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Synergistic effects of Lanthanum substitution on enhancing the thermoelectric properties of β-Zn4Sb3
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Synergistic effects of Lanthanum substitution on enhancing the thermoelectric properties of b-Zn4Sb3 Tianhua Zou a, Wenjie Xie a,*, Xiaoying Qin b, Menghan Zhou c, Marc Widenmeyer a, Jiangfeng Xu a, Jian He c, Anke Weidenkaff a,** a
b
Institute for Materials Science, University of Stuttgart, 70569 Stuttgart, Germany Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, 230031 Hefei, China c Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA Received 22 March 2016; revised 28 May 2016; accepted 2 June 2016 Available online 21 June 2016
Abstract A core challenge of thermoelectric research is decoupling the otherwise inversely interdependent properties electrical conductivity, thermopower, and lattice thermal conductivity offering synergistic effects. Herein, we present a systematic study in which we have substituted Lanthanum into the Zn-site in b-Zn4Sb3 compound. We observed that La-substitution not only simultaneously enhances electrical conductivity and thermopower over a wide temperature range but also substantially reduces the lattice thermal conductivity. These synergistic effects of Lasubstitution are discussed in terms of the substitution-induced variation in carrier concentration and effective mass as well as stronger phonon scattering by point defects. As a result, a ~30% increase of the power factor and a ~23% reduction in the lattice thermal conductivity led to a state-of-the-art ZT ~1.3 at 648 K for the bulk sample of b-La0.01Zn3.99Sb3. © 2016 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Thermoelectric; Band engineering; Rare earth; Phonon scattering
1. Introduction In the wake of increasing energy demand and the environmental detriments of using fossil fuels, the requirement for alternative energy technologies has stimulated research of energy-related materials including thermoelectrics, the simplest technology for heat-to-electricity conversion. The conversion efficiency of a thermoelectric (TE) material is gauged by its dimensionless figure of merit, ZT ¼ (sS2/k)T, where s, S, k are the electrical conductivity, thermopower, and total thermal conductivity, respectively. k can be expressed as the sum of the carrier thermal conductivity ke and the lattice * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (W. Xie), weidenkaff@imw. uni-stuttgart.de (A. Weidenkaff). Peer review under responsibility of The Chinese Ceramic Society.
thermal conductivity kL. A high ZT value requires a low kL and a high power factor PF ¼ sS2. In recent decades, most advances in enhancing ZT values were made by reducing kL via nanostructuring [1,2], “phonon liquid” [3,4], all-scale hierarchical microstructures [5,6], anharmonicity [7], phonon localization due to random stacking [8], complex crystal structures [9], phase diagram approach [10] and alloying [11]. As kL of start-of-the-art TE materials approaches the “amorphous limit” [12,13], the room for further reduction of kL declines. Now is the time to shift the focus of TE research to enhancing the PF. PF is a function of s and S, both of which depend on the electron band structure and the scattering mechanisms. Attention should especially concentrate on S, because PF increases with the square of S but only proportional to s. According to the Mott relation, S for a degenerate semiconductor can be expressed as:
http://dx.doi.org/10.1016/j.jmat.2016.06.002 2352-8478/© 2016 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
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p2 kB2 T vlnðsðEÞÞ S¼ 3q vE E¼EF 2 2 p kB T 1 vpðEÞ 1 vmðEÞ þ ¼ 3q p vE m vE E¼EF
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2.2. Sample characterization
ð1Þ
with the carrier mobility m(E )¼qt/m* in the Drude model, where q is the carrier charge, E the energy, p(E ) and m(E ) the energy dependent carrier concentration and mobility, kB the Boltzmann constant, m* the effective mass, and EF the Fermi energy, respectively. In most cases where non-resonant scattering dominates, the relaxation time t follows a power law behavior t¼t0El1/2, where l is the scattering parameter and t0 a constant. Eq. (1) indicates that S increases with increasing electron density of states (eDOS) near EF [14]. However, due to the inverse inter-dependence of s and S, improving S often impairs s. Consequently, the simultaneous increase of s and the S must result in synergistic effects. In this work, we show this by taking the example of La-substituted b-Zn4Sb3. b-Zn4Sb3 is a promising class of novel TE materials featuring a glasslike low kL and a relatively high PF in the temperature range of common applications [15]. Calculations predict that substitution with f-elements such as rare earth elements may introduce additional density of states near the Fermi level, thus, enhancing the thermopower. Indeed, substituting b-Zn4Sb3 with Sm (6s24f6), Pr (6s24f3) and Gd (6s24f65d1) enhances the power factor [16e18]. This begs the question of the effect of substituting b-Zn4Sb3 with La (6s25d1), the only rare earth element without f-electrons. To date, studies on the effect of La-substitution on the TE properties of b-Zn4Sb3 are scarce. The prime motivation of this work is, therefore, to reveal the role of f-electrons in rare earth element substituted b-Zn4Sb3. We will demonstrate that La-substitution of b-Zn4Sb3 has synergistic effects by simultaneously reducing the electrical resistivity due to a higher carrier concentration, enhancing the thermopower due to an enhanced effective mass, and reducing the lattice thermal conductivity due to point defect scattering of heat-carrying phonons. As a result, the ZT of bLa0.01Zn3.99Sb3 reaches values of up to 1.3 at 648 K. 2. Experimental procedure 2.1. Sample preparation Polycrystalline b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) samples were synthesized by melting highpurity elemental Zn (99.9999%, powder), Sb (99.999%, powder) and La (99.999%, powder) according to the nominal composition. An excess of Zn of about 1% was added to compensate for the Zn loss during synthesis. The evacuated and sealed quartz glass tubes with the starting materials were heated at 1023 K for 12 h and then quenched in cold water. The as grown b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) ingot was hand-ground into a fine powder and hot pressed at a pressure of 600 MPa in vacuum at 650 K for 1 h to get disc-shaped samples for TE property characterization.
