Microstructure and thermoelectric performance evaluation of p-type (Bi, Sb)₂Te₃ materials synthesized using mechanical alloying and spark plasma sintering process

Abstract

In this paper, three p-type thermoelectric compounds, namely Bi_0.5Sb_1.5Te₃, Bi_0.3Sb_1.7Te₃, and Bi_0.2Sb_1.8Te₃ were manufactured by mechanical milling and spark plasma sintering method. The effects of chemical composition on microstructural and thermoelectric properties were investigated. In this order, Bi, Te, and Sb powders with different contents were mechanically milled for 6 hours. Then, they were consolidated using a spark plasma sintering process (SPS) at 400 °C under 60 MPa pressure. The phase composition was analyzed using XRD with Cu-Kα radiation. The microstructural characterization of the specimens was performed using scanning electron microscopy. Moreover, thermoelectric properties of the samples, including the Seebeck coefficient, electrical and thermal conductivity, power factor, and ZT were determined. Analysis of XRD patterns of fabricated compositions indicated that a single phase with a rhombohedral lattice structure was synthesized in all conditions. In addition, SEM results showed an integrated structure with a few scattered micropores. The thermoelectric results confirmed that Bi_0.5Sb_1.5Te₃ demonstrates the lowest thermal conductivity (0.85 W/m K), the highest electrical conductivity (4.48 S/cm), and the maximum figure of merit (1.03 × 10⁻²) at room temperature. Therefore, it is the best option among the fabricated compounds to be utilized as thermoelectric materials.

1 Introduction

Environmental pollution emerged from the increasing combustion of fossil fuels is a matter of global concern. Nevertheless, it provides a significant opportunity to investigate new methods to produce energy. In this regard, thermoelectric (TE) materials are introduced as a key solution. By definition, TE materials are semiconductors that can convert thermal energy to electricity and are employed in appliances such as solar cells and generators.

In recent decades, scientists have been trying to manufacture TE materials with suitable properties such as long life, no moving parts, and zero toxic gas emission [1,2,3]. Moreover, these materials are environmentally friendly and, thus, are good selections for exploiting wasted energy. The efficiency of TE materials is measured by a figure of merit obtained by electrons (for n-type) or holes (for p-type) and phonon conduction.

Bismuth telluride-based alloys are the best TE materials for using in the range of 300–500 K [4, 5]. The highest figure of merit of these materials was calculated at room temperature [6]. The group IV–VI compounds show good electrical transport properties, well-known semiconductors, benefit from their narrow band gap and highest figure of merit among the other thermoelectric materials at low temperatures [7, 8]. It has been reported that when thermoelectric materials are produced in the nano-sized scale, they demonstrate high thermoelectric performance [9]. The performance is evaluated using the dimensionless figure of merit, ZT which is defined as follows:

$$ZT = \left( {\frac{{\alpha^{2} \delta }}{k}} \right)T,$$

(1)

where α is the Seebeck coefficient, δ is the electrical conductivity, k is the thermal conductivity, and T is the temperature. As it is known, in TE materials, three parameters, namely electrical conductivity, thermal conductivity, and Seebeck coefficient are determinative parameters of their performance level.

The thermal conductivity (k) includes lattice thermal conductivity (k_L) along with the electronic component (k_el) [10]. These semiconductor materials can obtain high-performance levels or high dimensionless figure of merit when they have high electrical conductivity, high Seebeck coefficient, and low thermal conductivity. However, due to interdependent physical parameters in bulk samples, it is difficult to balance these three main parameters [11].

TE materials can be produced using a wide range of methods, including solvothermal [12], hydrothermal [8], melt spinning [13], microwave synthesis [14], and mechanical alloying (MA), followed by hot pressing or spark plasma sintering (SPS) [15]. The synthesis mechanism of thermoelectric material powder during ball milling includes four steps: plastic deformation, cold welding, fracture, and thermochemical reactions. The synthesized powder should be compacted and sintered to form bulk materials. There are different methods to sinter material powders. SPS is one of them. SPS is an appropriate method to prevent grain growth due to its high heating rate and short sintering time. Therefore, it can potentially attract researchers [16,17,18,19,20]. In specific, bismuth telluride antimony compounds are often synthesized using this method [17].

