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The Onsager–de Groot–Callen model describes thermoelectricity in the framework of the thermodynamics of irreversible processes , which uses rather abstract kinetic matrix and generalized forces to describe the flux of the substance-like quantities electric charge and thermal energy (“heat”). A brief review of the derivation of the basic equations according to this model is given. Primarily, this model relies on the total differential of energy as in Gibb’s thermodynamics, but it then removes entropy to capture the energy production rate as a measure of irreversibility. Depending on the fluxes of interest, “proper” generalized forces are identified. The use of Onsager’s reciprocal relations helps to determine the coefficients of a kinetic matrix to link the generalized forces with the generalized potentials. The present article places entropy back into the as-obtained basic equations. The equations are then transformed such that the flux densities of electric charge and entropy appear with equal ranks. The respective conjugated intensive variables electrochemical potential and temperature then appear as the thermodynamic potentials. Moreover, the thermoelectric material is described by a material-specific tensor, which is composed only of the isothermal electric conductivity, the Seebeck coefficient and the entropy conductivity. The result is identical to that recently obtained by Fuchs using a direct entropic approach, which does not require Onsager’s reciprocal relations as a prerequisite. The benefit of this approach is the appearance of a material-specific thermoelectric tensor rather than a so-called kinetic matrix , which not only provides a new quality to the discussion but also facilitates descriptions of the thermoelectric phenomenon and the underlying energy conversion process. The latter can easily be understood as the transfer of energy from thermal to electric phenomenon or vice versa when fluxes of entropy and electric charge, as well as the local thermodynamic potentials temperature and electrochemical potential, are known.

Engineering thermoelectric (TE) materials for applications in power generation and cooling requires an understanding of how anisotropy influences the TE properties. In this paper we use an angular-dependent, multivalley formalism to model the band structure and to explore the effect of anisotropy on the Seebeck and conductivity tensors. Specifically we explore the effect of degeneracy and relative orientation of the effective mass ellipsoids near critical points on the shape of these tensors. Examples of these types of anisotropic effects are explored within the above formalism and with the full band structures of two materials: half-Heusler ZrNiSn and (Sr,Ba)Nb 2 O 6 with the tetragonal tungsten bronze structure.

The concepts of dual leg, unileg and transversal oxide thermoelectric harvesting devices were compared with regard to the dimensionless figure of merit calculated from published data on common dual leg oxide thermoelectric generators. The analysis shows that the application of the transversal thermoelectric effect does not significantly reduce the expected electrical output power density of thermoelectric devices utilizing thermoelectric oxides. At the same time, the transversal device layout is simple in comparison to the common dual leg device. A transversal thermoelectric harvester consisting of a tilted multilayer stack La 1.97 Sr 0.03 CuO 4 /Ag was prepared and analyzed in detail. Simulations using the finite elements method were performed to verify the results. Based on this data, the electrical power density of the transversal oxide-metal device is estimated to be in the range of currently published data on oxide dual leg devices, thus allowing energy harvesting for low power applications.

This paper reports about a new four-step analysis method for thermoelectric (TE) materials. While the Seebeck coefficient is usually measured under small temperature gradient, we report here the measurement of TE materials under large temperature gradient. The examined materials were Ag- and Bi-doped Mg 2 Si, Si 80 Ge 20 , the ceramic composite NaTaO 3 -Fe 2 O 3 , the half-Heusler alloy (TiZr)NiSn, and the clathrates Ba 8 Cu x Si 48- x with x =8, 12. The results show that the latter two metallic-like material groups have a low internal resistance. Hence, their output power is achieved at large electric currents with high carrier concentrations, while ceramic and silicides show the maximum output power at lower carrier concentration, which is considered to be a result of their large effective masses. The Arrhenius plot of the output energy yielded isosbestic-like points for ceramic-like materials, while the metal-like specimens show constant activation energies in the order of less than 0.1 eV. While all compared materials have reported ZT values around 0.4, the output energy was similar and measured as around 0.01 mW. Advantages of the metallic TE materials are their high carrier concentration and easy processing, disadvantages are their sensitivity to impurities and oxidation.

This investigation presents cost-effective fabrication of n-type silicon germanium–iron disilicide nanocomposites using low-cost low-purity germanium–germanium oxide powder. Moreover, the probability of the reduction of oxide powders during the synthesis process was studied. X-ray diffraction (XRD) analysis indicated reduction of germanium oxide impurity in the synthesized material. Scanning electron microscopy (SEM) along with the energy-dispersive spectrometer (EDS) showed a structure of dispersed iron disilicide particles embedded in silicon germanium matrix. The nanocomposite structure showed a moderate figure-of-merit, ZT, equal to 0.8. The ZT enhancement was related to both the nanocomposite structure and the reduction of germanium oxide.

