1 Introduction

Thermoelectric materials are used to convert waste heat into electricity or electrical power directly into heating and cooling [1,2,3,4,5]. Bi2Te3-based alloys are the most important commercial thermoelectric materials near room temperature. Recently, high thermoelectric performance of Bi2Te3-based materials has been achieved by using many methods and strategies such as hot deformation [6,7,8,9], point defects [10], nanocomposites [11,12,13], nanostructures [14,15,16,17,18,19,20] and doping [21, 22]. High-efficiency thermoelectric materials require a large Seebeck coefficient, high electrical conductivity and low thermal conductivity. Owing to interdependence of the thermoelectric parameters, increasing the thermoelectric figure of merit (zT) value remains a challenge. It is well known that doping may determine thermoelectric properties of the thermoelectric materials. The alkali atoms tend to have soft rattling-type phonon modes, which results in very low thermal conductivity in Bi2Te3-based materials [23]. Ji et al. [24] had developed a novel alkali metal salt hydrothermal nanocoating treatment method to coat the polycrystalline P-type Bi2Te3 bulk grains with a thin layer, and all three constituent physical properties of zT are “decoupled” and can be modified individually by different alkali metal salt solutions. On the other hand, alkali metals doping can effectively improve the Seebeck coefficient. Substituting Ag with Na has great influence on electron band structure and can enhance the Seebeck coefficient effectively, while adding excess Te in Na-doped samples plays a great role in optimizing the electrical and thermal conductivity in AgSbTe2 compound [25]. Substituting three valence electrons for Sb with five valence electrons in the Bi0.5Sb1.5Te3 alloy can be expected to be beneficial to the optimization of the carrier concentration, which results in an improvement in Seebeck coefficient.

To research the feasibility of the co-doping to enhance thermoelectric properties of the Bi2Te3-based materials, In and Na double partial substitutions for Sb in the Bi0.5Sb1.5Te3 alloys have been done. In present work, the samples were prepared by vacuum melting and hot-pressing technique. The effects of In and Na co-doping on electrical and thermal transport properties were investigated.

2 Experimental

Elemental powders with In (99.99%), Bi (99.99%), Sb (99.99%), Te (99.99%) and bulk Na (99.5%) were weighed according to the atomic ratios of Bi0.5Sb1.5Te3, Bi0.5Sb1.4−xNaxIn0.1Te3 (x = 0.02, 0.04, 0.06, 0.08, 0.10, 0.20). They were charged into a vacuum quartz tube, respectively. The elemental mixtures were melted at 1073 K for 8 h. Then, they were cooled to room temperature in the furnace. The gained ingots were pulverized using the agate mortar in atmosphere environment. The sizes of powders were controlled using the 300-mesh sieve. The powders were hot-pressed in the graphite dies under 50 MPa at 753 K for 1 h. Bulk disk-shaped pellets with dimension of 12 mm × 2 mm were prepared by hot pressing.

The phase structure and microstructure were analyzed by X-ray diffractometer (XRD, Bruker, D8 Advance with Cu Kα radiation, λ = 0.15406 nm) and scanning electron microscope (SEM, VEGA–II LSU), respectively. The Seebeck coefficients (S) were achieved by testing thermoelectric voltage under a temperature gradient with an accuracy of ± 7% from 300 to 500 K. The electrical resistivity (ρ) was measured by four-point probe from 300 to 500 K. The measure error of electrical resistivity is about ± 5%. The electrical properties were tested perpendicular to the hot-pressing direction. The thermal diffusivity (λ) was tested by the laser flash diffusivity method using a laser flash method (LFA 457). The thermal diffusivity was tested at the parallel to the hot-pressing direction. The measure error of thermal conductivity is about ± 5%. The heat capacity (Cp) was obtained from differential scanning calorimetry (DSC, DSC-Q20). The thermal conductivity was calculated according to the equation: λ = κ/(DCp), where λ is the thermal diffusivity, D is the density of samples, Cp is the heat capacity, and κ is the thermal conductivity. Hall coefficients were measured by the bar method using a Hall measurement system (Accent HL5500PC) at 300 K. The applied magnetic field is perpendicular to the hot-pressing direction.

