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Highly enhanced thermoelectric properties of Cu1.8S by introducing PbS
Journal of Alloys and Compounds 764 (2018) 738e744
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Highly enhanced thermoelectric properties of Cu1.8S by introducing PbS Yi-Xin Zhang a, Zheng Ma b, Zhen-Hua Ge a, *, Peng Qin a, Fengshan Zheng b, Jing Feng a a b
Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming, 650093, China Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2018 Received in revised form 15 May 2018 Accepted 11 June 2018 Available online 14 June 2018
Digenite (Cu1.8S) has attracted extensive attention as candidate for use in thermoelectric applications due to its low-cost, low-toxicity characteristics, but the thermoelectric (TE) property is still not good. In this work, PbS was used for improving TE properties of polycrystalline Cu1.8S bulk. Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were fabricated via mechanical alloying (MA) and spark plasma sintering (SPS) techniques. The effects of adding PbS on the TE performance of Cu1.8S were investigated in detail at the temperature between 323 K and 773 K. According to the results, introducing PbS is an efficient approach for optimizing the TE properties of Cu1.8S, which is mainly due to the maintained electrical transport properties by the regulated hole carrier concentration and the modified band structure, as well as the reduced the thermal conductivity by the generated point defect and additional interfaces. An optimum thermoelectric figure of merit (ZT) value of 1.1 was obtained at 773 K for the Cu1.8S sample with 2 wt% PbS, which is 2.2 times higher than that of the pristine Cu1.8S (0.49 at 773 K). © 2018 Elsevier B.V. All rights reserved.
Keywords: Cu1.8S Thermoelectric PbS
1. Introduction Solid-state thermoelectric (TE) technology, capable of converting waste heat source to electrical energy by exploiting a temperature difference to excite inherent charge carrier to flow in a TE material like semiconductor, is looking forward to playing a key role in global energy efficiency and waste-heat recovery [1e5]. While the conversion efficiency is governed by the dimensionless thermoelectric figure of merit ZT ¼ S2sT/(ke þ kl), where S, s, ke, kl, T are the Seebeck coefficient, electrical conductivity, electrical thermal conductivity, lattice thermal conductivity and absolute temperature, respectively [6]. Whereby, a combination of high S with high s and low k is desired to acquire the optimal thermoelectric properties. Nevertheless, it's hard to optimize these properties individually due to the strong coupling of them [7]. Commonly, the most direct and effective approach is reducing lattice thermal conductivity kl by creating scattering source like point defects through substitutional or interstitial atoms [8,9], boundaries from impurities [10,11], nanopores [12,13], dislocations [14] and nanostructuring [15e17] etc., to scatter phonons. On the other side, in an
* Corresponding author. E-mail address: [email protected] (Z.-H. Ge). https://doi.org/10.1016/j.jallcom.2018.06.116 0925-8388/© 2018 Elsevier B.V. All rights reserved.
attempt to raise the power factor of TE materials, lots of efforts have been put to enhance Seebeck coefficient (i.e. increasing electronic effective mass m*) either through nanostructuring [7,18] or densityof-states adjustment [19,20], while these methods would reduce carrier mobility significantly in the meantime [7]. Copper sulfides, particularly for digenite, Cu2-xS (0＜x＜1), which appeared as the potential candidates for TE materials due to their advantages: Low cost, earth abundant, less toxicity of constituent elements [21,22]. Although lots of intermediate phases have been investigated such as Cu2S (chalcocite, Ch), Cu1.96S (djurleite; Dj), Cu1.8S (digenite; Dg), and Cu1.4S (anilite; An) [23]. Cu1.8S has been proved to be the most potential TE material and attracts lots of attention due to its chemical stability and ultrahigh electrical conductivity (>3000 Scm1) [33]. The crystal structure of Cu1.8S beyond phase transition temperature (>361 K) ought to be the face centered cubic lattice composed of S atoms, which is similar to Cu2S crystal, but with the exception that only 9/10 of the lattice sites are occupied by copper atoms [24,25]. Cu1.8S is a type of superionic conductor due to the high mobility of the Cu ions, which has often been used as a conductive fiber [26]. However, high thermal conductivity and low Seebeck coefficient of Cu1.8S restrain its application. In order to solve this problem, the TE properties of compositions lying on the Sn0.01Cu1.79S has been investigated recently, utilizing the second phase and nanopores to scatter
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phonons, ZT value of it was reached to 0.81 [27]. This motivated us to focus our investigations on Cu1.8S-based systems and use some of new concepts to optimize power factor and to reduce thermal conductivity for acquiring a higher ZT. Lead sulfide (PbS) has been confirmed to be an ideal candidate for widespread application of affordable and efficient TE material system due to high performance in both p-type (ZT~1.1 at 923 K) [28] and n-type (ZT~1.1 at 923 K) [29] have been achieved. PbS shares many characteristics with PbSe and PbTe (i.e. crystal structure and energy band configuration) [30]. The electronic effective mass of the conduction band at room temperature is slightly higher in PbS than in PbTe, and the room temperature band gap of 0.43 eV for PbS has been reported [16]. Zhao et al. has proved that valence band alignment can be achieved with appropriate CdS and PbS could suppress carrier scattering in p-type PbS by reducing hole transport obstacle at the common boundary, the ZT value could be further enhanced to ~ 1.3 at 923 K [31]. The above-mentioned approaches prompted us to investigate the TE properties of Cu1.8S embedded with other metal sulfides, especially those with narrow band gaps. In this work, it is shown that the significant improvements in ZT could be achieved in p-type Cu1.8S materials. Pb as a large and heavy atom was introduced to the Cu1.8S by adding PbS for trying to create point defect as scattering source to diminish thermal conduction and for tuning hole carrier concentration to enhance Seebeck coefficient. To prove the effectivity of this method, PbS compound was selected as Pb-source into Cu1.8S, and the TE properties of which would be investigated. The results confirm that PbS has indeed greatly positive contribution to optimize TE performance of Cu1.8S especially through the obvious reduction of thermal conductivity by producing multiscale scattering centers. 2. Experimental section Commercial high purity powders were used as raw materials in this study: 99.99% Cu (under 200 mesh), 99.95% S (under 200 mesh) and 99.9% PbS (under 200 mesh). Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were prepared as follows: The powders were weighted by the atomic ratio of Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) and subjected to MA in a planetary ball mill (QM-4F, Nanjing University, China), respectively, continuing 3 h under 425 rpm in protective gases with high-purity nitrogen (95%) and hydrogen (5%). With the weight ratio of ball to powder was kept at 20:1, using the stainless-steel vessels and balls. The MAed powders were sintered at 723 K for 5 min in a 420 mm graphite mold under axial