Madavali et al. [16] fabricated p-type (Bi₂Te₃)_x–(Sb₂Te₃)_1−x alloys with high TE performance by mechanical alloying followed by SPS. They found that the electrical conductivity increases with Sb content. Moreover, the Bi_0.3Sb_1.7Te₃ compound presented a ZT of 1.3 ± 0.06 at 400 K and 1.07 ± 0.06 at 300 K. This enhanced ZT was gained by increasing the Sb content. It was because of the increased carrier concentration and band gap of these samples.

Cho et al. [18] fabricated the Bi_0.5Sb_1.5Te₃ compound using SPS in the temperature ranging of 250 °C to 350 °C and investigated the microstructure and thermoelectric properties of this compound. As reported in their study, the highest figure of merit of 3.5 × 10⁻³ was obtained for this compound when it was sintered at 350 °C for 2 min using hydrogen-reduced powders.

Li et al. [19] manufactured the Bi_0.5Sb_1.5Te₃ compound using mechanical alloying and SPS methods. They reported the maximum figure of Merit (0.0048/K) for sintered samples produced in the milling time of 60 h, the ratio of ball to powder of 20:1, and the milling speed of 450 rpm.

Chen et al. [20] produced single-phase Bi_xSb_2−xTe₃ (x = 0.2, 0.25, 0.3, 0.34, 0.38, 0.42, 0.46, and 0.5) alloys prepared by SPS and MA processes. According to the research, with the increasing Sb, the electrical resistivity and the Seebeck coefficient decreased. The higher thermal conductivities at low temperatures were obtained at the compositions with lower Bi values. As a result, the maximum ZT values of 1.23 for Bi_0.3Sb_1.7Te₃ compound and of 0.6 for Bi_0.5Sb_1.5Te₃ compound were achieved at 423 K.

Fan et al. [21] manufactured p-type Bi_0.5Sb_1.5Te₃ thermoelectric alloys by MA and hot pressing methods. Due to the MA process performed for 12 h, Bi_0.5Sb_1.5Te₃ solid solution phase was formed and the amount of the solid solution phase increased with increasing the milling time. Moreover, the fine grain size remained unchanged after hot pressing. As a result, the maximum figure of merit was gained as 2.84 × 10⁻³ at room temperature.

According to the literature, there are some studies performed on the fabrication of Bi_0.5Sb_1.5Te₃ using mechanical alloying [16, 19, 20]. However, the main drawbacks of the mentioned researches are the long time as well as the high sintering temperature needed for achieving a single-phase resulting in undesired grain growth. Considering the mentioned challenges, the present work aims to decrease the processing time and sintering temperature to gain the smaller particle size and also to evaluate the effect of the chemical composition and the size of the particles on the thermoelectric properties. For that reason, in the current research, a comparative study on the effect of the chemical composition of p-type TE compounds of Bi_0.2Sb_1.8Te₃, Bi_0.3Sb_1.7Te₃, and Bi_0.5Sb_1.5Te₃, synthesized using mechanical alloying and SPS on the resultant microstructure and electronic/thermal transport properties was carried out. This research will be important for the development of various thermoelectric applications of this group of advanced materials.

2 Experimental procedure

2.1 Synthesis of micro–nano-powders TE materials

Bi_2−xSb_xTe₃ (x = 1.8, 1.7, and 1.5) powders were synthesized by mechanical alloying (MA) and SPS processes. For the nominal compositions in this work, pure Te (Sigma Aldrich, 99.8%), Bi (Sigma Aldrich, 99.95%), and Sb (Sigma Aldrich, 99.95%) as raw materials were used according to the stoichiometry ratios of these elements in the different compositions. The powders were mixed in stainless-steel vials using balls with diameters of 8 to 13 mm. The milling was carried out with ball to powder ratio of 15:1 under argon atmosphere with a speed of 300 rpm for 6 h in a planetary ball mill (PM 2400/made in Iran).

