# Electrical, Thermal, and Thermoelectric Transport Properties of Se-doped Polycrystalline Re_{2}Te_{5}

## Article information

## Abstract

Re_{2}Te_{5} is considered a potential thermoelectric material because of its intrinsically low thermal conductivity, due to its complex crystal structure. Herein, a series of Se-doped Re_{2}Te_{5} (Re_{2}Te_{5-x}Se_{x}, *x* = 0, 0.2, 1, and 2) samples were synthesized, and their electrical and thermal transport properties were investigated. Pure orthorhombic Re_{2}Te_{5} phases were successfully synthesized without any impurities for all compositions, and the continuous decrease in the calculated lattice parameters confirmed the substitution of Se atoms at the Te sites. A maximum power factor of 0.135 mW/mK^{2} was achieved for the sample with *x* = 0.2 at 880 K, mainly due to the increase in carrier concentration and electrical conductivity. The lattice thermal conductivity significantly decreased for all doped samples, which was attributed to the point defect phonon scattering caused by Se doping. The thermoelectric figure of merit, *zT* reached a maximum value of 0.20 at 880 K for Re_{2}Te_{4.8}Se_{0.2} (*x* = 0.2) sample, which was approximately 22% higher than that of the pristine Re_{2}Te_{5} sample. The weighted mobility, quality factor, and expected *zT* were calculated to evaluate the optimization of the power factor and *zT*.

**Keywords:**thermoelectric; doping; Re

_{2}Te

_{5}

## 1. INTRODUCTION

Numerous studies on eco-friendly energy-production technologies have been conducted in various fields [1]. In particular, thermoelectric technology can be used for reversible energy conversion—from heat to electricity based on the Seebeck and Peltier effects, respectively [2,3]. Thermoelectric performance is evaluated using the dimensionless thermoelectric figure of merit, *zT* = *S ^{2}σT*/

*κ*, where

_{tot}*S*,

*σ*,

*κ*and

_{tot}*T*are the Seebeck coefficient, electrical conductivity, total thermal conductivity, and absolute temperature, respectively. Generally,

*κ*is divided =

_{tot}*κ*and

_{ele}*κ*, where

_{latt}*κ*and

_{ele}*κ*are electrical and lattice thermal conductivities, respectively. The most important goal of research on thermoelectric materials is to e

_{latt}*n*ance

_{H}*zT*. However,

*κ*and

_{ele}*σ*are closely related to each other according to the Wiedemann-Franz law (

*κ*=

_{ele}*L*·

*σ*·

*T*, where

*L*is the Lorenz number) [4]; consequently, e

*n*ancing

_{H}*zT*is challenging. Therefore,

*zT*can be improved by either increasing the power factor (

*S*,

^{2}σ*PF*) or by decreasing

*κ*. Skutterudites are typical thermoelectric materials with high

_{tot}*PF*. CoSbCoSb

_{3}-based skutterudites have a relatively high

*κ*of 3W/mK or more and a high

_{tot}*PF*of approximately 5 mW/mK

^{2}[5]. Skutterudites show excellent thermoelectric performance at high temperatures, but relatively poor performance at low temperatures. Therefore, skutterudites are unsuitable for wearable devices or vehicle applications. The most effective strat

*E*y for improving

_{g}*zT*at low temperatures is to reduce

*κ*[6,7]. Chalcogenides have a very low

_{tot}*κ*owing to their weak van der Waals bonding between atomic layers; thus, they can be potential thermoelectric materials with a high

_{tot}*zT*even at room temperature [8].

Chalcogenides are being actively studied as modules for various devices such as wearable devices and generators for vehicles [9,10]. Defect engineering, such as doping and nanostructuring, is an effective approach for reducing *κ _{latt}* by increasing point-defect phonon scattering [11-13]. This strat

*E*y has been adopted in many studies to e

_{g}*n*ance

_{H}*zT*in chalcogenides [13-17]. Rhyee et al. reported that In

_{4}Se

_{2.35}exhibited a very high

*zT*value of 1.48 at 705 K via self-doping by Se deficiency [13]. Qin et al. synthesized Mndoped Bi

_{0.5}Sb

_{1.5}Te

_{3}and a maximum

*zT*of ~1.3 was achieved for Mn

_{0.0075}Bi

_{0.5}Sb

_{1.4925}Te

_{3}at 430 K [15].

