Phase Formation Behavior and Thermoelectric Transport Properties of S-Doped FeSe_2−xS_x Polycrystalline Alloys

Abstract

Some transition-metal dichalcogenides have been actively studied recently owing to their potential for use as thermoelectric materials due to their superior electronic transport properties. Iron-based chalcogenides, FeTe₂, FeSe₂ and FeS₂, are narrow bandgap (~1 eV) semiconductors that could be considered as cost-effective thermoelectric materials. Herein, the thermoelectric and electrical transport properties FeSe₂–FeS₂ system are investigated. A series of polycrystalline samples of the nominal composition of FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8) samples are synthesized by a conventional solid-state reaction. A single orthorhombic phase of FeSe₂ is successfully synthesized for x = 0, 0.2, and 0.4, while secondary phases (Fe₇S₈ or FeS₂) are identified as well for x = 0.6 and 0.8. The lattice parameters gradually decrease gradually with S content increase to x = 0.6, suggesting that S atoms are successfully substituted at the Se sites in the FeSe₂ orthorhombic crystal structure. The electrical conductivity increases gradually with the S content, whereas the positive Seebeck coefficient decreases gradually with the S content at 300 K. The maximum power factor of 0.55 mW/mK² at 600 K was seen for x = 0.2, which is a 10% increase compared to the pristine FeSe₂ sample. Interestingly, the total thermal conductivity at 300 K of 7.96 W/mK (x = 0) decreases gradually and significantly to 2.58 W/mK for x = 0.6 owing to the point-defect phonon scattering by the partial substitution of S atoms at the Se site. As a result, a maximum thermoelectric figure of merit of 0.079 is obtained for the FeSe_1.8S_0.2 (x = 0.2) sample at 600 K, which is 18% higher than that of the pristine FeSe₂ sample.

1. Introduction

Thermoelectric materials have been widely studied in recent years, owing to their ability to convert waste thermal gradients into electrical energy [1]. The energy-conversion efficiency of thermoelectric materials can be evaluated using the dimensionless thermoelectric figure of merit, zT, which is expressed by the following Equation (1).

$$zT=\frac{\sigma S^2}{{\kappa }_{tot}}T$$

(1)

where σ, S, T, and κ_tot are the electrical conductivity, Seebeck coefficient, absolute temperature, and total thermal conductivity, respectively [2,3,4]. Generally, κ_tot is divided into two terms:

$${\kappa }_{tot}={\kappa }_{elec}+{\kappa }_{latt}$$

(2)

where κ_elec and κ_latt are the electrical and lattice thermal conductivities, respectively. zT can be improved by increasing the power factor (σ∙S²) or reducing κ_tot. However, the trade-off between σ and S and the proportionate relationship between σ and κ_elec make it difficult to improve zT. One strategy to obtain a high zT is to reduce κ_latt via point-defect phonon scattering, which can be achieved by doping or using a partial solid solution [5,6]. For example, Asfandiyar et al. investigated the thermoelectric properties of alloyed samples in an SnS–SnSe system, and they reported that the κ_latt of the alloyed samples was lower than that of the nonalloyed samples, and that the zT of the alloyed samples was greatly enhanced [7].

Transition-metal dichalcogenides (TMDCs) such as HfSe₂ [8,9], HfTe₂ [10], MoSe₂ [11], and SnSe₂ [12,13] have attracted significant attention because of their high potential for use as thermoelectric materials. Generally, TMDCs have a large effective mass owing to the presence of local d- or f-orbital electrons, leading to a large magnitude of S [14]. Among these TMDCs, FeSe₂ and FeS₂ have been actively investigated as promising thermoelectric materials. FeSe₂ is a p-type semiconductor with a narrow direct bandgap of ~1 eV [15]. FeSe₂ is known to be thermally and structurally stable, as previous studies have reported [16,17]. It has a high carrier concentration, of 10¹⁸–10¹⁹ cm⁻³, and is considered a good candidate for thermoelectric applications [17,18]. FeS₂ is a semiconductor with a narrow bandgap (~1 eV) and is one of the most abundant sulfides in the Earth’s crust [19]. It is nontoxic, inexpensive, and is considered a promising cost-effective thermoelectric material. By combining the first-principles calculations with the Boltzmann transport theory, Harran et al. predicted that the zT of FeS₂ could reach approximately 0.45 [20,21].

In this study, the electrical and thermoelectric transport properties of a series of polycrystalline FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8) samples of the FeSe₂–FeS₂ system are investigated. The S substitution for the Se site was successful up to S content of x = 0.6. The σ increased gradually with the S content, whereas the positive S decreased gradually with the S content at 300 K. The weighted mobility of the samples is calculated and analyzed to understand the electrical transport properties better. With an increase in S content, the κ_latt decreases gradually and significantly.