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compressive stress 50 MPa in vacuum using a SPS system (Sumitomo SPS1050, Japan). The sintered specimens were disk-shaped with dimensions of 15 mm 4 mm, which were cut into bars with dimensions appropriate 12 mm 3 mm 3 mm that were polished and used for simultaneous measurement. The Seebeck coefficient and the electrical conductivity were measured by using a Seebeck coefficient/ electrical resistance measuring system (ZEM-3 Ulvac-Riko, Japan) under a helium atmosphere from 323 to 773 K. The uncertainty of the Seebeck coefficient and electrical conductivity measurements is 3%. The Hall coefficients (RH), carrier concentration (n), and carrier mobility (m) of the samples were measured at 300 K with an applied magnetic field of 0.545 T and an electrical current of 1 mA using a Hall effect measurement system (Ecopia, HMS-7000, Korea), the surface roughness and dimensions of bulk are strictly required (diameter about 6 mm with 0.5 mm thickness) for ensuring these values of the error is below 5%. Besides, the obtained SPSed specimens were cut and polished into coins of 4 z 6 mm and about 1e2 mm thickness, which were then coated graphite for thermal diffusivity measurements. The thermal diffusivity (D) was measured by laser flash method (NETZSCH, LFA457, Germany), and the specific heat capacity (Cp) was measured with both thermal analysis-based (STA449, Netzsch, Germany) in the range 323e773 K, while the density of the samples was measured by the Archimedes method. The total thermal conductivity (k) of the samples was calculated by the relationship k ¼ DCpr. The combined uncertainty for all thermal properties measurements involved in the calculation of ZT is around 10e15%. Phase identification of the bulk samples was analyzed by X-ray diffraction (XRD Bruker D8, Germany) using Cu Ka radiation (l ¼ 1.5406 Å) in the range of the diffraction angle of 2-theta during 20e60 . The fractured morphologies of the SPSed bulk samples were observed by scanning electron microscopy (SEM, JSM-6460, Japan), while the high angle annular dark fields (HAADF) were obtained by scanning transmission electron microscopy (STEM), and an energy dispersive X-ray spectrometer (EDS) to observe the composition and distribution of the elements. 3. Results and discussion The XRD patterns of Cu1.8S bulk samples with/without PbS addition are shown in Fig. 1(a and b). All the major diffraction peaks of the samples are well-matched to those of the hexagonal Cu1.8S phase (R-3m, PDF#23-0962). While the extra diffraction peaks belonged to cubic PbS phase (Fm-3m, PDF#01-0880) are appeared
Fig. 1. XRD patterns of the SPS-treated Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples (a), XRD patterns of 2q range from 44 to 47 (b), and the lattice parameters of Cu1.8S with different PbS content (c).
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in the sample with 3 wt% PbS. It is shown that the 2q angle of the (1 1 0) peak shifts to the lower angle after introducing PbS, indicative of the enlargement of the matrix lattice. According to the lattice parameters calculated by XRD (Fig. 1 (c)), the a value raises with increasing PbS content, this trend follows well with the solid line (Vegard's law), indicating that Pb has indeed entered into the matrix lattice. Herein, two equations related to the PbS doping are presented as follows: Cu1:8 S
xPb !xPb$Cu þ SS þ ð1:8 xÞCuCu þ xe0 Cu1:8 S
0 xPb !xPb$$ i þ SS þ 1:8CuCu þ 2xe
(1) (2)
Eq. (1) shows the substitution of Cuþ by Pb2þ, which would enlarge the lattice due to the larger ionic radius (r) of 1.19 Å for Pb2þ than 0.77 Å for Cuþ. Besides, the formation of the interstitial solid solution is shown in Eq. (2), generating two electrons when per atom of Pb entered into the interstitial sites in the matrix. Both of two doping mechanisms cause the expansion of lattice due to the large size of Pb2þ. Nevertheless, the varying for the diffraction peaks with increasing PbS content might be explained by the interstitial doping, lots of studies have proved that foreign ions particularly the large one are easier to get into the interstitial sites of Cu1.8S matrix than replacing of Cuþ, such as Ti4þ (0.61 Å) [32], Naþ (1.33 Å) [33] and Bi3þ (1.03 Å) [34]. For Pb2þ (1.19 Å) ion, it ought to enter into the lattice by means of the interstitial doping as well. The lattice parameter for the bulk sample with 3 wt% PbS deviates from the solid solution line, which suggests that the solubility limit of Pb in Cu1.8S matrix is around 2 wt%. The past studies [32e36] have proved that doping elemental substance into Cu1.8S normally caused the production of Cu1.96S and sulfide phases by volatilization of S as: SPS
Cu1:8 S!Cu1:96 S þ 0:089S[ þ 0:089VS€ þ 0:18e0
(3)
Which usually deteriorate the electrical properties due to both decreased hole carrier concentration and carrier mobility in Cu1.8S. This reaction occurred in the PbS-free sample, whereas the diffraction peak has not continued to shift left when adding content
is beyond 2 wt%, since that PbS can be regarded as both lead and sulfur source, thus the volatilization of S has been relieved. SEM micrographs of the fractured Cu1.8S with x wt% PbS bulk samples are shown in Fig. 2, showing a dense microstructure, corresponding to the high relative density (Table 1). Obviously, adding PbS to Cu1.8S might be helpful to maintain densification of samples. Due to S-source from the PbS is introduced into the matrix, which assists to diminish the volatilization of S, resulting in a still high hole carrier mobility for PbS-added Cu1.8S samples (Table 1). To further observe the morphology and crystal structure of the specimen, high angle annular dark field (HAADF) images for Cu1.8S with 2 wt% PbS have been taken into consideration using STEM, showing in Fig. 3. Adding PbS into Cu1.8S materials produced the chain shaped nanopores during synthesis process. And a tiny part of PbS nanoparticle (about 300 nm), which has not involved in doping, were left in the matrix and redistributed along the nanopores interfaces, confirming by the point scan results (Fig. 3(b and c)). The selected area electron diffraction pattern in Fig. 3(d) exhibits the polycrystalline diffraction rings instead of diffraction spots, implying that the significantly refined grain is obtained for PbSadded samples. And the colorful areas in Fig. 3(e) of HRTEM represent neighbor grains own individual crystal orientation, showing the very small average gain size of 10e20 nm. The nano grains would increase grain boundaries, which would be helpful for enhancement of scattering of phonons thus for reducing thermal conductivity. Fig. 4 (a) shows the UVeVis diffuse reflectance spectra of SPStreated Cu1.8S with x wt% PbS content bulk samples. For the crystalline semiconductor, it is well known that the optical absorption near the band edge follows the equation [37]:
ahv ¼ A hv Eg
n=2
(4)
where a is the absorption coefficient, h is the Planck constant, v is the light frequency, A is the proportionality constant and Eg is the band gap, respectively. The constant A is the slope of the tangent while the Eg is the value of the point of intersection with hv axis. The plot (ahv)2 vs hv is capable of estimating the band gap Eg by extrapolating the straightest line to (ahv)2 ¼ 0 [38]. Optical
Fig. 2. SEM patterns of the SPS-treated Cu1.8S with x wt% PbS bulk samples, x ¼ 0.5 (a), x ¼ 1 (b), x ¼ 2 (c), x ¼ 3 (d).