3 Results and discussion

3.1 Microstructure

XRD patterns of Bi0.5Sb1.5Te3 and Bi0.5Sb1.4−xNaxIn0.1Te3 bulk samples are presented in Fig. 1. All the characteristic peaks of the bulk samples can be indexed into rhombohedral Bi0.5Sb1.5Te3 (JCPDS No. 49-1713) phase with no impurities, which indicates the single-phase structure of the samples. The (00l) peaks including (006), (009), (0015), (0018) and (0021) can be observed in the diffraction spectrums from section perpendicular to hot-pressing direction, which indicates that the basal planes are preferentially orientated perpendicular to hot-pressing direction. Since the rhombohedral Bi2Te3-based alloys have a quasi-layered crystal structure, it is important to determine whether all the hot-pressed samples are textured or not. The orientation degree of the (00l) planes can be determined by the orientation factor f, which can be calculated using the following method:

$$f = \frac{{P - P_{0} }}{{1 - P_{0} }}$$
(1)

where P and P0 are the ratios of the integrated intensities of all (00l) planes to those of all (hkl) planes for the preferentially oriented and the randomly oriented samples, respectively.

$$P = \frac{{I\left( {00l} \right)}}{{\sum I\left( {hkl} \right)}}\quad P_{0} = \frac{{I_{0} \left( {00l} \right)}}{{\sum I_{0} \left( {hkl} \right)}}$$
(2)

where I0(hkl) and I(hkl) are the peak integral intensities for randomly oriented sample and measured samples, respectively. The result of the orientation factor (f) was 0.29 ± 0.01. Because all the samples were prepared under the same condition, the values of f were almost equal. Therefore, it is concluded that the preferentially oriented c-axis samples can be fabricated by the vacuum melting and hot-pressing method.

Fig. 1
figure 1

XRD patterns of Bi0.5Sb1.5Te3 bulk sample and Bi0.5Sb1.4−xNa−xIn0.1Te3 bulk samples

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SEM images of the Bi0.5Sb1.5Te3 and the Bi0.5Sb1.36Na0.04In0.1Te3 samples are shown in Fig. 2. Figure 2a, c shows a laminated structure composed of micro–nanolayers. The Bi0.5Sb1.36Na0.04In0.1Te3 sample is found to have some randomly spaced pores in Fig. 2d. The size of these pores ranges from 300 to 600 nm. The other samples also exhibit the similar microstructures due to the same sintering method, but there are few randomly spaced pores in Fig. 2b. The above results are also confirmed by the density of the samples, which are shown in Table 1. The density of Bi0.5Sb1.36Na0.04In0.1Te3 sample is the lowest among all the samples.

Fig. 2
figure 2

SEM images of bulk samples: a Bi0.5Sb1.5Te3 from sections parallel to hot-pressing direction; b Bi0.5Sb1.5Te3 from sections perpendicular to hot-pressing direction; c Bi0.5Sb1.36Na0.04In0.1Te3 from sections parallel to hot-pressing direction; d Bi0.5Sb1.36Na0.04In0.1Te3 from sections perpendicular to hot-pressing direction

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Table 1 Density (D), hole concentration (n) and mobility (μ) of bulk Bi0.5Sb1.4−xNaxIn0.1Te3 samples at room temperature
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3.2 Thermoelectric properties

The temperature dependences of the Seebeck coefficient, the electrical conductivity and the power factor for the samples are shown in Fig. 3. The effects of co-doping on the electrical transport properties of the Bi0.5Sb1.4−xNaxIn0.1Te3 (x = 0.02–0.20) were systematically investigated. All the samples exhibit the p-type semiconductor behavior within the whole test temperature range, as shown in Fig. 3a. Figure 3a also shows that the In and Na co-doping leads to the increase in the Seebeck coefficient from 300 to 350 K. This is attributed to the In and Na co-doping causing the change in the carrier concentration. As shown in Table 1, the co-doped samples result in the decrease in the hole concentration at room temperature. In this way, the Seebeck coefficients increase. Compared with the Bi0.5Sb1.5Te3 sample, Fig. 3b shows that the electrical conductivity of the In and Na co-doped samples is lower than that of the Bi0.5Sb1.5Te3 alloy within the whole test temperature range. The carrier concentration and mobility are mainly two factors, which can lead to the differences of the electrical conductivity. The carrier concentration is mainly related to the composition, while the mobility can be affected by the grain size, grain boundary density and defects [26]. The incorporation of In and Na in the structure of Bi0.5Sb1.5Te3 results in the decrease in the hole concentration and mobility in Table 1. Owing to the lower electrical conductivity, the power factors of the co-doped samples are lower slightly than that of the Bi0.5Sb1.5Te3 sample, as shown in Fig. 3c.

