Electronic, Thermal, and Thermoelectric Transport Properties of ReSe2 and Re2Te5

Bang, Joonho; Park, Okmin; Kim, Hyun-Sik; Hwang, Seung-Mee; Lee, Se Woong; Park, Sang Jeoung; Kim, Sang-il

doi:https://doi.org/10.1155/2023/2831961

International Journal of Energy Research

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Abstract Introduction Results Data Availability Conflicts of Interest Authors’ Contributions Acknowledgments Supplementary Materials References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 2831961 | https://doi.org/10.1155/2023/2831961

Electronic, Thermal, and Thermoelectric Transport Properties of ReSe₂ and Re₂Te₅

Joonho Bang,^1,2Okmin Park,³Hyun-Sik Kim,³Seung-Mee Hwang,³Se Woong Lee,³Sang Jeoung Park,³and Sang-il Kim³

Academic Editor: Tholkappiyan Ramachandran

Received26 Sept 2022

Revised02 Nov 2022

Accepted03 Nov 2022

Published06 Feb 2023

Abstract

Re-based chalcogenides have been studied in various fields such as strain engineering, photodetection, spintronics, and electromechanics, as well as in piezoelectric and photonic devices. In this study, the electrical, thermal, and thermoelectric transport properties of two representative Re-based chalcogenides, ReSe₂ and Re₂Te₅, are investigated systematically. Furthermore, their electronic band dispersions are calculated using density functional theory and compared with the phenomenological data. The maximum power factor values for the ReSe₂ and Re₂Te₅ were measured 0.0066 and 0.11 mW/mK² at 880 K, respectively. Thermal conductivity of layered ReSe₂ at room temperature was between 1.93 and 8.73 W/mK according to the measuring direction. For Re₂Te₅ with a complex orthorhombic crystal structure, the thermal conductivity was quite low in the range between 0.62 and 1.23 W/mK at room temperature. As a result, the maximum values of ReSe₂ were quite low as 0.0016 at 880 K due to very low power factor and high thermal conductivity. Meanwhile, the relatively high of 0.145 in Re₂Te₅ is obtained at 880 K, which is originated from the acceptable power factor value and the low thermal conductivity.

1. Introduction

Metal chalcogenides have been receiving increasing attention as potential energy materials due to their tunable electronic properties and unique crystal structures, as well as relatively higher electrical conductivity in comparison to their transition metal oxide counterparts [1–3]. In particular, semiconductor chalcogenides have been widely used in thermoelectric (TE) fields because they have high electrical conductivity and low thermal conductivity, or even due to their unique crystal structures [4–6]. Among them, the layered structure that occupies most of the chalcogenides secures low thermal conductivity due to weak layer-to-layer van der Waals bonding. This is a key point because TE materials’ performance is evaluated using a dimensionless thermoelectric figure of merit, (where , , , and are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively). Therefore, several studies on layered chalcogenides are still being conducted to search for new thermoelectric materials. In fact, layered chalcogenides such as Bi-Te-based materials, InSe, In₄Se₃, HfTe₂, and SnSe₂ are famous TE materials that have high and low [7–13]. Bi-Te-based materials with high at 300-400 K have been reported in various studies [7–9]. In₄Se₃ was reported to have a value of 1.48 at 705 K [11].

Transition metal chalcogenides (TMCs), which have mostly layered structures, are also applicable in the same context. Recently, TMCs have been applied to a wide range of applications including nanoelectronics, sensors, energy conversion, and energy storage as 2D materials [14]. In addition, among the layered TMCs, chalcogenide materials that are based on Zr, Ti, W, and Mo have been widely used in the TE field [15, 16].

ReSe₂ is a one-layered TMC and has been studied in various fields such as strain engineering, photodetection, spintronics, and electromechanics, as well as in piezoelectric and photonic devices [17–20]. In addition, ReSe₂ is semiconductor that has a distinct band gap (1.26 eV for bulk ReSe₂) according to the density functional theory (DFT) of generalized gradient approximation (GGA) calculations from Hafeez et al. and Wolverson et al. [21, 22]. Thus, ReSe₂ may exhibit good TE properties and could be more advantageous due to the interlayer distance being 0.7 nm longer than other layered TMCs such as MoS₂ and WS₂ [17, 23], which leads to lower . Since the interlayer distance is long, of ReSe₂ can be predicted to being substantially large between the - and -axes. Mahmoud and Joubert calculated lattice thermal conductivity () based on bulk ReSe₂ through first principles. In their study, of the (100) and (010) directions were 18.47 and 17.44 W/mK at 300 K, respectively. However, of the (001) direction was 0.69 W/mK [24]. If these characteristics are used well, ReSe₂ can be judged to having sufficient potential as a TE material.

