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Thermoelectric properties of Ag-doped bismuth sulfide polycrystals prepared by mechanical alloying and spark plasma sintering
Materials Chemistry and Physics 131 (2011) 216–222
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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Thermoelectric properties of Ag-doped bismuth sulfide polycrystals prepared by mechanical alloying and spark plasma sintering Yi-Qiang Yu, Bo-Ping Zhang ∗ , Zhen-Hua Ge, Peng-Peng Shang, Yue-Xing Chen School of Materials Science and Engineering, University of Science and Technology Beijing, Xueyuan Road 30, Beijing 100083, China
a r t i c l e
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Article history: Received 22 October 2010 Received in revised form 9 August 2011 Accepted 6 September 2011 Keywords: Semiconductors Sintering Electrical conductivity Thermal conductivity
a b s t r a c t Single orthorhombic phase Bi2−x Agx S3 (x = 0–0.07) bulk materials were prepared by combining mechanical alloying (MA) with spark plasma sintering (SPS) technique. The microstructure and electrical transport properties were investigated with a special emphasis on the influence of Ag content. All the samples have a high density (91.1–95.9%) and homogeneous grains of about 100–500 nm. Optimizing the Ag content greatly improves the electrical conductivity and leads to a peak value of 2.8 × 103 S m−1 at 523 K for the Bi1.99 Ag0.01 S3 composition. The absolute value of Seebeck coefficient shows an inversely varying trend to the electrical conductivity with Ag content, whereby a power factor at 523 K by adjusting Ag content is enhanced from 91 W mK−2 for Bi2 S3 to 235 W mK−2 for Bi1.99 Ag0.01 S3 . The thermal conductivity of Bi2−x Agx S3 ranges from 0.48 to 0.73 W mK−1 , which is lower than the reported values of Bi2 S3 compounds. An enhanced maximum ZT value 0.25 is achieved at 573 K for the Bi1.99 Ag0.01 S3 sample, which is the highest value in Bi2 S3 system in literature. The present work reveals that the non-toxic and cheap Bi2 S3 based compound is a promising candidate for the thermoelectric applications. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric (TE) power generators and refrigerators as solidstate devices without moving parts are silent, reliable and scalable, which is also ideal for small and distributed power generation [1]. They have many important applications such as thermopiles, thermal sensors, and TE cooler for laser diodes [2,3]. The efficiency of TE devices is determined by the dimensionless figure of merit (ZT), defined as ZT = ˛2 T/, where ˛, , , and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively. The compounds A2 B3 (where A = Bi, Sb, Pb and B = S, Se, Te) are considered to be most promising for TE applications [4]. Bi–Te-based [5] and Pb–Te-based [6,7] compounds show the best TE properties at room and middle temperatures, respectively. Although telluride-based materials usually exhibit good TE properties and hold dominant market shares in TE materials, it is necessary to develop alternative materials to replace the rare and toxic tellurium. Bismuth sulfide (Bi2 S3 ) belongs to the A2 B3 family just like Bi2 Te3 [8–10], while little attention has been paid to Bi2 S3 in TE development, because of its high electrical resistivity due to a 1.30 eV direct band gap at room temperature. Zhao et al. [9] recently reported that a low electrical resistivity of the sulfurdeficient Bi2 S3−x (x = 0, 0.05, 0.10, 0.15) was realized via enhancing
∗ Corresponding author. Tel.: +86 10 62334195. E-mail address: [email protected] (B.-P. Zhang). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.09.010
carrier concentration on the sulfur vacancies, where a large Seebeck coefficient was maintained at the same time. The textured Bi2 S2.90 prepared by hot-forging showed the highest ZT = 0.11 at 523 K, which is higher than the other reported value (∼0.05) of Bi2 S3 [10]. Kyratsi et al. [11] found the uneven distribution of atoms and electronic replacement phenomenon of atoms in the lattice for the quaternary alloys K–Bi–Sb–Se and Ag–Pb–Sb–Te. The complexity of these structures is beneficial to improve the TE performance. Cui et al. [12] reported that doping Ag into Bi–Te base alloys reduces thermal conductivities and contributes to the high ZT value, in which a Ag-doped (Bi2 Te3 )0.9 –(Bi1.6 Ag0.4 Se3 )0.1 alloy showed 30% TE improvement as compared with Ag-free alloys. The enhanced ZT is considered to be attributed to the increase both in the concentration and mobility of free electrons due to the substitution of Ag atom for Bi in the Bi2 Se3 , since Ag belongs to the IB group elements and the most outside orbital layer has one 5s1 , while the outermost orbit of Bi has three 6p3 electrons. The structure of Bi2 S3 is similar to that of Bi2 Se3 , so it is expected that the substitution of Ag for a part of Bi in Bi–S-based alloys also increases structural defects and then change the concentration, although little attention has been paid on Ag-doped bismuth sulfide alloys so far. Compared with conventional melting or grinding techniques, mechanical alloying (MA) has several advantages such as: avoiding segregation from melting state, preparing nanometer powder in short time, and has been recently applied to fabricate nano-sized alloys. Spark plasma sintering (SPS) is suitable for fabricating finegrained TE materials because of the low sintering temperature and the short sintering time [13]. In the present study, Ag-doped ternary
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Bi2−x Agx S3 (x = 0–0.07) alloys were fabricated by MA and SPS technique. The microstructure and TE properties were investigated with special emphases on the effect of Ag content. 2. Experimental procedure Commercial high-purity powders of 99.99% Bi, 99.9% Ag and 99.5% S under the same 100 mesh were used as raw materials. The powders with a chemical composition of Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) were ball-milled at 400 rpm for 15 h in a mixture atmosphere of argon (95%) and hydrogen (5%) gases using a planetary ball mill (QM-1SP2, Nanjing University, China), then were milled again at 350 rpm for 5 h in an alcohol solution. Stainless steel vessel and balls were used, and the weight ratio of ball to powder was kept at 20:1. The MA-treated powders were applied by SPS at 673 K for 5 min in a ˚20 mm graphite mould under a pressure of 40 MPa in vacuum using a SPS system (Sumitomo SPS1050, Japan), resulting in a disk-shaped bulk of ˚20 mm × 4 mm. Phase structure was analyzed by X-ray diffraction (XRD, CuK␣, BrukerD8, Germany). The morphologies of powder and fractographs of bulks were observed by a field emission scanning electron microscopy (FESEM, SUPRATM 55, Germany). The TE properties were evaluated along the sample section perpendicular to the pressing direction of SPS. The Seebeck coefficient and electrical resistivity were measured at 323–573 K in a helium atmosphere using a Seebeck coefficient/electric resistance measuring system (ZEM-2, Ulvac-Riko, Japan). The thermal diffusivity coefficient (D) was measured using a laser flash method (NETZSCH, LFA427, Germany). The specific heat (Cp ) was measured using a thermal analyzing apparatus (Dupont 1090B, USA). The density (d) of the sample was measured by the Archimedes method. The thermal conductivity () was calculated from the product of thermal diffusivity, specific heat (Cp = 0.24) and density, = DCp d. The combined uncertainty for the experimental determination of ZT is about 15–20%, which was caused by five kinds of respective measurement including electrical resistivity, Seebeck coefficient, thermal diffusion coefficient, specific heat, and density. The UV–Vis diffuse reflectance spectra of the products were measured and converted into absorption spectra according to the Kubelka–Munk (KM) method (Hitachi U-3310, Japan).
