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Enhanced thermoelectric performance of n-type PbTe doped with Na2Te
Intermetallics 92 (2018) 113–118
Contents lists available at ScienceDirect
Intermetallics journal homepage: www.elsevier.com/locate/intermet
Enhanced thermoelectric performance of n-type PbTe doped with Na2Te a
a
a,c
a,∗
MARK
b
Fong-Ren Sie , Hsin-Jung Liu , Chia-Hung Kuo , Chii-Shyang Hwang , Ya-Wen Chou , Chien-Hsuan Yehb a b c
Department of Materials Science and Engineering, National Cheng Kung University, Tainan City, 701, Taiwan, ROC Green Energy & Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu City, 310, Taiwan, ROC New Materials Research & Development Department, China Steel Corporation, Kaohsiung City, 812, Taiwan, ROC
A R T I C L E I N F O
A B S T R A C T
Keywords: n-type PbTe Planetary ball milling ZT Hot-pressed sintering
The n-type PbTe doped with Na2Te (0.5–1.5 mol%) powders was prepared via planetary ball milling and then compacted via hot-pressed sintering at 773 K and 50 MPa. The effect of Na2Te on the thermoelectric performance of PbTe was investigated. The results demonstrated that Na2Te doping not only increased the lattice parameter, but also transformed the conduction type from p- to n-type. Moreover, Na+ was located at the interstitial sites of PbTe and generated excess electrons, increasing carrier concentration and electrical conductivity. The enhancement in the power factor of PbTe doped with Na2Te samples was due to the higher Seebeck coefficient and electrical conductivity at a high measurement temperature. A maximum ZT value of 0.81 at 700 K was obtained for n-type PbTe doped with 1 mol% Na2Te due primarily to a significant increase in the power factor and a reduction in thermal conductivity.
1. Introduction PbTe and its alloys are well-known thermoelectric materials in the intermediate temperature range of 500–800 K [1]. The density of state can be controlled for heavily doped PbTe due to the coexistence of light-hole (L) and heavy-hole (Σ) valence bands in PbTe [2,3], which exhibits outstanding ZT performance. Many elements and compounds have been doped into PbTe, such as Ag [4], K [5], Tl [6,7], Na [8–11], Sn [12], Ag2Te [9,13], Cd [14], CdTe [15], and CaTe [16]. Ahn et al. [17] prepared p-type PbTe-2% HgTe-1% Na2Te bulk samples at 770 K using the melting method and spark plasma sintering and obtained an excellent ZT of 1.64. The HgTe precipitated evenly in the PbTe matrix with a size distribution of 2–12 nm, and thus played an important role in the reduction of lattice thermal conductivity. Ohta et al. [18] synthesized p-type PbTe-2% MgTe-2% Na2Te using the melting method. A maximum ZT of 1.6 at 780 K was obtained. Additionally, PbTe doped with Na2Te (1–2 mol%) also exhibited p-type characteristics in their work. Wang et al. [19] found that p-type Na0.2Pb0.8Te synthesized under appropriate hot-pressed conditions had an optimized ZT of 1.74 at 774 K. Pei et al. [20] reported that p-type Na-doped PbTe had a maximum ZT of 1.4 at 750 K with a high hole carrier concentration of approximately 1020 cm−3. In many of the aforementioned studies on ptype Na or Na2Te doped PbTe systems, Na substituted Pb as an effective acceptor and controlled the p-type carrier concentration. It also led to the decrease of the lattice parameter when Na substituted Pb atoms ∗
[21,22]. In our previous study, Na-doped PbTe synthesized via a combination of the melting method, attrition milling, and spark plasma sintering exhibited p-type transport properties [23]. However, n-type PbTe with Na2Te addition has not been studied. In the present work, n-type semiconductor was observed when Na+ was located at the interstitial sites in PbTe fabricated through planetary ball milling and hot-pressed sintering. The effect of Na2Te addition on the thermoelectric performance of PbTe was investigated. 2. Experimental Commercial PbTe (Alfa Aesar, 99.98%) and Na2Te (Alfa Aesar, 99.98%) powders were chosen to prepare PbTe doped with 0–1.5 mol% Na2Te. Then, PbTe and PbTe doped with Na2Te powders were milled by planetary ball milling (Pulverisette 7, Fritsch) at a rotor speed of 400 rpm for 4 h under an argon atmosphere using a stainless steel medium with a diameter of 3 mm. Subsequently, PbTe samples doped with 0–1.5 mol% Na2Te powders were hot-pressed into bulk samples under a uniaxial pressure of 50 MPa at 773 K for 2 h in an argon atmosphere. The crystal phases of the bulk samples were confirmed with X-ray diffraction (XRD, D8 DISCOVER, Bruker) at room temperature using Cu Kα radiation (λ = 0.15406 nm). Field-emission scanning electron microscopy (FE-SEM SU8000, Hitachi) was used to observe the microstructure of the sintered samples. The bulk samples were cut into
Corresponding author. E-mail address: [email protected] (C.-S. Hwang).
http://dx.doi.org/10.1016/j.intermet.2017.09.018 Received 7 June 2017; Received in revised form 1 September 2017; Accepted 3 September 2017 Available online 12 October 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
Intermetallics 92 (2018) 113–118
F.-R. Sie et al.