Re₂Te₅, which is another rhenium chalcogenide semiconductor, is not a layered TMC but has a complex orthorhombic crystal structure with 84 atoms ([Re₂₄] and [Te₆₀]) per unit cell. These atoms exhibit a cluster-type Chevrel phase with [Re₆] surrounded by [Te₈] [25–27]. One notable structural property of the Chevrel phase is the presence of 4 large vacancies. This causes the scattering of phonons, which effectively reduces . Because of this, of Re₂Te₅ is 1.3 W/mK, which is similar to that of layered TMCs [28, 29]. In addition, it has the merit of being able to enhance thermoelectric properties through various doping in the 4 vacancies. In fact, Caillat et al. reported that rattling was found in elements doped into the vacancies, resulting in reduced due to phonon scattering [30].

In this study, the electrical, thermal, and thermoelectric transport properties of ReSe₂ and Re₂Te₅ samples were investigated. Notably, the electrical transport properties of ReSe₂ and Re₂Te₅ can be analyzed in more detail using a single parabolic band model. Based on this, the density-of-state effective mass, , was calculated, and was evaluated to confirm the thermoelectric performances. In addition, the measured electrical transport properties were compared with calculated from first-principle DFT calculations.

2. Experimental Method

The ReSe₂ and Re₂Te₅ samples were synthesized via a conventional solid-state reaction process in a vacuum-sealed quartz tube. High-purity elements Te (99.999%), Se (99.999%), and Re (99.99%) powders were weighed with stoichiometric compositions, and mixed powder was loaded in the vacuum-sealed quartz tube. The loaded quartz ampoules were then heated to 950°C for 6 h and this temperature was maintained for 70 h. The synthesized ReSe₂ and Re₂Te₅ were pulverized into powders through high-energy ball milling (SPEX 8000D, SPEX) in Ar atmosphere. The ReSe₂ and Re₂Te₅ powders were placed into a graphite mold and pressed for sintering by spark plasma sintering (SPS, SPS-1030, Sumitomo Coal Mining Co., Ltd.). The ReSe₂ and Re₂Te₅ loaded into graphite molds were sintered at 950°C for 20 min under 70 MPa and 850°C for 10 min under 70 MPa, respectively. During the sintering, vacuum was maintained in the inside of the SPS chamber (~10^-5 Torr).

The crystalline phases of the samples were identified using powder X-ray diffraction (XRD) with a Bruker D8 Discover (Cu K, ) diffractometer at room temperature. XRD measurements for the sintered pellet samples were carried out in two different directions, perpendicular (⟂) and parallel (‖) directions to the SPS pressing direction. The thermoelectric transport properties ( and ) were measured simultaneously using a thermoelectric-property measurement system (ZEM-3, Advanced-Riko) in the two different directions within a temperature range of 300–880 K on the samples in He atmosphere. Power factor (PF) was calculated based on the measured and values. The Hall carrier concentrations and mobilities were calculated using the Hall-Van der Pauw measurement system (HMS5300, Ecopia) under a 0.548 T magnetic field. The values of each sample were calculated from its sample density (), heat capacity (), and thermal diffusivity (). was used as theoretical densities for ReSe₂ and Re₂Te₅. , as presented in Table 1, was measured using a differential scanning calorimeter (DSC8000, Perkin Elmer). Laser-flash analysis was conducted to measure (LFA457, Netzsch). was evaluated based on the measured data.

First-principle DFT calculations were performed using the generalized gradient approximation with the Perdew-Burke-Ernzerhof functional and the projector augmented plane-wave method implemented in the Vienna Ab initio Simulation program code [31–33]. The 5d/6s electrons of Re, the 4s/4p electrons of Se, and the 5s/5p electrons of Te were used as valence electrons. The plan-wave-basis cut-off energy was set to 600 eV. Self-consistency was carried out using unit cells containing 12 and 84 atoms, and and k-point meshes were used for the structural relaxation and the electronic structure calculation of ReSe₂ and Re₂Te₅, respectively. A van der Waals correction was included using the DFT-D3 method with Becke-Johnson rational damping [34, 35]. Structural relaxation was performed until the Hellmann-Feynman forces were less than eV A⁻¹. The atomic positions of the relaxed structures are provided in Table S1 in Supporting Materials.