2.2 Sintering of TE powders using SPS process

All the prepared powders were sintered in the same condition by SPS method (SPS, Dr. Sinter825). The process was performed with a heating rate of 30 °C/min up to 400 °C under 60 MPa pressure. The holding time was set to 10 min. Finally, the density of the solid-state synthesized powders was measured according to the Archimedes method.

2.3 Materials characterization

Characterization of the phases produced during mechanical milling of the raw powders was performed by X-ray diffraction (XRD) using a PANalytical X’Pert PRO Alpha-1 by Cu-Kα radiation (λ = 1.54 nm). The data were collected in the 2θ range from 20° to 55°.

Morphology of the powders was observed with a field-emission scanning electron microscope (FESEM, TESCAN MIRA30XMU) using an accelerating voltage of 10 kV with a secondary electron detector. To study the microstructure of the sintered compounds, scanning electron microscopy (SEM, Zeiss ultra 55) was utilized on the polished surface of the bulk samples. Composition of the samples was estimated by energy-dispersive X-ray spectra (EDS). Moreover, particle size of the milled powders was measured using Particle Size Analyzer, Vasco3-Cordouan.

2.4 Thermoelectric transport characterization

Thermal conductivity of the samples was determined according to

$$k = \lambda \rho C_{{\text{p}}},$$

(2)

in this equation, ρ represents the density of the samples, λ is the thermal diffusivity measured by LFA (Netzsch Laser Flash Apparatus), and specific heat (C_p) was measured by DSC (Netzsch-DSC404 pegasus 214 polyma).

Thermoelectric transport parameters including Seebeck coefficient (α) and electrical conductivity (δ) were measured in the temperature range of 299 to 679 K using (ULVA-RIKO ZEM3).

3 Results and discussion

3.1 Phase and structure

Figure 1 shows X-ray diffraction patterns of Bi_xSb_2−xTe₃ (x = 0.5, 0.3, 0.2) TE materials prepared by milling procedure. According to Fig. 1a, high pure Bi_0.5Sb_1.5Te₃ and Bi_0.2Sb_1.8Te₃ compositions were fabricated due to the suitable time of milling (6 h). However, it was found that six-hour milling is not enough to obtain a single phase of Bi_0.3Sb_1.7Te₃ (PDF#71-393) chemical composition because there are some impurities (Te(JCPDS:36-1452)) in the X-ray pattern. Kitamura et al. [22] reported that single-phase Bi_0.3Sb_1.7Te₃ with the best thermoelectric properties was achieved when milling time was 30 h at 110 rpm (maximum ZT = 1.01 at room temperature) [22]. XRD patterns for the two nominal compositions, i.e., Bi_0.5Sb_1.5Te₃ (ICDD:00-049-1713) and Bi_0.2Sb_1.8Te₃ (ICDD:00-049-1743), shown in Fig. 1a, confirm the rhombohedral structure of the space group R3m for the materials [23]. Moreover, the comparison between the enlarged (015) peaks of the three samples, as demonstrated in Fig. 1b, approves the presence of Sb. Substitution of Bi instead of Sb shows more intensity and d-spacing, which is because of the larger atomic radius of Bi (230 pm) compared with Sb (140 pm). Therefore, according to the Bragg equation,

$$n\lambda = 2d\sin \theta$$

(3)

the peaks with more Bi shift to lower angles. The diffraction peaks of samples Bi_0.5Sb_1.5Te₃ and Bi_0.2 Sb_1.8Te₃ are much sharper after sintering. It means that sintering has led to better crystallinity and comparatively larger grain size due to the grain growth.