Fig. 1. (a) XRD patterns and (b) lattice parameter a of bulk samples with various Na2Te contents and hot-pressed at 773 K for 2 h.
conduction behavior. Based on the lattice parameter and Hall measurements results, Na+ diffusion into the interstitial sites of PbTe increases the lattice parameter and simultaneously contributes extra electrons. These results are different from those reported in other studies [10,11,17–20], where Na+ substituted Pb2+ as a p-type semiconductor. Fig. 3 presents the relation between carrier mobility and total carrier concentration for PbTe doped with Na2Te. Accordingly, the carrier mobility of all PbTe doped with Na2Te are smaller than that of PbTe, which means that the number of carriers is generated to scatter carriers and causes the decrease of carrier mobility. Furthermore, the densification of sintered bulk samples also influences carrier mobility. The carrier mobility increased slightly from 31 to 78 cm2/Vs when the relative density is improved from 95.3% to 97.1%, even though the carrier concentration increases from 1.07 × 1019 cm−3 to 1.53 × 1019 cm−3. In addition, the carrier mobility as a function of carrier concentration that an approximate n−1.1 relation for PbTe doped with Na2Te system, as shown in the inset of Fig. 3. It reveals a rough consistency, which means that the dominant mechanism is acoustic phonon scattering rather than electron scattering. Fig. 4 (a) and (b) presents the temperature dependence of electrical conductivity and Seebeck coefficient for all sintered samples. Generally, undoped PbTe has a typical bipolar characteristic in hand grinding [4], ball milling [24] and zone melting process [25]. It demonstrates that the electrical conductivity firstly decreases and then increases, and the Seebeck coefficient can be changed from p- to n-type with increasing measured temperature, as shown in Fig. 4(a) and (b). All PbTe doped with Na2Te samples have larger values of electrical conductivity than that of PbTe in the temperature range of 350–700 K, which is due to the total carrier concentration increasing with Na2Te content. Moreover, a transformation of the electrical conduction behavior is observed in all PbTe doped with Na2Te samples at room temperature, as determined using Hall measurements, with the Fermi level moving from the valence band to the conduction band. As the measurement temperature is increased, all PbTe doped with Na2Te samples change from being a semiconductor to a degenerate semi-conductor (metallic). This reveals that the intrinsic carriers are excited at higher temperature, which induces that the Fermi level shifts into the conduction band (as in a degenerate semi-conductor). Also, all PbTe doped with Na2Te samples have a negative Seebeck coefficient throughout the measurement temperature range, indicating that electrical conduction behavior is contributed mainly by electrons, as shown in Fig. 4 (b). It provides a result that the conduction behavior and Fermi level can be changed because Na+ diffuses into the interstitial sites in PbTe. Fig. 4 (c) demonstrates the Seebeck coefficient as a function of the total carrier concentration for PbTe doped with Na2Te system. The Pisarenko relation between the Seebeck coefficient and carrier concentration provides a good explanation of the experimental data [18,26,27]. The black line is the theoretical Pisarenko line assuming a single parabolic band and an acoustic phonon scattering mechanism. In this approximation, the Seebeck coefficient and carrier concentration are calculated according
rectangular bars (3 mm × 3 mm × 15 mm) for the measurement of electrical conductivity and the Seebeck coefficient under a low inert-gas atmosphere at temperatures ranging from 300 to 700 K using commercial equipment (ZEM-3, Ulvac-Riko). The carrier concentration and mobility of the bulk samples were measured using four-probe Hall-effect measurements at room temperature. The thermal diffusivity (α), bulk density (ρ) and specific heat (Cp) were measured using a laser flash thermal constant analyzer (TC-9000, Ulvac-Riko), the Archimedes method, and differential scanning calorimetry (DSC, Setaram), respectively. The thermal conductivity (κ) was calculated using the equation κ = αρCp. 3. Results and discussion Fig. 1(a) shows XRD patterns of all bulk samples with 0–1.5 mol% Na2Te addition hot-pressed at 773 K for 2 h. All specimens have the face-centered-cubic rock salt structure of PbTe and belong to the Fm3m space group, which means that no other crystalline phases could be observed. Fig. 1(b) shows the lattice parameter a for all samples with various Na2Te contents. The lattice parameter increases from 6.4655 to 6.4707 Å when the amount of Na2Te is increased from 0 to 1.5 mol%. The ionic radii of Na+, Pb2+, and Te2− are 1.03, 1.32 and 2.11 Å, respectively. Usually, Na doping of p-type PbTe decreases the lattice parameter because the metallic ionic radius of Na (1.03 Å) is smaller than that of Pb (1.32 Å) [21,22]. However, in this study, all PbTe doped with Na2Te samples have a larger lattice parameter than that of PbTe, which means that Na+ in PbTe is located at the interstitial sites rather than substitution sites. Fig. 2 displays SEM images of the fractured surface for specimens hot-pressed at 773 K for 2 h. It shows that the grain sizes of all samples are similar (1–10 μm) and no secondary phase is observed in all PbTe doped with Na2Te samples. Besides, the number of pores decreases with increasing Na2Te content according to SEM results. When the amount of Na2Te is increased, the measured density increases from 7.51 to 7.92 g/ cm3, and the relative density increases from 92.0 to 97.1%, as shown in Table 1. Thus, adding Na2Te in PbTe results in the decrease of pores and the increase of measured density and relative density. Table 1 also lists the carrier concentration and carrier mobility for all samples. The conduction behavior also confirms p- to n- type semiconductor through Hall measurements. When the amount of Na2Te is increased from 0.5 to 1.5 mol%, the carrier concentration increases from 1.07 × 1019 cm−3 to 1.53 × 1019 cm−3, whereas the carrier mobility decreases from 607 to 31 cm2/Vs and then increases to 78 cm2/Vs at room temperature. Because the stainless steel jars and balls are used in high energy ball milling, the contamination of Fe may affect the conduction behavior. The ICP-MS is used to analysis in order to understand the amount of Fe in the samples. When the amount of Na2Te is increased from 0 to 1.5 mol%, the Fe content are 104.2, 75.7, 210.9 and 70.2 ppm, respectively. The contamination of Fe is relatively low in all samples, so it will not contribute huge influence on 114
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Fig. 2. SEM images of fractured surface of (a) PbTe and PbTe doped with (b) 0.5%, (c) 1.0%, and (d) 1.5% Na2Te and hot-pressed at 773 K for 2 h.
