Enhanced Thermoelectric Properties of Graphene/Cu₂SnSe₃ Composites

Abstract

Cu₂SnSe₃ material is regarded as a potential thermoelectric material due to its relatively high carrier mobility and low thermal conductivity. In this study, graphene was introduced into the Cu₂SnSe₃ powder by ball milling, and the bulk graphene/Cu₂SnSe₃ thermoelectric composites were prepared by spark plasma sintering. The graphene nanosheets distributed uniformly in the Cu₂SnSe₃ matrix. Meanwhile, some graphene nanosheets tended to form thick aggregations, and the average length of these aggregations was about 3 μm. With the fraction of graphene increasing, the electrical conductivity of graphene/Cu₂SnSe₃ samples increased greatly while the Seebeck coefficient was decreased. The introduction of graphene nanosheets can reduce the thermal conductivity effectively resulting from the phonon scattering by the graphene interface. When the content of graphene exceeds a certain value, the thermal conductivity of graphene/Cu₂SnSe₃ composites starts to increase. The achieved highest figure of merit (ZT) for 0.25 vol % graphene/Cu₂SnSe₃ composite was 0.44 at 700 K.

1. Introduction

Due to the dilemma between energy crisis and environmental stewardship, developing renewable energy technologies has attracted considerable research interest in the past decade. Thermoelectric materials, which can directly convert heat energy into electrical energy and vice versa, show great promise in the application of solid-state cooling, waste heat recovery, and power generation. The conversion efficiency of thermoelectric material is governed by the dimensionless figure of merit, ZT = σα²T/κ, where σ, α, T, and κ are the electrical conductivity, Seebeck coefficient, absolute temperature and thermal conductivity, respectively. The total thermal conductivity is composed of carrier thermal conductivity (κ_c) and lattice thermal conductivity (κ_l). Therefore, thermoelectric materials with good performance should have a large α and σ and low κ. As the fundamental material parameters (α, σ, and κ_c) are interrelated and conflicting via carrier concentration in bulk thermoelectric materials, it is a longstanding challenge to largely improve the overall ZT [1,2,3,4]. Therefore, concepts or strategies that can decouple these parameters to simultaneously optimize the electron and phonon transport are highly encouraging and imperative for the thermoelectric community. Specifically, band engineering and nanostructuring have been demonstrated as effective extrinsic approaches to separately enhance the power factor (PF = α²σ) and reduce the κ_l, respectively.

Several classes of thermoelectric materials, such as skutterudite [5,6], tellurides [7,8,9,10], half-Heuslers [11,12], and silicides [13,14], have been modified to reach high ZT value. Recently, ternary diamond-like semiconductor of Cu₂SnSe₃ has emerged as a new potential thermoelectric material due to its relatively high carrier mobility and quite low thermal conductivity. Since the Cu–Se bond network in the Cu₂SnSe₃ structure forms an electrically conductive framework and Sn orbitals contribute little to the carrier transport, the electrical conductivity of Cu₂SnSe₃ is allowed to be tuned to optimize the thermoelectric property by partial substitution of the Sn site. Some valuable work has been done on Cu₂SnSe₃ compound by doping, substitution, or solid solution [15,16]. The In-doped Cu₂In_xSn_1-xSe₃ was studied by Chen et al. and a maximum ZT of around 1.2 was obtained at 850 K for x = 0.1 [17]. Similarly, gallium doping was found to be an effective way to increase the ZT in Ga-doped Cu₂SnSe₃ compounds by Shi et al., and the maximum ZT increased to 0.43 at 700 K [18]. Moreover, isoelectronic alloying with Ge at the Sn site was confirmed to be effective in enhancing the ZT value by Morelli et al. [19]. Besides substitution, the introduction of a nanostructure phase into the matrix is also an attractive approach to enhance the dimensionless figure of merit of thermoelectric materials. So far, there are few studies about nanostructured Cu₂SnSe₃ matrix composites due to the unapparent enhancement of ZT resulting from the second nanostructured phase. Although a remarkable decrease in the lattice conductivity can be achieved by phonon scattering at nanophase/matrix interfaces, the electrical properties of thermoelectric composites also decrease, leading to a marginal change of the overall ZT value. Moreover, the selection of nanophase and the control of the microstructure of thermoelectric composites are also important for the enhancement of ZT value [20,21,22].

