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      Power Conversion and Its Efficiency in Thermoelectric Materials

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          Abstract

          The basic principles of thermoelectrics rely on the coupling of entropy and electric charge. However, the long-standing dispute of energetics versus entropy has long paralysed the field. Herein, it is shown that treating entropy and electric charge in a symmetric manner enables a simple transport equation to be obtained and the power conversion and its efficiency to be deduced for a single thermoelectric material apart from a device. The material’s performance in both generator mode (thermo-electric) and entropy pump mode (electro-thermal) are discussed on a single voltage-electrical current curve, which is presented in a generalized manner by relating it to the electrically open-circuit voltage and the electrically closed-circuited electrical current. The electrical and thermal power in entropy pump mode are related to the maximum electrical power in generator mode, which depends on the material’s power factor. Particular working points on the material’s voltage-electrical current curve are deduced, namely, the electrical open circuit, electrical short circuit, maximum electrical power, maximum power conversion efficiency, and entropy conductivity inversion. Optimizing a thermoelectric material for different working points is discussed with respect to its figure-of-merit zT and power factor. The importance of the results to state-of-the-art and emerging materials is emphasized.

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          Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals.

          The thermoelectric effect enables direct and reversible conversion between thermal and electrical energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelectric materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is absolute temperature), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for commercial deployment, especially for compounds free of Pb and Te. Here we report an unprecedented ZT of 2.6 ± 0.3 at 923 K, realized in SnSe single crystals measured along the b axis of the room-temperature orthorhombic unit cell. This material also shows a high ZT of 2.3 ± 0.3 along the c axis but a significantly reduced ZT of 0.8 ± 0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal conductivity in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grüneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal conductivity (0.23 ± 0.03 W m(-1) K(-1) at 973 K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelectric performance.
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            Convergence of electronic bands for high performance bulk thermoelectrics.

            Thermoelectric generators, which directly convert heat into electricity, have long been relegated to use in space-based or other niche applications, but are now being actively considered for a variety of practical waste heat recovery systems-such as the conversion of car exhaust heat into electricity. Although these devices can be very reliable and compact, the thermoelectric materials themselves are relatively inefficient: to facilitate widespread application, it will be desirable to identify or develop materials that have an intensive thermoelectric materials figure of merit, zT, above 1.5 (ref. 1). Many different concepts have been used in the search for new materials with high thermoelectric efficiency, such as the use of nanostructuring to reduce phonon thermal conductivity, which has led to the investigation of a variety of complex material systems. In this vein, it is well known that a high valley degeneracy (typically ≤6 for known thermoelectrics) in the electronic bands is conducive to high zT, and this in turn has stimulated attempts to engineer such degeneracy by adopting low-dimensional nanostructures. Here we demonstrate that it is possible to direct the convergence of many valleys in a bulk material by tuning the doping and composition. By this route, we achieve a convergence of at least 12 valleys in doped PbTe(1-x)Se(x) alloys, leading to an extraordinary zT value of 1.8 at about 850 kelvin. Band engineering to converge the valence (or conduction) bands to achieve high valley degeneracy should be a general strategy in the search for and improvement of bulk thermoelectric materials, because it simultaneously leads to a high Seebeck coefficient and high electrical conductivity. ©2011 Macmillan Publishers Limited. All rights reserved
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              High-performance bulk thermoelectrics with all-scale hierarchical architectures.

              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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                Author and article information

                Journal
                Entropy (Basel)
                Entropy (Basel)
                entropy
                Entropy
                MDPI
                1099-4300
                22 July 2020
                August 2020
                : 22
                : 8
                : 803
                Affiliations
                Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstraße 3A, D-30167 Hannover, Germany; armin.feldhoff@ 123456pci.uni-hannover.de ; Tel.: +49-511-762-2940
                Author information
                https://orcid.org/0000-0003-1599-432X
                Article
                entropy-22-00803
                10.3390/e22080803
                7517375
                c92e8595-b5de-45bf-b09e-36e815ef1f52
                © 2020 by the author.

                Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

                History
                : 26 June 2020
                : 18 July 2020
                Categories
                Article

                thermoelectrics,power conversion,efficiency,voltage-electrical current curve,working point,entropy pump mode,generator mode,power factor,figure of merit,altenkirch-ioffe model

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