Fig. 1: Visualizing cohesive fracture energy for mechanical integrity, processability, and thermoelectric performance.

a Schematic illustrating how cohesive fracture energy correlates with key microstructural parameters —including grain roundness, size, dislocation density, and fracture surface characteristics— driving a transition from transgranular to intergranular fracture. b Images of low fracture energy (L-FE) and high fracture energy (H-FE) YbZn₂Sb₂ samples after spark plasma sintering (left) and subsequent precision machining (right), highlighting improved processability in H-FE samples. c Correlation between lattice thermal conductivity (κ_l) and pre-formation cohesive energy^{15,16,17,18,19,20,21,22}. Here, the pre-formation cohesive energy (E_pre) represents the total cohesive energy of the constituent pure elements (A/B) before the formation of compound A_xB_y, serving as a baseline for calculating the cohesive energy of A_xB_y compounds. d Maximum energy conversion efficiency (η_max) of thermoelectric modules based on Zintl, CoSb₃, PbTe, and half-Heusler (HH) systems^23,24,25,26. The cold-side temperature for all modules is near room temperature. The Zintl-based modules demonstrate strong potential for energy harvesting in low- to medium-grade waste heat regimes.