Sample phases were checked by X-ray powder diffraction on a Philips-X PERT PRO® diffractometer using Cu-Ka radiation. Electrical resistivity r (¼ 1/s) and thermopower S were measured on a ZEM-3 (ULVAC-RIKO®) in Helium atmosphere in the range of 300 Ke650 K. Hall coefficients RH were measured on a physical property measurement system (PPMS, Quantum Design®) at room temperature. The hole concentration p was estimated using the relationship p ¼ 1/ eRH, where e is the elementary charge. The Hall mobility m was calculated using the relationship m ¼ sRH ¼ RH/r. The thermal diffusivity a was measured with a NETZSCH LFA457 ® apparatus in the range of 300 Ke650 K in an argon atmosphere using cylinder disks (2e3 mm in thickness) coated with graphite. The total thermal conductivity k was calculated according to k ¼ DCpa, where Cp is the isobaric specific thermal capacity measured on a differential scanning calorimeter (DSC, Perkin-Elmer®) in argon atmosphere and D the density measured by the Archimedes method. 3. Results and discussion 3.1. Phase characterization XRD patterns of the b-(Zn1xLax)4Sb3 (x ¼ 0, 0.0005, 0.0075, 0.01, and 0.0125) samples are shown in Fig. 1(a). All reflections can be indexed to b-Zn4Sb3 (JCPDS #89-1969; space group R3c) and no secondary phase is detected. Upon La substitution, the refinement lattice constant a obviously increases (Fig. 1(b)) accompanied by an increase of the FWHM as demonstrated for the reflection at 2Q z 25.3 (Table 1). Both observations are consistent with a substitution of Zn2þ with La3þ. The host lattice increase originates from the larger ionic radius of La (ionic radius La3þ: ~1.06 Å vs. ionic radius Zn2þ: ~0.74 Å). 3.2. Thermoelectric properties Fig. 2(a) shows the temperature dependence of the electrical conductivity (s ¼ 1/r) of all b-(Zn1xLax)4Sb3 samples. All samples follow a similar pattern exhibiting a shallow minimum near 500 K, which is ascribed to the onset of the bipolar effect [15,19]. Importantly, s increases with increasing La-substitution, which can be attributed to an increased carrier concentration (Table 1). The temperature dependence of the thermopower S of b(Zn1xLax)4Sb3 is displayed in Fig. 2(b). As with s, all samples exhibit the same temperature dependence. S is positive in the whole temperature range indicating a p-type conduction effected by means of holes. Magnitude and temperature dependence of S are typical of degenerate semiconductors. In general, S increases linearly with increasing temperature in the range of 300 Ke500 K before reaching a plateau between 500 K and 550 K indicating the onset of the bipolar effect. We have made two interesting observations: (i) trivalent La (3þ) substituting divalent Zn (2þ) increased the carrier (hole)
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Fig. 1. (a) XRD patterns of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) and (b) La-content dependent lattice parameters a and c of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125). Table 1 Physical parameters of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) obtained at 300 K. x FWHMa ( ) pb (1019 cm3) mc (cm2/Vs) md*/med Le (108UWK2) a(A)f c(A)f D*g (%) Cph (Jg1 K1) ai (mm2/s) a b c d e f g h i
0 0.102 12.1 18.6 1.51 1.87 12.207 12.420 96 0.29 0.73
0.005 0.102 14.1 20.3 1.73 1.85 12.210 12.423 97 0.29 0.63
0.0075 0.119 15.1 18.4 1.92 1.84 12.224 12.428 96 0.30 0.56
0.01 0.143 17.3 15.8 2.10 1.84 12.226 12.425 96 0.30 0.52
0.0125 0.158 17.3 15.0 2.16 1.83 12.228 12.428 97 0.30 0.52
FWHM is the full width at half maximum of the XRD reflection at 25.3 . p is the hole concentration. m is the Hall mobility. md*/me is the radio of effective mass to that of free electron. L is the Lorenz number. a and c are the lattice parameters. D* is the relative density of the bulk samples. Cp is the specific heat capacity. a is the thermal diffusivity.