The transport properties of ReSe₂ and Re₂Te₅ were estimated using the Shankland-Koelling-Wood interpolation as implemented in the BoltzTraP2 code [36, 37]. First, the band structures obtained by DFT calculations were interpolated using the extended Shankland algorithm [38–40]. Next, the Onsager transport coefficients were determined using the linearized Boltzmann transport equation based on the rigid-band approximation [35]. For the calculation of the transport properties, dense and k-point meshes were used for ReSe₂ and Re₂Te₅, respectively.

3. Results and Discussions

Figures 1(a) and 1(c) depict the triclinic (space group: P1[2]) and orthorhombic (space group: Pbca [61]) crystal structures of ReSe₂ and Re₂Te₅, respectively. Figures 1(b) and 1(d) show XRD patterns of the ReSe₂ and Re₂Te₅ polycrystalline bulk samples at the 2θ range from 10° to 50°. In addition, to consider anisotropy for the samples, the measurements were performed along the directions perpendicular (⟂) and parallel (‖) to the sintering pressure direction. From the measured XRD patterns, it was observed that ReSe₂ and Re₂Te₅ have a single triclinic phase and a single orthorhombic phase without impurity, respectively. The lattice parameters are presented in Table 1 with the calculated lattice parameter by DFT calculation. The lattice parameters derived from the experiment were matched to those of JCPDS within an error less than 0.3%. In addition, the lattice parameters were similar with the calculated lattice parameters, while it is commonly known that the calculated lattice parameters by first-principle DFT had a larger value than those of the experimental data.

(a)

(b)

(c)

(d)

Figure 2 shows the measured thermoelectric transport properties for the ReSe₂ and Re₂Te₅ according to measurement directions. ReSe₂ and Re₂Te₅ demonstrated semiconductor transport behavior. As shown in Figures 2(a) and 2(d), the of ⟂ReSe₂ and ‖ReSe₂ are 0.0021 and S/cm at 370 K, respectively, and ⟂Re₂Te₅ and ‖Re₂Te₅ are 0.12 and 0.10 S/cm at 300 K, respectively. of ⟂ReSe₂ (‖ReSe₂) and ⟂Re₂Te₅ (‖Re₂Te₅) gradually increased to 0.56 (0.28) and 32 (25.8) S/cm at 880 K, respectively. In the case of ReSe₂, the -axis was superior to -axis; this is typical in the transport properties of a general layered structure material. Meanwhile, Re₂Te₅ did not differ significantly between the two directions. The maximum of the ReSe₂ in Figure 2(b) was 948 μV/K at 370 K, which was measured in ⟂ direction. However, in the case of Re₂Te₅ shown in Figure 2(e), at 300 K has a maximum value of 515 μV/K. Consequently, the calculated PF shows a maximum value in the ⟂ direction in both cases. The maximum PF values for the ReSe₂ and Re₂Te₅ were 0.0066 and 0.11 mW/mK², respectively.

(a)

(b)

(c)

(d)

(e)

(f)

Table 2 indicates the results of the Hall measurement and at room temperature. As presented, the large difference in is caused mainly by the fact that of Re₂Te₅ is 10⁴ times larger than the of ReSe₂ ( denotes hole concentration). The , which was calculated using Equation (1) [38], for ReSe₂ and Re₂Te₅, was 0.154 and 1.97 ( is the rest mass of an electron), respectively. The fact that the of ReSe₂ is significantly low is also the reason why the of the ReSe₂ is smaller than Re₂Te₅ by a factor of 12 despite its being higher than that of Re₂Te₅. Furthermore, as function of at 300 K was plotted for the ReSe₂ and Re₂Te₅ into insets of Figures 2(b) and 2(e).

Commonly, was estimated using Equation (2). However, because the is only accurate when is lower than 137 μV K^-1 [41], using Equation (2) for ReSe₂ and Re₂Te₅ ( μV K^-1) is not appropriate. Therefore, Equation (1), which is accurate for all degeneracy, was used instead.

Meanwhile, according to the measuring direction, the and values of layered ReSe₂ were 3.12 and 0.251 cm²/Vs, respectively. The and values of Re₂Te₅ were confirmed as 0.308 and 0.273 cm²/Vs, respectively.