Graphene has high electrical and thermal properties due to its unique 2D structure. The carrier mobility, electrical conductivity, and thermal conductivity of graphene is 2 × 10⁵ cm²·V⁻¹·s⁻¹, 1 × 10⁶ S/m, and 5 × 10³ Wm⁻¹·K⁻¹ at room temperature, respectively. Meanwhile, the carrier of graphene with zero bandgap can continuously vary from electron to hole, which can benefit the electrical transport in the p–n interfacial region. Wang et al. even confirmed that the introduction of 0.2 vol % graphene enhanced the ZT value of Bi₂Te₃ material [23]. Kim et al. confirmed that the peak ZT value for the 0.05 wt % graphene/Bi₂Te_2.7Se_0.3 composite increased to 0.8 at 400 K, which is 23% larger than that of the pristine sample [24]. Chen et al. also showed that an improved ZT value of 0.4 in graphene/CuInTe₂ composites was obtained due to a lower κ_l [25]. In this contribution, it is highly possible that incorporating graphene nanosheets into Cu₂SnSe₃ material will also lead to reduced κ_l, which perhaps will further improve the thermoelectric properties of graphene/Cu₂SnSe₃ composites.

In the present work, graphene nanosheets were incorporated into the Cu₂SnSe₃ matrix by ball-milling method, and the graphene/Cu₂SnSe₃ thermoelectric composites were fabricated by spark plasma sintering (SPS). The transport properties of graphene/Cu₂SnSe₃ composites were studied with the aim of enhancing thermoelectric performance of Cu₂SnSe₃.

2. Experimental Procedures

Cu₂SnSe₃ was synthesized by the reacting stoichiometric copper (powder, 99.96%), tin (powder, 99.999%), and selenium (shot, 99.999%) in evacuated fused-silica ampoules at 1173 K for 12 h, then slowly cooling the melt down to 873 K for 24 h, followed by annealing at this temperature for 2 days. Finally, the obtained ingots were reground into fine powder. Commercially available graphene powder (single layer, average diameter: 2 μm, thickness: 0.8 nm; XFNANO, Nanjing, China) was chosen as the second nanophase, just as shown in Figure 1. The graphene powder was incorporated into the Cu₂SnSe₃ powder at volume fractions of 0.25, 0.50, 0.75, and 1.0 vol %, respectively. Then, the graphene-added Cu₂SnSe₃ powders were mechanically milled with a planetary ball-milling machine. The ball-to-powder ratio was 5:1, and the ball-milling process was carried out in Ar atmosphere for 240 min at 150 rpm. The SPS process was used to consolidate the as-milled powders at 860 K for 8 min in a vacuum of 0.1 Pa under a pressure of 50 MPa.

The constituent phases of the samples were characterized by X-ray diffractometry on a Rigaku Rint2000 powder diffractometer equipped with Cu K_α radiation. The microstructure of all graphene/Cu₂SnSe₃ samples was observed using field-emission scanning electron microscopy (FESEM) and high-resolution transmission electron microscopy (HRTEM, JEM2100F, JEOL, Tokyo, Japan). The thermal diffusivity (λ) of all samples was measured on the disk-shaped specimen by laser flash technique using a Netzsch LFA427 (Netzsch, Berlin, German) setup in a flowing Ar atmosphere with temperature ranging from 300 to 700 K. The thermal conductivity was then calculated as κ = dλC_p, where d is the density measured by Archimedes method, and C_p is the Dulong–Petit approximation for the specific heat capacity. A bar-shaped specimen of 2 × 2 × 10 mm³ was cut with a diamond saw from the sample for the measurement of electrical transport properties. Both electrical conductivity and Seebeck coefficient were determined simultaneously using ZEM-3 equipment (ULVAC-RIKO, Tokyo, Japan) with temperature ranging from 300 to 700 K in Ar atmosphere. The Hall coefficients (R_H) were measured by van der Pauw’s method in a vacuum of 0.1 Pa under a magnetic field of 2 T. The carrier mobility (μ_H) and carrier concentration (p) were calculated through the formulae of μ_H = R_Hσ and p_H = 1/(R_He) based on the assumption of single-band model, where e is the electron charge. The experimental uncertainty on the electrical conductivity, Seebeck coefficient, thermal conductivity, and Hall coefficient are estimated to be 5%, 5%, 8%, and 4%, respectively.

3. Results and Discussion

3.1. Phase Analysis and Microstructure

Figure 2 displays the SEM image of the 1.0 vol % graphene-added Cu₂SnSe₃ powder after ball milling for 240 min at 150 rpm. It can be observed that the average diameter of graphene nanosheets in the mixed Cu₂SnSe₃ powder was about 1 μm. Figure 3 is the X-ray diffraction patterns of sintered graphene/Cu₂SnSe₃ composites. The diffraction peaks in Figure 3 are identified as JCPDS card 65-4145 (cubic Cu₂SnSe₃). No diffraction peak of graphene is found in the XRD results as the fraction of graphene in the composites is very low. All graphene/Cu₂SnSe₃ composites show the same XRD patterns as the pristine Cu₂SnSe₃.