to the Boltzmann transport equation and it can be expressed as follows [8,26,27]:
S=±
kB ⎛ (γ + 5/2) Fγ + 3/2 (η) − η⎞⎟ ⎜ e ⎝ (γ + 3/2) Fγ + 1/2 (η) ⎠
(1)
3
p (n) =
4π (2kB Tm∗) 2 F 1 (η) 2 h3
Fn (η) =
∫ 1 +χe χ −η dχ
∞
(2)
n
(3)
0
where kB is the Boltzmann's constant, e is the electron charge, γ is the scattering parameter (−1/2 for acoustic phonon scattering and +3/2 for ionized impurity scattering), m∗ is the effective mass, η is the reduced Fermi level, Fn(η) is the Fermi integral, and h is the Planck constant, respectively. Based on Fig. 3, acoustic phonon scattering is main scattering mechanism and thus the γ value equals −1/2. The effective mass m∗ can be calculated according to the results of Seebeck coefficient and carrier concentration at 300 K, as shown in Table 1. The experimental values and the theoretical Pisarenko line (m* = 0.3 m0) are in good agreement, indicating that acoustic phonon scattering is dominant. As shown in Fig. 4 (d), the power factor increases from 0.11 to 1.28 mW/m-K2 at 700 K when the Na2Te content is increased from 0 mol% to 1.5 mol%, indicating the power factor is increased by the addition of Na2Te. The temperature dependence of the total thermal conductivity for all samples is shown in Fig. 5 (a). It exhibits that total thermal conductivity of all PbTe doped with Na2Te samples is smaller than that of the PbTe sample at high measurement temperature, which decreases
Fig. 3. Carrier mobility as function of carrier concentration for PbTe doped with various Na2Te content levels. Solid line represents the μ - n−1.1 relation.
from 2.56 to 1.09 W/m-K. In comparison with PbTe sample, the bipolar effect is eliminated for all PbTe doped with Na2Te samples due to a change in the energy band structure, which is consistent with the experimental results for electrical conductivity. The total thermal conductivity (κ) is made up of the electronic thermal conductivity (κe) and the phonon thermal conductivity (κL) and can be expressed as κ = κL + κe = κL + LσT, where L is the Lorentz number. The electronic thermal conductivity (κe) can be estimated using the Wiedemann-Frantz equation (κe = LσT). The temperature dependence of the Lorentz number is calculated based on equations (1) and (4) [26,28].
Table 1 Measured density (D), relative density (DR), hall charge carrier concentration (nH), Hall mobility (μH), Seebeck coefficient (S), electrical conductivity (σ), effective mass (m*), and Lorentz number (L) for PbTe doped with various Na2Te samples measured at room temperature. Sample (mol% Na2Te)
D (g/cm3)
DR (%)
Type (p/n)
nH (×1019cm−3)
μH (cm2/Vs)
S (μV/K)
σ (S/cm)
m* (m0)
L (10−8 V2·K−2)
0 0.5 1.0 1.5
7.51 7.78 7.81 7.92
92.0 95.3 95.6 97.1
p n n n
0.09 1.07 1.49 1.53
607.8 31.4 32.4 78.1
325 −112 −100 −75
84.03 53.52 77.40 191.25
0.34 0.28 0.31 0.23
1.52 1.86 1.91 2.05
115
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Fig. 4. Temperature dependence of (a) electrical conductivity, (b) Seebeck coefficient, (c) Pisarenko plots at 300 K (Seebeck coefficient as function of carrier concentration. Solid line represents Pisarenko relations for effective mass of 0.3 m0.), and (d) power factor for PbTe doped with Na2Te (0–1.5 mol%).