Fig. 1

XRD pattern of: a as-milled powders, b the enlarged (015) diffraction peak of different samples, and c sintered alloys (Bi_xSb_2−xTe₃ with x = 0.5, 0.2, and 0.3)

Figure 1c demonstrates the XRD pattern following sintering at 673 K for all samples. As can be seen, there are small extra peaks of Te at 27.5° in the compositions. The presence of Te in the SPSed samples can be described according to the observation of Kitamura et al. [22], in which they reported that the eutectic temperature of Te and Bi₂Te₃ is 673K. Certainly, Te element remained in the compositions and the heterogeneous structure have negative effects on thermoelectric properties. It should be mentioned that many investigators have reported the presence of trace amounts of some initial elements or oxides in the fabricated compounds due to the insufficient milling time, the collisions of powders with jar and balls during milling, or low vacuum in the SPS process [21, 24]. In the current study, like the above-mentioned researches, trace amounts of Sb₂O₃ and Te element in all Bi_0.3Sb_1.7Te₃ compounds were detected after the sintering process which may be due to the low vacuum in the SPS process. Table 1 presents the trace amounts of Sb₂O₃ and Te and the Sb₂O₃/Te ratio for all the samples calculated by the area of the peaks using the Origin Software. Although, Likha et al. [25] claimed that a small enhancement in the oxygen content has not an important effect on the thermoelectric properties of materials.

Table 1 Sb₂O₃/Te ratio of the different compounds calculated by the area of the peaks using the Origin Software

3.2 Microstructure analysis

SEM morphologies of raw materials are demonstrated in Fig. 2 along with EDS analysis. As can be seen, the raw materials are multi-dimensional with rough surfaces and particle size smaller than 150 µm. In addition, according to the figure and the relevant EDS analysis, the raw materials include some oxygen. Moreover, Fig. 2a demonstrates Bi as regions with silver and white colors, while the created oxide as an iridescent sheen. Due to oxidation that sticks some particles together, some of them are bigger compared with others. The morphology of Sb and Te powders and their composition analysis can be seen in Fig. 2b and c, respectively.

Fig. 2

Morphologies of the raw materials: a Bi, b Sb, and c Te powder with EDS spectrums

Figure 3 illustrates SEM images of Bi_2−xSb_xTe₃ (x = 1.8, 1.7, 1.5) milled powders. Based on the figure, an increase in the Bi content up to 0.5 at.% leads to the reduction of particle size and the uniform size distribution of powders. Specially, it can be seen that a rise in Bi content from 0.3 to 0.5 at.% results in the smaller particle size and homogenous distribution. Sb atoms, against Bi atoms, could diffuse in a conductor due to a highly effective charge for electromigration-induced atomic diffusion. Therefore, the weak electromigration behavior of Bi atoms compared with Sb atoms leads to the lattice strain during the milling process. It means that the microstructural strain causes the fracture of powders. Hence, the refinement of particles and uniform size distribution of Bi_0.5Sb_1.5Te₃ alloy powders during the milling process occur [26]. The results of the particle size analysis of the synthesized powders showed that the average particle size of the Bi_0.5Sb_1.5Te₃ sample is smaller than the others. The mean particle size of Bi_0.5Sb_1.5Te₃, Bi_0.3Sb_1.7Te_3, and Bi_0.2Sb_1.8Te₃ was 23.15 nm, 24.58 nm, and 26.07 nm, respectively.

Fig. 3

SEM micrographs and the relevant EDS spectra of: a, b Bi_0.2Sb_1.8Te₃ powder, c, d Bi_0.3Sb_1.7Te₃ powder, and e, f Bi_0.5Sb_1.5Te₃ powder

It is worth noting that an increase in the Sb-to-Bi ratio in Bi_xSb_2xTe₃ causes increasing Sb_Te defects as a result, the carrier density increases which in turn, electrical resistance reduces. Moreover, diffusion of atoms can occur in a conductor under a high-density electric current, which is named electromigration. Sb atoms with a high effective charge (140e) and susceptible to electromigration are the suitable choices for atomic diffusion [16, 17].