2. Experimental Section

Polycrystalline FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8) samples were synthesized via a conventional solid-state reaction in vacuum-sealed quartz tubes. High-purity raw materials: Fe (99.9%, Kojundo Chemical Laboratory Co., Ltd., Tolya, Japan), Se (99.999%, 5 N Plus), and S (99.995%, Sigma-Aldrich, St. Louis, MO, USA) were weighed stoichiometrically and heated at 833 K for 48 h. The obtained ingots were pulverized into powder using a ball-milling machine (SPEX 8000D, SPEX, Costa Mesa, CA, USA). Each powder sample was densified through spark plasma sintering (SPS-1030, Sumitomo Coal Mining Co. Ltd., Japan) at 803 K for 7 min under a pressure of 75 MPa. The crystalline structures of the sintered samples were identified through X-ray diffraction (XRD, D8 Discover, Bruker, Billerica, MA, USA) using Cu K_α1 radiation. Energy-dispersive X-ray spectroscopy (EDS) and EDS mapping were measured by secondary electron microscopy (SEM). The thermoelectric transport properties (σ and S) of the samples were measured using a thermoelectric evaluation system (ZEM-3M8, Advance Riko, Kanagawa prefecture, Japan) in the temperature range of 300–600 K. Hall measurements were conducted in the van der Pauw configuration using a Hall measurement system (HMS-5300, Ecopia, Korea) at 300 K. The thickness of the specimen for Hall measurement were 0.75, 0.73, 0.70 and 0.70 mm for x = 0, 0.2, 0.4, and 0.6, respectively, and the applied electric current and magnitude of the magnetic field were 20 mA and 0.553 T, respectively. The κ_tot of each sample was calculated as follows:

$${\kappa }_{tot}=\alpha \rho C_p$$

(3)

where α, ρ, and C_p are the thermal diffusivity, density, and specific heat capacity, respectively. The α of the samples were measured in the range of 300–600 K through laser flash analysis (LFA457, Netzsch, Germany). Theoretical densities (D_x) of FeSe₂ and FeS₂ are 7.125 and 4.882 g/cm³ (JCPDS #01-079-1892 and JCPDS #00-037-0375) respectively, and the D_x for the alloyed samples were considered to be the average value according to the solid solution ratio; the D_x values for the samples were 7.13, 6.90, 6.68, 6.45, and 6.23 g/cm³ for x = 0, 0.2, 0.4, 0.6, and 0.8, respectively. The bulk densities for the samples were measured using the Archimedes method, and the relative densities were obtained from D_x and bulk densities. The calculated relative density values were 99.7, 98.9, 98.3, 98.3, and 97.8% for x = 0, 0.2, 0.4, 0.6, and 0.8, respectively. The C_p for the samples was measured using a differential scanning calorimeter (DSC8000, Perkin Elmer, Waltham, MA, USA).

3. Results and Discussion

Figure 1a shows the XRD patterns of the sintered samples of FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8). The samples with x = 0, 0.2, and 0.4 exhibited a single orthorhombic phase (FeSe₂, JCPDS #01-079-1892) without any impurity. However, for the samples with higher S content (x = 0.6 and 0.8), a secondary phase (Fe₇S₈, JCPDS #01-089-1954) was identified. For the sample with x = 0.8, the peak intensity of the Fe₇S₈ secondary phase was increased and a small amount of FeS₂ was observed. The relative peak intensities remain similar for the samples with x = 0, 0.2, 0.4, and 0.6 (See Table S1 in Supplementary Materials). In addition, the grain sizes D for the samples (x = 0, 0.2, 0.4, and 0.6) were estimated using the Scherrer equation [22]:

$$D=\frac{K\lambda }{\beta \cos \theta }$$

(4)

where K, λ, θ, and β are the Scherrer constant, the wavelength of the X-ray beam, Bragg angle, and full width at half maximum, respectively. The K value of 0.94 was used, assuming the spherical crystallites. The calculated D values for the samples were 39.8, 39.2, 32.2, and 24.8 nm for x = 0, 0.2, 0.4, and 0.6, respectively. Even though the grain size of x = 0.6 is a bit smaller (possibly due to secondary phase formation), it can be known that there is no large difference in microstructures between samples of x = 0, 0.2, 0.4, and 0.6. The lattice parameters a, b, and c for the FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8) crystal structures were calculated and are shown with error bars in Figure 1b. All lattice parameters decreased gradually with an increase in S content when x < 0.8, which confirmed that S atoms were successfully substituted at Se sites in the FeSe₂ crystal structure (the ionic radii of S²⁻ and Se²⁻ are 170 and 184 pm, respectively). However, the lattice parameters a, b, and c for x = 0.8, exhibited values similar to that for x = 0.6, suggesting that further S substitution at Se sites was limited. The EDS-SEM results are shown in Figure S1 and the atomic ratios measured by EDS-SEM are shown in Table S2 (Supplementary Information). The S-excess/Se-deficient regions are seen for x = 0.8, where the secondary phases started to be seen. The overall compositional ratios of S increases as S doping increases (Table S2 in Supplementary Information).

