Rare Metals

, Volume 37, Issue 4, pp 343–350 | Cite as

Thermoelectric transport properties of Pb–Sn–Te–Se system

  • Bing-Chao Qin
  • Yu Xiao
  • Yi-Ming Zhou
  • Li-Dong Zhao


IV–VI compounds are considered as promising thermoelectric materials, and high thermoelectric performance was achieved in IV–VI solid solutions. In this work, the thermoelectric properties of Pb–Sn–Te–Se-based solid solutions were systematically investigated. Among these solid solutions, it is found that a figure of merit (ZT) peak value of 1.0 at 873 K can be obtained in (PbTe)0.5(SnTe)0.5, on account of the combination of superior electrical properties in SnTe and low thermal conductivity in PbTe. Furthermore, we investigated and summarized the thermoelectric transport properties and proposed the thermoelectric performance maps for the IV–VI solid solutions in Pb–Sn–Te–Se system. This comprehensive investigation on Pb–Sn–Te–Se-based solid solutions can effectively guide and scan thermoelectric performance for a given unknown composition and enhance the thermoelectric properties in IV–VI compounds.

Graphical Abstract


Thermoelectric materials Electrical conductivity Thermal conductivity Pb–Sn–Te–Se system Solid solutions 

1 Introduction

Thermoelectric materials provide an alternative way to directly and reversibly convert between heat and electricity, making them particularly appealing in waste heat recovery and fuel efficiency improvement [1, 2, 3]. Researchers are making great efforts to explore and design high-performance thermoelectric materials for practical applications [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. The efficiency of a thermoelectric material is governed by the dimensionless figure of merit, ZT = (S 2 σT/κ), where S, σ, T and κ are the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity, respectively [2, 14]. It is supposed to exhibit high S and σ, and low κ simultaneously in a superior thermoelectric material. However, the interdependence of these parameters complicates the efforts in thermoelectric designing [2].

Noticeably, some state-of-the-art thermoelectric materials are from the IV–VI systems, including lead chalcogenides (PbTe [15, 16, 17], PbSe [18, 19, 20] and PbS [21, 22]) and tin chalcogenides (SnTe [23, 24, 25, 26], SnSe [7, 8, 27, 28] and SnS [29]). Interestingly, solid solutions between these compounds are confirmed to exhibit superior performance than end-members through successfully manipulating nanostructures and electronic band structures, such as PbTe–PbSe [13, 30, 31, 32], PbTe–PbS [15, 33, 34, 35], PbSe–PbS [36, 37, 38], SnSe–SnS [39], PbSe–SnSe [40], Pb1−x Sn x Te–PbS [41] and PbTe–PbSe–PbS [16, 42]. These outstanding thermoelectric materials motivate us to re-investigate IV–VI systems, and the composition is expected to be optimized through scanning the thermoelectric properties for the solid solutions between every two end-member.

In this paper, solid solutions with different ingredients in Pb–Sn–Te–Se system were synthesized by melting method and pulverizing followed by spark plasma sintering (SPS). It is found that PbSnTeSe possesses strong phonon scattering in solid solutions. Namely, a low lattice thermal conductivity of ~ 0.8 W·m−1·K−1 at 873 K can be achieved when PbTe is alloyed with SnSe. In addition, PbTe–SnTe solid solutions simultaneously possess promising thermal and electrical transport properties, and thus, the ZT value exceeds 1.0 at 873 K in (PbTe)0.5(SnTe)0.5. The present results show that (PbTe)0.5(SnTe)0.5 possesses the best thermoelectric performance among Pb–Sn–Te–Se-based solid solutions. Based on the investigated thermoelectric transport properties of IV–VI solid solutions, we proposed one performance map for Pb–Sn–Te–Se system. The comprehensive investigations on Pb–Sn–Te–Se-based solid solutions can effectively guide and scan thermoelectric performance for a given unknown composition and enhance the thermoelectric properties in IV–VI compounds.

2 Experimental

2.1 Raw materials

The raw materials include Pb granules (99.99%, Aladdin element, China), Sn pieces (99.99%, Aladdin element, China), Te pieces (99.999%, Aladdin element, China), Se pieces (99.999%, Aladdin element, China).