Fig. 3
figure 3

Temperature dependence of electrical properties of Bi0.5Sb1.4−xNaxIn0.1Te3 (x = 0.02–0.20) samples: a Seebeck coefficient (S); b electrical conductivity (σ); c power factor (PF)

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The thermal properties and zT values are shown in Fig. 4. As shown in Fig. 4a, the total thermal conductivity is the sum of contributions of the electronic thermal conductivity (κe) and the lattice thermal conductivity (κL). The electronic thermal conductivity (κe) is quantified through the Wiedemann–Franz law: κe = L0T/ρ, where L0 is the Lorenz number, T is the absolute temperature, and ρ is the electrical resistivity [27]. The classical value of the Lorentz number L0 = 2.45 × 10−8 V2·K−2 and is valid for a degenerate electron gas. In this paper, L0= 2.0 × 10−8 V2·K−2 is taken, which is used for a heavily doped semiconductor [28]. The total thermal conductivity of the Bi0.5Sb1.4−xNaxIn0.1Te3 (x = 0.02–0.06) samples is lower than that of the Bi0.5Sb1.5Te3 sample from 300 to 500 K. The alkali atoms tend to have soft rattling-type phonon modes, which results in very low thermal conductivity. With the Na substitution fraction increasing from 0.08 to 0.20, the thermal conductivity of the Bi0.5Sb1.4−xNaxIn0.1Te3 samples is larger than that of the Bi0.5Sb1.5Te3 sample. Figure 4b shows that the electrical thermal conductivity of the Bi0.5Sb1.4−xNaxIn0.1Te3 samples is lower than that of the Bi0.5Sb1.5Te3 sample from 300 to 500 K. The observed decreases are associated with the decrease in the hole concentration and mobility, which are shown in Table 1. As shown in Fig. 4c, the lattice thermal conductivity of the co-doping samples increases with Na substitution fraction increasing from 0.08 to 0.20. Because the electronegativity difference between Na and Te (1.17) is much larger than that between Sb and Te (0.05), replacing Sb with Na should result in much stronger bonding between anions and cations. So, the anharmonicity of the lattice vibrational spectrum is decreased and a rise in κL can be expected. With Na substitution fraction increasing from 0.02 to 0.04, the Bi0.5Sb1.36NaxIn0.1Te3 samples show lower κL over the whole temperature region. The x = 0.04 sample has the lowest lattice thermal conductivity. Besides solid solutions scattering high frequency phonons, decrease of the lattice thermal conductivity may be caused by the randomly spaced pores. The spaced pores are shown in Fig Fig. 2d. The randomly spaced pores are beneficial to the scattering of phonons, which contributes to the observed lower lattice thermal conductivity [29,30,31]. Figure 4d shows temperature dependence of zT value of all the samples. For the Bi0.5Sb1.5Te3 sample, the zT value of 1.01 is obtained at 323 K. Compared with the Bi0.5Sb1.5Te3 sample, the zT values of the Bi0.5Sb1.4−xNaxIn0.1Te3 samples decrease with the increasing Na substitution fraction from x = 0.06–0.2 in the whole temperature range. The Bi0.5Sb1.36Na0.04In0.1Te3 sample shows the highest zT values from 300 to 450 K. The increases in zT values can be attributed to the lower thermal conductivity. The zT value of 1.42 is obtained at 323 K. The value represents 40% enhancement with respect to the Bi0.5Sb1.5Te3 sample at the same temperature.

Fig. 4
figure 4

Temperature dependence of thermal conductivity of Bi0.5Sb1.4−xNaxIn0.1Te3 (x = 0.02–0.20) samples: a total thermal conductivity (κT); b electrical thermal conductivity (κE); c lattice thermal conductivity (κL); d figure of merit (zT)

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4 Conclusion

XRD results show that all the characteristic peaks of the bulk samples can be indexed into rhombohedral Bi0.5Sb1.5Te3 phase with no impurities. It is concluded that the preferentially oriented c-axis samples can be fabricated by the vacuum melting and hot-pressing method. SEM results show a laminated structure composed of micro–nanolayers. Compared with the Bi0.5Sb1.5Te3 sample, the In and Na co-doped Bi0.5Sb1.5Te3 samples bring about substantial increase in Seebeck coefficient at near room temperature. The electrical conductivity of the In and Na co-doping samples is lower than that of Bi0.5Sb1.5Te3 alloy within the whole test temperature range. For the Bi0.5Sb1.36Na0.04In0.1Te3 sample, a minimal thermal conductivity of 0.45 W·m−1·K−1 is obtained, with the maximal zT value reaching 1.42 at 323 K. The value represents 40% enhancement with respect to the Bi0.5Sb1.5Te3 alloy at the same temperature. The results show that the In and Na dual substitutions for Sb are effective in enhancing thermoelectric performance of Bi0.5Sb1.5Te3 alloy.