However, the thermoelectric performance of rhenium chalcogenide compounds has not been extensively investigated. According to density functional theory calculations by Hafeez et al. [18], ReS_{2} and ReSe_{2} have different band gaps:1.58 eV (1.50 eV) for monolayer (bulk) ReS_{2} and 1.32 eV (1.26 eV) for monolayer (bulk) ReSe_{2}. Sreeparvathy reported that ReX_{2} (*x* = *S* and Se) has flat bands aligned in both the valence and conduction bands, which contribute to the enhancement of *S* [19]. Sreeparvathy also showed that ReS_{2} has the potential to have a large *S* of 540-600 μV/K at 300 K. Re_{2}Te_{5}, a rhenium chalcogenide, does not have a layered structure but has a complex orthorhombic (space group: Pbca [61]) crystal structure with 84 atoms ([Re_{2}4] and [Te_{60}]) per unit cell. These atoms exhibit a cluster-type Chevrel phase, with [Re6] surrounded by [Te8] [20-22].

One of the structural properties of the Chevrel phase is the presence of four large vacancies. This causes scattering of phonons, effectively reducing *κ _{latt}*. Inevitably,

*κ*of Re

_{tot}_{2}Te

_{5}is 1.3 W/mK which is as low as that of chalcogenides which have layered structures [21]. Further, Caillat et al. reported that rattling was observed in elements doped into vacancies, resulting in reduced

*κ*due to increasing phonon scattering [23]. Therefore, the application of defect engineering to Re

_{tot}_{2}Te

_{5}is a reasonable approach for improving thermoelectric performance.

In this study, the thermoelectric transport properties of Se-doped Re_{2}Te_{5} samples were investigated. We synthesized a series of ReTe_{5-x}Se_{x} (*x* = 0, 0.2, 1, and 2) samples. The electrical and thermal transport properties of the samples were investigated, and Hall measurements were conducted to analyze the electrical transport properties of the samples in detail. The density-of-state effective mass was calculated from the measured parameters. *zT* was evaluated to determine the optimum composition for Se-doped Re_{2}Te_{5}.

## 2. EXPERIMENTAL

A series of Re_{2}Te_{5-x}Se_{x} (*x* = 0, 0.2, 1, and 2) samples were stoichiometrically synthesized using a conventional solidstate reaction process. High-purity element Te (99.999%), Se (99.999%), and Re (99.999%) powders were mixed and loaded in a vacuum quartz tube. The loaded vacuum quartz tube was then heated to 950°C for 6 hours and then maintained for 70 hours. After heating, the samples were cooled to room temperature in a furnace. The synthesized Sedoped Re_{2}Te_{5} samples were pulverized into powder by highenergy ball milling (SPEX 8000D, SPEX). The powder samples were placed in graphite molds and cold-pressed to form the green bodies. The samples were sintered using spark plasma sintering (SPS-1030, Sumitomo Coal Mining Co., Ltd.) under vacuum at 850°C for 10 min under 70 MPa. The crystal structures of the samples and the presence of impurities were identified using X-ray diffraction (XRD, D8 Discover, Bruker) analysis. Furthermore, *σ* and *S* were measured simultaneously using a thermoelectric-property measurement system (ZEM-3, Advanced-Riko) in the temperature range of 300-880 K in a He atmosphere. The error margins for *σ* and *S* were less than 3% and 5%, respectively.

The Hall carrier concentrations (*n _{H}*) and Hall carrier mobilities (

*μ*) were measured using a Hall measurement system (HMS5300, Ecopia) under a 0.548

_{H}*T*magnetic field. The

*κ*value of each sample was calculated using the density (

_{tot}*ρ*), heat capacity (Cp), and thermal diffusivity (

_{s}*α*).