concentration (Table 1); and (ii) the magnitude of S increases with increasing carrier (hole) concentration (Fig. 2(b)). We have not come up with a satisfactory explanation to these observations yet. Therefore, we employ a single parabolic band model, by which the DOS effective mass md* and S can be estimated according to [20,21]: 2=3 h2 p 2kB T 4pF1=2 ðxF Þ
ð3Þ
kB ½ðl þ 2ÞFlþ1 ðxF Þ xF e ½ðl þ 1ÞFl ðxF Þ
ð4Þ
m*d ¼
S¼
with the Fermi integral of order i Z∞ Fi ðxF Þ ¼ 0
xi dx 1 þ eðxxF Þ
ð5Þ
where h is the Planck constant, xF the reduced Fermi level EF/ (kBT ) and l the scattering parameter. We are well aware that a single parabolic band model is insufficient for a complex material like b-(Zn1xLax)4Sb3. Nonetheless, Eqs. (3)e(5) allow a semi-quantitative or qualitative explanation of the md* variations, which is key to understanding the synergistic effects of La-substitution. In other words, we focus on the trend of md* rather than its numeric value. Room temperature values of md* are calculated assuming a scattering parameter l ¼ 0 for electron-acoustic phonon scattering [14] and listed in Table 1. At room temperature, md* of unsubstituted b-Zn4Sb3 is about 1.51me. Inserting this value in Eqs. (3) and (4), we can plot S of unsubstituted bZn4Sb3 at 300 K as a function of the carrier concentration (black solid line in Fig. 2(c)). We found that S of b(Zn1xLax)4Sb3 samples with x ¼ 0.005, 0.0075, 0.01, and 0.0125 exceeds the values of the unsubstituted b-Zn4Sb3 by ~15, 23, 30 and 32 mV/K, respectively. As displayed in Fig. 2(c), md* of La-substituted b-(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) is 1.73me, 1.92me, 2.10me and 2.16me, respectively. Larger md* values suggest a larger eDOS near EF. Therefore, it is reasonable to assume that Lasubstitution enhances the eDOS near EF and thus increases S. Further eDOS calculations of b-Zn4Sb3 with and without Lasubstitution above 300 K are highly desirable to confirm the influence of La-substitution on the eDOS. With improved S and reduced r, the PF of all substituted b(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) samples is higher than that of unsubstituted b-Zn4Sb3 over the entire
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Fig. 2. Temperature dependence of (a) electrical conductivity, (b) thermopower, (d) power factor of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) specimens and (c) Pisarenko plot of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) at room temperature (300 K). The black solid line belongs to pristine b-Zn4Sb3 with md* ¼ 1.51me.
temperature range studied (Fig. 2(d)). In particular, the PF values of b-(La0.0075Zn0.9925)4Sb3 and b-(La0.01Zn0.99)4Sb3 at 650 K are 13.6 104 W/mK2 and 13.5 104 W/mK2, respectively, exceeding that of unsubstituted b-Zn4Sb3 by ~ 30%. This is the consequence of both an increased s due to increased p and an improved S due to an enhanced md*, a synergistic effect induced by La-substitution. Fig. 3(a) displays the temperature dependence of the total thermal conductivity k of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) samples. k of all samples decreases
with increasing temperature in the range of room temperature to 500e550 K, then rising again slightly with increasing temperature forming a shallow minimum or change of slope near 500 K. In a semiconductor, the bipolar thermal conductivity kB is not negligible and is allowed for by k ¼ kB þ kL þ kc, where kL is the lattice thermal conductivity and kc the carrier thermal conductivity (Fig. 3(b)). kc is usually assessed by the WiedemanneFranz relation: kc ¼ LsT, where L is the Lorenz number. This leads to the relation: kB þ kL ¼ k LsT. It is known that L depends on the reduced
Fig. 3. Temperature dependence of (a) total thermal conductivity, (b) carrier thermal conductivity, (c) calculated Lorenz number L (d) bipolar thermal conductivity and lattice thermal conductivity of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) specimens.
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Fig. 4. (a) Temperature dependence of the figure of merit ZT of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) and (b) average ZT values of b(Zn1xLax)4Sb3 and other substituted b-Zn4Sb3 samples between 300 K and 650 K.
