Electrical and Thermal Transport of Layered Bismuth-Sulfide EuBiS₂F at Temperatures between 300 and 623 K

Searching for novel thermoelectric materials is the most fundamental issue for the development of thermoelectrics because the maximum conversion efficiency of a thermoelectric device is primarily determined by the material's dimensionless figure of merit, \(\mathit{ZT}= S^{2}T\rho^{-1}\kappa^{-1}\), where T, S, ρ, and κ denote the temperature, Seebeck coefficient, electrical resistivity, and thermal conductivity, respectively.¹⁾ Bismuth telluride (Bi₂Te₃) and its related compounds have been the state-of-the-art thermoelectric materials at around room temperature since the 1950s with a \(\mathit{ZT}\) value as high as 1.4 in a nanocrystalline bulk specimen.²⁾ Compared with tellurides and selenides, little attention has been paid to the thermoelectric properties of bismuth-based sulfides because of their low \(\mathit{ZT}\) value. However, recent studies on sulfide systems have clearly shown that sulfides also exhibit attractive thermoelectric properties.³⁾ Aside from thermoelectricity, the superconductivity of layered bismuth sulfides, such as Bi₄S₃O₄ and LaBiS₂O\(_{1-x}\)F_x,^4,5) has led to novel studies on superconductivity (the chemical formula is written according to standard nomenclature⁶⁾). The crystallographic structures of these compounds are basically composed of alternate stacks of BiS₂ and oxide/fluoride layers, as shown in the inset of Fig. 1. The conduction band near the Fermi level is primarily composed of in-plane Bi \(6p\) orbitals. The thermoelectric properties of LaBiS₂O are suppressed by F substitution,⁷⁾ whereas they are improved by Se substitution.⁸⁾ Recently, EuBiS₂F has been reported as a possible compound that exhibits charge-density-wave-like order below 280 K and superconductivity below 0.3 K without element substitution.⁹⁾ Specific heat measurement showed significant hybridization between Eu \(4f\) and Bi \(6p\) electrons, while density functional theory (DFT) calculation indicates that the valence band maximum consists of Eu \(4f\) orbitals.⁹⁾ Given the results shown in the previous study, it was controversial from the viewpoint of thermoelectricity, whether Eu \(4f\) and Bi \(6p\) hybridized orbitals are effective in modulating the Fermi surface and enhancing S,¹⁰⁾ or reducing S owing to the coexistence of electrons and holes, i.e., mixed conduction. In this study, we demonstrate the electrical and thermal transport of EuBiS₂F at temperatures between 300 and 623 K.

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Figure 1. (Color online) XRD pattern of EuBiS₂F and the results of Rietveld analysis. The arrows denote the diffraction peaks due to unknown impurities. The lattice parameters were calculated to be \(a = 0.40488(1)\) nm and \(c = 1.353240(6)\) nm. The reliability factor (\(R_{\text{wp}}\)) is 8.48%. The inset shows the crystallographic structure of EuBiS₂F.

Polycrystalline EuBiS₂F was prepared by a solid-state reaction using a sealed silica tube, following the method reported by Zhai et al.⁹⁾ The sample purity was examined by X-ray diffraction (XRD) collected using Cu Kα radiation (Rigaku RINT 2500). Rietveld analysis was performed using the RIETAN-FP code.¹¹⁾ The relative density of the sample was calculated to be 90%.

The Hall coefficient (\(R_{\text{H}}\)) at room temperature was measured using the four-probe geometry under magnetic fields (H) of up to \(\mu_{0}H =\pm 1\) Tesla. The measurements of ρ, S, and κ were conducted between room temperature and about 623 K using a lamp heating unit (Ulvac MILA-5000), which was described elesewhere.¹²⁾ Measurements of the electrical and thermal transport of the polycrystalline sample were performed in the same direction.

Figure 1 shows the XRD pattern of the sample and the results of Rietveld refinement. Almost all diffraction peaks corresponded to those of the EuBiS₂F phase, indicating that this phase was dominant in the samples. Although diffraction peaks due to unknown impurities were also observed, the diffraction intensities of the impurity phases relative to those of EuBiS₂F were ∼1%, suggesting that the amount of impurities was at these levels in the sample. The bond valence sum (BVS) of Eu was calculated to be 2.16(1),^13,14) which was consistent with the previously reported value,⁹⁾ indicating electron doping into the BiS₂ conduction layer. The negative polarity of \(R_{\text{H}}\) at 300 K confirms that the dominant carriers are electrons at this temperature. \(n_{\text{H}}\) was calculated to be \(3.2(2)\times 10^{21}\) cm⁻³ assuming a single-band model.