Fig. 5. Temperature dependence of (a) thermal conductivity, (b) Lorentz number, (c) electronic thermal conductivity, and (d) lattice thermal conductivity for PbTe doped with Na2Te (0–1.5 mol%).
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from p- to n-type, the Fermi level moves, and the bipolar effect of PbTe is eliminated. Moreover, all PbTe doped with Na2Te samples show a conversion feature from a semiconductor to a degenerate semiconductor with increasing measurement temperature. For PbTe doped with Na2Te system, the ZT value increases with temperature owing to a higher power factor and lower thermal conductivity at higher measurement temperature, which are controlled by the concentration of Na2Te. The maximum ZT value for n-type PbTe doped with 1 mol% Na2Te (0.81) is higher than that of the PbTe sample (0.03) at 700 K. Acknowledgement The authors gratefully appreciate the financial support received for this work from the Ministry of Science and Technology of Taiwan, R.O.C., under grant MOST 103-2221-E-006-069-MY3 and the Bureau of Energy, Ministry of Economic Affairs, Taiwan, R.O.C. Fig. 6. Temperature dependence of dimensionless ZT values for PbTe doped with Na2Te (0–1.5 mol%).
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2
(γ + 5/2) Fγ + 3/2 (η) ⎤ ⎞ k 2 ⎛ (γ + 7/2) Fγ + 5/2 (η) −⎡ L = ⎛ B⎞ ⎜ ⎢ (γ + 3/2) Fγ + 1/2 (η) ⎥ ⎟ ⎝ e ⎠ ⎝ (γ + 3/2) Fγ + 1/2 (η) ⎣ ⎦⎠
(4)
The Lorentz number of all samples as a function of temperature is shown in Fig. 5 (b). All Lorentz numbers are in the range from the nondegenerate limit (1.5 × 10−8 V2K−2) to the degenerate limit (2.45 × 10−8 V2K−2). At room temperature, the Lorentz numbers increase with increasing Na2Te addition, indicating that the Fermi level has shifted. An obvious upturn at high temperature is observed for the undoped PbTe sample because it is a bipolar narrow semiconductor. In contrast, the PbTe doped with Na2Te samples do not exhibit an upturn in the whole measurement temperature range, indicating that the bipolar effect is eliminated. Based on the above calculation for the Lorenz number, the electronic thermal conductivity and lattice thermal conductivity for all samples are shown in Fig. 5 (c) and (d). As seen in Fig. 5 (c), the electronic thermal conductivity increases with increasing the amount of Na2Te because the electrical conductivity is enhanced. Moreover, the higher electrical conductivity and electronic thermal conductivity always result in a decrease in lattice thermal conductivity, as shown in Fig. 5 (d). The lattice thermal conductivity of all PbTe doped with Na2Te samples is smaller than that of the PbTe sample at high measurement temperature because the bipolar effect is eliminated when Na2Te is added. Moreover, the porosity could efficiently scatter phonons and play a role in the PbTe doped with Na2Te samples. The enhancement of relative density for PbTe doped with Na2Te samples leads to an increase in lattice thermal conductivity as increasing the amount of Na2Te. Fig. 6 presents the temperature dependence of ZT value for all samples. All PbTe doped with Na2Te samples have relatively larger ZT values than that of the PbTe sample. Especially, the highest ZT value is about 0.81 at 700 K for PbTe doped with 1 mol% Na2Te, which means that the addition of Na2Te significantly increases ZT value. The ZT value can be improved by an increase in the electrical conductivity and Seebeck coefficient and a decrease in thermal conductivity at higher temperature due to Na2Te addition. Although the ZT value in this work is not higher than those of p-type Na-doped PbTe, n-type PbTe doped with Na2Te was easily prepared by combining planetary ball milling and hot-pressed sintering. 4. Conclusions n-type PbTe doped with Na2Te was fabricated via planetary ball milling and hot-pressed sintering. The results reveal that the lattice parameter increase with increasing Na2Te content, indicating that the addition of Na2Te leads to Na+ being located at the interstitial sites of PbTe. When Na2Te is added to PbTe, the electrical conduction changes 117
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[25] G. Ding, J. Si, H. Wu, S. Yang, J. Zhao, G. Wang, Thermoelectric properties of melt spun PbTe with multi-scaled nanostructures, J. Alloys Compd. 662 (2016) 368–373. [26] L.D. Zhao, S.H. Lo, J. He, H. Li, K. Biswas, J. Androulakis, C.I. Wu, T.P. Hogan, D.Y. Chung, V.P. Dravid, M.G. Kanatzidis, High performance thermoelectrics from earth-abundant materials: enhanced figure of merit in Pbs by Second phase nanostructures, J. Am. Chem. Soc. 133 (2011) 20476–20487. [27] S. Johnsen, J. He, J. Androulakis, V.P. Dravid, I. Todorov, D.Y. Chung, M.G. Kanatzidis, Nanostructures boost the thermoelectric performance of PbS, J. Am. Chem. Soc. 133 (2011) 3460–3470. [28] S. Wang, X. Tan, G. Tan, X. She, W. Liu, H. Li, H. Liu, X. Tang, The realization of a high thermoelectric figure of merit in Ge-substituted β-Zn4Sb3 through band structure modification, J. Mater. Chem. 22 (2012) 13977.