*ρ*was considered to be the theoretical density of orthorhombic Re

_{s}_{2}Te

_{5}(8.423 g/cm

^{3}[2]). The Cp of each sample was measured by differential scanning calorimetry (DSC8000, Perkin Elmer). The

*α*value of each sample was measured by laser flash analysis (LFA457, Netzsch). The error margin for

*α*was less than 7%. The

*zT*values of the samples were calculated based on measured data.

## 3. RESULTS AND DISCUSSION

Figures 1(a) and 1(b) show the XRD patterns and calculated lattice parameters of the series of Re_{2}Te_{5-x}Se_{x} (*x* = 0, 0.2, 1, and 2) samples, respectively. As shown in Figure 1(a), single orthorhombic Re_{2}Te_{5} phases were synthesized without impurities. The (200) and (020) diffraction peaks for the samples with *x* = 0, 0.2, and 1 appeared as a single peak, and the calculated lattice parameters, a and b of these samples were almost identical. However, for the sample with *x* = 2, the (200) and (020) peaks were separated. Therefore, the calculated lattice parameters, a and b for *x* = 2 exhibited significantly different values of 12.68 and 12.95 Å, respectively. The lattice parameters along the three axes gradually decreased with increasing Se doping content, which is attributed to the difference in ionic radii between Se^{2−} (184 pm) and Te^{2−} (207 pm). Therefore, this result confirms that Se atoms were successfully substituted at Te sites.

Figure 2 shows the thermoelectric transport properties measured perpendicular to the pressing axis. As shown in Figure 2(a), *σ* for the samples with *x* = 0, 0.2, 1, and 2 were 0.106, 0.112, 0.020, and 0.005 S/cm at 300 K, respectively. All the samples exhibited typical semiconductor behavior, and *σ _{i}*ncreased to 33.74, 36.71, 3.88, and 2.25 S/cm at 880 K for Re

_{2}Te

_{5-x}Se

_{x}with

*x*= 0, 0.2, 1, and 2, respectively. The maximum σ value was observed for Re

_{2}Te

_{5-x}Se

_{x}with

*x*= 0.2. Figure 2(b) shows the temperature dependence of

*S*for the samples. At 300 K, the

*S*values were 574, 497, 424, and 299 μV/K for Re

_{2}Te

_{5-x}Se

_{x}with

*x*= 0, 0.2, 1, and 2, respectively; at 300 K

*S*decreased gradually with increasing

*x*.

Generally, the magnitude of *S* increases when *σ* decreases because of the trade-off relationship between *S* and *σ*. However, the *S* of the samples with *x* = 1 and 2 at 300 K decreased despite the decrease in *σ* of these samples. This result can be explained by the bipolar effect. The samples with *x* = 1 and 2 initially increased with *T* and then decreased following their maximum values at approximately 580 K, suggesting that bipolar excitation dominates the transport [25]. Therefore, the relationship between the measured *S* completely reversed at 880 K; the values of *S* were 190, 192, 245, and 286 for *x* = 0, 0.2, 1, and 2, respectively at 880 K.

The *PF* values of the samples calculated from the measured σ and *S* values are shown in Figure 2(c). The *PF* values of the samples with *x* = 0 and 0.2 are very similar up to 670 K, but at *T* > 670 K, the *PF* value of the sample with *x* = 0.2 is higher than that of the sample with *x* = 0. Therefore, a maximum *PF* of 0.135 mW/mK^{2} was achieved for *x* = 0.2 at 880 K. However, the samples with *x* = 1 and 2 exhibited very low *PF* values of 0.023 and 0.019 mW/mK^{2} at 880 K, respectively. The decrease in *PF* for these samples is attributed to the reduction in σ and the small increase in *S* due to the amplified bipolar effect.