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Table 1 Carrier concentration, carrier mobility and relative density of Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) at room temperature (300 K). Bulk sample Cu1.8S Cu1.8Sþ0.5% Cu1.8Sþ1.0% Cu1.8Sþ2.0% Cu1.8Sþ3.0%
PbS PbS PbS PbS
Measured density (gcm3)
Relative density (%)
Hall carrier concentration nH (cm3)
Hall carrier mobility mH (cm2/sec)
5.40 5.47 5.44 5.10 4.79
96.4 97.51 96.80 90.43 84.64
4.93 4.49 4.33 4.24 4.16
38.03 37.96 37.78 37.56 36.92
Eþ20 Eþ20 Eþ20 Eþ20 Eþ20
Fig. 3. HAADF images (a-c, e) and diffraction pattern (d) of SPS-treated Cu1.8S with 2 wt% PbS bulk sample, black areas in the enlarged picture are catenarian nanopores, and the diffraction pattern fits well with the crystal structure of Cu1.8S.
Fig. 4. The plot (ahv)2 vs hv of the MA-treated Cu1.8S bulk samples with x wt% PbS (x ¼ 0.5, 1, 2, 3), (a); The schematic drawing shows the effect of doping Pb on band structure character (b).
absorption of SPSed pure Cu1.8S bulk exhibits that the direct band gap of the Cu1.8S is 1.80 eV. Although the calculated value of band gap for Cu1.8S is 1.20 eV, which then seems consistent with an optical gap of 1.7e1.8 eV experimentally [24,39]. The band gaps were estimated as an inverse trend with increasing PbS content, which can be explained by the introduction of the impurity level beyond
the valence band after adding Pb2þ which is similar to Ag in Bi2S3 [38], the Pb2þ 6p electrons might contribute to the density of states (DOS) of Cu and S, leading to the enhancement of total DOS and finally to narrow the Eg, whose schematic representation of the modified band structure is shown in Fig. 4(b). Meanwhile, the intrinsic narrow Eg semiconductor PbS (0.43 eV [31]) is introduced,
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which would be another reason for the variation of band gap. That provides a possibility of tailoring the band gap by doping Pb, an observation which could be utilized in the enhancement of electrical transport properties using adjustment of band gap. This modified band structure should correspond to the enhancement of the carrier mobility [40], which would also optimize the electrical transport. The temperature dependent electrical conductivity (s) among the 323 Ke773 K for SPSed Cu1.8S with x wt% PbS bulk samples are illustrated in Fig. 5 (a). The s values for all samples increased at first and then decreased when beyond around 375 K due to the phase transition of Cu1.8S at 361 K [41]. Cu1.8S material is a p-type semiconductor with the major carrier as a hole. The s value is directly proportional to the carrier mobility (m), carrier concentration (n) and electronic charge (e), by the expression: s ¼ nem. The Hall carrier concentration (nH) and Hall mobility (mH) of all samples at room temperature are shown in Table 1, appearing a decreased trend of nH and mH for the sample with increasing PbS content. Introducing PbS results in the dropped hole carrier concentration due to Pb2þ occupied the interstitial sites, the holes as major carrier may annihilate with the extrinsic electrons deriving from the interstitial doping. On the other side, though the Eg has been narrowed, the mH finally decreased after adding PbS due to the scattering of carriers by the introduced extra phase interfaces and few nanopores boundaries, which also corresponds to the slightly decreased mass density. Furthermore, PbS as dopant makes sulfur content adequate, inhibiting the production of sulfur vacancies derived from Cu1.8S, which is beneficial to maintain the hole carrier concentration. Thus the s values only decreased slightly for Cu1.8S after adding PbS. The Seebeck coefficients of the Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) were checked as a function of carrier concentration at room temperature (300 K). Assuming a parabolic band and an acoustic phonon scattering mechanism, the Pisarenko relation between the Seebeck coefficient and carrier concentration is established in Fig. 5 (d), which gives a good description of the experimental data. The
Seebeck coefficient S and Hall carrier concentration nH for a single parabolic band are given by the relationship [16,29]:
" # kB ð5=2 þ lÞFlþ3=2 S¼ h e ð3=2 þ lÞFlþ1=2
(5)
* 3=2 2m kB T F1=2 nH ¼ 4p h2
(6)
In the above equations, h is the reduced Fermi energy, kB is the Boltzmann constant, m* is the effective mass, h is the Planck constant, e is the electron charge, Fi(h) is the ith order Fermi integral, which could be described as:
Fi ðhÞ ¼
Z∞ 0
xi dx 1 þ expðx hÞ
(7)
The SPB model was calculated using the experimentally measured S, the reduced Fermi level h and Eqs. (5) and (6) by allowing the value of m* to be adjusted for a better description of the carrier concentration data. Fig. 5 (d) illustrates the confirmed assumptions, which is immune to the introduction of PbS, and the estimated m* value get increased from 0.48 to 0.55 m0 with increasing PbS, which all well lie on the theoretically predicted line by the SPB model. The Pb doping via adding PbS might complicate the DOS near the Fermi level thus increase the carrier effective mass and enhance the seebeck coefficient. As shown in Fig. 5 (b), the Seebeck coefficients (S) are positive for all samples, implying that the p-type semi-conductive behavior has not changed after introducing PbS. The S value increased from 14.8 to 100.6 mVK1 for pristine Cu1.8S in the temperature range of 323 Ke773 K. According to the expression: a ¼ g ln n, where g and n are scattering factor and carrier concentration, respectively [35]. The increased S values of the Cu1.8S bulk samples with PbS are ascribed to the decreased major carrier concentration by interstitial doping and to the
Fig. 5. Temperature dependence of electrical conductivity (a), Seebeck coefficient (b), power factor (c), Pisarenko plots at 300 K (d). Seebeck coefficients as a function of carrier concentration. The lines correspond to the theoretically expected curves for the pristine Cu1.8S with m*~xm0 (x ¼ 0.42, 0.48, 0.54, 0.60), thermal conductivity (e), ZT value (f) for Cu1.8S bulk samples with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3).
