Hee Seok Kim

Relationship between thermoelectric figure of merit and energy conversion efficiency

Significance Thermoelectric materials generate electricity from temperature gradients. The dimensionless figure of merit, ZT = S2ρ−1κ−1T, is calculated from the Seebeck coefficient (S), electrical resistivity (ρ), and thermal conductivity (κ). The calculated efficiency based on ZT using the conventional formula is not reliable in some cases due to the assumption of temperature-independent S, ρ, and κ. We established a new efficiency formula by introducing an engineering figure of merit (ZT)eng and an engineering power factor (PF)eng to predict reliably and accurately the efficiency of materials at a large temperature difference between the hot and cold sides, unlike the conventional ZT and PF providing performance only at specific temperatures. These new formulas will profoundly impact the search for new thermoelectric materials. The formula for maximum efficiency (ηmax) of heat conversion into electricity by a thermoelectric device in terms of the dimensionless figure of merit (ZT) has been widely used to assess the desirability of thermoelectric materials for devices. Unfortunately, the ηmax values vary greatly depending on how the average ZT values are used, raising questions about the applicability of ZT in the case of a large temperature difference between the hot and cold sides due to the neglect of the temperature dependences of the material properties that affect ZT. To avoid the complex numerical simulation that gives accurate efficiency, we have defined an engineering dimensionless figure of merit (ZT)eng and an engineering power factor (PF)eng as functions of the temperature difference between the cold and hot sides to predict reliably and accurately the practical conversion efficiency and output power, respectively, overcoming the reporting of unrealistic efficiency using average ZT values.

n-type thermoelectric material Mg2Sn0.75Ge0.25 for high power generation

Significance Thermoelectric materials have been extensively studied for applications in conversion of waste heat into electricity. The efficiency is related to the figure-of-merit, ZT = (S2σ/κ)T, where S, σ, and κ are the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively. Pursuing higher ZT for higher efficiency has been the focus by mainly reducing the thermal conductivity. In this paper, we point out, for a given ZT, higher power factor (S2σ) should be pursued for achieving more power because power is determined by (Th − Tc)2(S2σ)/L, where Th, Tc, and L are the hot and cold side temperatures, and leg length, respectively. We found a new material, Mg2Sn0.75Ge0.25, having both high ZT and high power factor. Thermoelectric power generation is one of the most promising techniques to use the huge amount of waste heat and solar energy. Traditionally, high thermoelectric figure-of-merit, ZT, has been the only parameter pursued for high conversion efficiency. Here, we emphasize that a high power factor (PF) is equivalently important for high power generation, in addition to high efficiency. A new n-type Mg2Sn-based material, Mg2Sn0.75Ge0.25, is a good example to meet the dual requirements in efficiency and output power. It was found that Mg2Sn0.75Ge0.25 has an average ZT of 0.9 and PF of 52 μW⋅cm−1⋅K−2 over the temperature range of 25–450 °C, a peak ZT of 1.4 at 450 °C, and peak PF of 55 μW⋅cm−1⋅K−2 at 350 °C. By using the energy balance of one-dimensional heat flow equation, leg efficiency and output power were calculated with Th = 400 °C and Tc = 50 °C to be of 10.5% and 6.6 W⋅cm−2 under a temperature gradient of 150 °C⋅mm−1, respectively.

Achieving high power factor and output power density in p-type half-Heuslers Nb1-xTixFeSb.

Significance Thermoelectric technology can boost energy consumption efficiency by converting some of the waste heat into useful electricity. Heat-to-power conversion efficiency optimization is mainly achieved by decreasing the thermal conductivity in many materials. In comparison, there has been much less success in increasing the power factor. We report successful power factor enhancement by improving the carrier mobility. Our successful approach could suggest methods to improve the power factor in other materials. Using our approach, the highest power factor reaches ∼106 μW⋅cm−1⋅K−2 at room temperature. Such a high power factor further yields a record output power density in a single-leg device tested between 293 K and 868 K, thus demonstrating the importance of high power factor for power generation applications. Improvements in thermoelectric material performance over the past two decades have largely been based on decreasing the phonon thermal conductivity. Enhancing the power factor has been less successful in comparison. In this work, a peak power factor of ∼106 μW⋅cm−1⋅K−2 is achieved by increasing the hot pressing temperature up to 1,373 K in the p-type half-Heusler Nb0.95Ti0.05FeSb. The high power factor subsequently yields a record output power density of ∼22 W⋅cm−2 based on a single-leg device operating at between 293 K and 868 K. Such a high-output power density can be beneficial for large-scale power generation applications.

The bridge between the materials and devices of thermoelectric power generators

While considerable efforts have been made to develop and improve thermoelectric materials, research on thermoelectric modules is at a relatively early stage because of the gap between material and device technologies. In this review, we discuss the cumulative temperature dependence model to reliably predict the thermoelectric performance of module devices and individual materials for an accurate evaluation of the p–n configuration compared to the conventional model used since the 1950s. In this model, the engineering figure of merit and engineering power factor are direct indicators, and they exhibit linear correlations to efficiency and output power density, respectively. To reconcile the strategy for high material performance and the thermomechanical reliability issue in devices, a new methodology is introduced by defining the engineering thermal conductivity. Beyond thermoelectric materials, the device point of view needs to be actively addressed before thermoelectric generators can be envisioned as power sources.