Table 2 presents the chemical composition of the samples determined by EDS results. The obtained values show that all samples have Bi:Te:Sb ratio confirming the near-stoichiometric and homogenous composition. It means that the milling procedure successfully distributes the elements in Bi_2−xSb_xTe₃ (x= 1.8, 1.7, 1.5) TE alloys.

Table 2 The chemical composition (at.%) of the samples obtained from EDS analyses of powders

Figure 4 indicates grain size distribution of Bi_0.2Sb_1.8Te₃, Bi_0.3Sb_1.7Te₃, and Bi_0.5Sb_1.5Te₃-sintered samples. The grain size of the sintered bulk samples was measured by Digimizer software using SEM microstructures. The results showed that the mean grain size of bulk Bi_0.2Sb_1.8Te₃, Bi_0.3Sb_1.7Te₃, and Bi_0.5Sb_1.5Te₃ samples is 165, 155, and 150 nm, respectively, indicating that with an increase in Bi content, the average particle size decreases. Moreover, it can be attributed to the initial particle size of the synthesized materials after the milling process and before SPS.

Fig. 4

Grain size distribution in samples: a Bi_0.2Sb_1.8Te₃, b Bi_0.3Sb_1.7Te₃, and c Bi_0.5Sb_1.5Te₃

Li et al. [19] found that particle size decreases and particle distribution becomes more uniform with increasing milling time. As a result, the minimum particle size of 300–800 nm could be reached. They showed that after ball milling at 500 rpm for 18 h, the particle size reduces to about 100 nm; however, the particle size increases by the annealing process of sintered samples at 300 °C for 2 h [19]. In comparison with the work of Li et al. [19], the particle size obtained in the current study is smaller. Therefore, developed thermoelectric properties are expected.

Fracture surfaces of the sintered samples in the SPS condition of 400 °C/60 MPa are shown in Fig. 5. As can be seen, the grain size of the samples increases following the SPS process due to the high-temperature sintering [10].

Fig. 5

SEM micrographs of SPSed materials: a, b Bi_0.2Sb_1.8Te₃, c, d Bi_0.3Sb_1.7Te₃, and e, f Bi_0.5Sb_1.5Te₃. Red circles indicate Sb₂O₃ particles (Color figure online)

According to Fig. 5, all samples show dense structures with some sub-micron voids, which are effective in thermoelectric properties. It is worth noting that sub-micron pores can affect the electron/hole transformation and scattering and also thermal conductivity and, thus, thermoelectric properties of the material. According to SEM images, the average pore size in the Bi_0.3Sb_1.7Te₃ sample is bigger than the average pore size in the other samples.

Pakdel et al. [27] found that the addition of Sb₂O₃ nanoparticles (0, 1, 4, and 6 wt.%) leads to the dispersion at grain boundaries as Zenner pinning particles. Moreover, these nanoparticles are dispersed in the matrix as pinning sites. According to the research, the SEM image shown in Fig. 5, consists of Sb₂O₃ compound introduced as white particles. The existence of Sb₂O₃ compound has been confirmed by XRD pattern presented in Fig. 1c.

Density measurement of SPS-sintered samples shows that the experimental density of the samples is in the range of 78–80% of their theoretical density; therefore, 20–22% porosity could be present in the samples. The average pore size of the samples was measured less than 1 µm. It should be mentioned that the small particle size of milled powders of the higher Bi content sample has increased its compressibility and sinterability and led to the minimum pore size.

As mentioned above, the porous structure maintains the heat in the pores and decreases the thermal conductivity. Following the sintering process, grain growth is observed; however, since sintering time in SPS is shorter than other sintering processes, it is not observed too much [28].

The integrated structure confirmed the suitable sintering temperature of 400 °C; however, all samples have sub-micron pores. Definitely, with enhancing sintering temperature, the porosity of the bulk sample decreases due to the increase in the amount of melted particles, although the purity of the ternary compound reduces. Sintering at higher temperatures such as 450 °C was not suitable since according to the triple diagram for Bi, Sb, and Te, all samples should melt at this temperature. For instance, melting of Bi_0.5Sb_1.5Te₃ compound (with nano-size particle) starts at 413 °C; therefore, at 450 °C, the Te was observed as a liquid phase in the structure. Therefore, 400 °C was selected as the sintering temperature of all samples.