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enhancement of carrier scattering by introducing complicated interfaces, especially for the sample with 2% PbS, which acquires the highest S value of 105 mVK1 at 773 K. According to the s and a, the calculated power factor (PF ¼ a2 s) for Cu1.8S with different PbS content is displayed in Fig. 5 (c). In this work, the pristine Cu1.8S still possesses the highest PF value of 1237 mWm1K2 at 773 K due to its original ultrahigh electrical conductivity. Nevertheless, it's worth noting that the PF value for the sample with 2 wt% PbS ups to 1198 mWm1K2 at 773 K, and other values of this specimen in the low to mid temperature range are even higher than those of the pristine Cu1.8S, primarily due to the maintained electrical conductivity by modifying band structure as well as the enhanced Seebeck coefficient by tuning hole carrier concentration. And the reduced thermal performance for Cu1.8S by adding PbS is expected as well. For Cu1.8S system TE materials, the vital strategy to improve TE properties is to reduce k value through introducing scattering centers. In thermoelectric materials, dopants not only supply carriers to optimize the power factor, but also induce point defect to scatter short-wavelength phonons to suppress lattice thermal conductivity (klat) [8]. Besides, adding foreign nanoparticles into materials would introduce extra phase interfaces then scatter longwavelength phonons to reduce klat. Thus the thermal properties for PbS-added Cu1.8S samples were studied, the total thermal conductivity and ZT value as the function of temperature are shown in Fig. 5 (e and f). The k value was calculated by k ¼ DCp r, where D, Cp, r are the thermal diffusivity (Fig. 5 (d)), heat capacity and mass density, respectively. Obviously, the k values decreased monotonically with the increased PbS, and the Cu1.8S with 2% PbS bulk sample exhibits the lowest measured k values compared to others, which is from 0.8 to 2.2 Wm1K1 in the entire measurement temperature, significantly lower than that of the pristine SPSed Cu1.8S bulk sample. The k value usually is the sum of the electronic thermal conductivity (kele) and the lattice part (klat). For the most thermoelectric materials, the electronic part (kele) is proportional to the electrical conductivity (s) through the WiedemannFranz relation, kele ¼ LsT, where L is the Lorenz number. However, this relation has been proved to be unsuitable for Cu1.8S system superionic conductor, which might due to the different thermal transport properties between electron/hole carriers and ion carrier [33,34]. The ultralow k value of the Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples can be simply understood by the introduced multiscale scattering centers: 1) although the doping content is little, the Pb2þ that entered into the matrix strongly distorted the lattice and scattered short-wavelength phonons; 2) a part of PbS nanoparticles has indeed existed in the matrix, and the nanopores were also produced by introducing PbS, these extra interfaces would effectively scatter long-wavelength phonons. When Pb2þ occupies the interstitial sites, the huge mass (Pb2þ: 207, Cuþ: 64) and the size (Pb2þ: 1.19 Å, Cuþ: 0.73 Å) differences cause a strong mass fluctuation scattering, and the scattering factor A could be expressed as follow [42,43]:
A¼
V0 DM 2 xð1 xÞ M 4pv2
(8)
where the V0, v, x, DM and M are unit cell volume, phonon speed, doping fraction, difference of atomic mass between guest atom and host atom, average mass of cells, respectively. The A value is the factor multiplying the Rayleigh term for point-defect scattering in the relaxation time of the Debye-Callaway expression for the thermal conductivity. According to this equation, the Pb2þ got into the matrix results in a strong interatomic coupling force, which diminished uniformity of the lattice structure or even distorted it.
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Hence the scattering of phonons would be more strongly strengthened by comparison of other light dopants due to the intense mass and strain fluctuations. And the klat should decrease with greater PbS contents. Moreover, adding PbS also brought extra phase interfaces and nanopores boundaries, which would contribute to the reduction of klat by scattering long-wavelength phonons at low temperature. It's noteworthy that the thermal conductivity for the specimens undergoes a hump or a fluctuation with increasing temperature after the phase transition, this phenomenon also appears in other copper sulfides [22,33e35]. Nevertheless, there are few clear discussions to explain the reason. The mechanism of the thermal conductivity variation for Cu1.8S specimen is still an open question or a pending issue. But two possible explanations are proposed as follows: heat transport is very sensitive to the exact configuration of Cu ions, thus when the measuring temperature increases beyond the phase transition temperature, a low temperature hexagonal phase changes to a high temperature cubic phase, thermal conductivity for Cu1.8S often goes through a fluctuation. On the other side, nanopores generated after introducing PbS. The average velocity of gas molecules increases with the temperature increased, which would dominant the heat transport though the mean free path decreases. Because of the existence of pores, the thermal conductivity might increase temporarily with increasing temperature. The reduced thermal conductivity for the Cu1.8S with PbS samples are much helpful for optimizing ZT value, which is observed in Fig. 5 (f). Eventually, the peak ZT value of 1.1 was obtained in the Cu1.8S with 2 wt% PbS bulk sample at 773 K. This result indicates that PbS as lead source into Cu1.8S has optimized the electrical transport properties as well as significantly diminished the thermal conduction, which is an efficient method in enhancing TE performance for Cu1.8S. It is expected to further optimize TE properties of Cu1.8S compounds through other heavy atoms doping and band engineering to adjust Cu vacancies concentration in superionic conductor as well as including other strategies like nanostructuring and/or structure designing. 4. Conclusions Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were fabricated through mechanical alloying (MA) and spark plasma sintering (SPS) techniques by using PbS as the additive. The results in this study indicate that adding PbS contributes greatly in enhancing TE properties of Cu1.8S. Lead was introduced in Cu1.8S by adding PbS for tuning carrier concentration to improve Seebeck coefficient and modifying band structure to maintain the electrical properties as well as for causing lattice distortion to reduce thermal conductivity, both effects seems reflected in this study. Besides, the refinement of grains and produced nanopores after introducing PbS create additional phase interfaces and pores boundaries, which obviously suppress the lattice thermal conductivity for the samples. A peak ZT value reaches to 1.1 at 773 K for the Cu1.8S bulk sample with 2 wt% PbS, which is 2.2 times higher than that of the pure Cu1.8S sample (0.49 at 773 K). Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51501086 and 11764025). References [1] M.G. Kanatzidis, Nanostructured thermoelectrics: the new paradigm? Chem. Mater. 22 (2010) 648e659.