Figures 3(a) and 3(b) show the measured electrical transport properties of the samples at 300 K. The *n _{H}* value marginally increased from 3.37 × 10

^{18}cm

^{-3}to 4.11 × 10

^{18}cm

^{-3}when a small amount of Se (~0.03 at. %) was doped to pristine Re

_{2}Te

_{5}sample. However,

*n*decreased with a further increase in Se content. The

_{H}*μ*values of the samples measured at 300 K were 0.20, 0.18, 0.12, and 0.11 cm

_{H}^{2}/Vs for

*x*= 0, 0.2, 1, and 2, respectively. The

*μ*values decreased gradually as the Se content increased. The increase in σ for

_{H}*x*= 0.2 and the decrease in σ for

*x*= 1 and 2, were due to the improved

*n*for the sample with

_{H}*x*= 0.2, and the reduced

*n*and

_{H}*μ*for the samples with

_{H}*x*= 1 and 2.

S as a function of *n _{H}* at 300 K is plotted for the series of samples (Pisarenko plot) in Figure 3(c). The dotted lines in Figure 3(c) indicate the contours of the density-of-state effective mass (

*m*, expressed with respect to the free electron mass,

_{d}^{*}*m*

_{0}) according to the Mott relationship [26].

where *h, e*, and *k* are the Planck’s constant, elementary charge, and Boltzmann constant, respectively. Figure 3(d) shows the change in *m _{d}^{*}* of the Re

_{2}Te

_{5-x}Se

_{x}(

*x*= 0, 0.2, 1, and 2) samples with respect to

*x*. As the Se content increased, the

*m*value gradually decreased. The

_{d}^{*}*m*values of the samples were 0.64, 0.63, 0.16, and 0.06

_{d}^{*}*m*

_{0}for the samples with

*x*= 0, 0.2, 1, and 2, respectively.

Figure 4(a) shows the plot of *κ _{tot}* vs temperature for the Re

_{2}Te

_{5-x}Se

_{x}(

*x*= 0, 0.2, 1, and 2) samples. The measured

*κ*value of the undoped sample gradually decreased with

_{tot}*T*from 1.33 to 0.59 W/mK up to 740 K, but then increased to 0.66 W/mK at 880 K. The

*κ*values of the doped samples were significantly low (below ~0.85 W/mK), and notably, the samples with

_{tot}*x*= 1 and 2 exhibited very low

*κ*values of 0.23-0.53 W/mK. Figure 4(b) shows the temperature dependence of

_{tot}*κ*of the samples, and the

_{ele}*κ*values exhibited a trend similar to that of the σ values. However, the influence of

_{ele}*κ*on

_{ele}*κ*was marginal, because the measured σ was less than 50 S/cm. Consequently, the

_{tot}*κ*values were almost identical to the

_{latt}*κ*values, as shown in Figure 4(c). Further,

_{tot}*κ*gradually decreased with increasing Se content over the entire temperature range; this was attributed to the point defect phonon scattering by Se doping.

_{latt}The gradual decrease in lattice parameters a, b, and c suggests an increase in lattice distortion, which leads to a decrease in *κ _{latt}*. Furthermore, the scattering parameters are proportional to the difference in mass (ΔM) in the pointdefect scattering mechanism [27]. Therefore, the difference between the atomic masses of Te (127.6 u) and Se (79.0 u) also contributed to the decrease in

*κ*.

_{latt}Next, the *zT* values were calculated using the measured *σ*, *S*, and *κ _{tot}* values of the samples (Figure 5(a)). The error margin for

*zT*was less than 15%. The highest

*zT*value of 0.20 was achieved for the sample with

*x*= 0.2 at 880 K, which is ~22% higher than that of the pristine Re

_{2}Te

_{5}sample. The

*zT*enhancement for

*x*= 0.2 was attributed to the marginal increase in

*PF*and decrease in

*κ*. However, the other doped samples (

_{tot}*x*= 1 and 2) exhibited reduced

*zT*values because of the significant decrease in

*PF*, despite the very low

*κ*values.