New insight into the material parameter B to understand the enhanced thermoelectric performance of Mg2Sn1−x−yGexSby

Historically, a material parameter B incorporating weighted mobility and lattice thermal conductivity has guided the exploration of novel thermoelectric materials. However, the conventional definition of B neglects the bipolar effect which can dramatically change the thermoelectric energy conversion efficiency at high temperatures. In this paper, a generalized material parameter B* is derived, which connects weighted mobility, lattice thermal conductivity, and the band gap. Based on the new parameter B*, we explain the successful tuning of the electron and phonon transport in Mg2Sn1−x−yGexSby, with an improved ZT value from 0.6 in Mg2Sn0.99Sb0.01 to 1.4 in Mg2Sn0.73Ge0.25Sb0.02. We uncover that the Ge alloying approach simultaneously improves all the key variables in the material parameter B*, with an ∼25% enhancement in the weighted mobility, ∼27% band gap widening, and ∼50% reduction in the lattice thermal conductivity. We show that a higher generalized parameter B* leads to a higher optimized ZT in Mg2Sn0.73Ge0.25Sb0.02, and some common thermoelectric materials. The new parameter B* provides a better characterization of materials thermoelectric transport, particularly at high temperatures, and therefore can facilitate the search for good thermoelectric materials.

Investigating the thermoelectric properties of p-type half-Heusler Hfx(ZrTi)1−xCoSb0.8Sn0.2 by reducing Hf concentration for power generation

Based on the fact that Hf is much more expensive than other commonly used elements in HfCoSb-based half-Heusler materials, we studied the thermoelectric properties of the p-type half-Heusler Hfx(ZrTi)1−xCoSb0.8Sn0.2 by reducing Hf concentration. A peak ZT of ∼1.0 was achieved at 700 °C with the composition of Hf0.19Zr0.76Ti0.05CoSb0.8Sn0.2 by keeping the Hf/Zr ratio at 1/4 and Hf/Ti at 4/1. This composition has much reduced cost and similar thermoelectric performance compared with our previously reported best p-type half-Heusler: Hf0.44Zr0.44Ti0.12CoSb0.8Sn0.2. Due to the decreased usage of Hf, it is more favorable for consideration in applications. In addition, a higher output power is expected because of the higher power factor even though the conversion efficiency is the same due to the same ZT.

Thermoelectric properties of Bi-based Zintl compounds Ca1−xYbxMg2Bi2

Bi-based Zintl compounds, Ca1−xYbxMg2Bi2 with the structure of CaAl2Si2, have been successfully prepared by mechanical alloying followed by hot pressing. We found that the electrical conductivity, Seebeck coefficient, carrier concentration, and thermal conductivity can be adjusted by changing the Yb concentration. All Ca1−xYbxMg2Bi2 samples have low carrier concentrations (∼2.4 to 7.2 × 1018 cm−3) and high Hall mobility (∼119 to 153 cm2 V−1 s−1) near room temperature. The partial substitution of Ca with Yb causes structural disorders, which lowers the thermal conductivity. The highest figure of merit of ∼1.0 is observed in Ca0.5Yb0.5Mg2Bi2, and ∼0.8 in the unsubstituted CaMg2Bi2 and YbMg2Bi2. A small amount of free Bi was found in all the samples except YbMg2Bi2. By reducing the initial Bi concentration, we succeeded in obtaining phase pure samples in all compositions, which resulted in a much better thermoelectric performance, especially much higher (ZT)eng and a conversion efficiency near 11%. Such a high efficiency makes this material competitive with half-Heuslers and skutterudites.

Thermoelectric properties of Zintl compound Ca1−xNaxMg2Bi1.98

Motivated by good thermoelectric performance of Bi-based Zintl compounds Ca1−xYbxMg2Biy, we further studied the thermoelectric properties of Zintl compound CaMg2Bi1.98 by doping Na into Ca as Ca1−xNaxMg2Bi1.98 via mechanical alloying and hot pressing. We found that the electrical conductivity, Seebeck coefficient, power factor, and carrier concentration can be effectively adjusted by tuning the Na concentration. Transport measurement and calculations revealed that an optimal doping of 0.5 at. % Na achieved better average ZT and efficiency. The enhancement in thermoelectric performance is attributed to the increased carrier concentration and power factor. The low cost and nontoxicity of Ca1−xNaxMg2Bi1.98 makes it a potentially promising thermoelectric material for power generation in the mid-temperature range.

Efficiency and output power of thermoelectric module by taking into account corrected Joule and Thomson heat

The maximum conversion efficiency of a thermoelectric module composed of p- and n-type materials has been widely calculated using a constant property model since the 1950s, but this conventional model is only valid in limited conditions and no Thomson heat is accounted for. Since Thomson heat causes the efficiency under- or over-rated depending on the temperature dependence of Seebeck coefficient, it cannot be ignored especially in large temperature difference between the hot and cold sides. In addition, incorrect Joule heat is taken into consideration for heat flux evaluation of a thermoelectric module at thermal boundaries due to the assumption of constant properties in the conventional model. For this reason, more practical predictions for efficiency and output power and its corresponding optimum conditions of p- and n-type materials need to be revisited. In this study, generic formulae are derived based on a cumulative temperature dependence model including Thomson effect. The formulae reliably predict the maximum efficiency and output power of a thermoelectric module at a large temperature.