chemical potential xF, the band structure and details of the scattering process [22]. Kim et al. proposed a satisfactory approximation for the Lorenz number [23]: S L ¼ 1:5 þ exp ð6Þ 116 The temperature dependent L calculated by Eq. (6) is presented in Fig. 3(c). It is evident that the calculated L values are far below the standard L0 ¼ 2.45 108UWK2, which is to be expected for metals and degenerate semiconductors and marked by a dotted line at the top in Fig. 3(c). Actually, the calculated L values are close to the non-degenerate limit marked by the dotted line at the bottom in Fig. 3(c). The low L values thus imply a partially degenerate character of the samples, which may be related to the large DOS near the valence band [24e26]. Due to the effective phonon scattering by the intrinsic disorder and the La dopant, the (kB þ kL) values of b(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) are lower than that of pristine b-Zn4Sb3 (Fig. 3(d)). For instance, the (kB þ kL) value of b-La0.01Zn3.99Sb3 is 0.65 W/K m at 300 K, which is about 30% lower than that of the pristine sample. Cahill et al. developed a model for the minimum lattice thermal conductivity kmin based on random walk of Einstein modes [27,28]: i p1=3 X T 2 Z x3 ex 2=3 kmin ¼ k B na vi 2 dx 6 qI ðex 1Þ i
q =T
ð7Þ
0
where qi¼vi(Z/kB)(6p2na)1/3 is the cut-off frequency, na the number density of atoms, Z the reduced Planck constant and vi the sound velocity for each polarization mode. Based on the data from Caillat et al. [29], kmin of Zn4Sb3 is calculated and plotted in Fig. 3(d). At elevated temperatures, the (kB þ kL) values of the substituted samples are close to the amorphous limit confirming the ‘‘phonon-glass’’ nature of b-Zn4Sb3 [30e32].
Fig. 4(a) shows the temperature dependence of the ZT of b(Zn1xLax)4Sb3. Owing to the above-mentioned synergistic effects of La-substitution on PF and kL, the ZT values of all substituted b-(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) samples are significantly higher than those of unsubstituted b-Zn4Sb3. Specifically, b-La0.01Zn3.99Sb3 has a ZT value of about 1.3 at 648 K, which is about 73% higher than that of unsubstituted b-Zn4Sb3. In addition, in the studied temperature range the average ZT is higher compared to other, differently substituted b-Zn4Sb3 compounds (Fig. 4(b)) [18,28,31,33,34]. 4. Summary In summary, the TE properties of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) have been studied in the range of 300 Ke650 K. The synergistic effects of La3þ-substitution led to a simultaneous increase of carrier concentration (holes) and effective mass, enhanced PF, and reduced kL. As a result, a state-of-the-art ZT ~1.3 at 648 K for b-La0.01Zn3.99Sb3 is obtained. Acknowledgements We would like to thank Dr. Angelika Veziridis for a critical reading of our manuscript and polishing the English. T.H.Z, W.J.X and A.W. acknowledge the Deutsche Forschungsgemeinschaft for financial support through the DFG Priority Program SPP 1386 (Grant WE 2803/2-2). X.Y.Q. gratefully acknowledges financial support from the National Natural Science Foundation of China (Nos. 11174292, 11374306, 51101150, 21521001). M.H.Z and J.H. acknowledge the support of NSF DMR 1307740. References [1] Xie W, He J, Kang HJ, Tang X, Zhu S, Laver M, et al. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites. Nano Lett 2010;10(9):3283e9.
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Tianhua Zou, University of Stuttgart. Tianhua Zou is a PhD candidate in Institute for Materials Science at University of Stuttgart, Germany. He received his Bachelor's degree of Science in physics from Xiangtan University, China in 2011 and Master's degree of Science in condensed matter physics from Institute of Solid State Physics, Chinese Academy of Sciences in 2014. His research interests include characterization of electrical, thermal, optical, magnetic properties and microstructures about thermoelectric materials, understanding the fundamental physics and chemistry of thermoelectrics and developing new materials and synthesis technology. Email: [email protected]
Dr. Wenjie Xie, University of Stuttgart. Wenjie Xie received his BE (2004), ME (2007), and PhD (2011) from Wuhan University of Technology, China. He was visiting student at Clemson University from 2008 to 2010. From 2011 to 2012 he worked as assistant Professor at Wuhan University of Technology, and afterwards he joined Empa (Switzerland) as a postdoc fellow funded by Marie Curie fellowship. Since 2014 he leads the thermoelectric research activities of Chair III at Institute for Materials Chemistry, University of Stuttgart, Germany. He has so far published over 40 publications which receive total citations over 1500, and two granted Chinese patents. He was the winner of annual Goldsmid Award in 2011. Email: [email protected]
T. Zou et al. / J Materiomics 2 (2016) 273e279 Prof. Dr. Anke Weidenkaff, University of Stuttgart. Anke Weidenkaff is full professor for Materials Chemistry at the University of Stuttgart since 2013. She completed her PhD degree in Chemistry at ETH Zu¨rich in 2000, received the Venia Legendi for Solid State Chemistry and Materials Sciences from the University of Augsburg in 2006 and became section head at Empa as well as professor at the University of Bern, Switzerland. She published some 220 SCI rated publications on materials research in energy conversion technologies, is president of the European Thermoelectric Society (ETS), elected member of the MRS board of directors, the E-MRS Executive Committee and was co-chair of the E-MRS spring meeting in 2013. In 2011 she was awarded with the Kavli Foundation Lectureship prize. Email: [email protected]
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Synergistic effects of Lanthanum substitution on enhancing the thermoelectric properties of b-Zn4Sb3 Tianhua Zou a, Wenjie Xie a,*, Xiaoying Qin b, Menghan Zhou c, Marc Widenmeyer a, Jiangfeng Xu a, Jian He c, Anke Weidenkaff a,** a
b
