During the last two decades, we have witnessed great progress in research on thermoelectrics. There are two primary focuses. One is the fundamental understanding of electrical and thermal transport, enabled by the interplay of theory and experiment; the other is the substantial enhancement of the performance of various thermoelectric materials, through synergistic optimisation of those intercorrelated transport parameters. Here we review some of the successful strategies for tuning electrical and thermal transport. For electrical transport, we start from the classical but still very active strategy of tuning band degeneracy (or band convergence), then discuss the engineering of carrier scattering, and finally address the concept of conduction channels and conductive networks that emerge in complex thermoelectric materials. For thermal transport, we summarise the approaches for studying thermal transport based on phonon-phonon interactions valid for conventional solids, as well as some quantitative efforts for nanostructures. We also discuss the thermal transport in complex materials with chemical-bond hierarchy, in which a portion of the atoms (or subunits) are weakly bonded to the rest of the structure, leading to an intrinsic manifestation of part-crystalline part-liquid state at elevated temperatures. In this review, we provide a summary of achievements made in recent studies of thermoelectric transport properties, and demonstrate how they have led to improvements in thermoelectric performance by the integration of modern theory and experiment, and point out some challenges and possible directions. INTRODUCTION Thermoelectric (TE) materials are materials that can generate useful electric potentials when subjected to a temperature gradient (known as the Seebeck effect). Conversely, they also transfer heat against the temperature gradient when a current is driven against this potential (known as the Peltier effect). They are promising energy materials with many applications, such as waste heat harvesting, radioisotope TE power generation, and solid state Peltier refrigeration, all of which are driving growing research interest. A key challenge is to improve the TE properties in order to obtain more efficient energy conversion and in turn enable new practical applications. Good TE materials must have excellent electrical transport properties, measured by the TE power factor ( = S 2 σ, where S is the Seebeck coefficient and σ is the electrical conductivity), and also a very low thermal conductivity κ (composed of the electronic contribution κ e , the lattice contribution κ L , and the bipolar contribution κ bi ). Combining the two aspects gives us the dimensionless figure of merit ZT,

Understanding thermal and phonon transport in solids has been of great importance in many disciplines such as thermoelectric materials, which usually requires an extremely low lattice thermal conductivity (LTC). By analyzing the finite-temperature structural and vibrational characteristics of typical thermoelectric compounds such as filled skutterudites and Cu 3 SbSe 3 , we demonstrate a concept of part-crystalline part-liquid state in the compounds with chemicalbond hierarchy, in which certain constituent species weakly bond to other part of the crystal. Such a material could intrinsically manifest the coexistence of rigid crystalline sublattices and other fluctuating noncrystalline sublattices with thermally induced largeamplitude vibrations and even flow of the group of species atoms, leading to atomic-level heterogeneity, mixed part-crystalline partliquid structure, and thus rattling-like thermal damping due to the collective soft-mode vibrations similar to the Boson peak in amorphous materials. The observed abnormal LTC close to the amorphous limit in these materials can only be described by an effective approach that approximately treats the rattling-like damping as a "resonant" phonon scattering.sublattice melting | partial Grüneisen parameter | first principles | anharmonicity U nderstanding thermal and phonon transport in solids has been of great importance in many disciplines such as thermoelectrics (1-3), phononic materials (4), and thermal management composites (5). The interplay among chemical bonds, lattice dynamics, and thermal transport in materials is also an attractive topic in condensed matter physics (6) and materials science (7). Thermal transport is a key issue in thermoelectric (TE) energy-conversion materials, which are regarded among the potential candidates for revolutionizing waste-heat recovery (2, 7-9). The dimensionless figure of merit of a TE material is defined as ZT = TS 2 σ=κ, where T, S, σ, and κ are the absolute temperature, Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively. To improve the efficiency of TE conversion, many approaches aim at reducing the thermal conductivity, especially the lattice part, to a minimum level, namely the realization of phonon-glass-like thermal transport (1, 7).TE materials research primarily focuses on solid and crystalline thermoelectrics. It has been long viewed that all solids contain strong interatomic interactions without even an exception, and thus the established approaches to describe thermal transports in crystalline solids, including TE solids, are solely based on the perturbative "small-parameter" approximation to lattice dynamics of atoms around their equilibrium positions, i.e., phonons and phonon-phonon interactions (10, 11). As a result, crystallographic homogeneity at the atomic level in solid materials has overwhelmingly been accepted. However, recent work on exploring novel TE materials went noticeably beyond the conventional knowledge of solid TE compounds being ideally crystalline, atomically...

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