Figure 2 shows the electrical and thermal transport properties versus the temperature of EuBiS₂F. ρ is 3.9 mΩ cm at 300 K and it slightly decreases with increasing temperature, as shown in Fig. 2(a). On the other hand, Zhai et al. reported ρ of ∼2.2 mΩ cm at 300 K with a positive temperature coefficient (\(d\rho/dT\)) between 300 and 350 K.⁹⁾ This different ρ–T plot is probably due to self-doping owing to the mixed valence of Eu and/or inevitable Bi off-stoichiometry, which is previously examined using X-ray diffraction¹⁵⁾ and scanning tunneling microscopy.¹⁶⁾

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Figure 2. (Color online) (a) Electrical resistivity (ρ), (b) Seebeck coefficient (S), and (c) thermal conductivity (κ) of EuBiS₂F.

Figure 2(b) shows S as a function of temperature. The absolute value of S is ∼32 µV K⁻¹ at 300 K and it increases almost linearly up to 623 K. Both ρ–T and S–T plots are similar to those of LaBiS₂O\(_{1-x}\)F_x (\(x\approx 0.5\)),⁷⁾ suggesting that the charged carrier transport of EuBiS₂F at these temperatures is primarily determined by the carrier concentration provided by oxide/fluoride layer, not by the hybridization between Eu \(4f\) and Bi \(6p\) electrons.

Figure 2(c) shows the total thermal conductivity (\(\kappa_{\text{tot}}\)) versus temperature. The lattice thermal conductivity (\(\kappa_{\text{l}}\)) was calculated by subtracting the electronic thermal conductivity (\(\kappa_{\text{el}}\)) from \(\kappa_{\text{tot}}\). \(\kappa_{\text{el}}\) was obtained by the Wiedemann–Franz relation using the Lorenz number of \(2.45\times 10^{-8}\) W Ω K⁻². \(\kappa_{\text{l}}\) was 1.5–2.0 W m⁻¹ K⁻¹ at temperatures between 300 and 623 K. This value is distinctly lower than that of isostructural SrBiS₂F (\(\kappa_{\text{l}}\approx 2.7\) W m⁻¹ K⁻¹),¹⁷⁾ which is attributed to the lower speed of sound resulting from the heavier atomic mass of the Eu ions than that of Sr ions.¹⁸⁾ Notably, the relative density of the sample in this study is 90%. According to the effective medium theory (EMT) by Maxwell Garnett, a 14% reduction in κ is expected from the sample with a relative density of 90% under the assumption that 10% of the pores are randomly distributed and separated spheres.¹⁹⁾ A fully dense sample will be required to elucidate the detailed thermal transport mechanism of these compounds. Furthermore, the EMT predicts an increase in 16% in ρ for the sample with a relative density of 90%. The dimensionless figure of merit is calculated to be 0.02 at 623 K.

We briefly discuss a possible method of improving \(\mathit{ZT}\) for these compounds. A typical way of enhancing \(\mathit{ZT}\) is by tuning \(n_{\text{H}}\). \(\mathit{ZT}\) for state-of-the-art thermoelectric materials, such as Bi₂Te₃ and PbTe, is optimized at \(n_{\text{H}}\) of \(10^{19}\)–\(10^{20}\) cm⁻³,¹⁾ while \(n_{\text{H}}\) for EuBiS₂F is \(3.2(2)\times 10^{21}\) cm⁻³, as described above. However, \(\mathit{ZT}\) for LaBiS₂O, which has \(n_{\text{H}}\) of \({\sim}10^{19}\) cm⁻³,²⁰⁾ is on the same order as that for EuBiS₂F, suggesting that simply tuning \(n_{\text{H}}\) is not an effective way of improving \(\mathit{ZT}\) for these compounds. Band engineering is a more reasonable way of improving \(\mathit{ZT}\), as demonstrated by Se substitution in LaBiS₂O.⁸⁾ Notably, the detailed mechanism of the enhancement of \(\mathit{ZT}\) in Se-doped LaBiS₂O has not been clarified yet. DFT calculation is considered to be effective in shedding light on the issue as well as measurements of the transport properties of fully dense samples.

In summary, we demonstrated the electrical and thermal transport of the layered bismuth-based sulfide EuBiS₂F at temperatures between 300 and 623 K. Although significant hybridization between Eu \(4f\) and Bi \(6p\) electrons was previously reported, the charged carrier transport of EuBiS₂F is similar to that of F-doped LaBiS₂O, at least above 300 K. These results indicate that electron doping into the BiS₂ layer is detrimental to the thermoelectric properties of layered bismuth-chalcogenides. \(\kappa_{\text{l}}\) is distinctly lower than that for isostructural SrBiS₂F, which is probably due to the heavier atomic mass of Eu ions than that of Sr ions.

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