Fig. 1. XRD patterns of the MA-treated Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) powders.
the diffraction peaks of samples with higher Ag content (x = 0.03, 0.05 and 0.07) shift conversely to a large angle, indicating the expansion of the host lattice. This kind of the discontinuous varying for the diffraction peaks with Ag content might be explained from below two aspects. One possible explanation refers on the valence of Ag ions. The ionic radius of Ag+ and Ag2+ is 0.126 nm and 0.089 nm, respectively, whereas that of Bi3+ is 0.096 nm. If a part
3. Results and discussion Fig. 1 shows the XRD patterns of the Bi2−x Agx S3 powders (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07). All the Bi2−x Agx S3 powders show a well-matched pattern to the binary Bi2 S3 (PDF#17-0320), which indicates that a single phase with an orthorhombic symmetry could be successfully synthesized by the MA method. The XRD patterns of the Bi2−x Agx S3 bulks obtained by applying SPS at 673 K for 5 min using MA-treated powders are shown in Fig. 2, which coincide roughly with those of the MA-treated powders. The tiny difference between the MA-treated Bi2−x Agx S3 powders (dot lines) and the SPS-treated counterparts (solid lines) are compared in Fig. 3 by using the enlarged patterns in 2 ranges 24–27◦ , 28–29◦ , 31–32◦ , 46–47◦ , in which the Miller indices of the diffraction peak are indexed as (1 3 0), (3 1 0), (2 1 1), (2 2 1) and (2 4 0), respectively. Compared with the XRD patterns of the powders, the SPS-treated bulks have a sharp diffraction peak with a narrowed full width at half maximum (FWHM), which indicates the grain growth and the improvement of the crystallinity after sintering the powders to the bulks. Note that the main diffraction peaks around 24.9◦ , 28.6◦ , 31.8◦ , and 46.4◦ shift slightly with increasing Ag content. Compared with Bi2 S3 (x = 0), the diffraction peaks of Bi2−x Agx S3 samples (x = 0.005, 0.01, 0.015) shift to lower diffraction angles, indicating that the size of unit cell is enlarged. Otherwise,
Fig. 2. XRD patterns of the SPS-treated Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) bulks.
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Fig. 3. XRD patterns of Bi2−x Agx S3 powders (dot lines) and SPS-treated bulks (solid lines) in 2 range 24–27◦ , 28–29◦ , 31–32◦ , 46–47◦ .
of Bi3+ (0.096 nm) is substituted by Ag+ (0.126 nm), which should induce the expansion of the host lattice, whereas the shrinkage of the unite cell might be caused if a part of Bi3+ (0.096 nm) is substituted by Ag2+ (0.089 nm). However, it is unknown why the valence state of Ag changes with increasing Ag-doping content. Any other evidence for the change of valence state of Ag ions is also difficult to provide because of the light doping level of Ag. Another possible explanation is that Ag gets into an interstitial site similar to Cu in Bi2 Te3 [14], and works as a definitely n-type doping that increases the lattice parameter as 0 < x < 0.01. When the concentration of Ag is beyond the solution limit, which is likely x = 0.01, the Ag2+ likely gets into the Bi sub-lattice and decreases the lattice parameter as 0.01 < x < 0.07. These two explanations will be relevant to the microstructure and electrical transport properties as discussed later. Fig. 4(a) shows the UV–Vis diffuse reflectance spectra of Bi2−x Agx S3 MA-treated powders. The absorptions of all Ag-added samples are obviously different from the pure Bi2 S3 sample, indicating that Ag is introduced into bismuth sulfide. For a crystalline semiconductor, it is known that the optical absorption near the band edge follows the equation [15] ˛h = A(h − Eg )
n/2
(1)
in which ˛, h, , A, and Eg are absorption coefficient, Planck constant, light frequency, proportionality constant, and band gap, respectively. The constant A is the slope of the straightest line and the Eg is the value of the point of intersection with h axis. The plot (˛h)2 vs h can be used to evaluate the band gap Eg by extrapolating the straightest line to (˛h)2 = 0. In the equation, n depends on whether the transition is direct (n = 1) or indirect (n = 4). As well-known, Bi2 S3 material belongs to direct band gap semiconductor [8–10]. The value of n for the Bi2 S3 was determined to be 1 from Fig. 4(a). The plot (˛h)2 vs h (Fig. 4(b)) can be used to evaluate the band gap Eg by extrapolating the straightest line to the h axis intercept. The values of the band gap were estimated as follows: 1.29 eV for Bi2 S3 , 1.20 eV for Bi1.995 Ag0.005 S3 , and all 1.05 eV for Bi1.99 Ag0.01 S3 , Bi1.985 Ag0.015 S3 and Bi1.97 Ag0.03 S3 . The band gap of the as-prepared pure Bi2 S3 (1.29 eV) is basically coincident with the reported value 1.30 eV [9]. It is found from Fig. 4(b) that the band gap decreases
with increasing Ag content after doping Ag to Bi2 S3 until x = 0.01, and becomes constant as x > 0.01. The initially decreased band gap may be due to the introduction of the impurity level after doping Ag less than 0.01, whereas the band gap will be constant by adding Ag more than this limit. Since the band gap is inversely proportional to carrier mobility [16], so the decreased band gap should correspond to the enhancement of the carrier mobility and affect the electrical conductivity which will be discussed later. Fig. 5 shows the FESEM micrographs of the fractured surfaces for Bi2−x Agx S3 bulks obtained by applying SPS at 673 K. The fractured surface of Bi2 S3 in Fig. 5(a) shows a lamellar structure with an average grain size of about 200 nm, which is finer than those (about 400 nm) of the samples Bi2 S3−x (x = 0, 0.05, 0.10, 0.15) MA-treated at 350 rpm for 15 h and then sintered at 673 K for 5 min [9]. The fined grain size is attributed to the fine powder which was ball-milled at a high speed (400 rpm). The grain sizes grow when doping Ag to 0.01, while decrease to 200 nm and 100 nm as further increasing Ag content to 0.03 (Fig. 5(e)) and 0.07 (Fig. 5(f)). If the discontinuous shifting for the diffraction peaks with Ag content (Fig. 3) caused by the variation of valence of Ag ions, the grain size should show a monotonic change with Ag content. Therefore, the nonmonotonic change on the grain size with Ag content may be attributed to the formation of interstitial solid solution and substitution solid solution depending on the Ag content. The large diffusion rate and