys that shift pristine materials toward the $κ_\mathrm{L}/κ$ approaching 0.5 regime. Ultimately, by integrating rapid screening with PGEC-guided optimization, our data-driven framework effectively bridges the critical gap between materials discovery and performance enhancement.

Figures (7)

• Figure 1: Relationships between $ZT$ and thermal conductivity in the literature from Starrydata. (a) shows the relation between $ZT$, $\kappa_\mathrm{L}$, and $\kappa_\mathrm{e}$ at approximately fixed total $\kappa$. (b) shows $ZT$ versus $\kappa_\mathrm{L}/\kappa$ (lattice-to-total thermal conductivity ratio) for the full curated dataset.
• Figure 2: Relationships between $ZT$ and the lattice-to-total thermal conductivity ratio ($\kappa_\mathrm{L}/\kappa$), for two representative TE material families: (a) CoSb$_3$ and (b) GeTe. Pristine compositions, defined as those whose reduced formula exactly matches the corresponding stoichiometric compound (CoSb$_3$ or GeTe), are shown as filled crosses, while optimized variants are shown as semi-transparent circles.
• Figure 3: Fine-tuned model's performance on the held-out test set for lattice thermal conductivity $\kappa_{\mathrm{L}}$ and electronic thermal conductivity $\kappa_{\mathrm{e}}$.
• Figure 4: Performance on the held-out test set for total thermal conductivity $\kappa$ obtained (a) by summing the predicted $\kappa_{\mathrm{L}}$ and $\kappa_{\mathrm{e}}$ (additive model) and (b) from a baseline model trained directly on $\kappa$.
• Figure 5: SHAP beeswarm plots for the (a) $\kappa_{\mathrm{L}}$ and (b) $\kappa_{\mathrm{e}}$ Random Forest models, computed on the entire training set. Features are ordered by mean $|\mathrm{SHAP}|$.