Measurement of thermal conductivity and specific heat by impedance spectroscopy of Bi2Te3 thermoelectric element

Abstract

The thermal conductivity (κ) and specific heat (Cp) of a thermoelectric element consisting of Bi2Te3 (SRM 3451) were obtained by impedance spectroscopy and using only electrometric measurements. The dimensionless figure of merit (zT) was successfully estimated by the four-probe method from the frequency dependence of the impedance, and the result was compared with that obtained using the two-probe method. The calculated values of zT and resistivity were 0.577 and 13.4 µΩ m, respectively, at 300 K, which allowed us to obtain κ = 2.11 W/(m K) and Cp = 165 J/(kg K) by using a Seebeck coefficient of −233 µV/K, a thermal diffusivity of 1.68 mm2/s, and a mass density of 7.60 g/cm3 from our earlier electrometric measurements. The calculated κ and Cp are quite reasonable when compared to reported values. We thus conclude that, without relying on calorimetric measurements, impedance spectroscopy is a powerful technique for determining not only zT but also the thermal properties of thermoelectric materials via the Peltier effect.

Dimensionless figure of merit of constantan estimated using impedance spectroscopy

“…The zT is calculated as a result of measuring each of the parameters, S, ρ, and κ. 1) Additionally, impedance spectroscopy has been introduced to determine the zT of merit directly from the frequency dependence of the impedance Z(ω) as follows: [5][6][7][8][9][10][11][12] where ΔT is the temperature difference along the length of the sample in the frequency domain, I is the alternating current, R ohm and R TE are the ohmic resistance and impedance derived from the thermoelectric effect, respectively, K is the thermal conductance, A and L are the cross-section and length of each thermoelectric element, respectively, and ω TE is the characteristic angular frequency proportional to α/L 2 , where α is the thermal diffusivity. Further, this technique has the advantage of estimating the κ without controlling the heat flux using the thermoelectric material after measuring the Seebeck coefficient from the definition of the zT:…”

“…Several authors have reported different models and experimental techniques to evaluate the zT using materials that exhibit high zT values such as bismuth telluride, which has zT ∼ 1. [5][6][7][8][9][10][11][12] On the other hand, impedance spectroscopy can be applied to assess the thermoelectric parameters of materials with significantly low values of the zT. Therefore, in this study, we investigated the feasibility of employing impedance spectroscopy for estimating thermoelectric parameters using constantan, which has a larger S compared to metals.…”

“…We conclude believe that this was the primary reason for observing a slightly higher experimental value of the resistivity compared to the value from the literature (ρ B > ρ l ). Although the four-probe method can be used to avoid the contact resistance when the sample resistance is significantly larger than the contact resistance or the appropriate binder is not found, 12) high contact resistance prevents driving the Peltier heat. Additionally, the desirable results of κ B = 24 W mK −1 were advantageously obtained in the experimental configuration.…”

Electronic structure and thermal conductance of the MASnI3/Bi2Te3 interface: a first-principles study

“…The results indicate that the effective thermal conductivity of Bi 2 Te 3 /MASnI 3 asymptotically approaches 0.17 W/(m·K) at a film thickness sufficiently larger than 1 µm. This value is calculated from the experimental values of Bi 2 Te 3 and MASnI 3 : 2.11 W/(m·K) 62 and 0.09 W/(m·K) 41 , respectively. This upper limit does not depend on the interfacial thermal conductance because the influence of the interface is negligible in the limit of large D. In contrast, when the film thickness is sufficiently smaller than 1 µm, the interfacial thermal conductance significantly influences the effective thermal conductivity.…”

Determining phonon transport properties of bismuth telluride thin films with extremely small grain size using nanoindentation and 3ω method

“…Therefore, phonon MFP of the Bi 2 Te 3 film was estimated using the group velocity and lattice thermal conductivity presented in Tables I and II while specific heat C was used with a literature value of 165 J (kg −1 •K −1 ). 28) Thus, the phonon MFP of the Bi 2 Te 3 film was determined to be 0.49 nm, which was 35% of the value for the singlecrystal. In addition, the phonon MFP of the Bi 2 Te 3 film was 14% for the grain size, indicating that the phonons were scattered inside the grains at point defects such as atomic vacancies and grain boundaries.…”