3.3 Electrical conductivity

The electrical conductivity of the samples is demonstrated in Fig. 6. According to Eqs. (1) and (6), some thermoelectric properties such as power factor and the figure of merit demonstrate a proportional relation with electrical conductivity. According to the literature, the reason for the increase in electrical conductivity can be attributed to impurities and defects that cause the electron to scatter. In general, electrical conductivity (S/cm) is calculated by the following equation [29, 30]:

$$\delta = ne\mu$$

(4)

in this case, n and μ are the density the mobility of the carriers, respectively. The results from all the three samples confirm that Bi_0.5Sb_1.5Te₃ presents the best electrical conductivity. This is due to the uniform distribution of fine cavities and the improvement of load-bearing motion. It should also be noted that increasing the amount of Sb to the optimal value in the Bi_2−xSb_xTe₃ (x = 1.5) sample results in an increase in the electrical conductivity [10].

Fig. 6

Electrical conductivity of the SPSed Bi_0.5Sb_1.5Te₃, Bi_0.2Sb_1.8Te₃, and Bi_0.3Sb_1.7Te₃ samples

As mentioned, electrical resistivity depends on two factors: carrier concentration and carrier mobility. The carrier mobility changes by density, grain size, and defects [31]. Therefore, as it was expected, the results show that electrical conductivity decreases by an increase of the grain size.

3.4 Seebeck coefficient

The Seebeck results for the three samples (Fig. 7) show that increasing Bi in the chemical composition of the materials has a positive effect on the Seebeck coefficient. The positive Seebeck coefficient demonstrates that all the samples are p-type. In specific, the highest Seebeck coefficient is reported for Bi_0.5Sb_1.5Te₃ at room temperature (256 µV/K), while it is 79 µV/K for the Bi_0.3Sb_1.5Te₃ compound. As shown in SEM images, the material has integrated structure in which there is a lower carrier concentration, and thus, a lower scattering [32]. Therefore, the carrier movement is easier, and the Seebeck coefficient is higher. In addition, as can be seen in Fig. 7, there is a decreasing trend in the curves from 400 K to 700 K. The Seebeck coefficient obtained in the current study is lower compared with those obtained from some other studies. It can be related to the higher milling time, ratio of ball to powder, and milling rate in the researches [19]. These factors lead to the smaller particle size, decrease of carrier concentration, and the increase of the Seebeck coefficient. A donor-like effect (an interaction between anti-site defects and vacancies) resulted from the heavy plastic deformation during the milling process can be the reason. Li et al. [19] reported that the increase in the milling rate, the ball to powder ratio, and the milling time lead to the formation of extra electron carriers in the lattice and the negative Seebeck coefficient [19]. The study showed that at first, carriers are positive and then with increasing milling time, carriers change to the electron with a negative Seebeck value. However, in the current study, positive Seebeck coefficient was achieved, and it shows that carriers in these semiconductors are holes, instead of electrons. It might be because of the lower energy applied during the synthesize of the compounds using ball-milling process.

Fig. 7

Seebeck coefficient of Bi_0.5Sb_1.5Te₃, Bi_0.2Sb_1.8Te₃, and Bi_0.3Sb_1.7Te₃ samples SPSed at 400 °C

Pan et al. [33] ball-milled p-type Bi_0.5Sb_1.5Te₃ and n-type Bi₂Te_2.7Se_0.3 at 450 rpm for 3 h in a purified argon atmosphere with the ball to powder weight ratio of 20:1. The powders were sintered by SPS under uniaxial stress of 50 MPa at 673 K in a vacuum for 5 min. They reported that during the MA process and mechanical deformation, some vacancies are produced and collision of the anti-site defects and vacancies results in the decrease of the hole concentration and the increase of the Seebeck coefficient.

