A record thermoelectric efficiency in tellurium-free modules for low-grade waste heat recovery

Low-grade heat accounts for >50% of the total dissipated heat sources in industries. An efficient recovery of low-grade heat into useful electricity not only reduces the consumption of fossil-fuels but also releases the subsequential environmental-crisis. Thermoelectricity offers an ideal solution, yet low-temperature efficient materials have continuously been limited to Bi2Te3-alloys since the discovery in 1950s. Scarcity of tellurium and the strong property anisotropy cause high-cost in both raw-materials and synthesis/processing. Here we demonstrate cheap polycrystalline antimonides for even more efficient thermoelectric waste-heat recovery within 600 K than conventional tellurides. This is enabled by a design of Ni/Fe/Mg3SbBi and Ni/Sb/CdSb contacts for both a prevention of chemical diffusion and a low interfacial resistivity, realizing a record and stable module efficiency at a temperature difference of 270 K. In addition, the raw-material cost to the output power ratio in this work is reduced to be only 1/15 of that of conventional Bi2Te3-modules.

Thermoelectric efficiency measurements: The power output (P) and conversion efficiency (η) of the Mg3SbBi/CdSb modules under different temperature differences were measured in vacuum (Supplementary Fig. 1) 1 . The cold-side temperature was maintained by water-cooling system. The heater, module and heat-flow meter (Cu bar) were assembled under a uniaxial pressure to improve the thermal contacts. Thermal grease (QM850) was used to improve the thermal contact between the heater and module and between the module and heat-flow meter. K-type thermocouples (Omega) were adhered to Al2O3 ceramics using silver paste for measuring the temperature difference between the hot (Th) and cold (Tc) side temperatures of the module. Two tubular heaters (Omega) were embedded in a graphite block for heating the module at hot side. Graphite was chosen for its high thermal conductivity and low thermal expansion coefficient. Circulating water cooling block along with a thermoelectric cooling plate were used to cool the temperature of the cold side. A Cu bar with a cross-sectional area identical to that of the module (10×10 mm 2 ) is used as a heat-flow meter with known thermal conductivity 1 for measuring the heat flow through the thermoelectric module. Two K-type thermocouples (Omega) with a wire-diameter of only 0.6 mm for reducing heat loss were embedded and soldered to the heat-flow meter for determining the temperature difference. The distance between these two thermocouples is 17 mm.

Cu block
The typical temperature differences between the hot-and cold-side of the heat-flow meter (ΔTCu) are 0.4-1.6 K (Supplementary Table 1, Supplementary Fig. 2a), depending on the temperature differences applied to the module (ΔT). The linear relationship between ΔT and ΔTCu ( Supplementary Fig. 2b) nicely suggests the consistent responsivity of the heat-flow meter. In order to ensure the accuracy in determining the temperature difference of the heat-flow meter, two K-type thermocouples (Omega, wire-diameter of 0.6 mm) are buried inside the copper-bar with a further soldering, and each thermocouple takes 60 measurements for averaging ( Supplementary Fig. 2a). As can be seen, even at the smallest ΔTCu of ~0.64 K, the relative standard deviation (RSD) for these 60 measurements can be ensured to be within 3%, indicating the sufficiently large signal to noise ratio.
A measurement of thermoelectric efficiency was enabled by measuring the output power (P=IV) and the heat flow in vacuum, where I is the current and V is the output voltage. By varying the load resistance and measuring the corresponding load voltage and current, the maximum output power can be obtained.
The heat flow can be obtained by: where Q, ACu, LCu, ΔTCu=T1-T2 and Cu are the heat flow, cross-sectional area of the copper bar, distance between the thermocouples, temperature difference and thermal conductivity of the heat-flow meter (Cu block). Because of the small temperature difference (ΔTCu), the thermal conductivity (Cu) is approximated as temperature independent. Therefore, the efficiency () can be estimated according to =P/(P+Q). The maximum efficiency (max) can be obtained by varying the load resistance in the circuit, and measuring the corresponding output power and heat flow. To minimize the system error, we measured each parameter (including temperature, voltage and current) for 60 times for averaging.