Insets of Figures 2(c) and 2(f) are results that calculated weighted mobilities as a function of the temperature for the ReSe₂ and Re₂Te₅. The values were calculated from the measured and ; can be obtained via a simple analytical expression, wherein the exact Drude-Sommerfeld free-electron model is approximated using Equation (3) for μV/K [42]. where is the mass of an electron. is proportional to the maximum PF that a sample can reach when is optimized. Therefore, of ReSe₂ shows as significant difference as in PF with regard to the direction. However, unlike PF, maximum values of these were observed at 480 K (14.5 cm²/Vs, ) and at 580 K (1.40 cm²/Vs, ), respectively. While the difference between and of ReSe₂ decreases for temperatures higher than 480 K, the difference between corresponding PF increases for all temperatures. The large difference in PF observed at 880 K despite the small difference in and suggests that the of ReSe₂ is rapidly shifting away from the optimal . In the case of Re₂Te₅, values about the two directions were 2.47 and 2.036 cm²/Vs, respectively. This is similar to the PF trend at 880 K.

Figures 3(a) and 3(b) show the temperature dependence of the and (: relaxation time) values for ReSe₂ and Re₂Te₅, respectively. For this calculation, we adopt the values of for ReSe₂ and for Re₂Te₅, which are obtained by the Hall effect measurements at 300 K (see Table 2). Both compounds exhibit similar behavior; i.e., the value decreases as temperature increases, whereas the (: relaxation time) value is increased with the increase of temperature. Such trends are in good agreement with the experimental observations (Figures 2(a), 2(b), 2(d), and 2(e)), indicating that our calculational approach is suitable for the present systems. It is noted that there are distinct differences in the transport properties between ReSe₂ and Re₂Te₅: (i) the values of Re₂Te₅ are higher than that of ReSe₂ throughout the whole temperature range, and (ii) the maximum value of ReSe₂ (~1293 μV K⁻¹ at 330 K) is about two times higher than that of Re₂Te₅ (~601 μV K⁻¹ at 500 K).

(a)

(b)

(c)

(d)

(e)

(f)

We also calculated the doping dependence of the and (: relaxation time) values for both compounds (Figures 3(c) and 3(d)). The calculated values are 1330 μV/K for ReSe₂ and 594 μV/K for Re₂Te₅ when the values are and , respectively. These values reasonably agree with the experimental data (see Table 2 and Figures 2(b), 2(c), and 2(e)) but are slightly overestimated. When the increases, the values of both compounds decrease, whereas the values sharply increase. As a result, the values, which are directly correlated with the PF, increase rapidly at the higher until the maximum is reached. This result indicates that the higher PF of Re₂Te₅ compared with that of ReSe₂ in our experimental observation (Figures 2(c) and 2(f)) mainly originates from the ~10⁴ times higher of Re₂Te₅, rather than other parameters such as maximum PF. The optimal values to achieve the maximum PF can be estimated as ~10²⁰ cm⁻³ for both compounds, suggesting that the thermoelectric performance can be further improved by introducing additional hole carriers into ReSe₂ and Re₂Te₅.

The electronic band structures and density of states (DOS) for ReSe₂ and Re₂Te₅ are calculated to elucidate the correlation between the thermoelectric properties and the electronic structure. The calculated band structures and DOS for ReSe₂ and Re₂Te₅ are shown in Figures 3(e) and 3(f), respectively. Both compounds have finite band gaps with values of ~0.9 eV and ~0.7 eV, consistent with the experimentally observed semiconducting transport behavior (Figures 2(a) and 2(d)). By comparing the electronic band structures of ReSe₂ and Re₂Te₅, it was found that Re₂Te₅ has a more complex band structure near the valence band maximum as compared with that of ReSe₂. Such higher band degeneracy facilitates the substantial enhancement of the DOS near the valence band maximum, which mainly consists of Te 5p orbitals (right panel in Figure 3(f)). The high band degeneracy and effective DOS near the valence band maximum are beneficial to achieve a higher power factor in the p-type doping regime [43]. This distinct difference in electronic structures can be understood by comparing their different crystal structure; i.e., the Re cations in ReSe₂ are only bound to the nearby Se anions (Figure 1(a)), whereas the crystal structure of Re₂Te₅ consists of the mixture of the homopolar Te–Te bonds and heteropolar Re–Te bonds (Figure 1(c)), inducing a complex electronic structure.