Impurities such as Fe entered from milling vessel and balls during the MA process can produce the anti-site defects and thus Seebeck coefficient [32]. According to Fig. 1, there are not such impurities in the synthesized powders, and it may be a reason for the lower Seebeck coefficient in these samples.

Based on Fig. 3, a rise in Bi content from 0.2 to 0.5 at.% results in the reduction of the particle size of the produced powders. Furthermore, it can be noted that the decrease in the size of the produced powders leads to a decrease in carrier concentration and, of course, a decrease in their scattering. As a result, the movement of the carriers is less disturbed, and the Seebeck coefficient increases [34]. The higher Seebeck coefficient of the Bi_0.5Sb_1.5Te₃ sample is due to the uniform distribution of fine cavities and the improvement of the charge carrier mobility, which can be cited by visual analysis of SEM images. Moreover, it indicates the effect of additives (Bi content) in all samples. According to Fig. 7, increasing the amount of Bi reduces the size of the cavities in the sample and also increases the Seebeck coefficient at ambient temperature which has a positive effect on TE properties.

The Seebeck coefficient variation in the temperature range of 300–700 K can be explained with two factors. The first one is the interaction of the anti-site defects and Te vacancy affecting the carrier concentrations. The second one is the effect of temperature on the mobility of carriers [29]. According to these parameters, the Bi_0.5Sb_1.5Te₃ composition showed the best Seebeck coefficient at room temperature.

3.5 Thermal conductivity

Thermal conductivity was calculated according to the following equation:

$$k = \, k_{{{\text{el}}}} + k_{{\text{L}}}$$

(5)

where k_el and k_L are the electronic and lattice thermal conductivity, respectively [10]. Figure 8 shows thermal conductivity curves. As can be observed, the thermal conductivity of the Bi_0.5Sb_1.5Te₃ specimen is the lowest at room temperature (0.856 W/m K). Also, due to low k_el and k_L, it demonstrates the highest phonon scattering in comparison with the other two specimens.

Fig. 8

The temperature-dependent thermal conductivity of Bi_0.5Sb_1.5Te₃, Bi_0.2Sb_1.8Te₃, and Bi_0.3Sb_1.7Te₃ samples SPSed at 400 °C

Among other significant factors affecting thermal conductivity, the addition of Bi as a doping agent to the sample Bi_0.5Sb_1.5Te₃ on the one hand increases grain boundaries which in turn, increases phonon scattering. On the other hand, Bi is a heavy element and can decrease lattice fluctuation and, in conclusion, decreases the phonon scattering.

According to Hyoung’s study [34], decreasing the grain size causes decreasing of K_lat by increasing of phonon scattering. Thus, reduction of the grain size can improve the thermoelectric performance of p-type Bi_0.5Sb_1.5Te₃ alloy by controlling both electronic and thermal transport properties.

In comparison with other results, the thermal conductivity measured in this study was lower. Some sample specifications affecting thermal conductivity have been mentioned in the literature such as the amount of impurity, microstructure, and grain size [21]. These parameters are controlled by synthesis parameters.

3.6 Power factor

Figure 9 exhibits the power factor for all the three samples of this study. As can be seen, the power factor is the highest for Bi_0.5Sb_1.5Te₃ at room temperature. Since the power factor is an important parameter influencing the efficiency of thermoelectric properties, the power factor was determined according to the following equation:

$$PF = \delta^{2} \alpha$$

(6)

in which, δ is the electrical conductivity and α is the Seebeck coefficient. According to the equation, the highest power factor is obtained with the highest Seebeck coefficient and electrical conductivity. As Fig. 9 indicates, the Bi_0.5Sb_1.5Te₃ sample demonstrates the highest power factor among the three samples studied in this research followed by Bi_0.2Sb_1.8Te₃, while Bi_0.3Sb_1.7Te₃ shows the lowest power factor among the samples. In this research, the power factor of 0.29 µW/K² cm was achieved for the sample Bi_0.5Sb_1.5Te₃ at room temperature. The power factor of these three compositions is resulted from the electrical conductivity and Seebeck coefficient. It means that the trend of power factor coefficient with temperature is affected by the variation of electrical conductivity and Seebeck coefficient. Therefore, the variation of the power factor comes from the concentration and mobility of holes [29].