Estimation of heat radiation and leakage:
In this work, a control experiment is carried out to figure out the main origin leading to the discrepancy between measured and predicted heat flows. In order to measure the vertical thermal radiation between the uncovered inner surfaces of the alumina-ceramic substrates of the module, two alumina-ceramic substrates of the same size are respectively fixed to the heater (hot side of the module) and the heat-flow meter (cold side of the module) with an exact separation of 3 mm (the total length of the leg and contacts of Module-1). The cold-side temperature is kept at 280 K, and varying the hot-side temperature enables a measurement of the corresponding vertical radiative heat flows under different temperature differences. As shown in Supplementary Fig. 3, an exact measurement setup of Module-1 but without thermoelectric materials is used to estimate the induced vertical heat flow due to heat radiation (vertical) between the substrates of the module. This corresponds to the extreme case of a zero-filling-fraction module, and the heat flow [Qrad(f=0)] of which can be used to estimate the case of a real case of module with a filling fraction of f=0.315 for Module-1 by [Qrad(f≠0)=Qrad(f=0)×(1-f)]. This helps understand that the discrepancy between measured and predicted heat flow increases with increasing ΔT, due to the increase in vertical heat radiation from the unfilled portion of hot-side substrate to the cold-side one at high temperatures ( Supplementary Fig. 3). The heat radiated from the surfaces of legs to the surroundings (horizontal) can be estimated by the following equation 2,3 : where the Qrad is the horizontal heat radiation, ε is the emissivity, θ is the Stefan-Boltzmann constant, C is the total outer side surface area of thermoelectric legs, ΔT is the temperature gradient, Th is the hot-side temperature, Tc is the cold-side temperature, T is the temperature distribution, and TS is the surrounding temperature. The emissivity of 0.5 is used according to the previous reports of thermoelectric materials [2][3][4] . The surrounding temperature is measured by two thermocouples in the vacuum chamber, and average ( Supplementary Fig. 4). The estimated horizontal heat radiation increases with increasing temperature, leading to a heat loss of 2% at Th=550 K and Tc=280 K of Module-2 with a leg length of 4 mm. Since the horizontal heat radiation is proportional to the radiative surface area, Module-1 with a shorter leg length of 2 mm reduces the heat radiation loss to be only 0.63% at the same temperature gradient of 270 K ( Supplementary Fig. 4). Compared to the total heat-flow, the horizontal heat radiation loss for Module-1 is negligible. In this work, both horizontal and vertical heat radiations are taken into account for estimating the efficiency, and the corresponding maximum efficiency are listed in Supplementary Table 3. Note again that vertical radiation between unfilled module substrates leads to an overestimation in heat flow but horizontal one leads to an underestimation.  Heat leakages can be important sources causing measurement uncertainties. Indeed, we used thermocouples and Cu wires with as thin as possible diameters. Thermocouples/wires shown in Supplementary Fig. 1b come with insulation/shielding accessories, which make them look bigger than they actually are. In this work, note that the heat-flow meter locates underneath the cold-side of the module, the temperature of which is actually lower than the surrounding temperature ( Supplementary Fig. 3).
Nevertheless, heat transferred between the heat-flow meter and the surroundings is estimated to be only about 0.9% of the total heat Q. Even operating at a hot-side temperature of 550 K, additional heat transferred due to the thermal conduction of thermocouples, wires attached to the module and heat-flow meter, is estimated to be not greater than 2% of Q according to the Fourier's law. Due to the small contribution, this work does not take into account the effect of heat transferred by these wires and thermocouples shown in Supplementary Fig. 1b.