The microstructure of the sintered pristine Cu₂SnSe₃ and 0.75 vol % graphene/Cu₂SnSe₃ sample is illustrated in Figure 4a,b, respectively. It is evident that the graphene nanosheets distributed uniformly in the Cu₂SnSe₃ matrix. Meanwhile, some graphene nanosheets tended to form thick aggregations and the average length of aggregations was about 3 μm. A similar phenomenon was also observed by Zhao et al. in the graphene/CoSb₃ nanocomposite [26]. The results of energy dispersive X-ray spectroscopy (EDS) for graphene/Cu₂SnSe₃ sample identify that the matrix consisted of 33.17 atom % copper, 16.79 atom % tin, and 50.04 atom % selenium, indicating the Cu₂SnSe₃ phase, just as shown in Figure 5. The black phase in Figure 5a only contains the C element, corresponding to the graphene phase. It can be observed from HRTEM in Figure 6 that most of the graphene nanosheets is of the multilayered form (<10 layers), which is consistent with SEM results. The fringe spacing of 0.81 nm in the lattice image corresponds to the interplanar distance of the (111) plane of Cu₂SnSe₃. Figure 7 shows the FESEM image of the fractured surface of the sintered graphene/Cu₂SnSe₃ sample. The graphene nanosheets are homogeneously embedded in the Cu₂SnSe₃ matrix. According to the classic band theory [27,28], nanostructures distributed in the material can result in strain fields, then lead to a change in the energy-band structure of thermoelectric material. At the same time, nanophases can greatly influence the phonon and electronic transport of thermoelectric materials.

3.2. Electrical Properties

Figure 8 presents the σ of graphene/Cu₂SnSe₃ composites as a function of temperature. It can be observed that the σ of the pristine Cu₂SnSe₃ sample declines steeply with the temperature increasing across the overall temperature range, showing a typical heavily doped degenerate semiconducting behavior. It is noteworthy that graphene/Cu₂SnSe₃ samples show an obvious increased σ compared with pristine Cu₂SnSe₃ due to the introduction of conductivity graphene nanosheets. In addition, the σ of graphene/Cu₂SnSe₃ samples increases with the increasing fraction of graphene. The σ of 1.0 vol % graphene/Cu₂SnSe₃ sample at room temperature is about 350 Ω⁻¹·cm⁻¹, which is about 3 times the value of the pristine Cu₂SnSe₃. Even at the high-temperature region, the σ of graphene/Cu₂SnSe₃ sample still retains a high value. The σ of 0.25 vol % graphene/Cu₂SnSe₃ sample is around 124 Ω⁻¹·cm⁻¹ at 700 K. The enhancement in σ for graphene/Cu₂SnSe₃ samples may be ascribed to either an increase of carrier concentration (p), or the increment in carrier mobility (μ_H), or both.

Table 1. Chemical composition and some physical and structural parameters of graphene/Cu₂SnSe₃ composites at room temperature.

x (vol %)	Relative Density	σ (Ω−1·cm−1)	p (1019 cm−3)	μH (cm2/V·s)	α (μV/K)	κl (W·m−1·K−1)	m* (m0)
0	98.7%	127	3.74	21.2	131	2.65	2.6
0.25	98.1%	255	5.43	29.3	99.8	2.36	2.8
0.50	98.0%	285	5.86	30.4	92.0	2.59	2.9
0.75	97.8%	313	6.13	31.9	78.7	2.92	2.7
1.00	97.5%	448	8.16	34.3	69.9	3.24	3.1

x: volume fraction; σ: electrical conductivity; p: charge carrier concentration; μ_H: carrier mobility; α: Seebeck coefficient; κ_l: thermal conductivity; m*: density of states effective mass

lists some physical and structural parameters of the graphene/Cu₂SnSe₃ composites at room temperature. As shown in Table 1, the carrier concentration of graphene/Cu₂SnSe₃ composites is higher than that of pristine Cu₂SnSe₃. The carrier mobility increases from 21.2 cm²/V·s for Cu₂SnSe₃ to 34.3 cm²/V·s for the 1.0 vol % graphene/Cu₂SnSe₃ sample. Therefore, it can be concluded that incorporating graphene nanosheets into a Cu₂SnSe₃ matrix can improve the electrical conductivity, which is attributed to the increment in both carrier concentration and mobility. This is reasonable because the multilayered graphene is p-type thermoelectric material, and the graphene itself can afford the charged carrier [29]. In addition, the graphene has a relatively high mobility, which is beneficial to increase the carrier mobility of graphene/Cu₂SnSe₃ composites.