small diffusion activation energy of the interstitial solid solution contributes to the growth of grain as compared with the substitution solid solution. The relative density of the Bi2−x Agx S3 samples (when x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, and 0.07) was 94.7%, 93.8%, 95.9%, 94.2%, 94.1%, 93.5% and 91.1%, respectively. It is obvious that excessive adding Ag (x > 0.015) not only decreases the relative density but also suppresses the grain growth as corresponding with the FESEM micrographs (Fig. 5(e) and (f)). Fig. 6 shows the temperature dependence of electrical transport properties for Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.07). The electrical conductivity () increases for all the Bi2−x Agx S3 samples with increasing temperature, being indicative of a semiconductor conducting behavior. The value of Bi2 S3 ranges from 4 × 101 to 4 × 102 S m−1 at 323–573 K and increases firstly and then decreases with increasing Ag content, which shows a maximum value 2.8 × 103 S m−1 at 523 K as x = 0.01. When the Ag atoms
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Fig. 4. UV–Vis-DRS (a) and the plot (˛h)2 vs h of the MA-treated Bi2−x Agx S3 powders (x = 0, 0.005, 0.01, 0.015, 0.03).
Fig. 5. Field emission scanning electron microscopy of the fractured surfaces for the Bi2−x Agx S3 bulks. (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.015, (e) x = 0.03, and (f) x = 0.07.
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Fig. 6. Temperature dependence of electrical conductivity (a), Seebeck coefficient (b), and power factor (c) for the different Bi2−x Agx S3 (x = 0–0.07) alloys.
entered into the Bi2 S3 crystal lattice, two defect equations corresponding to the interstitial and substitutional types could be expressed as follows: 2Bi S
2 3 2Agi • + 3SS + 2BiBi + 2e 2Ag −→
Bi2 S3
••
AgS −→ 2AgBi + Ss + Vs
(2) (3)
The defect Eqs. (2) and (3) describe the formation of interstitial solid solution and substitution solid solution, respectively. According to the XRD results in Fig. 3, the defect equation is dominant in form of Eq. (2) as 0 < x ≤ 0.01 and becomes dominant in Eq. (3) as x > 0.01. When Ag gets into interstitial site, the electrons
concentration could be increased in system as shown in Eq. (2). When Ag2+ replaces Bi3+ , holes concentration could be increased in system (Eq. (3)). In the n-type Bi2−x Agx S3 materials, the major carrier is electron. Since the value is directly proportional to the mobility (), carrier concentration (n), electronic charge (e), according to the expression = ne, the increased value as increasing x from 0 to 0.01 should attribute to the increased e to increase carrier concentration, which contributes to the enhancement of the value in the semiconductors [17]. However, the replacement of Ag ions to Bi ions (x > 0.01) will offer the holes (Vs •• ) to recombination with electrons and reduce the carrier concentration leading to diminution of the value, although the carrier mobility increases continuously with increasing Ag content, this result is well-matched with the calculation of the diminishing band gap [16] (from 1.29 to 1.05 eV, when x from 0 to 0.03), as shown in Fig. 4(b). Fig. 6(b) shows the temperature dependence of Seebeck coefficient (˛) for Bi2−x Agx S3 with different Ag content. The negative values of Seebeck coefficient indicate that all the samples are n-type and the major carrier is electron. The absolute values of Seebeck coefficient (|˛|) for the Bi2 S3 are around 500 V K−1 at 423–573 K. With increasing Ag content, the |˛| value decreases firstly and then increases, which shows an inverse varying tendency to the electrical conductivity. A minimum |˛| of 250 V K−1 occurs at 323 K in the sample Bi1.99 Ag0.01 S3 . As further increasing Ag content to x = 0.07, a maximum |˛| of 800 V K−1 was achieved at 323 K, which shows a decreasing trend with increasing temperature. According to the expression ˛ = (k/e)( − ln(n/N0 )), where n and are carrier concentration and scattering factor, respectively, the |˛| value is proportional to scattering factor and inversely proportional to carrier concentration. The initial decreased |˛| as 0 < x ≤ 0.01 attributes to the increased carrier concentration as discussed by the defect Eqs. (2) and (3). On the other hand, the subsequently increased |˛| as 0.01 < x ≤ 0.07 may be due to a strong phonon scattering which caused by the lattice defects (Fig. 3) and the reduced carrier concentration which caused by compounding partly holes with electrons. Fig. 6(c) shows the temperature dependence of power factor (PF = ˛2 ) for Bi2−x Agx S3 with different Ag content. The PF of the Bi2 S3 sample is 10.2 W mK−2 at 323 K and increases to 91.4 W mK−2 as raising temperature to 573 K. All samples show a similar positive-temperature dependence of PF, while have different slopes. With increasing Ag content, the PF of Bi2−x Agx S3 first increases and then decreases. This trend is similar to the variation of but is inverse to that of the ˛, which reveals that the gives more contribution to PF than that of ˛. The Bi1.99 Ag0.01 S3 sample shows higher PF than other samples at high temperature, and has a maximum of 235 W mK−2 at 523 K. The above results indicate that the electrical properties of Bi2−x Agx S3 can be increased by doping Ag, and have an optimal doping concentration at x = 0.01. Fig. 7(a) shows the temperature dependence of thermal conductivity for Bi2−x Agx S3 (x = 0–0.03) bulks sintered at 673 K. The thermal conductivity of the samples Bi2−x Agx S3 (x = 0–0.015) decreases with increasing temperatures, which suggests the dominant mechanism of the phonon scattering. The thermal conductivity of the sample Bi2 S3 increases from 0.54 W mK−1 to 0.69 W mK−1 in the whole measuring temperature ranges from 327 to 573 K. The values are lower than 0.84–0.88 W mK−1 of the sample with the same composition Bi2 S3 reported by Zhao et al. [9], whose sample had a larger average grain size (400 nm) than that (200 nm in Fig. 6(a)) of the present sample Bi2 S3 . The total thermal conductivity is the sum of lattice and carrier contributions in which they were estimated according to the Wiedemann–Franz law as follows:
= lattice + carrier
(4)
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Fig. 8. Temperature dependences of merit ZT for the different Bi2−x Agx S3 (x = 0–0.03) alloys.