Figures 4(a) and 4(d) show calculated of ReSe₂ and Re₂Te₅. values of ReSe₂ were gradually decreased in both ⟂ and ‖ directions as the temperature changed. and were 1.93 and 8.73 W/mK at 300 K, respectively, which are quite large. The large difference between two directions is due to the layered structure. The and were gradually decreased to 0.920 and 3.75 W/mK at 880 K. For Re₂Te₅, which has the complex crystal structure, the value was in the range between 0.62 and 1.23 W/mK. The of Re₂Te₅ can be further reduced by possible doping in 4 large vacancies in the unit cell, which can cause rattling effect [27].

(a)

(b)

(c)

(d)

(e)

(f)

Figures 4(b) and 4(e) show evaluated as a function of temperature, while the insets show a dimensionless thermoelectric quality factor for ReSe₂ and Re₂Te₅. The maximum values of ReSe₂ and Re₂Te₅ were 0.0016 and 0.145, respectively, in the ⟂ direction at 880 K. The of ReSe₂ is very low due to low and high , which are not adequate for the good thermoelectric materials. Meanwhile, the relatively high of 0.145 in Re₂Te₅ is originated from the acceptable PF higher than 0.1 mW/mK² and the low-enough smaller than 1.0 W/mK.

The dimensionless thermoelectric quality factor [39] (the insets of Figures 4(b) and 4(e)) is another measure of thermoelectric performance of materials, which can be obtained using the following [39]:

of ReSe₂ is quite low and shows similar trend to , which shows the maximum values at midtemperature. of Re₂Se₅ shows the maximum value of 0.039 at 880 K.

Figures 4(c) and 4(f) depict the plot of the experimental of ReSe₂ and Re₂Te₅ (in symbol) and the calculated of ReSe₂ and Re₂Te₅ (in line) as a function of at 300 K using a single parabolic band (SPB) model under acoustic phonon scattering assumption: where ( is the reduced electrochemical potential) is the Fermi integral of order .

According to the SPB model, both of ReSe₂ and Re₂Te₅ can be significantly improved once is optimized. For example, the maximum at 300 K predicted for ReSe₂ and Re₂Te₅ are and at 300 K, respectively. Based on appropriate tuning, of ReSe₂ and Re₂Te₅ can be improved by more than a factor of 83 () and 4 (), respectively. The optimization of by proper doping in Re₂Te₅ by various strategies, including cation/anion doping and impurity control, may further increase the .

In this study, the electrical, thermal, and thermoelectric transport properties of ReSe₂ and Re₂Te₅ polycrystalline alloys are systematically investigated. The maximum power factor values for the ReSe₂ and Re₂Te₅ were measured 0.0066 and 0.11 mW/mK² at 880 K, respectively. The differences in electronic transport properties between ReSe₂ and Re₂Te₅ were verified with density of state and electronic dispersion calculated from first-principle density functional theory. Thermal conductivity of layered ReSe₂ at room temperature was between 1.93 and 8.73 W/mK according to the measuring direction, which of both are relatively high. For Re₂Te₅ with the complex crystal structure, the thermal conductivity was low in the range between 0.62 and 1.23 W/mK at room temperature. As a result, the maximum thermoelectric figure of merit values of ReSe₂ was quite low as 0.0016 at 880 K due to very low power factor and high thermal conductivity. On the other hand, the relatively high of 0.145 in Re₂Te₅ is seen due to the decent power factor value and the low thermal conductivity. Indeed, adequate doping can enhance the of Re₂Te₅ by further enhancing the power factor by controlling the carrier concentration and reducing the thermal conductivity by filling the 4 large vacancies in the unit cell by rattling effect.

Data Availability

Data are available upon request.

Conflicts of Interest

There is no conflict of interest.

Authors’ Contributions

Joonho Bang, Okmin Park, and Hyun-Sik Kim contributed equally to this work.

Acknowledgments

This research was supported by Nano·Material Technology Development Program through National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2022M3H4A1A04076667).

Supplementary Materials

Additional supporting information may be found in the online version of the article at the publisher’s website. The atomic positions of the relaxed structures of ReSe₂ and Re₂Te₅ are provided in Table S1 in Supporting Materials. (Supplementary Materials)

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Copyright © 2023 Joonho Bang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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