2.2 Synthesis

The ingots of the Pb–Sn–Te–Se systems were prepared by putting the high-purity materials (Pb, Sn, Te and Se) into quartz tubes; then, the tubes were evacuated (< 1.3 × 10−2 Pa) and sealed. The sealed tubes were slowly heated to 823 K over 12 h, then quickly heated to 1423 K over 6 h, kept at this temperature for 6 h and furnace-cooled to room temperature. The obtained ingots were crushed into fine powders and densified using spark plasma sintering (SPS) in a 15-mm-diameter graphite dies under 50 MPa at 873 K for 6 min; disk-shaped samples with dimension of Φ 15 mm × 8 mm were obtained.

2.3 Phase and microstructure

Samples pulverized with an agate mortar were used for X-ray powder diffraction. The diffraction patterns were recorded with Cu Kα (λ = 0.15418 nm) radiation in a reflection geometry on an INEL diffractometer operating at 40 kV and 20 mA using a position-sensitive detector. Scanning electron microscope (SEM, JSM7500, JEOL, Tokyo, Japan) and energy-dispersive spectroscopy (EDS) experiments were carried out. SEM specimens were prepared by conventional methods, including cutting, grinding, dimpling and polishing, etc.

2.4 Electrical transport properties

The obtained SPS-processed pellets were cut into bars with 3 mm × 3 mm × 10 mm that were used for simultaneous measurement of the electrical conductivity and Seebeck coefficient using CTA and Ulvac-Riko ZEM-3 instrument under a helium atmosphere from room temperature to 873 K. The samples were coated with a thin layer of boron nitride to protect the instrument from the influence of evaporation.

2.5 Thermal transport properties

The obtained SPS-processed pellets were cut and polished into a Φ 6-mm disk shape with a 1–2 mm thickness for thermal diffusivity measurements. The disks were coated with a thin layer of graphite to minimize errors from the emissivity of the materials. The thermal conductivity was calculated according to the formula κ = D × ρ×C p , where the thermal diffusivity (D) was measured using laser-flash diffusivity method with a Netzsch LFA457 instrument, ρ is the sample density determined using the dimensions and mass of the sample and C p is the specific heat capacity estimated with Dulong–Petit law. The thermal diffusivity data were analyzed using a Cowan model with pulse correction. Noticeably, all the properties described in this study were measured perpendicular to the sintering pressure direction, which is the same to the direction for electrical transport properties measurement.

3 Results and discussion

In this work, solid solutions with cubic structure in Pb–Sn–Te–Se systems were firstly investigated, including SnTe–PbTe, PbTe–PbSe and PbSe–SnTe. Then, polycrystalline SnSe in the solid solutions was introduced aiming to reduce the thermal conductivity. In general, all the solid solutions formed by binary compounds in Pb–Sn–Te–Se systems were studied. Our study covers different components on each composition line shown in Fig. 1.
Fig. 1

Investigated solid solutions in Pb–Sn–Te–Se system

Among the materials suitable for thermoelectric applications, PbTe possesses excellent thermoelectric performance [43]. PbSe and PbTe have exactly the same crystal structure, but the thermoelectric properties of PbSe system are lower than those of PbTe system due to poor electrical conductivity in PbSe [44, 45]. SnTe is considered to be a potential non-toxic substitute for PbTe, but possesses higher carrier concentrations and higher thermal conductivity [46]. Firstly, the thermoelectric performance of PbSe–SnTe solid solution was investigated to check the optimized composition between these two end-members. As shown in Fig. 2a, all samples possess cubic structure since PbSe and SnTe both have the rock-salt (NaCl) structure. XRD peaks slowly shift from PbSe pattern to SnTe pattern with the content of SnTe increasing, which suggests that PbSe and SnTe can form solid solution. Obviously, the lattice parameter in PbSe–SnTe solutions increases with SnTe content increasing, due to that the lattice parameter in SnTe (~ 0.634 nm) is larger than that in PbSe (~ 0.612 nm), as shown in Fig. 2b.
Fig. 2