and thermoelectric properties of NaXPb1−XTe0.85Se0.15, J. Electron. Mater 43 (2013) 353–358. [22] J. Androulakis, I. Todorov, D.-Y. Chung, S. Ballikaya, G. Wang, C. Uher, M. Kanatzidis, Thermoelectric enhancement in PbTe with K or Na codoping from tuning the interaction of the light-and heavy-hole valence bands, Phys. Rev. B 82 (11) (2010). [23] C.H. Kuo, M.S. Jeng, J.R. Ku, S.K. Wu, Y.W. Chou, C.S. Hwang, P-type PbTe thermoelectric bulk materials with nanograins fabricated by attrition milling and Spark Plasma Sintering, J. Electron. Mater 38 (2009) 1956–1961. [24] A. Schmitz, C. Stiewe, K. Zabrocki, J. de Boor, K. Mull, E. Müller, Current assisted sintering of PbTe—effects on thermoelectric and mechanical properties, Mater. Res. Bull. 86 (2017) 159–166.
118
Contents lists available at ScienceDirect
Intermetallics journal homepage: www.elsevier.com/locate/intermet
Enhanced thermoelectric performance of n-type PbTe doped with Na2Te a
a
a,c
a,∗
MARK
b
Fong-Ren Sie , Hsin-Jung Liu , Chia-Hung Kuo , Chii-Shyang Hwang , Ya-Wen Chou , Chien-Hsuan Yehb a b c
Department of Materials Science and Engineering, National Cheng Kung University, Tainan City, 701, Taiwan, ROC Green Energy & Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu City, 310, Taiwan, ROC New Materials Research & Development Department, China Steel Corporation, Kaohsiung City, 812, Taiwan, ROC
A R T I C L E I N F O
A B S T R A C T
Keywords: n-type PbTe Planetary ball milling ZT Hot-pressed sintering
The n-type PbTe doped with Na2Te (0.5–1.5 mol%) powders was prepared via planetary ball milling and then compacted via hot-pressed sintering at 773 K and 50 MPa. The effect of Na2Te on the thermoelectric performance of PbTe was investigated. The results demonstrated that Na2Te doping not only increased the lattice parameter, but also transformed the conduction type from p- to n-type. Moreover, Na+ was located at the interstitial sites of PbTe and generated excess electrons, increasing carrier concentration and electrical conductivity. The enhancement in the power factor of PbTe doped with Na2Te samples was due to the higher Seebeck coefficient and electrical conductivity at a high measurement temperature. A maximum ZT value of 0.81 at 700 K was obtained for n-type PbTe doped with 1 mol% Na2Te due primarily to a significant increase in the power factor and a reduction in thermal conductivity.
1. Introduction PbTe and its alloys are well-known thermoelectric materials in the intermediate temperature range of 500–800 K [1]. The density of state can be controlled for heavily doped PbTe due to the coexistence of light-hole (L) and heavy-hole (Σ) valence bands in PbTe [2,3], which exhibits outstanding ZT performance. Many elements and compounds have been doped into PbTe, such as Ag [4], K [5], Tl [6,7], Na [8–11], Sn [12], Ag2Te [9,13], Cd [14], CdTe [15], and CaTe [16]. Ahn et al. [17] prepared p-type PbTe-2% HgTe-1% Na2Te bulk samples at 770 K using the melting method and spark plasma sintering and obtained an excellent ZT of 1.64. The HgTe precipitated evenly in the PbTe matrix with a size distribution of 2–12 nm, and thus played an important role in the reduction of lattice thermal conductivity. Ohta et al. [18] synthesized p-type PbTe-2% MgTe-2% Na2Te using the melting method. A maximum ZT of 1.6 at 780 K was obtained. Additionally, PbTe doped with Na2Te (1–2 mol%) also exhibited p-type characteristics in their work. Wang et al. [19] found that p-type Na0.2Pb0.8Te synthesized under appropriate hot-pressed conditions had an optimized ZT of 1.74 at 774 K. Pei et al. [20] reported that p-type Na-doped PbTe had a maximum ZT of 1.4 at 750 K with a high hole carrier concentration of approximately 1020 cm−3. In many of the aforementioned studies on ptype Na or Na2Te doped PbTe systems, Na substituted Pb as an effective acceptor and controlled the p-type carrier concentration. It also led to the decrease of the lattice parameter when Na substituted Pb atoms ∗
[21,22]. In our previous study, Na-doped PbTe synthesized via a combination of the melting method, attrition milling, and spark plasma sintering exhibited p-type transport properties [23]. However, n-type PbTe with Na2Te addition has not been studied. In the present work, n-type semiconductor was observed when Na+ was located at the interstitial sites in PbTe fabricated through planetary ball milling and hot-pressed sintering. The effect of Na2Te addition on the thermoelectric performance of PbTe was investigated. 2. Experimental Commercial PbTe (Alfa Aesar, 99.98%) and Na2Te (Alfa Aesar, 99.98%) powders were chosen to prepare PbTe doped with 0–1.5 mol% Na2Te. Then, PbTe and PbTe doped with Na2Te powders were milled by planetary ball milling (Pulverisette 7, Fritsch) at a rotor speed of 400 rpm for 4 h under an argon atmosphere using a stainless steel medium with a diameter of 3 mm. Subsequently, PbTe samples doped with 0–1.5 mol% Na2Te powders were hot-pressed into bulk samples under a uniaxial pressure of 50 MPa at 773 K for 2 h in an argon atmosphere. The crystal phases of the bulk samples were confirmed with X-ray diffraction (XRD, D8 DISCOVER, Bruker) at room temperature using Cu Kα radiation (λ = 0.15406 nm). Field-emission scanning electron microscopy (FE-SEM SU8000, Hitachi) was used to observe the microstructure of the sintered samples. The bulk samples were cut into
Corresponding author. E-mail address: [email protected] (C.-S. Hwang).