Fig. 7. Temperature dependences of thermal conductivity (a), the ratios of carrier / (b) and lattice / (c) for the different Bi2−x Agx S3 (x = 0–0.03) alloys.
carrier = LT
(5)
where lattice , carrier and L are the lattice thermal conductivity, carrier thermal conductivity and the Lorenz number, respectively. The Lorenz number was calculated as the fellow equation [18,19]: L=
k 2 3F ()F () − 4F 2 () 0 2 B 1 e
F0 ()
(6)
where the kB , e, Fr , and are the Boltzmann constant, unit charge, Fermi integration of order r, and reduced Fermi energy which is obtained from the Seebeck coefficient value according to the fellow equation [18,19]: ˛=
kB e
2F1 () − F0 ()
factors on the thermal conductivity, the relative ratios of the carrier and lattice to total are shown in Fig. 7(b) and (c), respectively. The ratio of carrier / for all samples in Fig. 7(b) increases with increasing temperature, which might be attributed to an ambipolar contribution arising from the diffusion of electron–hole pairs with the onset of intrinsic contribution [20]. The temperature dependence of the carrier / ratio increases firstly and then decreases with increasing Ag content, whose trend is similar to that of the electrical conductivity (Fig. 6(a)). Nevertheless, it is noticed that even the highest proportion of the carrier to is not excess 2.75% for the Bi1.99 Ag0.01 S3 sample at 523 K. It is concluded that the total should be strongly relative to the variation of lattice as shown in Fig. 7(c). The lattice for all samples decreases with increasing temperature, which is ascribed to the strong phonon scattering. The proportion of the lattice to for Ag-free Bi2 S3 is nearly 100% at 273 K and downs to about 99.7% at 573 K. Increasing Ag doping content leads to the initial decrease and later increase in the lattice / ratio, while a minimum value attained at x = 0.01. This trend is well agreement with that of the Seebeck coefficient (˛) (Fig. 6(b)). Compared with the lattice thermal conductivity at room temperature for the optimized n-type Bi2 (Se, Te)3 polycrystalline materials (0.7 W mK−1 ) [21], we note that the majority of the total thermal conductivity for all the Ag-doped samples which varies between 0.48 and 0.73 W mK−1 are still lower than this value. Such surprising low thermal conductivity of the Bi2−x Agx S3 bulks indicates their great potentials to satisfy one of the key requirements for a useful TE material at least from the perspective of thermal transport. Fig. 8 shows the temperature dependence of the dimension less figure of merit, ZT, for the different Bi2−x Agx S3 (x = 0–0.03) alloys. All samples show an enhanced ZT values with raising measuring temperature which owing to the increased powder factor (Fig. 6(c)) and decreased thermal conductivity (Fig. 7(a)). Doping Ag to 0.01 mol leads to initial increase in the ZT values but decrease in ones by further increasing Ag over 0.01 mol. The enhanced ZT value is mainly ascribed to the improved electrical transport properties (Fig. 6) and the decreased lattice thermal conductivity (lattice ) (Fig. 7(c)) since the contribution of the carrier thermal conductivity (carrier ) is quite weak (Fig. 7(c)). The maximum ZT value reaches about 0.25 for the sample Bi1.99 Ag0.01 S3 at 573 K, which is about 178% higher than that of Bi2 S3 (0.09) at the same temperature and is also the largest value in Bi2 S3 system in literature reported so far.
(7)
By inserting into Eq. (6), L values were calculated to be in the range from 1.68 × 10−8 to 1.76 × 10−8 V2 K−2 , which were used to estimate carrier thermal conductivity. In order to discuss the effect
4. Conclusions Bi2−x Agx S3 polycrystals with a single orthorhombic phase were synthesized by MA and SPS technique. The electrical
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conductivity increases firstly and then decreases with increasing Ag content, which shows a maximum value 2.8 × 103 S m−1 at 523 K as x = 0.01. The absolute value of Seebeck coefficient shows an opposite trend, whereby the power factor is enhanced from 91 W mK−2 for Bi2 S3 to 235 W mK−2 for Bi1.99 Ag0.01 S3 . The thermal conductivity of Bi2−x Agx S3 ranges from 0.48 to 0.73 W mK−1 . An enhanced maximum ZT value of 0.25 was achieved at 573 K for the Bi1.99 Ag0.01 S3 sample, which is the highest value in the Bi2 S3 system reported so far. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 50972012), High-Tech 863 Program of China (Grant No. 2009AA03Z216), and National Basic Research Program of China (Grant No. 2007CB607500). References [1] D.M. Rowe, Thermoelectrics Handbook: Macro to Nano, CRC Press, Boca Raton, 2006. [2] T.M. Tritt, Science 283 (1999) 804.