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Highly enhanced thermoelectric properties of Cu1.8S by introducing PbS Yi-Xin Zhang a, Zheng Ma b, Zhen-Hua Ge a, *, Peng Qin a, Fengshan Zheng b, Jing Feng a a b
Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming, 650093, China Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 March 2018 Received in revised form 15 May 2018 Accepted 11 June 2018 Available online 14 June 2018
Digenite (Cu1.8S) has attracted extensive attention as candidate for use in thermoelectric applications due to its low-cost, low-toxicity characteristics, but the thermoelectric (TE) property is still not good. In this work, PbS was used for improving TE properties of polycrystalline Cu1.8S bulk. Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were fabricated via mechanical alloying (MA) and spark plasma sintering (SPS) techniques. The effects of adding PbS on the TE performance of Cu1.8S were investigated in detail at the temperature between 323 K and 773 K. According to the results, introducing PbS is an efficient approach for optimizing the TE properties of Cu1.8S, which is mainly due to the maintained electrical transport properties by the regulated hole carrier concentration and the modified band structure, as well as the reduced the thermal conductivity by the generated point defect and additional interfaces. An optimum thermoelectric figure of merit (ZT) value of 1.1 was obtained at 773 K for the Cu1.8S sample with 2 wt% PbS, which is 2.2 times higher than that of the pristine Cu1.8S (0.49 at 773 K). © 2018 Elsevier B.V. All rights reserved.
Keywords: Cu1.8S Thermoelectric PbS
1. Introduction Solid-state thermoelectric (TE) technology, capable of converting waste heat source to electrical energy by exploiting a temperature difference to excite inherent charge carrier to flow in a TE material like semiconductor, is looking forward to playing a key role in global energy efficiency and waste-heat recovery [1e5]. While the conversion efficiency is governed by the dimensionless thermoelectric figure of merit ZT ¼ S2sT/(ke þ kl), where S, s, ke, kl, T are the Seebeck coefficient, electrical conductivity, electrical thermal conductivity, lattice thermal conductivity and absolute temperature, respectively [6]. Whereby, a combination of high S with high s and low k is desired to acquire the optimal thermoelectric properties. Nevertheless, it's hard to optimize these properties individually due to the strong coupling of them [7]. Commonly, the most direct and effective approach is reducing lattice thermal conductivity kl by creating scattering source like point defects through substitutional or interstitial atoms [8,9], boundaries from impurities [10,11], nanopores [12,13], dislocations [14] and nanostructuring [15e17] etc., to scatter phonons. On the other side, in an
* Corresponding author. E-mail address: [email protected] (Z.-H. Ge). https://doi.org/10.1016/j.jallcom.2018.06.116 0925-8388/© 2018 Elsevier B.V. All rights reserved.
attempt to raise the power factor of TE materials, lots of efforts have been put to enhance Seebeck coefficient (i.e. increasing electronic effective mass m*) either through nanostructuring [7,18] or densityof-states adjustment [19,20], while these methods would reduce carrier mobility significantly in the meantime [7]. Copper sulfides, particularly for digenite, Cu2-xS (0＜x＜1), which appeared as the potential candidates for TE materials due to their advantages: Low cost, earth abundant, less toxicity of constituent elements [21,22]. Although lots of intermediate phases have been investigated such as Cu2S (chalcocite, Ch), Cu1.96S (djurleite; Dj), Cu1.8S (digenite; Dg), and Cu1.4S (anilite; An) [23]. Cu1.8S has been proved to be the most potential TE material and attracts lots of attention due to its chemical stability and ultrahigh electrical conductivity (>3000 Scm1) [33]. The crystal structure of Cu1.8S beyond phase transition temperature (>361 K) ought to be the face centered cubic lattice composed of S atoms, which is similar to Cu2S crystal, but with the exception that only 9/10 of the lattice sites are occupied by copper atoms [24,25]. Cu1.8S is a type of superionic conductor due to the high mobility of the Cu ions, which has often been used as a conductive fiber [26]. However, high thermal conductivity and low Seebeck coefficient of Cu1.8S restrain its application. In order to solve this problem, the TE properties of compositions lying on the Sn0.01Cu1.79S has been investigated recently, utilizing the second phase and nanopores to scatter
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phonons, ZT value of it was reached to 0.81 [27]. This motivated us to focus our investigations on Cu1.8S-based systems and use some of new concepts to optimize power factor and to reduce thermal conductivity for acquiring a higher ZT. Lead sulfide (PbS) has been confirmed to be an ideal candidate for widespread application of affordable and efficient TE material system due to high performance in both p-type (ZT~1.1 at 923 K) [28] and n-type (ZT~1.1 at 923 K) [29] have been achieved. PbS shares many characteristics with PbSe and PbTe (i.e. crystal structure and energy band configuration) [30]. The electronic effective mass of the conduction band at room temperature is slightly higher in PbS than in PbTe, and the room temperature band gap of 0.43 eV for PbS has been reported [16]. Zhao et al. has proved that valence band alignment can be achieved with appropriate CdS and PbS could suppress carrier scattering in p-type PbS by reducing hole transport obstacle at the common boundary, the ZT value could be further enhanced to ~ 1.3 at 923 K [31]. The above-mentioned approaches prompted us to investigate the TE properties of Cu1.8S embedded with other metal sulfides, especially those with narrow band gaps. In this work, it is shown that the significant improvements in ZT could be achieved in p-type Cu1.8S materials. Pb as a large and heavy atom was introduced to the Cu1.8S by adding PbS for trying to create point defect as scattering source to diminish thermal conduction and for tuning hole carrier concentration to enhance Seebeck coefficient. To prove the effectivity of this method, PbS compound was selected as Pb-source into Cu1.8S, and the TE properties of which would be investigated. The results confirm that PbS has indeed greatly positive contribution to optimize TE performance of Cu1.8S especially through the obvious reduction of thermal conductivity by producing multiscale scattering centers. 2. Experimental section Commercial high purity powders were used as raw materials in this study: 99.99% Cu (under 200 mesh), 99.95% S (under 200 mesh) and 99.9% PbS (under 200 mesh). Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were prepared as follows: The powders were weighted by the atomic ratio of Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) and subjected to MA in a planetary ball mill (QM-4F, Nanjing University, China), respectively, continuing 3 h under 425 rpm in protective gases with high-purity nitrogen (95%) and hydrogen (5%). With the weight ratio of ball to powder was kept at 20:1, using the stainless-steel vessels and balls. The MAed powders were sintered at 723 K for 5 min in a 420 mm graphite mold under axial
739
