For the single-leg n-type ZrCo0.9Ni0.1Bi0.85Sb0.15, the thermoelectric materials were polished for a cross-section of 1.51 × 2.35 mm2 and length of ~8.54 mm. For the unicouple of ZrCoBi-based materials, the dimensions are 1.51 × 2.35 × 8.54 mm3 for the n-type ZrCo0.9Ni0.1Bi0.85Sb0.15 and 1.61 × 2.42 × 8.54 mm3 for the p-type ZrCoBi0.65Sb0.15Sn0.2. The cold-side temperature was maintained at ~303 K by water circulation. Because of the increasing of heat flow, the cold-side temperature will rise with the hot-side temperature. The difference between the measured efficiency and the predicted value increases with increasing hot-side temperature because the predicted value is calculated on the basis of the fixed cold-side temperature (room temperature). The experiments were conducted under high vacuum (below 10−6 mbar) to reduce parasitic conduction and convection losses. To measure conversion efficiency (η), the input power from the hot side (Qin) and the generated power (P) from the thermoelectric leg were measured at the same time. The direct measurement of Qin is greatly challenging because of the heavy heat loss at high temperature. According to Fourier’s law, a bulk polycrystalline graphite with measured geometry and thermal conductivity was placed below the cold-side end to measure the heat flow out of the cold-side end (Qout). The thermal conductivity of the bulk polycrystalline graphite was confirmed by the method described above in the discussion on thermoelectric property measurements. To measure temperature differences of the leg and graphite bulk, K-type thermocouples were embedded at the interfaces. It should be noted that the hot-side temperature of graphite can be regarded as the cold-side temperature of the leg if the setup is working under a large pressure. The total Qin equals the sum of Qout, P, and radiation loss from the leg (Qrad). Therefore, the conversion efficiency (η) can be written as followsη=PQin=PQout+P+Qrad(4)

Because Qrad cannot be directly measured, in real measurement, Qin is composed of Qout and P, which leads to the measurement error of η. By tuning the current in the circuit, a series of Qin, P can be measured at the same time. Therefore, both maximum η and P can be found. The main sources of error in this system are the radiation heat, the rise of the cold-side temperature, the Seebeck coefficient of copper wire, and the parasitic electrical and heat loss. In the measurement of p-type leg efficiency (42), to offset the radiation loss, copper foil working as a radiation shield was brazed with copper plate at the hot side. Because this radiation shield is at a higher temperature than the leg, it will add additional heat flow into the leg so that the measured Qout will actually be higher than without the shield. This should lead to a more conservative value of efficiency for the p-type leg, especially at high temperature.

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