Fig. 9

Power factor of Bi_0.5Sb_1.5Te₃, Bi_0.2Sb_1.8Te₃, and Bi_0.3Sb_1.7Te₃ samples SPSed at 400 °C

3.7 Figure of merit

Figure 10 shows the dependency of the figure of merit on temperature for all the three samples synthesized in this study. The figure of merit is a dimensionless parameter that exhibits the productivity of the TE materials and is determined using Eq. (1). Moreover, figure of merit of Bi₂Te₃-based thermoelectric materials could be improved using the nanostructured materials [35]. The results confirm that the sample with high electrical conductivity, high Seebeck coefficient, and low thermal conductivity, i.e., Bi_0.5Sb_1.5Te₃ sample shows the highest ZT (1.70 × 10⁻²) at 468 K, while for Bi_0.3Sb_1.7Te₃ and Bi_0.2Sb_1.8Te₃ samples, this parameter is 0.244 × 10⁻² and 0.951 × 10⁻², respectively. Fan et al. [21] fabricated Bi_0.5Sb_1.5Te₃ compounds using hot pressing at 300, 400, 450, and 500 °C. They found that ZT increases with increasing sintering temperature. The results showed that the sample sintered at 500 °C presents the maximum figure of merit of 2.84 × 10⁻³ at room temperature which is lower in comparison with the figure of merit of the specimen synthesized in the current study.

Fig. 10

Figure of merit of Bi_0.5Sb_1.5Te₃, Bi_0.2Sb_1.8Te₃, and Bi_0.3Sb_1.7Te₃ samples SPSed at 400 °C

Table 3 summarizes the thermoelectric properties of the synthesized compounds at 468 K, at which the higher ZT value has been obtained. In this research, Bi_0.5Sb_1.5Te₃ was compared with other TE materials such as Bi_0.2Sb_1.8Te₃ and Bi_0.3Sb_1.7Te₃ and exhibited better thermoelectric properties, including higher electrical conductivity and lower thermal conductivity. Finally, the Bi_0.5Sb_1.5Te₃ compound demonstrated the highest figure of merit.

Table 3 Thermoelectric properties of Bi_2−xSb_xTe₃ samples: total thermal conductivity (k_tot), Seebeck coefficient (S), electrical conductivity (σ), power factor (PF), and the figure of merit (ZT) at room temperature

4 Conclusions

In this study, three p-type thermoelectric compounds, i.e., Bi_2−xSb_xTe₃ with x = (1.2, 1.3, 1.5), were fabricated using mechanical alloying and spark plasma sintering (SPS). The microstructure and thermoelectric properties of the samples were analyzed and the following results were achieved:

• 1. A 6-h milling led to the formation of single phases of Bi_0.5Sb_1.5Te₃ and Bi_0.2Sb_1.8Te₃ rhombohedral structures; however, some impurities were seen along with the formation of the Bi_0.3Sb_1.7Te₃ single phase.

• 2. SEM images showed micropores with sizes of less than 50 microns uniformly distributed in the structure of Bi_0.5Sb_1.5Te₃ TE material.

• 3. Increasing the Bi content from 0.2 to 0.5 at.% resulted in a higher amount of power factor (0.294 µW/K² cm⁻¹), lower thermal conductivity (0.856 (W/mK)) and an increase in the electrical conductivity (0.854 S/cm) at room temperature.

• 4. A comparison of the three synthesized compounds confirmed that Bi_0.5Sb_1.5Te₃ material with the highest homogeneity and the lowest grain size demonstrates the highest ZT (1.70 × 10⁻²) at 468 K.