compressive stress 50 MPa in vacuum using a SPS system (Sumitomo SPS1050, Japan). The sintered specimens were disk-shaped with dimensions of 15 mm 4 mm, which were cut into bars with dimensions appropriate 12 mm 3 mm 3 mm that were polished and used for simultaneous measurement. The Seebeck coefficient and the electrical conductivity were measured by using a Seebeck coefficient/ electrical resistance measuring system (ZEM-3 Ulvac-Riko, Japan) under a helium atmosphere from 323 to 773 K. The uncertainty of the Seebeck coefficient and electrical conductivity measurements is 3%. The Hall coefficients (RH), carrier concentration (n), and carrier mobility (m) of the samples were measured at 300 K with an applied magnetic field of 0.545 T and an electrical current of 1 mA using a Hall effect measurement system (Ecopia, HMS-7000, Korea), the surface roughness and dimensions of bulk are strictly required (diameter about 6 mm with 0.5 mm thickness) for ensuring these values of the error is below 5%. Besides, the obtained SPSed specimens were cut and polished into coins of 4 z 6 mm and about 1e2 mm thickness, which were then coated graphite for thermal diffusivity measurements. The thermal diffusivity (D) was measured by laser flash method (NETZSCH, LFA457, Germany), and the specific heat capacity (Cp) was measured with both thermal analysis-based (STA449, Netzsch, Germany) in the range 323e773 K, while the density of the samples was measured by the Archimedes method. The total thermal conductivity (k) of the samples was calculated by the relationship k ¼ DCpr. The combined uncertainty for all thermal properties measurements involved in the calculation of ZT is around 10e15%. Phase identification of the bulk samples was analyzed by X-ray diffraction (XRD Bruker D8, Germany) using Cu Ka radiation (l ¼ 1.5406 Å) in the range of the diffraction angle of 2-theta during 20e60 . The fractured morphologies of the SPSed bulk samples were observed by scanning electron microscopy (SEM, JSM-6460, Japan), while the high angle annular dark fields (HAADF) were obtained by scanning transmission electron microscopy (STEM), and an energy dispersive X-ray spectrometer (EDS) to observe the composition and distribution of the elements. 3. Results and discussion The XRD patterns of Cu1.8S bulk samples with/without PbS addition are shown in Fig. 1(a and b). All the major diffraction peaks of the samples are well-matched to those of the hexagonal Cu1.8S phase (R-3m, PDF#23-0962). While the extra diffraction peaks belonged to cubic PbS phase (Fm-3m, PDF#01-0880) are appeared
Fig. 1. XRD patterns of the SPS-treated Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples (a), XRD patterns of 2q range from 44 to 47 (b), and the lattice parameters of Cu1.8S with different PbS content (c).
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in the sample with 3 wt% PbS. It is shown that the 2q angle of the (1 1 0) peak shifts to the lower angle after introducing PbS, indicative of the enlargement of the matrix lattice. According to the lattice parameters calculated by XRD (Fig. 1 (c)), the a value raises with increasing PbS content, this trend follows well with the solid line (Vegard's law), indicating that Pb has indeed entered into the matrix lattice. Herein, two equations related to the PbS doping are presented as follows: Cu1:8 S
xPb !xPb$Cu þ SS þ ð1:8 xÞCuCu þ xe0 Cu1:8 S
0 xPb !xPb$$ i þ SS þ 1:8CuCu þ 2xe
(1) (2)
Eq. (1) shows the substitution of Cuþ by Pb2þ, which would enlarge the lattice due to the larger ionic radius (r) of 1.19 Å for Pb2þ than 0.77 Å for Cuþ. Besides, the formation of the interstitial solid solution is shown in Eq. (2), generating two electrons when per atom of Pb entered into the interstitial sites in the matrix. Both of two doping mechanisms cause the expansion of lattice due to the large size of Pb2þ. Nevertheless, the varying for the diffraction peaks with increasing PbS content might be explained by the interstitial doping, lots of studies have proved that foreign ions particularly the large one are easier to get into the interstitial sites of Cu1.8S matrix than replacing of Cuþ, such as Ti4þ (0.61 Å) [32], Naþ (1.33 Å) [33] and Bi3þ (1.03 Å) [34]. For Pb2þ (1.19 Å) ion, it ought to enter into the lattice by means of the interstitial doping as well. The lattice parameter for the bulk sample with 3 wt% PbS deviates from the solid solution line, which suggests that the solubility limit of Pb in Cu1.8S matrix is around 2 wt%. The past studies [32e36] have proved that doping elemental substance into Cu1.8S normally caused the production of Cu1.96S and sulfide phases by volatilization of S as: SPS
Cu1:8 S!Cu1:96 S þ 0:089S[ þ 0:089VS€ þ 0:18e0
(3)
Which usually deteriorate the electrical properties due to both decreased hole carrier concentration and carrier mobility in Cu1.8S. This reaction occurred in the PbS-free sample, whereas the diffraction peak has not continued to shift left when adding content
is beyond 2 wt%, since that PbS can be regarded as both lead and sulfur source, thus the volatilization of S has been relieved. SEM micrographs of the fractured Cu1.8S with x wt% PbS bulk samples are shown in Fig. 2, showing a dense microstructure, corresponding to the high relative density (Table 1). Obviously, adding PbS to Cu1.8S might be helpful to maintain densification of samples. Due to S-source from the PbS is introduced into the matrix, which assists to diminish the volatilization of S, resulting in a still high hole carrier mobility for PbS-added Cu1.8S samples (Table 1). To further observe the morphology and crystal structure of the specimen, high angle annular dark field (HAADF) images for Cu1.8S with 2 wt% PbS have been taken into consideration using STEM, showing in Fig. 3. Adding PbS into Cu1.8S materials produced the chain shaped nanopores during synthesis process. And a tiny part of PbS nanoparticle (about 300 nm), which has not involved in doping, were left in the matrix and redistributed along the nanopores interfaces, confirming by the point scan results (Fig. 3(b and c)). The selected area electron diffraction pattern in Fig. 3(d) exhibits the polycrystalline diffraction rings instead of diffraction spots, implying that the significantly refined grain is obtained for PbSadded samples. And the colorful areas in Fig. 3(e) of HRTEM represent neighbor grains own individual crystal orientation, showing the very small average gain size of 10e20 nm. The nano grains would increase grain boundaries, which would be helpful for enhancement of scattering of phonons thus for reducing thermal conductivity. Fig. 4 (a) shows the UVeVis diffuse reflectance spectra of SPStreated Cu1.8S with x wt% PbS content bulk samples. For the crystalline semiconductor, it is well known that the optical absorption near the band edge follows the equation [37]:
ahv ¼ A hv Eg
n=2
(4)
where a is the absorption coefficient, h is the Planck constant, v is the light frequency, A is the proportionality constant and Eg is the band gap, respectively. The constant A is the slope of the tangent while the Eg is the value of the point of intersection with hv axis. The plot (ahv)2 vs hv is capable of estimating the band gap Eg by extrapolating the straightest line to (ahv)2 ¼ 0 [38]. Optical
Fig. 2. SEM patterns of the SPS-treated Cu1.8S with x wt% PbS bulk samples, x ¼ 0.5 (a), x ¼ 1 (b), x ¼ 2 (c), x ¼ 3 (d).