_{tot}Figure 5(b) shows the weighted mobility (*μ _{w}*) as a function of the temperature for the samples.

*μ*is proportional to the maximum

_{w}*PF*that a sample can reach when

*n*is optimized. The

_{H}*μ*value of each sample was calculated from the measured

_{w}*σ*and

*S*;

*μ*can be obtained from a simple analytical form that approximates the exact Drude-Sommerfeld free-electron model given in Equation (2) for |

_{w}*S*| > 20 μV/K [28].

where *m _{e}* is the mass of the electron. The calculated

*μ*values at 880 K were 2.73, 3.03, 0.59, and 0.56 cm

_{w}^{2}/Vs for

*x*= 0, 0.2, 1, and 2, respectively. The

*μ*values increased at

_{w}*x*= 0.2, and then decreased with increasing

*x*, which is in agreement with the

*PF*trend at 880 K. Therefore, the

*PF*of the sample with

*x*= 0.2 can be further improved by appropriate

*n*tuning. In addition,

_{H}*μ*is closely related to

_{w}*m*as shown in Equation (3) [29].

_{d}^{*}where *μ*_{0} is the non-d*E _{g}*enerate mobility. The

*μ*values of the samples at 300 K were 3.70, 1.61, 0.12, and 0.08 cm

_{w}^{2}/Vs for

*x*= 0, 0.2, 1, and 2, respectively. The

*μ*values at 300 K decreased with x, which can also be observed in the

_{w}*m*trend.

_{d}^{*}Figure 5(c) shows the dimensionless thermoelectric quality factor (*B*) of each sample, calculated from *μ _{w}* and

*κ*.

_{latt}*B*was calculated using Equation (4) [28]:

*B* is related to the maximum *zT* that a material can achieve when *n _{H}* is optimized. The general trend of

*B*closely followed that of

*zT*:

*B*increased at

*x*= 0.2, and decreased with a further increase in Se content. Figure 5(d) shows the plot of the expected

*zT*of pristine Re

_{2}Te

_{5}as a function of

*n*at 300 K using a single parabolic band model. The parabolic line in Figure 5(d) was calculated using Equation (5) [29].

_{H}where *F _{x}*

*η*(

*η*is the reduced electrochemical potential) and

*τ*are the Fermi int

_{ac}*E*ral and relaxation time of acoustic phonon scattering, respectively.

_{g}Therefore, maximum *zT* can be achieved when *n _{H}* is ~1020cm

^{-3}. Accordingly, the

*zT*of Re

_{2}Te

_{5}can be substantially e

*n*anced by appropriate cation doping, such as Zr

_{H}^{4+}, Sn

^{4+}and Hf

^{4+}, in Re

^{5+}-site, considering the significant decrease in

*κ*due to Se doping.

_{tot}## 4. CONCLUSIONS

A series of Re_{2}Te_{5-x}Se_{x} (*x* = 0, 0.2, 1, and 2) polycrystalline samples were prepared to investigate their electrical and thermal transport properties. Pure orthorhombic Re_{2}Te_{5} phases were synthesized without any impurities, and the lattice parameters *a, b*, and *c* gradually decreased with increasing Se content, confirming the substitution of Se atoms at the Te sites. A maximum power factor of 0.135 mW/mK^{2} was obtained for the sample with *x* = 0.2 at 880 K, predominantly due to the increase in the *n _{H}* and

*σ*. The lattice thermal conductivity significantly decreased with increasing Se content, which was attributed to the point defect phonon scattering by Se doping. Further,

*zT*reached a maximum value of 0.20 at 880 K for the Re

_{2}Te

_{4.8}Se

_{0.2}(

*x*= 0.2) sample, an enhancement of approximately 22% compared to the pristine Re

_{2}Te

_{5}sample. The single parabolic band model predicted that

*zT*can be further improved by appropriate

*n*tuning.

_{H}## Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF-2019R1C1C1005254, NRF-2019R1A6A1A11055660, NRF-2022R1F1A1063054).