Institute for Materials Science, University of Stuttgart, 70569 Stuttgart, Germany Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, 230031 Hefei, China c Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA Received 22 March 2016; revised 28 May 2016; accepted 2 June 2016 Available online 21 June 2016
Abstract A core challenge of thermoelectric research is decoupling the otherwise inversely interdependent properties electrical conductivity, thermopower, and lattice thermal conductivity offering synergistic effects. Herein, we present a systematic study in which we have substituted Lanthanum into the Zn-site in b-Zn4Sb3 compound. We observed that La-substitution not only simultaneously enhances electrical conductivity and thermopower over a wide temperature range but also substantially reduces the lattice thermal conductivity. These synergistic effects of Lasubstitution are discussed in terms of the substitution-induced variation in carrier concentration and effective mass as well as stronger phonon scattering by point defects. As a result, a ~30% increase of the power factor and a ~23% reduction in the lattice thermal conductivity led to a state-of-the-art ZT ~1.3 at 648 K for the bulk sample of b-La0.01Zn3.99Sb3. © 2016 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Thermoelectric; Band engineering; Rare earth; Phonon scattering
1. Introduction In the wake of increasing energy demand and the environmental detriments of using fossil fuels, the requirement for alternative energy technologies has stimulated research of energy-related materials including thermoelectrics, the simplest technology for heat-to-electricity conversion. The conversion efficiency of a thermoelectric (TE) material is gauged by its dimensionless figure of merit, ZT ¼ (sS2/k)T, where s, S, k are the electrical conductivity, thermopower, and total thermal conductivity, respectively. k can be expressed as the sum of the carrier thermal conductivity ke and the lattice * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (W. Xie), weidenkaff@imw. uni-stuttgart.de (A. Weidenkaff). Peer review under responsibility of The Chinese Ceramic Society.
thermal conductivity kL. A high ZT value requires a low kL and a high power factor PF ¼ sS2. In recent decades, most advances in enhancing ZT values were made by reducing kL via nanostructuring [1,2], “phonon liquid” [3,4], all-scale hierarchical microstructures [5,6], anharmonicity [7], phonon localization due to random stacking [8], complex crystal structures [9], phase diagram approach [10] and alloying [11]. As kL of start-of-the-art TE materials approaches the “amorphous limit” [12,13], the room for further reduction of kL declines. Now is the time to shift the focus of TE research to enhancing the PF. PF is a function of s and S, both of which depend on the electron band structure and the scattering mechanisms. Attention should especially concentrate on S, because PF increases with the square of S but only proportional to s. According to the Mott relation, S for a degenerate semiconductor can be expressed as:
http://dx.doi.org/10.1016/j.jmat.2016.06.002 2352-8478/© 2016 The Chinese Ceramic Society. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
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p2 kB2 T vlnðsðEÞÞ S¼ 3q vE E¼EF 2 2 p kB T 1 vpðEÞ 1 vmðEÞ þ ¼ 3q p vE m vE E¼EF
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2.2. Sample characterization
ð1Þ
with the carrier mobility m(E )¼qt/m* in the Drude model, where q is the carrier charge, E the energy, p(E ) and m(E ) the energy dependent carrier concentration and mobility, kB the Boltzmann constant, m* the effective mass, and EF the Fermi energy, respectively. In most cases where non-resonant scattering dominates, the relaxation time t follows a power law behavior t¼t0El1/2, where l is the scattering parameter and t0 a constant. Eq. (1) indicates that S increases with increasing electron density of states (eDOS) near EF [14]. However, due to the inverse inter-dependence of s and S, improving S often impairs s. Consequently, the simultaneous increase of s and the S must result in synergistic effects. In this work, we show this by taking the example of La-substituted b-Zn4Sb3. b-Zn4Sb3 is a promising class of novel TE materials featuring a glasslike low kL and a relatively high PF in the temperature range of common applications [15]. Calculations predict that substitution with f-elements such as rare earth elements may introduce additional density of states near the Fermi level, thus, enhancing the thermopower. Indeed, substituting b-Zn4Sb3 with Sm (6s24f6), Pr (6s24f3) and Gd (6s24f65d1) enhances the power factor [16e18]. This begs the question of the effect of substituting b-Zn4Sb3 with La (6s25d1), the only rare earth element without f-electrons. To date, studies on the effect of La-substitution on the TE properties of b-Zn4Sb3 are scarce. The prime motivation of this work is, therefore, to reveal the role of f-electrons in rare earth element substituted b-Zn4Sb3. We will demonstrate that La-substitution of b-Zn4Sb3 has synergistic effects by simultaneously reducing the electrical resistivity due to a higher carrier concentration, enhancing the thermopower due to an enhanced effective mass, and reducing the lattice thermal conductivity due to point defect scattering of heat-carrying phonons. As a result, the ZT of bLa0.01Zn3.99Sb3 reaches values of up to 1.3 at 648 K. 2. Experimental procedure 2.1. Sample preparation Polycrystalline b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) samples were synthesized by melting highpurity elemental Zn (99.9999%, powder), Sb (99.999%, powder) and La (99.999%, powder) according to the nominal composition. An excess of Zn of about 1% was added to compensate for the Zn loss during synthesis. The evacuated and sealed quartz glass tubes with the starting materials were heated at 1023 K for 12 h and then quenched in cold water. The as grown b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) ingot was hand-ground into a fine powder and hot pressed at a pressure of 600 MPa in vacuum at 650 K for 1 h to get disc-shaped samples for TE property characterization.