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Table 1 Carrier concentration, carrier mobility and relative density of Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) at room temperature (300 K). Bulk sample Cu1.8S Cu1.8Sþ0.5% Cu1.8Sþ1.0% Cu1.8Sþ2.0% Cu1.8Sþ3.0%
PbS PbS PbS PbS
Measured density (gcm3)
Relative density (%)
Hall carrier concentration nH (cm3)
Hall carrier mobility mH (cm2/sec)
5.40 5.47 5.44 5.10 4.79
96.4 97.51 96.80 90.43 84.64
4.93 4.49 4.33 4.24 4.16
38.03 37.96 37.78 37.56 36.92
Eþ20 Eþ20 Eþ20 Eþ20 Eþ20
Fig. 3. HAADF images (a-c, e) and diffraction pattern (d) of SPS-treated Cu1.8S with 2 wt% PbS bulk sample, black areas in the enlarged picture are catenarian nanopores, and the diffraction pattern fits well with the crystal structure of Cu1.8S.
Fig. 4. The plot (ahv)2 vs hv of the MA-treated Cu1.8S bulk samples with x wt% PbS (x ¼ 0.5, 1, 2, 3), (a); The schematic drawing shows the effect of doping Pb on band structure character (b).
absorption of SPSed pure Cu1.8S bulk exhibits that the direct band gap of the Cu1.8S is 1.80 eV. Although the calculated value of band gap for Cu1.8S is 1.20 eV, which then seems consistent with an optical gap of 1.7e1.8 eV experimentally [24,39]. The band gaps were estimated as an inverse trend with increasing PbS content, which can be explained by the introduction of the impurity level beyond
the valence band after adding Pb2þ which is similar to Ag in Bi2S3 [38], the Pb2þ 6p electrons might contribute to the density of states (DOS) of Cu and S, leading to the enhancement of total DOS and finally to narrow the Eg, whose schematic representation of the modified band structure is shown in Fig. 4(b). Meanwhile, the intrinsic narrow Eg semiconductor PbS (0.43 eV [31]) is introduced,
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which would be another reason for the variation of band gap. That provides a possibility of tailoring the band gap by doping Pb, an observation which could be utilized in the enhancement of electrical transport properties using adjustment of band gap. This modified band structure should correspond to the enhancement of the carrier mobility [40], which would also optimize the electrical transport. The temperature dependent electrical conductivity (s) among the 323 Ke773 K for SPSed Cu1.8S with x wt% PbS bulk samples are illustrated in Fig. 5 (a). The s values for all samples increased at first and then decreased when beyond around 375 K due to the phase transition of Cu1.8S at 361 K [41]. Cu1.8S material is a p-type semiconductor with the major carrier as a hole. The s value is directly proportional to the carrier mobility (m), carrier concentration (n) and electronic charge (e), by the expression: s ¼ nem. The Hall carrier concentration (nH) and Hall mobility (mH) of all samples at room temperature are shown in Table 1, appearing a decreased trend of nH and mH for the sample with increasing PbS content. Introducing PbS results in the dropped hole carrier concentration due to Pb2þ occupied the interstitial sites, the holes as major carrier may annihilate with the extrinsic electrons deriving from the interstitial doping. On the other side, though the Eg has been narrowed, the mH finally decreased after adding PbS due to the scattering of carriers by the introduced extra phase interfaces and few nanopores boundaries, which also corresponds to the slightly decreased mass density. Furthermore, PbS as dopant makes sulfur content adequate, inhibiting the production of sulfur vacancies derived from Cu1.8S, which is beneficial to maintain the hole carrier concentration. Thus the s values only decreased slightly for Cu1.8S after adding PbS. The Seebeck coefficients of the Cu1.8S with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) were checked as a function of carrier concentration at room temperature (300 K). Assuming a parabolic band and an acoustic phonon scattering mechanism, the Pisarenko relation between the Seebeck coefficient and carrier concentration is established in Fig. 5 (d), which gives a good description of the experimental data. The
Seebeck coefficient S and Hall carrier concentration nH for a single parabolic band are given by the relationship [16,29]:
" # kB ð5=2 þ lÞFlþ3=2 S¼ h e ð3=2 þ lÞFlþ1=2
(5)
* 3=2 2m kB T F1=2 nH ¼ 4p h2
(6)
In the above equations, h is the reduced Fermi energy, kB is the Boltzmann constant, m* is the effective mass, h is the Planck constant, e is the electron charge, Fi(h) is the ith order Fermi integral, which could be described as:
Fi ðhÞ ¼
Z∞ 0
xi dx 1 þ expðx hÞ
(7)
The SPB model was calculated using the experimentally measured S, the reduced Fermi level h and Eqs. (5) and (6) by allowing the value of m* to be adjusted for a better description of the carrier concentration data. Fig. 5 (d) illustrates the confirmed assumptions, which is immune to the introduction of PbS, and the estimated m* value get increased from 0.48 to 0.55 m0 with increasing PbS, which all well lie on the theoretically predicted line by the SPB model. The Pb doping via adding PbS might complicate the DOS near the Fermi level thus increase the carrier effective mass and enhance the seebeck coefficient. As shown in Fig. 5 (b), the Seebeck coefficients (S) are positive for all samples, implying that the p-type semi-conductive behavior has not changed after introducing PbS. The S value increased from 14.8 to 100.6 mVK1 for pristine Cu1.8S in the temperature range of 323 Ke773 K. According to the expression: a ¼ g ln n, where g and n are scattering factor and carrier concentration, respectively [35]. The increased S values of the Cu1.8S bulk samples with PbS are ascribed to the decreased major carrier concentration by interstitial doping and to the
Fig. 5. Temperature dependence of electrical conductivity (a), Seebeck coefficient (b), power factor (c), Pisarenko plots at 300 K (d). Seebeck coefficients as a function of carrier concentration. The lines correspond to the theoretically expected curves for the pristine Cu1.8S with m*~xm0 (x ¼ 0.42, 0.48, 0.54, 0.60), thermal conductivity (e), ZT value (f) for Cu1.8S bulk samples with x wt% PbS (x ¼ 0, 0.5, 1, 2, 3).