Figure 2a shows the σ values of the FeSe_2−xS_x (x = 0, 0.2, 0.4, and 0.6) samples. The sample with x = 0.8 with extensive secondary phases, which did not show the gradual decrease in lattice parameters, exhibited much higher σ values ~440 S/cm at 300 K (Not shown in Figure 2a). The thermoelectric measurement data of the x = 0.8 sample is not included due to the non-systematic change due to the existence of the secondary phases. The σ of the samples increased with temperature, exhibiting intrinsic semiconducting behavior. The σ values were 12.4, 15.3, 19.8, and 49.6 S/cm at 300 K, and 247, 315, 353, 442, and 1170 S/cm at 600 K for x = 0, 0.2, 0.4, and 0.6, respectively. The value of σ increased gradually with an increase in S content, over the entire temperature range. The relationship between σ and T can be expressed by the Arrhenius relationship [23]:

$$\sigma ={\sigma }_0\exp \left(-E_a/kT\right)$$

(5)

where k is the Boltzmann constant and E_a is the activation energy. The inset in Figure 2b shows the Arrhenius relationship (logarithmic σ as a function of 1000/T) for the samples and Figure 2b shows the calculated E_a with respect to x. Noticeable changes in the slope were observed at 400–450 K (Inset of Figure 2b). The calculated E_a values of the samples were 0.033, 0.032, 0.028, 0.013, and 0.006 eV in the low-temperature range and 0.123, 0.115, 0.114, 0.108, and 0.048 eV in the high-temperature range for x = 0, 0.2, 0.4, 0.6, and 0.8, respectively. The E_a decreased gradually with an increase in S content in both low- and high-temperature ranges.

Figure 2c shows S as a function of the temperature for the FeSe_2−xS_x (x = 0, 0.2, 0.4, and 0.6) samples. The S values of the samples at 300 K were 445, 146, 85, and 6 μV/K for x = 0, 0.2, 0.4, and 0.6, respectively. All the samples exhibited positive S values at 300 K, showing p-type conduction: however, the conduction changes to n-type at 400–500 K. At higher temperatures, the S values of all the samples became negative and the S values of the samples at 600 K were gradually decreases from −143 to −62 μV/K. Interestingly, the magnitude of S decreased gradually with increasing S content at both 300 and 600 K.

Figure 2d,e shows the calculated power factors of the samples where the conduction is p- and n-type, respectively, according to the temperature range. In Figure 2d, the power factor of p-type conduction was the highest for the pristine FeSe₂ sample (x = 0), exhibiting a maximum value of 0.31 mW/mK² at 350 K. The power factors of the alloyed samples (x = 0, 0.2, 0.4, and 0.6) were lower than that of the pristine sample, despite the increase in σ, mainly owing to the significant decrease in S at the low-temperature range. However, when considering the power factor of the n-type conduction, the power factor at 600 K of x = 0.2 and 0.4 was comparable to the pristine sample (the power factors of the samples at 600 K were 0.50, 0.55, 0.48, 0.17, and 0.051 mW/mK² for x = 0, 0.2, 0.4, 0.6, and 0.8, respectively). The power factor of the sample with x = 0.2 was the highest, which could be attributed to an increase in σ and a small decrease in the magnitude of S. Therefore, a maximum power factor of 0.55 mW/mK² was achieved for the sample with x = 0.2 at 600 K, which was 10% higher than that of pristine FeSe₂. The sample of x = 0.6 exhibits lower power factors due to a large decrease in the magnitude of S.

Figure 3a,b present the Hall carrier concentration (n_H) and Hall mobility (μ_H) of the samples, measured at 300 K. The n_H values were 1.67 × 10¹⁹, 1.81 × 10¹⁹, 1.91 × 10¹⁹, and 3.80 × 10¹⁹ cm⁻³ and the μ_H values were 4.01, 4.90, 5.97, and 6.44 cm²/Vs, for x = 0, 0.2, 0.4, and 0.6, respectively. All the samples exhibited positive n_H values at 300 K, and n_H and μ_H increased gradually with an increase in x. Thus, the increase in the σ of the samples could be due to the simultaneous increase in n_H and μ_H. Furthermore, an increase in carrier concentration generally leads to a decrease in the magnitude of S, according to the Mott relationship [24]:

$$S=\frac{8{\pi }^2{k}^2}{3e{h}^2}{m}_d^{*}T{\left(\frac{\pi }{3n}\right)}^{\frac{2}{3}},$$

(6)

where m_d*, e, and h are the density-of-state effective mass, elementary charge, and Planck’s constant, respectively. Therefore, the decrease in the magnitude of S for the alloyed samples at 300 K could be attributed to the increase in n_H. Figure 3c,d show the m_d* values of the samples at 300 K calculated using the measured S and n_H, based on the relationship in Equation (6). The m_d* values of the samples were 1.45, 0.50, 0.30, and 0.04 m₀ for x = 0, 0.2, 0.4, and 0.6, respectively. The m_d* values decreased gradually with an increase in S content.