Sample phases were checked by X-ray powder diffraction on a Philips-X PERT PRO® diffractometer using Cu-Ka radiation. Electrical resistivity r (¼ 1/s) and thermopower S were measured on a ZEM-3 (ULVAC-RIKO®) in Helium atmosphere in the range of 300 Ke650 K. Hall coefficients RH were measured on a physical property measurement system (PPMS, Quantum Design®) at room temperature. The hole concentration p was estimated using the relationship p ¼ 1/ eRH, where e is the elementary charge. The Hall mobility m was calculated using the relationship m ¼ sRH ¼ RH/r. The thermal diffusivity a was measured with a NETZSCH LFA457 ® apparatus in the range of 300 Ke650 K in an argon atmosphere using cylinder disks (2e3 mm in thickness) coated with graphite. The total thermal conductivity k was calculated according to k ¼ DCpa, where Cp is the isobaric specific thermal capacity measured on a differential scanning calorimeter (DSC, Perkin-Elmer®) in argon atmosphere and D the density measured by the Archimedes method. 3. Results and discussion 3.1. Phase characterization XRD patterns of the b-(Zn1xLax)4Sb3 (x ¼ 0, 0.0005, 0.0075, 0.01, and 0.0125) samples are shown in Fig. 1(a). All reflections can be indexed to b-Zn4Sb3 (JCPDS #89-1969; space group R3c) and no secondary phase is detected. Upon La substitution, the refinement lattice constant a obviously increases (Fig. 1(b)) accompanied by an increase of the FWHM as demonstrated for the reflection at 2Q z 25.3 (Table 1). Both observations are consistent with a substitution of Zn2þ with La3þ. The host lattice increase originates from the larger ionic radius of La (ionic radius La3þ: ~1.06 Å vs. ionic radius Zn2þ: ~0.74 Å). 3.2. Thermoelectric properties Fig. 2(a) shows the temperature dependence of the electrical conductivity (s ¼ 1/r) of all b-(Zn1xLax)4Sb3 samples. All samples follow a similar pattern exhibiting a shallow minimum near 500 K, which is ascribed to the onset of the bipolar effect [15,19]. Importantly, s increases with increasing La-substitution, which can be attributed to an increased carrier concentration (Table 1). The temperature dependence of the thermopower S of b(Zn1xLax)4Sb3 is displayed in Fig. 2(b). As with s, all samples exhibit the same temperature dependence. S is positive in the whole temperature range indicating a p-type conduction effected by means of holes. Magnitude and temperature dependence of S are typical of degenerate semiconductors. In general, S increases linearly with increasing temperature in the range of 300 Ke500 K before reaching a plateau between 500 K and 550 K indicating the onset of the bipolar effect. We have made two interesting observations: (i) trivalent La (3þ) substituting divalent Zn (2þ) increased the carrier (hole)
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Fig. 1. (a) XRD patterns of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) and (b) La-content dependent lattice parameters a and c of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125). Table 1 Physical parameters of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) obtained at 300 K. x FWHMa ( ) pb (1019 cm3) mc (cm2/Vs) md*/med Le (108UWK2) a(A)f c(A)f D*g (%) Cph (Jg1 K1) ai (mm2/s) a b c d e f g h i
0 0.102 12.1 18.6 1.51 1.87 12.207 12.420 96 0.29 0.73
0.005 0.102 14.1 20.3 1.73 1.85 12.210 12.423 97 0.29 0.63
0.0075 0.119 15.1 18.4 1.92 1.84 12.224 12.428 96 0.30 0.56
0.01 0.143 17.3 15.8 2.10 1.84 12.226 12.425 96 0.30 0.52
0.0125 0.158 17.3 15.0 2.16 1.83 12.228 12.428 97 0.30 0.52
FWHM is the full width at half maximum of the XRD reflection at 25.3 . p is the hole concentration. m is the Hall mobility. md*/me is the radio of effective mass to that of free electron. L is the Lorenz number. a and c are the lattice parameters. D* is the relative density of the bulk samples. Cp is the specific heat capacity. a is the thermal diffusivity.