Y.-X. Zhang et al. / Journal of Alloys and Compounds 764 (2018) 738e744
enhancement of carrier scattering by introducing complicated interfaces, especially for the sample with 2% PbS, which acquires the highest S value of 105 mVK1 at 773 K. According to the s and a, the calculated power factor (PF ¼ a2 s) for Cu1.8S with different PbS content is displayed in Fig. 5 (c). In this work, the pristine Cu1.8S still possesses the highest PF value of 1237 mWm1K2 at 773 K due to its original ultrahigh electrical conductivity. Nevertheless, it's worth noting that the PF value for the sample with 2 wt% PbS ups to 1198 mWm1K2 at 773 K, and other values of this specimen in the low to mid temperature range are even higher than those of the pristine Cu1.8S, primarily due to the maintained electrical conductivity by modifying band structure as well as the enhanced Seebeck coefficient by tuning hole carrier concentration. And the reduced thermal performance for Cu1.8S by adding PbS is expected as well. For Cu1.8S system TE materials, the vital strategy to improve TE properties is to reduce k value through introducing scattering centers. In thermoelectric materials, dopants not only supply carriers to optimize the power factor, but also induce point defect to scatter short-wavelength phonons to suppress lattice thermal conductivity (klat) [8]. Besides, adding foreign nanoparticles into materials would introduce extra phase interfaces then scatter longwavelength phonons to reduce klat. Thus the thermal properties for PbS-added Cu1.8S samples were studied, the total thermal conductivity and ZT value as the function of temperature are shown in Fig. 5 (e and f). The k value was calculated by k ¼ DCp r, where D, Cp, r are the thermal diffusivity (Fig. 5 (d)), heat capacity and mass density, respectively. Obviously, the k values decreased monotonically with the increased PbS, and the Cu1.8S with 2% PbS bulk sample exhibits the lowest measured k values compared to others, which is from 0.8 to 2.2 Wm1K1 in the entire measurement temperature, significantly lower than that of the pristine SPSed Cu1.8S bulk sample. The k value usually is the sum of the electronic thermal conductivity (kele) and the lattice part (klat). For the most thermoelectric materials, the electronic part (kele) is proportional to the electrical conductivity (s) through the WiedemannFranz relation, kele ¼ LsT, where L is the Lorenz number. However, this relation has been proved to be unsuitable for Cu1.8S system superionic conductor, which might due to the different thermal transport properties between electron/hole carriers and ion carrier [33,34]. The ultralow k value of the Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples can be simply understood by the introduced multiscale scattering centers: 1) although the doping content is little, the Pb2þ that entered into the matrix strongly distorted the lattice and scattered short-wavelength phonons; 2) a part of PbS nanoparticles has indeed existed in the matrix, and the nanopores were also produced by introducing PbS, these extra interfaces would effectively scatter long-wavelength phonons. When Pb2þ occupies the interstitial sites, the huge mass (Pb2þ: 207, Cuþ: 64) and the size (Pb2þ: 1.19 Å, Cuþ: 0.73 Å) differences cause a strong mass fluctuation scattering, and the scattering factor A could be expressed as follow [42,43]:
A¼
V0 DM 2 xð1 xÞ M 4pv2
(8)
where the V0, v, x, DM and M are unit cell volume, phonon speed, doping fraction, difference of atomic mass between guest atom and host atom, average mass of cells, respectively. The A value is the factor multiplying the Rayleigh term for point-defect scattering in the relaxation time of the Debye-Callaway expression for the thermal conductivity. According to this equation, the Pb2þ got into the matrix results in a strong interatomic coupling force, which diminished uniformity of the lattice structure or even distorted it.
743
Hence the scattering of phonons would be more strongly strengthened by comparison of other light dopants due to the intense mass and strain fluctuations. And the klat should decrease with greater PbS contents. Moreover, adding PbS also brought extra phase interfaces and nanopores boundaries, which would contribute to the reduction of klat by scattering long-wavelength phonons at low temperature. It's noteworthy that the thermal conductivity for the specimens undergoes a hump or a fluctuation with increasing temperature after the phase transition, this phenomenon also appears in other copper sulfides [22,33e35]. Nevertheless, there are few clear discussions to explain the reason. The mechanism of the thermal conductivity variation for Cu1.8S specimen is still an open question or a pending issue. But two possible explanations are proposed as follows: heat transport is very sensitive to the exact configuration of Cu ions, thus when the measuring temperature increases beyond the phase transition temperature, a low temperature hexagonal phase changes to a high temperature cubic phase, thermal conductivity for Cu1.8S often goes through a fluctuation. On the other side, nanopores generated after introducing PbS. The average velocity of gas molecules increases with the temperature increased, which would dominant the heat transport though the mean free path decreases. Because of the existence of pores, the thermal conductivity might increase temporarily with increasing temperature. The reduced thermal conductivity for the Cu1.8S with PbS samples are much helpful for optimizing ZT value, which is observed in Fig. 5 (f). Eventually, the peak ZT value of 1.1 was obtained in the Cu1.8S with 2 wt% PbS bulk sample at 773 K. This result indicates that PbS as lead source into Cu1.8S has optimized the electrical transport properties as well as significantly diminished the thermal conduction, which is an efficient method in enhancing TE performance for Cu1.8S. It is expected to further optimize TE properties of Cu1.8S compounds through other heavy atoms doping and band engineering to adjust Cu vacancies concentration in superionic conductor as well as including other strategies like nanostructuring and/or structure designing. 4. Conclusions Cu1.8Sþ x wt% PbS (x ¼ 0, 0.5, 1, 2, 3) bulk samples were fabricated through mechanical alloying (MA) and spark plasma sintering (SPS) techniques by using PbS as the additive. The results in this study indicate that adding PbS contributes greatly in enhancing TE properties of Cu1.8S. Lead was introduced in Cu1.8S by adding PbS for tuning carrier concentration to improve Seebeck coefficient and modifying band structure to maintain the electrical properties as well as for causing lattice distortion to reduce thermal conductivity, both effects seems reflected in this study. Besides, the refinement of grains and produced nanopores after introducing PbS create additional phase interfaces and pores boundaries, which obviously suppress the lattice thermal conductivity for the samples. A peak ZT value reaches to 1.1 at 773 K for the Cu1.8S bulk sample with 2 wt% PbS, which is 2.2 times higher than that of the pure Cu1.8S sample (0.49 at 773 K). Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51501086 and 11764025). References [1] M.G. Kanatzidis, Nanostructured thermoelectrics: the new paradigm? Chem. Mater. 22 (2010) 648e659.
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