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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Thermoelectric properties of Ag-doped bismuth sulfide polycrystals prepared by mechanical alloying and spark plasma sintering Yi-Qiang Yu, Bo-Ping Zhang ∗ , Zhen-Hua Ge, Peng-Peng Shang, Yue-Xing Chen School of Materials Science and Engineering, University of Science and Technology Beijing, Xueyuan Road 30, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 22 October 2010 Received in revised form 9 August 2011 Accepted 6 September 2011 Keywords: Semiconductors Sintering Electrical conductivity Thermal conductivity
a b s t r a c t Single orthorhombic phase Bi2−x Agx S3 (x = 0–0.07) bulk materials were prepared by combining mechanical alloying (MA) with spark plasma sintering (SPS) technique. The microstructure and electrical transport properties were investigated with a special emphasis on the influence of Ag content. All the samples have a high density (91.1–95.9%) and homogeneous grains of about 100–500 nm. Optimizing the Ag content greatly improves the electrical conductivity and leads to a peak value of 2.8 × 103 S m−1 at 523 K for the Bi1.99 Ag0.01 S3 composition. The absolute value of Seebeck coefficient shows an inversely varying trend to the electrical conductivity with Ag content, whereby a power factor at 523 K by adjusting Ag content is enhanced from 91 W mK−2 for Bi2 S3 to 235 W mK−2 for Bi1.99 Ag0.01 S3 . The thermal conductivity of Bi2−x Agx S3 ranges from 0.48 to 0.73 W mK−1 , which is lower than the reported values of Bi2 S3 compounds. An enhanced maximum ZT value 0.25 is achieved at 573 K for the Bi1.99 Ag0.01 S3 sample, which is the highest value in Bi2 S3 system in literature. The present work reveals that the non-toxic and cheap Bi2 S3 based compound is a promising candidate for the thermoelectric applications. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Thermoelectric (TE) power generators and refrigerators as solidstate devices without moving parts are silent, reliable and scalable, which is also ideal for small and distributed power generation [1]. They have many important applications such as thermopiles, thermal sensors, and TE cooler for laser diodes [2,3]. The efficiency of TE devices is determined by the dimensionless figure of merit (ZT), defined as ZT = ˛2 T/, where ˛, , , and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively. The compounds A2 B3 (where A = Bi, Sb, Pb and B = S, Se, Te) are considered to be most promising for TE applications [4]. Bi–Te-based [5] and Pb–Te-based [6,7] compounds show the best TE properties at room and middle temperatures, respectively. Although telluride-based materials usually exhibit good TE properties and hold dominant market shares in TE materials, it is necessary to develop alternative materials to replace the rare and toxic tellurium. Bismuth sulfide (Bi2 S3 ) belongs to the A2 B3 family just like Bi2 Te3 [8–10], while little attention has been paid to Bi2 S3 in TE development, because of its high electrical resistivity due to a 1.30 eV direct band gap at room temperature. Zhao et al. [9] recently reported that a low electrical resistivity of the sulfurdeficient Bi2 S3−x (x = 0, 0.05, 0.10, 0.15) was realized via enhancing
∗ Corresponding author. Tel.: +86 10 62334195. E-mail address: [email protected] (B.-P. Zhang). 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.09.010
carrier concentration on the sulfur vacancies, where a large Seebeck coefficient was maintained at the same time. The textured Bi2 S2.90 prepared by hot-forging showed the highest ZT = 0.11 at 523 K, which is higher than the other reported value (∼0.05) of Bi2 S3 [10]. Kyratsi et al. [11] found the uneven distribution of atoms and electronic replacement phenomenon of atoms in the lattice for the quaternary alloys K–Bi–Sb–Se and Ag–Pb–Sb–Te. The complexity of these structures is beneficial to improve the TE performance. Cui et al. [12] reported that doping Ag into Bi–Te base alloys reduces thermal conductivities and contributes to the high ZT value, in which a Ag-doped (Bi2 Te3 )0.9 –(Bi1.6 Ag0.4 Se3 )0.1 alloy showed 30% TE improvement as compared with Ag-free alloys. The enhanced ZT is considered to be attributed to the increase both in the concentration and mobility of free electrons due to the substitution of Ag atom for Bi in the Bi2 Se3 , since Ag belongs to the IB group elements and the most outside orbital layer has one 5s1 , while the outermost orbit of Bi has three 6p3 electrons. The structure of Bi2 S3 is similar to that of Bi2 Se3 , so it is expected that the substitution of Ag for a part of Bi in Bi–S-based alloys also increases structural defects and then change the concentration, although little attention has been paid on Ag-doped bismuth sulfide alloys so far. Compared with conventional melting or grinding techniques, mechanical alloying (MA) has several advantages such as: avoiding segregation from melting state, preparing nanometer powder in short time, and has been recently applied to fabricate nano-sized alloys. Spark plasma sintering (SPS) is suitable for fabricating finegrained TE materials because of the low sintering temperature and the short sintering time [13]. In the present study, Ag-doped ternary
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Bi2−x Agx S3 (x = 0–0.07) alloys were fabricated by MA and SPS technique. The microstructure and TE properties were investigated with special emphases on the effect of Ag content. 2. Experimental procedure Commercial high-purity powders of 99.99% Bi, 99.9% Ag and 99.5% S under the same 100 mesh were used as raw materials. The powders with a chemical composition of Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) were ball-milled at 400 rpm for 15 h in a mixture atmosphere of argon (95%) and hydrogen (5%) gases using a planetary ball mill (QM-1SP2, Nanjing University, China), then were milled again at 350 rpm for 5 h in an alcohol solution. Stainless steel vessel and balls were used, and the weight ratio of ball to powder was kept at 20:1. The MA-treated powders were applied by SPS at 673 K for 5 min in a ˚20 mm graphite mould under a pressure of 40 MPa in vacuum using a SPS system (Sumitomo SPS1050, Japan), resulting in a disk-shaped bulk of ˚20 mm × 4 mm. Phase structure was analyzed by X-ray diffraction (XRD, CuK␣, BrukerD8, Germany). The morphologies of powder and fractographs of bulks were observed by a field emission scanning electron microscopy (FESEM, SUPRATM 55, Germany). The TE properties were evaluated along the sample section perpendicular to the pressing direction of SPS. The Seebeck coefficient and electrical resistivity were measured at 323–573 K in a helium atmosphere using a Seebeck coefficient/electric resistance measuring system (ZEM-2, Ulvac-Riko, Japan). The thermal diffusivity coefficient (D) was measured using a laser flash method (NETZSCH, LFA427, Germany). The specific heat (Cp ) was measured using a thermal analyzing apparatus (Dupont 1090B, USA). The density (d) of the sample was measured by the Archimedes method. The thermal conductivity () was calculated from the product of thermal diffusivity, specific heat (Cp = 0.24) and density, = DCp d. The combined uncertainty for the experimental determination of ZT is about 15–20%, which was caused by five kinds of respective measurement including electrical resistivity, Seebeck coefficient, thermal diffusion coefficient, specific heat, and density. The UV–Vis diffuse reflectance spectra of the products were measured and converted into absorption spectra according to the Kubelka–Munk (KM) method (Hitachi U-3310, Japan).