In this study, we investigate the changes occurring in the microstructure and thermoelectric properties of PbTe 0.9 S 0.1 alloy (PbTe–PbS) under varying thermal treatment conditions. Transmission electron microscopy (TEM) studies were utilized to reveal the distribution of nano-precipitates in the annealed alloy. PbTe 0.9 S 0.1 alloy with PbS phase precipitates displayed a significant reduction in the thermal conductivity and an enhancement in the Seebeck coefficient. The 47% reduction in lattice thermal conductivity at the measurement temperature of 300°C in the alloy annealed at 400°C was attributed to the phonon scattering occurring due to the presence of nano-precipitates. The annealed alloy displayed higher electrical conductivity at room temperature than that of the alloy without annealing. The maximum figure of merit, ZT , was found to be 0.76 at 300°C in the alloy annealed at 400°C.

During the last decade oxide-based thermoelectric materials have received increased attention due to their high stability and thermal robustness at high temperatures as well as the availability and nontoxic nature of a number of promising candidates. In the present study we are investigating the thermoelectric properties of an n-type La-substituted SrTiO 3 with the specific composition (La 0.12 Sr 0.88 ) 0.05 TiO 3 . Nanosized powder precursors were spark plasma sintered (SPS) for 5 minutes between 900 and 1,200°C, resulting in densities between 73 and 98% and crystallite sizes between 40 nm and 1 μm. The formation of a rutile phase (TiO 2 ) was observed in samples sintered at 1,150 and 1,200°C; at lower temperatures only single-phase cubic perovskite was observed. There was no clear evidence that the presence of rutile affected the thermal conductivity ( κ ). A significant reduction in κ was observed both with increasing porosity and reducing crystallite size, showing a minimum at ~700°C corresponding to ~1.3 W m −1 K −1 .

ZnO-based compositions are of great interest for high-temperature thermoelectric applications. In this study, n -type Al-doped ZnO was sintered under varying atmospheres and the changes in electrical conductivity along with chemical defects were analyzed. The electrical conductivity of Al-doped ZnO (ZnO-Al) exhibited large variation from 10 −5 to 10 3 S/cm as the sintering atmosphere was changed from air to nitrogen to vacuum. The low oxygen partial pressure assisted Al substitution in ZnO and increased the interstitial Zn, which increased the carrier concentration and improved the electrical conductivity. Using vacuum sintering, the electrical conductivity of ZnO was enhanced as the concentration of Al doping was increased from 1 to 3 at.%. Two sets of starting powders were used for sintering studies, one synthesized through the ball-milling and other through the sol–gel chemical synthesis. It was found that the Al substitution is improved by using chemically synthesized ZnO-Al powders.

This article presents a solution for the thermoelectric power supply of wireless sensor nodes for condition monitoring of marine gearboxes. Among the different ambient energy sources in marine gearboxes, frictional heat has been identified to be appropriate to thermally power a thermoelectric generator (TEG). The such generated electricity may power wireless sensor nodes for detecting temperature, vibration, torque and rotational speed. Requirements for a corresponding energy supply are formulated, constructive solutions are presented and thermal simulations and practical experiments are reviewed. The results are evaluated and a solution is selected for further implementation, which provides for an actively cooled TEG in the area of the ship gearbox’s heat exchanger. This can provide continuous electrical power of up to 14 mW, thus supplying the planned sensor nodes. The disadvantage of this solution is that a comparatively extensive mechanical modification, for example, to the oil and cooling water pipelines is required.

A versatile finite-element simulation tool was developed to predict the electric power output, the distributions of the electric and entropy potentials (i.e., the absolute temperature) and the local flux densities of electric charge and thermal energy (i.e., heat) for a thermoelectric generator. The input parameters are the thermogenerator architecture (i.e., geometries of different components and number of legs) and material properties such as specific electric conductivity, Seebeck coefficient and thermal conductivity. The finite-element simulation tool was validated by modeling a commercially available thermoelectric generator, which was based on semiconducting n- and p-type Bi 2–x Sb x Te 3 with ceramic cover plates, and comparing the modeled voltage–current characteristics and power characteristics with experimental values for different temperature conditions. The geometric parameters could easily be determined from photomicrography and cross-sectional scanning electron microscopy observations. The electric conductivity and Seebeck coefficient were measured, as functions of temperature, from the integer module as leg-averaged values. The thermal conductivity was taken from literature data, which required estimating the compositions of components using energy-dispersive X-ray spectroscopy in the scanning electron microscope and their crystal structures using X-ray diffraction. Good agreement was found between the simulated and measured voltage–current and power–current characteristics. The finite-element simulation tool is versatile because it uses a script-based approach, which allows easy parameter changes and allows it to be adapted to thermogenerators consisting of different geometries and materials, including novel materials.