Figure 9 demonstrates the α of graphene/Cu₂SnSe₃ samples as a function of temperature. It can be seen that the α of all graphene/Cu₂SnSe₃ samples across the whole temperature range was positive, indicating the major charge carriers in the samples are holes. Moreover, the α of all graphene/Cu₂SnSe₃ composites and pristine Cu₂SnSe₃ samples increases approximately linearly with increasing temperature. For example, the α of pristine Cu₂SnSe₃ increases from 130 μV/K to 255 μV/K in the temperature range of 300–700 K. At the same time, the introduction of graphene nanosheets decreased the Seebeck coefficients of Cu₂SnSe₃ samples evidently. Compared with the α of pristine Cu₂SnSe₃ sample, the α of graphene/Cu₂SnSe₃ samples decreases with the increasing fraction of graphene. At room temperature, the α decreases from 130 μV/K for Cu₂SnSe₃ matrix to 70 μV/K for the 1.0% graphene/Cu₂SnSe₃ composite. The decrease of α for graphene/Cu₂SnSe₃ composites can be explained by the equation

$$\mathsf{\alpha }=\pm \frac{{\mathrm{k}}_B}{e}\left[2+\ln \frac{2{\left(2\mathsf{\pi }{m}^{\ast }{\mathrm{k}}_{B}T\right)}^{\frac{3}{2}}}{{\mathrm{h}}^{3}p}\right]$$

(1)

where k_B, m*, h, and p are Boltzmann constant, density of states effective mass, Planck’s constant, and charge carrier concentration, respectively. The introduction of graphene nanosheets leads to the improved carrier density. Herein, according to the equation, the α is reduced.

The μ_H of graphene/Cu₂SnSe₃ composites as a function of temperature is displayed in Figure 10. The μ_H of graphene/Cu₂SnSe₃ composites increases with the increasing fraction of graphene. Moreover, the μ_H of graphene/Cu₂SnSe₃ samples in this study is between 20 and 35 cm²·V⁻¹·s⁻¹ at room temperature, which is close with that of CoSb₃ [30,31]. This may be attributed to the similar carrier effective mass (m*) of Cu₂SnSe₃ and skutterudite compounds. The m* can be calculated by the following equations based on single parabolic band model.

Table 1 lists the evaluated equivalent m* of graphene/Cu₂SnSe₃ samples at room temperature. Meanwhile, it can also be observed in Figure 10 that the μ_H of pristine Cu₂SnSe₃ shows a temperature dependence of T^−3/2 above 520 K, suggesting that the dominant scattering mechanism is phonon scattering in the temperature range from 520 K to 700 K. Below 520 K, the μ_H of pristine Cu₂SnSe₃ proportional to T^−3/2 is weak, and the relationship of μ_H as function of temperature dependence of T^−0.5 can be seen, showing that alloy scattering is the dominate mechanism in this temperature range. However, the μ_H of graphene/Cu₂SnSe₃ samples deviates from the T^−1.5 or T^−0.5 dependence across the entire temperature range, indicating the dominative mechanism is mixed scattering in these composites.