Fig. 1. XRD patterns of the MA-treated Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) powders.
the diffraction peaks of samples with higher Ag content (x = 0.03, 0.05 and 0.07) shift conversely to a large angle, indicating the expansion of the host lattice. This kind of the discontinuous varying for the diffraction peaks with Ag content might be explained from below two aspects. One possible explanation refers on the valence of Ag ions. The ionic radius of Ag+ and Ag2+ is 0.126 nm and 0.089 nm, respectively, whereas that of Bi3+ is 0.096 nm. If a part
3. Results and discussion Fig. 1 shows the XRD patterns of the Bi2−x Agx S3 powders (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07). All the Bi2−x Agx S3 powders show a well-matched pattern to the binary Bi2 S3 (PDF#17-0320), which indicates that a single phase with an orthorhombic symmetry could be successfully synthesized by the MA method. The XRD patterns of the Bi2−x Agx S3 bulks obtained by applying SPS at 673 K for 5 min using MA-treated powders are shown in Fig. 2, which coincide roughly with those of the MA-treated powders. The tiny difference between the MA-treated Bi2−x Agx S3 powders (dot lines) and the SPS-treated counterparts (solid lines) are compared in Fig. 3 by using the enlarged patterns in 2 ranges 24–27◦ , 28–29◦ , 31–32◦ , 46–47◦ , in which the Miller indices of the diffraction peak are indexed as (1 3 0), (3 1 0), (2 1 1), (2 2 1) and (2 4 0), respectively. Compared with the XRD patterns of the powders, the SPS-treated bulks have a sharp diffraction peak with a narrowed full width at half maximum (FWHM), which indicates the grain growth and the improvement of the crystallinity after sintering the powders to the bulks. Note that the main diffraction peaks around 24.9◦ , 28.6◦ , 31.8◦ , and 46.4◦ shift slightly with increasing Ag content. Compared with Bi2 S3 (x = 0), the diffraction peaks of Bi2−x Agx S3 samples (x = 0.005, 0.01, 0.015) shift to lower diffraction angles, indicating that the size of unit cell is enlarged. Otherwise,
Fig. 2. XRD patterns of the SPS-treated Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, 0.07) bulks.
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Fig. 3. XRD patterns of Bi2−x Agx S3 powders (dot lines) and SPS-treated bulks (solid lines) in 2 range 24–27◦ , 28–29◦ , 31–32◦ , 46–47◦ .
of Bi3+ (0.096 nm) is substituted by Ag+ (0.126 nm), which should induce the expansion of the host lattice, whereas the shrinkage of the unite cell might be caused if a part of Bi3+ (0.096 nm) is substituted by Ag2+ (0.089 nm). However, it is unknown why the valence state of Ag changes with increasing Ag-doping content. Any other evidence for the change of valence state of Ag ions is also difficult to provide because of the light doping level of Ag. Another possible explanation is that Ag gets into an interstitial site similar to Cu in Bi2 Te3 [14], and works as a definitely n-type doping that increases the lattice parameter as 0 < x < 0.01. When the concentration of Ag is beyond the solution limit, which is likely x = 0.01, the Ag2+ likely gets into the Bi sub-lattice and decreases the lattice parameter as 0.01 < x < 0.07. These two explanations will be relevant to the microstructure and electrical transport properties as discussed later. Fig. 4(a) shows the UV–Vis diffuse reflectance spectra of Bi2−x Agx S3 MA-treated powders. The absorptions of all Ag-added samples are obviously different from the pure Bi2 S3 sample, indicating that Ag is introduced into bismuth sulfide. For a crystalline semiconductor, it is known that the optical absorption near the band edge follows the equation [15] ˛h = A(h − Eg )
n/2
(1)
in which ˛, h, , A, and Eg are absorption coefficient, Planck constant, light frequency, proportionality constant, and band gap, respectively. The constant A is the slope of the straightest line and the Eg is the value of the point of intersection with h axis. The plot (˛h)2 vs h can be used to evaluate the band gap Eg by extrapolating the straightest line to (˛h)2 = 0. In the equation, n depends on whether the transition is direct (n = 1) or indirect (n = 4). As well-known, Bi2 S3 material belongs to direct band gap semiconductor [8–10]. The value of n for the Bi2 S3 was determined to be 1 from Fig. 4(a). The plot (˛h)2 vs h (Fig. 4(b)) can be used to evaluate the band gap Eg by extrapolating the straightest line to the h axis intercept. The values of the band gap were estimated as follows: 1.29 eV for Bi2 S3 , 1.20 eV for Bi1.995 Ag0.005 S3 , and all 1.05 eV for Bi1.99 Ag0.01 S3 , Bi1.985 Ag0.015 S3 and Bi1.97 Ag0.03 S3 . The band gap of the as-prepared pure Bi2 S3 (1.29 eV) is basically coincident with the reported value 1.30 eV [9]. It is found from Fig. 4(b) that the band gap decreases
with increasing Ag content after doping Ag to Bi2 S3 until x = 0.01, and becomes constant as x > 0.01. The initially decreased band gap may be due to the introduction of the impurity level after doping Ag less than 0.01, whereas the band gap will be constant by adding Ag more than this limit. Since the band gap is inversely proportional to carrier mobility [16], so the decreased band gap should correspond to the enhancement of the carrier mobility and affect the electrical conductivity which will be discussed later. Fig. 5 shows the FESEM micrographs of the fractured surfaces for Bi2−x Agx S3 bulks obtained by applying SPS at 673 K. The fractured surface of Bi2 S3 in Fig. 5(a) shows a lamellar structure with an average grain size of about 200 nm, which is finer than those (about 400 nm) of the samples Bi2 S3−x (x = 0, 0.05, 0.10, 0.15) MA-treated at 350 rpm for 15 h and then sintered at 673 K for 5 min [9]. The fined grain size is attributed to the fine powder which was ball-milled at a high speed (400 rpm). The grain sizes grow when doping Ag to 0.01, while decrease to 200 nm and 100 nm as further increasing Ag content to 0.03 (Fig. 5(e)) and 0.07 (Fig. 5(f)). If the discontinuous shifting for the diffraction peaks with Ag content (Fig. 3) caused by the variation of valence of Ag ions, the grain size should show a monotonic change with Ag content. Therefore, the nonmonotonic change on the grain size with Ag content may be attributed to the formation of interstitial solid solution and substitution solid solution depending on the Ag content. The large