a Powder XRD patterns and b lattice parameters for (PbSe)1−x (SnTe) x

As shown in Fig. 3a, the electrical conductivity of all solid solutions decreases with temperature increasing, which shows a typical metallic behavior. The electrical conductivity in PbSe–SnTe solid solutions is largely enhanced with SnTe content increasing due to the ultrahigh carrier concentration in the pristine SnTe [47]. The electrical conductivity of the sample (PbSe)0.2(SnTe)0.8 exceeds 4000 S·cm−1 at room temperature. The Seebeck coefficient of all samples in the measurement temperature range is positive, indicating the p-type conduction. When PbSe is the dominant component (e.g., x = 0.2, 0.4), Seebeck coefficient rises with temperature and then decreases at high temperature. This case usually happens in PbSe system because of its narrow band gap [48, 49]. When SnTe becomes the main component (e.g., x = 0.5–0.8), the Seebeck coefficient mounts with the temperature rising and reaches 160 μV·K−1 at 873 K. As a result, the maximum power factor of ~ 15 μW·cm−1·K−2 is achieved in (PbSe)0.2(SnTe)0.8 at 673 K. At 873 K, the power factor of ~ 12 and ~ 11 μW·cm−1·K−2 in (PbSe)0.2(SnTe)0.8 and (PbSe)0.5(SnTe)0.5 (also be written as PbSnTeSe) is also achieved, respectively.
Fig. 3

Thermoelectric transport properties as a function of temperature for (PbSe)1−x (SnTe) x : a electrical conductivity, b Seebeck coefficient, c power factor, d total thermal conductivity, e lattice thermal conductivity, f ZT values

As shown in Fig. 3d, the variation tendencies of thermal conductivities for all solid solutions are consistent with those of their electrical conductivities. κ tot is a sum of the electronic (κ ele) and lattice thermal conductivity (κ lat). κ ele is directly proportional to the electrical conductivity (σ) through the Wiedemann–Franz relation, κ ele = LσT, where L is the Lorenz number [50]. The typical method of Lorenz number calculation is adopted [21]. When the SnTe component gradually rises in the solid solution, the Lorenz number of ~ 2.45 × 10−8 W·Ω·K−2 shows a property of degenerate semiconductor [50]. As shown in Fig. 3d, the overall trend of the total thermal conductivity of each sample decreases first and then rises at high temperature, indicating the existence of bipolar effect. The minimum thermal conductivity of solid solutions reaches ~ 1.0 W·m−1·K−1 at 473 K in (PbSe)0.8(SnTe)0.2. At high temperature, the thermal conductivity of each sample is superior to those of PbSe and SnTe; a lattice thermal conductivity of ~ 0.8 W·m−1·K−1 is obtained in (PbSe)0.5(SnTe)0.5 at 873 K (Fig. 3e). Owing to the special valence band characteristic of PbSe and high carrier concentration brought by SnTe, the ZT values of ~ 0.6, ~ 0.5 and ~ 0.6 are obtained in samples with x = 0.5, 0.6 and 0.8 at 773 K. In (PbSe)0.5(SnTe)0.5, the ZT value of ~ 0.72 is achieved at 873 K.

To further explore the mechanism of the excellent performance of the solid solution (PbSe)0.5(SnTe)0.5, SEM and EDS experiments were carried out (Fig. 4). SEM image and EDS mappings show that the distribution of each element in the sample is pretty uniform, except for some precipitates in small areas. As shown in Fig. 4b, most of the precipitates are indeed enriched in Se. The partial enrichment of Se will lead to a decrease in the electrical transport properties, indicating that the thermoelectric properties of the (PbSe)0.5(SnTe)0.5 can potentially be further optimized with Se enrichment disappearing after annealing homogenization.
Fig. 4

a SEM image and EDS elemental maps (b Pb, c Te, d Sn, e Se) of (PbSe)0.5(SnTe)0.5