Uncertainty analyses:
In this work, an oxygen-free Cu-bar is used as the heat-flow meter. The thermal conductivity (к) of Cu is determined by к=dCpD, where d, Cp, D are density, heat capacity and thermal diffusivity. The density was estimated by mass/volume and the thermal diffusivity was measured by a laser flash technique (Netzsch LFA457), the uncertainty in the measurement of к is about 5% (Supplementary Fig. 2). The uncertainties of cross-area (ACu) and length (LCu) are less than 1%. At given steady temperature gradients applied to the module, the corresponding ΔTCu=T1-T2 fluctuate within 2~8% (Supplementary Table 2). Note that the uncertainty of ΔTCu decreases with increasing temperature gradient of the module (ΔT), leading to a small uncertainty of ~2% at the high-efficiency temperature gradient of ΔT=270 K. Moreover, to verify the accuracy and sensitivity of the heat-flow meter, intentionally varied hot-side temperature Th of the module lead to corresponding synchronous variations in T1 and T2 of the heat meter, however, ΔTCu=T1-T2 easily gets stabilized ( Supplementary Fig. 5). No matter how the temperature gradient of the module is applied, steady or fluctuated, ΔTCu shows a rough linear increase with increasing ΔT (Supplementary Fig. 5f and Supplementary   Fig. 2d). The open-circuit voltage (Voc) responds quickly to the hot-side temperature ( Supplementary Fig. 6), further suggests the high responsivity of the measurement setup. In addition, the nice agreement in module efficiencies measured either by a steady-temperature-gradient or by oscillating-temperature-gradient techniques, confirms the excellent responsivity of the measurement setup (Supplementary Fig. 26 and Supplementary Fig. 27). All these features confirm the overall good stability/reliability/sensitivity of the heat-flow meter ( Supplementary Fig. 2c).
Therefore, the overall uncertainty of the efficiency measurement in this work is about 7~12%, depending on the temperature gradients applied to the module, and a larger temperature gradient tends to reduces the uncertainty (Supplementary Table 2).

Prediction of heat-flow:
In this work, the heat-flow of a thermoelectric module is estimated by a simplified analytical one-dimensional model 5 . The internal resistance of the module (Rin) is: where Rmaterials is the total resistance of the thermoelectric materials, Rcontact is the total contact resistance, N is the number of pairs of couples, L is the length of each thermoelectric leg, Ap and An are respectively the cross-sectional areas of p-leg and n-leg,ρp andρn are respectively the average resistivity of p-type material and n-type material. The open-circuit voltage (Voc) and the output power (P) of the module are: where Th and Tc are respectively the hot-side and cold-side temperatures,Sp andSn are respectively the average Seebeck coefficient of p-type and n-type materials, I is the current.
The open-circuit heat-flow (Qoc) of the module is: whereκp andκn are respectively the average thermal conductivity of p-type and n-type materials.
The input heat at the hot side (Qinput) of the module: where βp and βn are combined coefficient of p-type and n-type materials, respectively. S7 The heat-flow at the cold-side of the module (Q) can be estimated by: The prediction of Q is shown in Supplementary Fig. 24b.

Calibration of the module measurement system:
In this work, the measurement accuracy has also been double checked with the results measured by the commercial instruments from both material and module levels.
For the module level, a commercial Bi2Te3 module HT-01702 from TECooler Technology 6 Fig. 7 and Supplementary Fig. 8). The output power P=VI measured by our setup is distinguishable to that by Mini-PEM (Advance Riko, Japan), indicating the nice accuracy here in electrical properties measurements. More importantly, the heat-flow (Q) measured by this system is also highly comparable to that by Mini-PEM. This leads the maximum conversion efficiencies (ηmax) of the commercial Bi2Te3 module measured by different apparatus and that disclosed by TECooler Technology to be almost the same, ensuring the accuracy of the system here for efficiency measurements (Supplementary Fig. 9). For the materials level, the average thermal conductivity (κavg) of p-type CdSb and n-type Mg3SbBi alloys is measured by a laser flash technique (Netzsch LFA467) and the steady-state technique using the exact heat-flow meter. The dimensions of the pand n-type materials are 10×10×2.1 mm 3 and 10×10×2.3 mm 3 , respectively. As shown in Supplementary Fig. 10, the laser flash method tends to show a lower thermal conductivity than that measured by a steady-state technique, which was indeed confirmed by our measurements in both n-and p-type materials (red data points by LFA467 locating slightly underneath those by heat-flow meter). Furthermore, we also corrected the measurement results by the steady-state technique (using the heat-flow meter), taking into account the effect of horizontal thermal radiations (absence of vertical ones in this measurement). Note that the steady-state technique (using the heat-flow meter) leads to a higher thermal conductivity than that measured by the laser flash method in both n-and p-type materials ( Supplementary Fig. 10).   Supplementary Fig. 19. SEM images and EDS mapping of Ni/ CdSb after 14-days aging at temperature of 550 K.  Module-3     CdSb (a, b, c) and Ni/Fe /Mg3SbBi (d, e, f) interfaces.