With about two-thirds of all used energy being lost as waste heat, there is a compelling need for high-performance thermoelectric materials that can directly and reversibly convert heat to electrical energy. However, the practical realization of thermoelectric materials is limited by their hitherto low figure of merit, ZT, which governs the Carnot efficiency according to the second law of thermodynamics. The recent successful strategy of nanostructuring to reduce thermal conductivity has achieved record-high ZT values in the range 1.5-1.8 at 750-900 kelvin, but still falls short of the generally desired threshold value of 2. Nanostructures in bulk thermoelectrics allow effective phonon scattering of a significant portion of the phonon spectrum, but phonons with long mean free paths remain largely unaffected. Here we show that heat-carrying phonons with long mean free paths can be scattered by controlling and fine-tuning the mesoscale architecture of nanostructured thermoelectric materials. Thus, by considering sources of scattering on all relevant length scales in a hierarchical fashion--from atomic-scale lattice disorder and nanoscale endotaxial precipitates to mesoscale grain boundaries--we achieve the maximum reduction in lattice thermal conductivity and a large enhancement in the thermoelectric performance of PbTe. By taking such a panoscopic approach to the scattering of heat-carrying phonons across integrated length scales, we go beyond nanostructuring and demonstrate a ZT value of ∼2.2 at 915 kelvin in p-type PbTe endotaxially nanostructured with SrTe at a concentration of 4 mole per cent and mesostructured with powder processing and spark plasma sintering. This increase in ZT beyond the threshold of 2 highlights the role of, and need for, multiscale hierarchical architecture in controlling phonon scattering in bulk thermoelectrics, and offers a realistic prospect of the recovery of a significant portion of waste heat.

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The morphology of crystalline precipitates in a solid-state matrix is governed by complex but tractable energetic considerations driven largely by volume strain energy minimization and anisotropy of interfacial energies. Spherical precipitate morphologies are favored by isotropic systems, while anisotropic interfacial energies give energetic preference to certain crystallographically oriented interfaces, resulting in a faceted precipitate morphology. In conventional solid-solution precipitation, a precipitate's morphological evolution is mediated by surface anchoring of capping molecules, which dramatically alter the surface energy in an anisotropic manner, thereby providing exquisite morphology control during crystal growth. Herein, we present experimental evidence and theoretical validation for the role of a ternary element (Na) in controlling the morphology of nanoscale PbS crystals nucleating in a PbTe matrix, an important bulk thermoelectric system. The PbS nanostructures formed by phase separation from a PbI(2)-doped or undoped PbTe matrix have irregular morphologies. However, replacing the iodine dopant with Na (1-2 mol %) alters dramatically the morphology of the PbS precipitates. Segregation of Na at PbTe/PbS interfaces result in cuboidal and truncated cuboidal morphologies for PbS. Using analytical scanning/transmission electron microscopy and atom-probe tomography, we demonstrate unambiguously that Na partitions to the precipitates and segregates at the matrix/precipitate interfaces, inducing morphological anisotropy of PbS precipitates. First-principles and semiclassical calculations reveal that Na as a solute in PbTe has a higher energy than in PbS and that Na segregation at a (100) PbTe/PbS interface decreases the total energy of matrix/precipitate system, resulting in faceting of PbS precipitates. These results provide an impetus for a new strategy for controlling morphological evolution in matrix/precipitate systems, mediated by solute partitioning of ternary additions.