http://dx.doi.org/10.1016/j.intermet.2017.09.018 Received 7 June 2017; Received in revised form 1 September 2017; Accepted 3 September 2017 Available online 12 October 2017 0966-9795/ © 2017 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) XRD patterns and (b) lattice parameter a of bulk samples with various Na2Te contents and hot-pressed at 773 K for 2 h.
conduction behavior. Based on the lattice parameter and Hall measurements results, Na+ diffusion into the interstitial sites of PbTe increases the lattice parameter and simultaneously contributes extra electrons. These results are different from those reported in other studies [10,11,17–20], where Na+ substituted Pb2+ as a p-type semiconductor. Fig. 3 presents the relation between carrier mobility and total carrier concentration for PbTe doped with Na2Te. Accordingly, the carrier mobility of all PbTe doped with Na2Te are smaller than that of PbTe, which means that the number of carriers is generated to scatter carriers and causes the decrease of carrier mobility. Furthermore, the densification of sintered bulk samples also influences carrier mobility. The carrier mobility increased slightly from 31 to 78 cm2/Vs when the relative density is improved from 95.3% to 97.1%, even though the carrier concentration increases from 1.07 × 1019 cm−3 to 1.53 × 1019 cm−3. In addition, the carrier mobility as a function of carrier concentration that an approximate n−1.1 relation for PbTe doped with Na2Te system, as shown in the inset of Fig. 3. It reveals a rough consistency, which means that the dominant mechanism is acoustic phonon scattering rather than electron scattering. Fig. 4 (a) and (b) presents the temperature dependence of electrical conductivity and Seebeck coefficient for all sintered samples. Generally, undoped PbTe has a typical bipolar characteristic in hand grinding [4], ball milling [24] and zone melting process [25]. It demonstrates that the electrical conductivity firstly decreases and then increases, and the Seebeck coefficient can be changed from p- to n-type with increasing measured temperature, as shown in Fig. 4(a) and (b). All PbTe doped with Na2Te samples have larger values of electrical conductivity than that of PbTe in the temperature range of 350–700 K, which is due to the total carrier concentration increasing with Na2Te content. Moreover, a transformation of the electrical conduction behavior is observed in all PbTe doped with Na2Te samples at room temperature, as determined using Hall measurements, with the Fermi level moving from the valence band to the conduction band. As the measurement temperature is increased, all PbTe doped with Na2Te samples change from being a semiconductor to a degenerate semi-conductor (metallic). This reveals that the intrinsic carriers are excited at higher temperature, which induces that the Fermi level shifts into the conduction band (as in a degenerate semi-conductor). Also, all PbTe doped with Na2Te samples have a negative Seebeck coefficient throughout the measurement temperature range, indicating that electrical conduction behavior is contributed mainly by electrons, as shown in Fig. 4 (b). It provides a result that the conduction behavior and Fermi level can be changed because Na+ diffuses into the interstitial sites in PbTe. Fig. 4 (c) demonstrates the Seebeck coefficient as a function of the total carrier concentration for PbTe doped with Na2Te system. The Pisarenko relation between the Seebeck coefficient and carrier concentration provides a good explanation of the experimental data [18,26,27]. The black line is the theoretical Pisarenko line assuming a single parabolic band and an acoustic phonon scattering mechanism. In this approximation, the Seebeck coefficient and carrier concentration are calculated according
rectangular bars (3 mm × 3 mm × 15 mm) for the measurement of electrical conductivity and the Seebeck coefficient under a low inert-gas atmosphere at temperatures ranging from 300 to 700 K using commercial equipment (ZEM-3, Ulvac-Riko). The carrier concentration and mobility of the bulk samples were measured using four-probe Hall-effect measurements at room temperature. The thermal diffusivity (α), bulk density (ρ) and specific heat (Cp) were measured using a laser flash thermal constant analyzer (TC-9000, Ulvac-Riko), the Archimedes method, and differential scanning calorimetry (DSC, Setaram), respectively. The thermal conductivity (κ) was calculated using the equation κ = αρCp. 3. Results and discussion Fig. 1(a) shows XRD patterns of all bulk samples with 0–1.5 mol% Na2Te addition hot-pressed at 773 K for 2 h. All specimens have the face-centered-cubic rock salt structure of PbTe and