Owing to the limited length of this article, thermoelectric transport properties of other solid solution systems depicted in Figs. S1–S16 in detail are shown in the supplementary information. Here we only show some experimental data of these systems, as listed in Table 1.
Table 1

Thermoelectric properties of solid solutions in Pb–Sn–Te–Se system


σ(300 K)/(S·cm−1)



κ tot (min)/(W·m−1·K−1)

κ lat (min)/(W·m−1·K−1)
















(PbTe)0. 5(SnTe)0. 5





































































































































In order to fully show the thermoelectric properties of solid solutions in Pb–Sn–Te–Se system, contouring diagrams are plotted according to these data. The electrical conductivity at 300 K, the maximum of Seebeck coefficient and power factor are shown in Fig. 5, respectively. The peak of the electrical conductivity appears near SnTe, due to the high hole carrier concentration of pristine SnTe. In addition, in the PbTe- or PbSe-riched PbTe–SnTe and PbSe–SnTe solid solutions, the electrical conductivity is enhanced compared with that of pristine PbTe/PbSe. The high Seebeck coefficient appears in two regions: One is near SnSe, which is caused by the high Seebeck coefficient of polycrystalline SnSe, and the other is near the PbTe–PbSe line. As a result, in solid solutions, high power factor value is achieved near the SnTe–PbTe line and PbSe–PbTe line.
Fig. 5

a Electrical conductivity, b Seebeck coefficient, c power factor of Pb–Sn–Te–Se system

Similarly, thermal transport properties are shown in Fig. 6. The minimum total thermal conductivity among all solid solutions appears near SnSe due to its intrinsically low thermal conductivity from weak phonon propagation and strong interface scattering from layered structure [7, 27, 51, 52]. The minimum lattice thermal conductivity is achieved near the SnSe-rich solid solution. Compared with the pristine compounds, the total and lattice thermal conductivity of solid solutions shows different degrees of reduction, which may arise from strong phonon scattering caused by the lattice distortion and defects in the high-entropy solid solutions [53]. Finally, the ZT values of the Pb–Sn–Te–Se system are shown in Fig. 7. The maximum ZT is achieved in the solid solutions near (SnTe)0.5(PbTe)0.5. Besides, ZT values over 0.7 are obtained near SnTe, SnSe and solid solution PbSnTeSe.
Fig. 6

Minimum a total thermal conductivity and b lattice thermal conductivity of Pb–Sn–Te–Se system

Fig. 7

Maximum ZT values of Pb–Sn–Te–Se system

4 Conclusion

In this work, a systematic study on solid solutions in Pb–Sn–Te–Se system was presented. In the PbSe–SnTe system, the ZT value of ~ 0.72 is achieved at 873 K in PbSnTeSe. In the SnTe–PbTe system, due to the effective combination of SnTe and PbTe, the complementary performance of two compounds is achieved and both electrical and thermal transport properties are significantly enhanced. In (SnTe)0.5(PbTe)0.5, the ZT value exceeds 1.0 at 773–873 K. Present results indicate that (1) SnTe can effectively enhance the electrical conductivity in PbTe, PbSe and SnSe because of its high carrier concentration; (2) SnSe can largely suppress the lattice thermal conductivity in PbTe, PbSe and SnTe due to its low thermal conductivity; (3) the relatively high ZT values appear in PbSe–SnTe and SnTe–PbTe solid solutions. Noticeably, these results in this work are acquired only using alloying method; therefore, higher performance is worthy to be expected after optimizing the carrier concentration.



This work was financially supported by the National Natural Science Foundation of China (Nos. 51671015, 51571007 and 51772012), the 111 project (No. B17002), the Beijing Municipal Science and Technology Commission (No. Z171100002017002) and the Shenzhen Peacock Plan Team (No. KQTD2016022619565991).

Compliance with ethical standards

Ethical standards

On behalf of all the authors, we declare that all the experiments comply with the current laws of the country in which they were performed.

Supplementary material

12598_2017_991_MOESM1_ESM.doc (4.2 mb)
Supplementary material 1 (DOC 4317 kb)


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Copyright information

© The Nonferrous Metals Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringBeihang UniversityBeijingChina

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