concentration (Table 1); and (ii) the magnitude of S increases with increasing carrier (hole) concentration (Fig. 2(b)). We have not come up with a satisfactory explanation to these observations yet. Therefore, we employ a single parabolic band model, by which the DOS effective mass md* and S can be estimated according to [20,21]: 2=3 h2 p 2kB T 4pF1=2 ðxF Þ
ð3Þ
kB ½ðl þ 2ÞFlþ1 ðxF Þ xF e ½ðl þ 1ÞFl ðxF Þ
ð4Þ
m*d ¼
S¼
with the Fermi integral of order i Z∞ Fi ðxF Þ ¼ 0
xi dx 1 þ eðxxF Þ
ð5Þ
where h is the Planck constant, xF the reduced Fermi level EF/ (kBT ) and l the scattering parameter. We are well aware that a single parabolic band model is insufficient for a complex material like b-(Zn1xLax)4Sb3. Nonetheless, Eqs. (3)e(5) allow a semi-quantitative or qualitative explanation of the md* variations, which is key to understanding the synergistic effects of La-substitution. In other words, we focus on the trend of md* rather than its numeric value. Room temperature values of md* are calculated assuming a scattering parameter l ¼ 0 for electron-acoustic phonon scattering [14] and listed in Table 1. At room temperature, md* of unsubstituted b-Zn4Sb3 is about 1.51me. Inserting this value in Eqs. (3) and (4), we can plot S of unsubstituted bZn4Sb3 at 300 K as a function of the carrier concentration (black solid line in Fig. 2(c)). We found that S of b(Zn1xLax)4Sb3 samples with x ¼ 0.005, 0.0075, 0.01, and 0.0125 exceeds the values of the unsubstituted b-Zn4Sb3 by ~15, 23, 30 and 32 mV/K, respectively. As displayed in Fig. 2(c), md* of La-substituted b-(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) is 1.73me, 1.92me, 2.10me and 2.16me, respectively. Larger md* values suggest a larger eDOS near EF. Therefore, it is reasonable to assume that Lasubstitution enhances the eDOS near EF and thus increases S. Further eDOS calculations of b-Zn4Sb3 with and without Lasubstitution above 300 K are highly desirable to confirm the influence of La-substitution on the eDOS. With improved S and reduced r, the PF of all substituted b(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) samples is higher than that of unsubstituted b-Zn4Sb3 over the entire
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Fig. 2. Temperature dependence of (a) electrical conductivity, (b) thermopower, (d) power factor of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) specimens and (c) Pisarenko plot of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) at room temperature (300 K). The black solid line belongs to pristine b-Zn4Sb3 with md* ¼ 1.51me.
temperature range studied (Fig. 2(d)). In particular, the PF values of b-(La0.0075Zn0.9925)4Sb3 and b-(La0.01Zn0.99)4Sb3 at 650 K are 13.6 104 W/mK2 and 13.5 104 W/mK2, respectively, exceeding that of unsubstituted b-Zn4Sb3 by ~ 30%. This is the consequence of both an increased s due to increased p and an improved S due to an enhanced md*, a synergistic effect induced by La-substitution. Fig. 3(a) displays the temperature dependence of the total thermal conductivity k of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) samples. k of all samples decreases
with increasing temperature in the range of room temperature to 500e550 K, then rising again slightly with increasing temperature forming a shallow minimum or change of slope near 500 K. In a semiconductor, the bipolar thermal conductivity kB is not negligible and is allowed for by k ¼ kB þ kL þ kc, where kL is the lattice thermal conductivity and kc the carrier thermal conductivity (Fig. 3(b)). kc is usually assessed by the WiedemanneFranz relation: kc ¼ LsT, where L is the Lorenz number. This leads to the relation: kB þ kL ¼ k LsT. It is known that L depends on the reduced
Fig. 3. Temperature dependence of (a) total thermal conductivity, (b) carrier thermal conductivity, (c) calculated Lorenz number L (d) bipolar thermal conductivity and lattice thermal conductivity of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) specimens.
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Fig. 4. (a) Temperature dependence of the figure of merit ZT of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) and (b) average ZT values of b(Zn1xLax)4Sb3 and other substituted b-Zn4Sb3 samples between 300 K and 650 K.