belong to the Fm3m space group, which means that no other crystalline phases could be observed. Fig. 1(b) shows the lattice parameter a for all samples with various Na2Te contents. The lattice parameter increases from 6.4655 to 6.4707 Å when the amount of Na2Te is increased from 0 to 1.5 mol%. The ionic radii of Na+, Pb2+, and Te2− are 1.03, 1.32 and 2.11 Å, respectively. Usually, Na doping of p-type PbTe decreases the lattice parameter because the metallic ionic radius of Na (1.03 Å) is smaller than that of Pb (1.32 Å) [21,22]. However, in this study, all PbTe doped with Na2Te samples have a larger lattice parameter than that of PbTe, which means that Na+ in PbTe is located at the interstitial sites rather than substitution sites. Fig. 2 displays SEM images of the fractured surface for specimens hot-pressed at 773 K for 2 h. It shows that the grain sizes of all samples are similar (1–10 μm) and no secondary phase is observed in all PbTe doped with Na2Te samples. Besides, the number of pores decreases with increasing Na2Te content according to SEM results. When the amount of Na2Te is increased, the measured density increases from 7.51 to 7.92 g/ cm3, and the relative density increases from 92.0 to 97.1%, as shown in Table 1. Thus, adding Na2Te in PbTe results in the decrease of pores and the increase of measured density and relative density. Table 1 also lists the carrier concentration and carrier mobility for all samples. The conduction behavior also confirms p- to n- type semiconductor through Hall measurements. When the amount of Na2Te is increased from 0.5 to 1.5 mol%, the carrier concentration increases from 1.07 × 1019 cm−3 to 1.53 × 1019 cm−3, whereas the carrier mobility decreases from 607 to 31 cm2/Vs and then increases to 78 cm2/Vs at room temperature. Because the stainless steel jars and balls are used in high energy ball milling, the contamination of Fe may affect the conduction behavior. The ICP-MS is used to analysis in order to understand the amount of Fe in the samples. When the amount of Na2Te is increased from 0 to 1.5 mol%, the Fe content are 104.2, 75.7, 210.9 and 70.2 ppm, respectively. The contamination of Fe is relatively low in all samples, so it will not contribute huge influence on 114
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Fig. 2. SEM images of fractured surface of (a) PbTe and PbTe doped with (b) 0.5%, (c) 1.0%, and (d) 1.5% Na2Te and hot-pressed at 773 K for 2 h.
to the Boltzmann transport equation and it can be expressed as follows [8,26,27]:
S=±
kB ⎛ (γ + 5/2) Fγ + 3/2 (η) − η⎞⎟ ⎜ e ⎝ (γ + 3/2) Fγ + 1/2 (η) ⎠
(1)
3
p (n) =
4π (2kB Tm∗) 2 F 1 (η) 2 h3
Fn (η) =
∫ 1 +χe χ −η dχ
∞
(2)
n
(3)
0
where kB is the Boltzmann's constant, e is the electron charge, γ is the scattering parameter (−1/2 for acoustic phonon scattering and +3/2 for ionized impurity scattering), m∗ is the effective mass, η is the reduced Fermi level, Fn(η) is the Fermi integral, and h is the Planck constant, respectively. Based on Fig. 3, acoustic phonon scattering is main scattering mechanism and thus the γ value equals −1/2. The effective mass m∗ can be calculated according to the results of Seebeck coefficient and carrier concentration at 300 K, as shown in Table 1. The experimental values and the theoretical Pisarenko line (m* = 0.3 m0) are in good agreement, indicating that acoustic phonon scattering is dominant. As shown in Fig. 4 (d), the power factor increases from 0.11 to 1.28 mW/m-K2 at 700 K when the Na2Te content is increased from 0 mol% to 1.5 mol%, indicating the power factor is increased by the addition of Na2Te. The temperature dependence of the total thermal conductivity for all samples is shown in Fig. 5 (a). It exhibits that total thermal conductivity of all PbTe doped with Na2Te samples is smaller than that of the PbTe sample at high measurement temperature, which decreases
Fig. 3. Carrier mobility as function of carrier concentration for PbTe doped with various Na2Te content levels. Solid line represents the μ - n−1.1 relation.
from 2.56 to 1.09 W/m-K. In comparison with PbTe sample, the bipolar effect is eliminated for all PbTe doped with Na2Te samples due to a change in the energy band structure, which is consistent with the experimental results for electrical conductivity. The total thermal conductivity (κ) is made up of the electronic thermal conductivity (κe) and the phonon thermal conductivity (κL) and can be expressed as κ = κL + κe = κL + LσT, where L is the Lorentz number. The electronic thermal conductivity (κe) can be estimated using the Wiedemann-Frantz equation (κe = LσT). The temperature dependence of the Lorentz number is calculated based on equations (1) and (4) [26,28].