diffusion rate and small diffusion activation energy of the interstitial solid solution contributes to the growth of grain as compared with the substitution solid solution. The relative density of the Bi2−x Agx S3 samples (when x = 0, 0.005, 0.01, 0.015, 0.03, 0.05, and 0.07) was 94.7%, 93.8%, 95.9%, 94.2%, 94.1%, 93.5% and 91.1%, respectively. It is obvious that excessive adding Ag (x > 0.015) not only decreases the relative density but also suppresses the grain growth as corresponding with the FESEM micrographs (Fig. 5(e) and (f)). Fig. 6 shows the temperature dependence of electrical transport properties for Bi2−x Agx S3 (x = 0, 0.005, 0.01, 0.015, 0.03, 0.07). The electrical conductivity () increases for all the Bi2−x Agx S3 samples with increasing temperature, being indicative of a semiconductor conducting behavior. The value of Bi2 S3 ranges from 4 × 101 to 4 × 102 S m−1 at 323–573 K and increases firstly and then decreases with increasing Ag content, which shows a maximum value 2.8 × 103 S m−1 at 523 K as x = 0.01. When the Ag atoms
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Fig. 4. UV–Vis-DRS (a) and the plot (˛h)2 vs h of the MA-treated Bi2−x Agx S3 powders (x = 0, 0.005, 0.01, 0.015, 0.03).
Fig. 5. Field emission scanning electron microscopy of the fractured surfaces for the Bi2−x Agx S3 bulks. (a) x = 0, (b) x = 0.005, (c) x = 0.01, (d) x = 0.015, (e) x = 0.03, and (f) x = 0.07.
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Fig. 6. Temperature dependence of electrical conductivity (a), Seebeck coefficient (b), and power factor (c) for the different Bi2−x Agx S3 (x = 0–0.07) alloys.
entered into the Bi2 S3 crystal lattice, two defect equations corresponding to the interstitial and substitutional types could be expressed as follows: 2Bi S
2 3 2Agi • + 3SS + 2BiBi + 2e 2Ag −→
Bi2 S3
••
AgS −→ 2AgBi + Ss + Vs
(2) (3)
The defect Eqs. (2) and (3) describe the formation of interstitial solid solution and substitution solid solution, respectively. According to the XRD results in Fig. 3, the defect equation is dominant in form of Eq. (2) as 0 < x ≤ 0.01 and becomes dominant in Eq. (3) as x > 0.01. When Ag gets into interstitial site, the electrons
concentration could be increased in system as shown in Eq. (2). When Ag2+ replaces Bi3+ , holes concentration could be increased in system (Eq. (3)). In the n-type Bi2−x Agx S3 materials, the major carrier is electron. Since the value is directly proportional to the mobility (), carrier concentration (n), electronic charge (e), according to the expression = ne, the increased value as increasing x from 0 to 0.01 should attribute to the increased e to increase carrier concentration, which contributes to the enhancement of the value in the semiconductors [17]. However, the replacement of Ag ions to Bi ions (x > 0.01) will offer the holes (Vs •• ) to recombination with electrons and reduce the carrier concentration leading to diminution of the value, although the carrier mobility increases continuously with increasing Ag content, this result is well-matched with the calculation of the diminishing band gap [16] (from 1.29 to 1.05 eV, when x from 0 to 0.03), as shown in Fig. 4(b). Fig. 6(b) shows the temperature dependence of Seebeck coefficient (˛) for Bi2−x Agx S3 with different Ag content. The negative values of Seebeck coefficient indicate that all the samples are n-type and the major carrier is electron. The absolute values of Seebeck coefficient (|˛|) for the Bi2 S3 are around 500 V K−1 at 423–573 K. With increasing Ag content, the |˛| value decreases firstly and then increases, which shows an inverse varying tendency to the electrical conductivity. A minimum |˛| of 250 V K−1 occurs at 323 K in the sample Bi1.99 Ag0.01 S3 . As further increasing Ag content to x = 0.07, a maximum |˛| of 800 V K−1 was achieved at 323 K, which shows a decreasing trend with increasing temperature. According to the expression ˛ = (k/e)( − ln(n/N0 )), where n and are carrier concentration and scattering factor, respectively, the |˛| value is proportional to scattering factor and inversely proportional to carrier concentration. The initial decreased |˛| as 0 < x ≤ 0.01 attributes to the increased carrier concentration as discussed by the defect Eqs. (2) and (3). On the other hand, the subsequently increased |˛| as 0.01 < x ≤ 0.07 may be due to a strong phonon scattering which caused by the lattice defects (Fig. 3) and the reduced carrier concentration which caused by compounding partly holes with electrons. Fig. 6(c) shows the temperature dependence of power factor (PF = ˛2 ) for Bi2−x Agx S3 with different Ag content. The PF of the Bi2 S3 sample is 10.2 W mK−2 at 323 K and increases to 91.4 W mK−2 as raising temperature to 573 K. All samples show a similar positive-temperature dependence of PF, while have different slopes. With increasing Ag content, the PF of Bi2−x Agx S3 first increases and then decreases. This trend is similar to the variation of but is inverse to that of the ˛, which reveals that the gives more contribution to PF than that of ˛. The Bi1.99 Ag0.01 S3 sample shows higher PF than other samples at high temperature, and has a maximum of 235 W mK−2 at 523 K. The above results indicate that the electrical properties of Bi2−x Agx S3 can be increased by doping Ag, and have an optimal doping concentration at x = 0.01. Fig. 7(a) shows the temperature dependence of thermal conductivity for Bi2−x Agx S3 (x = 0–0.03) bulks sintered at 673 K. The thermal conductivity of the samples Bi2−x Agx S3 (x = 0–0.015) decreases with increasing temperatures, which suggests the dominant mechanism of the phonon scattering. The thermal conductivity of the sample Bi2 S3 increases from 0.54 W mK−1 to 0.69 W mK−1 in the whole measuring temperature ranges from 327 to 573 K. The values are lower than 0.84–0.88 W mK−1 of the sample with the same composition Bi2 S3 reported by Zhao et al. [9], whose sample had a larger average grain size (400 nm) than that (200 nm in Fig. 6(a)) of the present sample Bi2 S3 . The total thermal conductivity is the sum of lattice and carrier contributions in which they were estimated according to the Wiedemann–Franz law as follows:
= lattice + carrier
(4)
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Fig. 8. Temperature dependences of merit ZT for the different Bi2−x Agx S3 (x = 0–0.03) alloys.