chemical potential xF, the band structure and details of the scattering process [22]. Kim et al. proposed a satisfactory approximation for the Lorenz number [23]: S L ¼ 1:5 þ exp ð6Þ 116 The temperature dependent L calculated by Eq. (6) is presented in Fig. 3(c). It is evident that the calculated L values are far below the standard L0 ¼ 2.45 108UWK2, which is to be expected for metals and degenerate semiconductors and marked by a dotted line at the top in Fig. 3(c). Actually, the calculated L values are close to the non-degenerate limit marked by the dotted line at the bottom in Fig. 3(c). The low L values thus imply a partially degenerate character of the samples, which may be related to the large DOS near the valence band [24e26]. Due to the effective phonon scattering by the intrinsic disorder and the La dopant, the (kB þ kL) values of b(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) are lower than that of pristine b-Zn4Sb3 (Fig. 3(d)). For instance, the (kB þ kL) value of b-La0.01Zn3.99Sb3 is 0.65 W/K m at 300 K, which is about 30% lower than that of the pristine sample. Cahill et al. developed a model for the minimum lattice thermal conductivity kmin based on random walk of Einstein modes [27,28]: i p1=3 X T 2 Z x3 ex 2=3 kmin ¼ k B na vi 2 dx 6 qI ðex 1Þ i
q =T
ð7Þ
0
where qi¼vi(Z/kB)(6p2na)1/3 is the cut-off frequency, na the number density of atoms, Z the reduced Planck constant and vi the sound velocity for each polarization mode. Based on the data from Caillat et al. [29], kmin of Zn4Sb3 is calculated and plotted in Fig. 3(d). At elevated temperatures, the (kB þ kL) values of the substituted samples are close to the amorphous limit confirming the ‘‘phonon-glass’’ nature of b-Zn4Sb3 [30e32].
Fig. 4(a) shows the temperature dependence of the ZT of b(Zn1xLax)4Sb3. Owing to the above-mentioned synergistic effects of La-substitution on PF and kL, the ZT values of all substituted b-(Zn1xLax)4Sb3 (x ¼ 0.005, 0.0075, 0.01, and 0.0125) samples are significantly higher than those of unsubstituted b-Zn4Sb3. Specifically, b-La0.01Zn3.99Sb3 has a ZT value of about 1.3 at 648 K, which is about 73% higher than that of unsubstituted b-Zn4Sb3. In addition, in the studied temperature range the average ZT is higher compared to other, differently substituted b-Zn4Sb3 compounds (Fig. 4(b)) [18,28,31,33,34]. 4. Summary In summary, the TE properties of b-(Zn1xLax)4Sb3 (x ¼ 0, 0.005, 0.0075, 0.01, and 0.0125) have been studied in the range of 300 Ke650 K. The synergistic effects of La3þ-substitution led to a simultaneous increase of carrier concentration (holes) and effective mass, enhanced PF, and reduced kL. As a result, a state-of-the-art ZT ~1.3 at 648 K for b-La0.01Zn3.99Sb3 is obtained. Acknowledgements We would like to thank Dr. Angelika Veziridis for a critical reading of our manuscript and polishing the English. T.H.Z, W.J.X and A.W. acknowledge the Deutsche Forschungsgemeinschaft for financial support through the DFG Priority Program SPP 1386 (Grant WE 2803/2-2). X.Y.Q. gratefully acknowledges financial support from the National Natural Science Foundation of China (Nos. 11174292, 11374306, 51101150, 21521001). M.H.Z and J.H. acknowledge the support of NSF DMR 1307740. References [1] Xie W, He J, Kang HJ, Tang X, Zhu S, Laver M, et al. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites. Nano Lett 2010;10(9):3283e9.
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Tianhua Zou, University of Stuttgart. Tianhua Zou is a PhD candidate in Institute for Materials Science at University of Stuttgart, Germany. He received his Bachelor's degree of Science in physics from Xiangtan University, China in 2011 and Master's degree of Science in condensed matter physics from Institute of Solid State Physics, Chinese Academy of Sciences in 2014. His research interests include characterization of electrical, thermal, optical, magnetic properties and microstructures about thermoelectric materials, understanding the fundamental physics and chemistry of thermoelectrics and developing new materials and synthesis technology. Email: [email protected]
Dr. Wenjie Xie, University of Stuttgart. Wenjie Xie received his BE (2004), ME (2007), and PhD (2011) from Wuhan University of Technology, China. He was visiting student at Clemson University from 2008 to 2010. From 2011 to 2012 he worked as assistant Professor at Wuhan University of Technology, and afterwards he joined Empa (Switzerland) as a postdoc fellow funded by Marie Curie fellowship. Since 2014 he leads the thermoelectric research activities of Chair III at Institute for Materials Chemistry, University of Stuttgart, Germany. He has so far published over 40 publications which receive total citations over 1500, and two granted Chinese patents. He was the winner of annual Goldsmid Award in 2011. Email: [email protected]
T. Zou et al. / J Materiomics 2 (2016) 273e279 Prof. Dr. Anke Weidenkaff, University of Stuttgart. Anke Weidenkaff is full professor for Materials Chemistry at the University of Stuttgart since 2013. She completed her PhD degree in Chemistry at ETH Zu¨rich in 2000, received the Venia Legendi for Solid State Chemistry and Materials Sciences from the University of Augsburg in 2006 and became section head at Empa as well as professor at the University of Bern, Switzerland. She published some 220 SCI rated publications on materials research in energy conversion technologies, is president of the European Thermoelectric Society (ETS), elected member of the MRS board of directors, the E-MRS Executive Committee and was co-chair of the E-MRS spring meeting in 2013. In 2011 she was awarded with the Kavli Foundation Lectureship prize. Email: [email protected]
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