Figure 3e shows the weighted mobility (μ_w) of the samples, obtained for a better understanding of the thermoelectric properties of the samples. The μ_w was calculated using the measured σ and S from a simple analytic form that approximates the exact Drude–Sommerfeld free-electron model for |S| > 20 μV/K [25]:

$${\mu }_w=\frac{3h^3\sigma }{8\pi e{\left(2m_{e}kT\right)}^{3/2}}\left[\frac{\exp \left[\frac{\left|S\right|}{k/e}-2\right]}{1+\exp \left[-5\left(\frac{\left|S\right|}{k/e}-1\right)\right]}+\frac{\frac{3}{{\pi }^2}\frac{\left|S\right|}{k/e}}{1+\exp \left[5\left(\frac{\left|S\right|}{k/e}-1\right)\right]}\right],$$

(7)

where m_e is the electron mass. μ_w is closely related to the theoretically optimum electrical performance of a thermoelectric material, and is relevant to the maximum power factor when n_H is tuned properly [26]. Therefore, the μ_w trend was very similar to that of the power factor. The values of μ_w at 600 K were 20.3, 22.7, 20.9, and 11.9 cm²/Vs for x = 0, 0.2, 0.4, and 0.6, respectively. The μ_w increased initially at x = 0.2 and decreased gradually at x > 0.2, which was in agreement with the power factor trend at 600 K.

Figure 4a,b show the κ_tot and κ_latt of the samples as functions of temperature. The inset of Figure 4a shows the temperature dependence of κ_elec. The κ_elec of the samples was calculated according to the Wiedemann–Franz law [27]:

$${\kappa }_{elec}=L\sigma T$$

(8)

where L is the Lorenz number. Subsequently, the κ_latt was calculated by subtracting κ_elec from κ_tot. The electronic contribution to κ_tot was not very significant; thus, κ_tot and κ_latt exhibited similar values. The κ_latt values of the samples were 7.96, 6.07, 4.47, and 2.58 W/mK at 300 K and 4.29, 3.85, 3.51, and 2.10 W/mK at 600 K, for x = 0, 0.2, 0.4, and 0.6, respectively. The κ_latt decreased gradually as the S content increased, over the entire temperature range, which was attributed to the point-defect phonon scattering caused by the partial substitution of S atoms at Se sites (the atomic masses of S and Se are 32.065 and 78.96 amu and the ionic radii of S²⁻ and Se²⁻ are 170 and 184 pm, respectively).

Figure 4c,d shows the calculated zT values of p- and n-type conduction, respectively. In Figure 4c, the maximum zT of the pristine sample was ~0.02, and the alloyed samples exhibited even lower zT values below 0.005. On the other hand, in Figure 4d of n-type conduction of high-temperature range, the samples with x = 0.2 and 0.4 exhibited zT values higher than that of the pristine sample, mainly owing to the decrease in κ_tot. Consequently, the FeSe_1.8S_0.2 (x = 0.2) sample exhibited a maximum zT value of 0.079, which was approximately 18% higher than that of the pristine FeSe₂ sample.

4. Conclusions

A series of FeSe_2−xS_x (x = 0, 0.2, 0.4, 0.6, and 0.8) polycrystalline samples were synthesized by a conventional solid-state reaction, and their thermoelectric transport properties were examined in an effort to search for the cost-effective thermoelectric materials. A single orthorhombic FeSe₂ phase was successfully synthesized for x = 0, 0.2, and 0.4; however, a secondary phase (Fe₇S₈ or FeS₂) was identified for x = 0.6 and 0.8. The lattice parameters decreased gradually with an increase in S content for x < 0.8, suggesting that S atoms were substituted at the Se sites in the FeSe₂ crystal structure. The electrical conductivity increased gradually with an increase in S content, whereas the magnitude of S decreased gradually with an increase in S content. As a result, the sample with x = 0.2 exhibited a maximum power factor of 0.55 mW/mK² at 600 K. The total thermal conductivity decreased significantly with an increase in S content, and thus a maximum thermoelectric figure of merit value of 0.079 was obtained for the FeSe_1.8S_0.2 (x = 0.2) sample at 600 K, which was approximately 18% higher than that of the FeSe₂ (x = 0) sample.