Table 1 Measured density (D), relative density (DR), hall charge carrier concentration (nH), Hall mobility (μH), Seebeck coefficient (S), electrical conductivity (σ), effective mass (m*), and Lorentz number (L) for PbTe doped with various Na2Te samples measured at room temperature. Sample (mol% Na2Te)
D (g/cm3)
DR (%)
Type (p/n)
nH (×1019cm−3)
μH (cm2/Vs)
S (μV/K)
σ (S/cm)
m* (m0)
L (10−8 V2·K−2)
0 0.5 1.0 1.5
7.51 7.78 7.81 7.92
92.0 95.3 95.6 97.1
p n n n
0.09 1.07 1.49 1.53
607.8 31.4 32.4 78.1
325 −112 −100 −75
84.03 53.52 77.40 191.25
0.34 0.28 0.31 0.23
1.52 1.86 1.91 2.05
115
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Fig. 4. Temperature dependence of (a) electrical conductivity, (b) Seebeck coefficient, (c) Pisarenko plots at 300 K (Seebeck coefficient as function of carrier concentration. Solid line represents Pisarenko relations for effective mass of 0.3 m0.), and (d) power factor for PbTe doped with Na2Te (0–1.5 mol%).
Fig. 5. Temperature dependence of (a) thermal conductivity, (b) Lorentz number, (c) electronic thermal conductivity, and (d) lattice thermal conductivity for PbTe doped with Na2Te (0–1.5 mol%).
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from p- to n-type, the Fermi level moves, and the bipolar effect of PbTe is eliminated. Moreover, all PbTe doped with Na2Te samples show a conversion feature from a semiconductor to a degenerate semiconductor with increasing measurement temperature. For PbTe doped with Na2Te system, the ZT value increases with temperature owing to a higher power factor and lower thermal conductivity at higher measurement temperature, which are controlled by the concentration of Na2Te. The maximum ZT value for n-type PbTe doped with 1 mol% Na2Te (0.81) is higher than that of the PbTe sample (0.03) at 700 K. Acknowledgement The authors gratefully appreciate the financial support received for this work from the Ministry of Science and Technology of Taiwan, R.O.C., under grant MOST 103-2221-E-006-069-MY3 and the Bureau of Energy, Ministry of Economic Affairs, Taiwan, R.O.C. Fig. 6. Temperature dependence of dimensionless ZT values for PbTe doped with Na2Te (0–1.5 mol%).
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2
(γ + 5/2) Fγ + 3/2 (η) ⎤ ⎞ k 2 ⎛ (γ + 7/2) Fγ + 5/2 (η) −⎡ L = ⎛ B⎞ ⎜ ⎢ (γ + 3/2) Fγ + 1/2 (η) ⎥ ⎟ ⎝ e ⎠ ⎝ (γ + 3/2) Fγ + 1/2 (η) ⎣ ⎦⎠
(4)
The Lorentz number of all samples as a function of temperature is shown in Fig. 5 (b). All Lorentz numbers are in the range from the nondegenerate limit (1.5 × 10−8 V2K−2) to the degenerate limit (2.45 × 10−8 V2K−2). At room temperature, the Lorentz numbers increase with increasing Na2Te addition, indicating that the Fermi level has shifted. An obvious upturn at high temperature is observed for the undoped PbTe sample because it is a bipolar narrow semiconductor. In contrast, the PbTe doped with Na2Te samples do not exhibit an upturn in the whole measurement temperature range, indicating that the bipolar effect is eliminated. Based on the above calculation for the Lorenz number, the electronic thermal conductivity and lattice thermal conductivity for all samples are shown in Fig. 5 (c) and (d). As seen in Fig. 5 (c), the electronic thermal conductivity increases with increasing the amount of Na2Te because the electrical conductivity is enhanced. Moreover, the higher electrical conductivity and electronic thermal conductivity always result in a decrease in lattice thermal conductivity, as shown in Fig. 5 (d). The lattice thermal conductivity of all PbTe doped with Na2Te samples is smaller than that of the PbTe sample at high measurement temperature because the bipolar effect is eliminated when Na2Te is added. Moreover, the porosity could efficiently scatter phonons and play a role in the PbTe doped with Na2Te samples. The enhancement of relative density for PbTe doped with Na2Te samples leads to an increase in lattice thermal conductivity as increasing the amount of Na2Te. Fig. 6 presents the temperature dependence of ZT value for all samples. All PbTe doped with Na2Te samples have relatively larger ZT values than that of the PbTe sample. Especially, the highest ZT value is about 0.81 at 700 K for PbTe doped with 1 mol% Na2Te, which means that the addition of Na2Te significantly increases ZT value. The ZT value can be improved by an increase in the electrical conductivity and Seebeck coefficient and a decrease in thermal conductivity at higher temperature due to Na2Te addition. Although the ZT value in this work is not higher than those of p-type Na-doped PbTe, n-type PbTe doped with Na2Te was easily prepared by combining planetary ball milling and hot-pressed sintering. 4. Conclusions n-type PbTe doped with Na2Te was fabricated via planetary ball milling and hot-pressed sintering. The results reveal that the lattice parameter increase with increasing Na2Te content, indicating that the addition of Na2Te leads to Na+ being located at the interstitial sites of PbTe. When Na2Te is added to PbTe, the electrical conduction changes 117
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