Fig. 7. Temperature dependences of thermal conductivity (a), the ratios of carrier / (b) and lattice / (c) for the different Bi2−x Agx S3 (x = 0–0.03) alloys.
carrier = LT
(5)
where lattice , carrier and L are the lattice thermal conductivity, carrier thermal conductivity and the Lorenz number, respectively. The Lorenz number was calculated as the fellow equation [18,19]: L=
k 2 3F ()F () − 4F 2 () 0 2 B 1 e
F0 ()
(6)
where the kB , e, Fr , and are the Boltzmann constant, unit charge, Fermi integration of order r, and reduced Fermi energy which is obtained from the Seebeck coefficient value according to the fellow equation [18,19]: ˛=
kB e
2F1 () − F0 ()
factors on the thermal conductivity, the relative ratios of the carrier and lattice to total are shown in Fig. 7(b) and (c), respectively. The ratio of carrier / for all samples in Fig. 7(b) increases with increasing temperature, which might be attributed to an ambipolar contribution arising from the diffusion of electron–hole pairs with the onset of intrinsic contribution [20]. The temperature dependence of the carrier / ratio increases firstly and then decreases with increasing Ag content, whose trend is similar to that of the electrical conductivity (Fig. 6(a)). Nevertheless, it is noticed that even the highest proportion of the carrier to is not excess 2.75% for the Bi1.99 Ag0.01 S3 sample at 523 K. It is concluded that the total should be strongly relative to the variation of lattice as shown in Fig. 7(c). The lattice for all samples decreases with increasing temperature, which is ascribed to the strong phonon scattering. The proportion of the lattice to for Ag-free Bi2 S3 is nearly 100% at 273 K and downs to about 99.7% at 573 K. Increasing Ag doping content leads to the initial decrease and later increase in the lattice / ratio, while a minimum value attained at x = 0.01. This trend is well agreement with that of the Seebeck coefficient (˛) (Fig. 6(b)). Compared with the lattice thermal conductivity at room temperature for the optimized n-type Bi2 (Se, Te)3 polycrystalline materials (0.7 W mK−1 ) [21], we note that the majority of the total thermal conductivity for all the Ag-doped samples which varies between 0.48 and 0.73 W mK−1 are still lower than this value. Such surprising low thermal conductivity of the Bi2−x Agx S3 bulks indicates their great potentials to satisfy one of the key requirements for a useful TE material at least from the perspective of thermal transport. Fig. 8 shows the temperature dependence of the dimension less figure of merit, ZT, for the different Bi2−x Agx S3 (x = 0–0.03) alloys. All samples show an enhanced ZT values with raising measuring temperature which owing to the increased powder factor (Fig. 6(c)) and decreased thermal conductivity (Fig. 7(a)). Doping Ag to 0.01 mol leads to initial increase in the ZT values but decrease in ones by further increasing Ag over 0.01 mol. The enhanced ZT value is mainly ascribed to the improved electrical transport properties (Fig. 6) and the decreased lattice thermal conductivity (lattice ) (Fig. 7(c)) since the contribution of the carrier thermal conductivity (carrier ) is quite weak (Fig. 7(c)). The maximum ZT value reaches about 0.25 for the sample Bi1.99 Ag0.01 S3 at 573 K, which is about 178% higher than that of Bi2 S3 (0.09) at the same temperature and is also the largest value in Bi2 S3 system in literature reported so far.
(7)
By inserting into Eq. (6), L values were calculated to be in the range from 1.68 × 10−8 to 1.76 × 10−8 V2 K−2 , which were used to estimate carrier thermal conductivity. In order to discuss the effect
4. Conclusions Bi2−x Agx S3 polycrystals with a single orthorhombic phase were synthesized by MA and SPS technique. The electrical
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conductivity increases firstly and then decreases with increasing Ag content, which shows a maximum value 2.8 × 103 S m−1 at 523 K as x = 0.01. The absolute value of Seebeck coefficient shows an opposite trend, whereby the power factor is enhanced from 91 W mK−2 for Bi2 S3 to 235 W mK−2 for Bi1.99 Ag0.01 S3 . The thermal conductivity of Bi2−x Agx S3 ranges from 0.48 to 0.73 W mK−1 . An enhanced maximum ZT value of 0.25 was achieved at 573 K for the Bi1.99 Ag0.01 S3 sample, which is the highest value in the Bi2 S3 system reported so far. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 50972012), High-Tech 863 Program of China (Grant No. 2009AA03Z216), and National Basic Research Program of China (Grant No. 2007CB607500). References [1] D.M. Rowe, Thermoelectrics Handbook: Macro to Nano, CRC Press, Boca Raton, 2006. [2] T.M. Tritt, Science 283 (1999) 804.
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