3.3. Thermal Conductivity

The κ and κ_l for graphene/Cu₂SnSe₃ samples as function of temperature is shown in Figure 11. The κ_l is obtained by directly subtracting the carrier thermal conductivity κ_c from the total thermal conductivity; κ_c can be calculated according to the Wiedemann–Franz law, κ_c = L₀σT, where the Lorenz constant L₀ is taken as 2.45 × 10⁻⁸ V²/K². The κ for all composites decreases with the increasing temperature. With the fraction of graphene increasing, the κ of graphene/Cu₂SnSe₃ composites firstly declines then starts to increase. The achieved κ of 0.25% graphene/Cu₂SnSe₃ sample at room temperature is 2.5 W/m·K, which is a 12% reduction from that of pristine Cu₂SnSe₃. On the contrary, the κ of the 1.0% graphene/Cu₂SnSe₃ sample at room temperature increases to 3.45 W/m·K. The κ_l of graphene/Cu₂SnSe₃ samples demonstrates similar changes compared to that of pure Cu₂SnSe₃. The lowest κ_l of 0.25% graphene/Cu₂SnSe₃ samples is 0.78 W/m·K, which is 22% lower than that of the pristine Cu₂SnSe₃ sample. As is known to all, nanostructuring will reduce the κ_l of material as the long-wavelength phonon scattering at grain boundaries was suppressed. Because graphene itself has high lattice thermal conductivity and large specific surface area, an opposite effect of graphene nanosheets on the κ of Cu₂SnSe₃ can be allowed. On one side, the addition of second phase with high κ may increase the total thermal conductivity of composite. On the other side, large specific surface area suggests more newly formed interfaces between the matrix and second phase, which are expected to scatter phonons to depress the κ_l. For 0.25% graphene/Cu₂SnSe₃, graphene nanosheets are homogeneously dispersed in the Cu₂SnSe₃ matrix, which means the dominative factor should be the influence of interface scattering. By comparison, when the content of graphene exceeds a certain value, the graphene in the composites tends to aggregate into thick flakes in the Cu₂SnSe₃ matrix, as mentioned above. Therefore, the interfacial increment due to the incorporation of graphene should not be significant. This can explain the change in κ_l of graphene/Cu₂SnSe₃ composites. The results also confirm that the κ_l of Cu₂SnSe₃ can be effectively reduced by introducing graphene nanosheets. The obtained minimum κ_l in the present work is 0.78 W/m·K at 700 K for the 1.0% graphene/Cu₂SnSe₃ sample. According to the basic kinetic theory, when the phonon mean free path is equal to the shortest interatomic distance, the lattice thermal conductivity can achieve the minimal value κ_lmin [32]. The κ_lmin can be calculated according to the formula κ_l = 1/3ν_mC_v·l, where ν_m, C_v, and l are the mean sound velocity, the isochoric specific heat of the system using Dulong and Petit value, and the mean free path of phonon, respectively. The ν_m is taken as the constant 2.3 × 10³ m/s [33]. It is assumed that the minimum mean free path of phonon l is the interatomic distance (0.238 nm) of the Cu₂SnSe₃ structure, and the achieved κ_lmin is 0.52 W·m⁻¹·K⁻¹, just as illustrated by the brown dashed line in Figure 11b. By controlling the content of graphene nanosheets and microstructure of composites, the κ_l of graphene/Cu₂SnSe₃ composites may approach the κ_lmin of Cu₂SnSe₃ in the high-temperature region. Further optimization will be studied in further work.

3.4. Figure of Merit

Figure 12 shows the ZT value of graphene/Cu₂SnSe₃ samples as a function of temperature. Like other related Cu-based ternary chalcogenide compounds with diamond-like structure [17,18], the ZT value of graphene/Cu₂SnSe₃ samples increases with increasing temperature. Compared with the figure of merit of pristine Cu₂SnSe₃, the ZT of graphene/Cu₂SnSe₃ samples is obviously improved. The 0.25% graphene/Cu₂SnSe₃ composite has the maximal ZT value of 0.44 at 700 K, 45% higher than that of pristine Cu₂SnSe₃. If the graphene/Cu₂SnSe₃ samples were coated by a coating film and the measured temperature increased to 850 K, the ZT value is capable of reaching 1.0–1.2. The enhancement of ZT for graphene/Cu₂SnSe₃ composites is basically ascribed to the depressed κ_l and the increased σ. The incorporation of graphene nanosheets into the Cu₂SnSe₃ could enhance the thermoelectric properties. Therefore, if we choose the material with optimized carrier concentration and mobility as the thermoelectric matrix, the thermoelectric composite with a higher ZT value could be achieved.

4. Conclusions

The graphene nanosheets were introduced into the Cu₂SnSe₃ matrix by ball milling and the graphene/Cu₂SnSe₃ composite was fabricated by spark plasma sintering. The graphene nanosheets distributed uniformly in the Cu₂SnSe₃ matrix. Meanwhile, some graphene nanosheets tended to form thick aggregations and the average length of aggregations was about 3 μm. With the increasing content of graphene, the electrical conductivity of graphene/Cu₂SnSe₃ samples greatly increased, while the Seebeck coefficient was decreased. The introduction of graphene nanosheets reduced the thermal conductivity, effectively resulting from the phonon scattering by the graphene interface. When the fraction of graphene exceeds a certain value, the thermal conductivity of graphene/Cu₂SnSe₃ composites starts to increase. The maximum figure of merit ZT for 0.25 vol % graphene/Cu₂SnSe₃ was 0.44 at 700 K.