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Thermoelectric properties of Spark plasma sintered PbTe synthesized
without any surfactant and organic solventMaterials Research
Express
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This content was downloaded from IP address 65.21.228.167 on 08/04/2022 at 07:03
PAPER
Thermoelectric properties of Spark plasma sintered PbTe synthesized without any surfactant and organic solvent
PradeepKumar Sharma1,2, TDSenguttuvan3, VK Sharma2, NKGupta1,M Saravanan3 and Sujeet Chaudhary1,∗
1 Thin Film Laboratory, Department of Physics, Indian Institute of TechnologyDelhi, NewDelhi 110 016, India 2 ShyamLal College, University ofDelhi, Delhi 110 032, India 3 CSIR-National Physical Laboratory, DrK. S. KrishnanMarg, NewDelhi 110 012, India ∗ Author towhomany correspondence should be addressed.
E-mail: [email protected]
Keywords: thermoelectrics, bulk nanostructuredmaterials, lead telluride, hydrothermal synthesis,figure ofmerit
Abstract We report a systematic investigation on structural and thermoelectric properties of Spark plasma sintered Lead telluride synthesized by hydrothermal route and a low temperature aqueous chemical routewithout using any organic solvent and surfactant. The as-synthesized powder samples obtained from these two different synthesis routes were identically subjected to spark plasma sintering. The size of nanocubes formed by the hydrothermalmethod, as evident fromTEM-HRTEM images, is 50 nm; however, the samples synthesized by aqueous chemical route showsmixedmorphologywith particle size<50 nm. The thermoelectric properties of spark plasma sintered bulk nanostructured samples have beenmeasured fromRT to 700K.Notably, large Seebeck coefficient and small electrical resistivity values are observed in the sample synthesized by the hydrothermal route, which is ascribed to the charge carrier energy filtering effect. Amaximum reduction of∼38%and∼58%has been observed in the sample synthesized by the hydrothermal route and aqueous chemical route, respectively, compared to the bulk ingot. Themaximumfigure ofmerit attained is 0.18 at 673K in the lead telluride sample synthesized by the hydrothermal route.
1. Introduction
Thermoelectric energy conversion technology utilizes the Seebeck and Peltier effect for the interconversion between thermal and electrical energy. There has been a renewed interest in thermoelectric technology due to a large interest in harvesting thewaste heat and solid-state refrigeration-based devices [1]. This technique ismore significant in the areas where there is ample quantity of waste heat and is likely to play a crucial part in clean and renewable energy [2]. The conversion efficiency of a thermoelectricmaterial is determined by the dimensionless figure ofmerit zT, which is, in turn, the function of the intrinsicmaterial parameters,
s k
=zT S
Where S,σ, andκ represent the Seebeck coefficient, electrical conductivity, and coefficient of thermal conductivity at the temperatureT [3]. Hence, to boost the thermoelectric performance of amaterial, the Seebeck coefficient and electrical conductivity need to be enhancedwhile simultaneouslymaintaining small values of thermal conductivity. However, the complicated relationship between thesematerial parameters impedes the efforts in obtaining highTE performance and thewidespread use of thermoelectric technology [4]. Nanostructured thermoelectricmaterials are of great interest as they offer a uniqueway to independently tune thesematerial parameters and hence enhance the zT value [5]. Recent advances show that it is possible to improve the zT values in nanostructuredmaterial by reducing the lattice component of thermal conductivity through the intensive scattering of the phonons at grain boundaries/crystal interfaces and enhancing the thermoelectric power factor by carrier energyfiltering and quantum confinement effects [6].
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7 July 2021
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In the present work, we report the synthesis of lead telluride by two different routes, a low-temperature aqueous chemical route and a hydrothermal route without using any organic surfactant or organic precursors, and the thermoelectric properties. The nanoparticles synthesized through both themethods are in sufficiently large quantities and are easily further processed through spark plasma sintering. The present study aims to investigate the outcome of nano-structuration on the thermoelectric properties of PbTe.We have systematically investigated the thermoelectric properties (S,σ andκ) across a broad temperature range 300–700K.One of the main outcomes of this study is that the total thermal conductivity of samples at room temperature synthesized by hydrothermal route and aqueous chemical route, respectively, are∼38%and 58% less than the thermal conductivity of bulk PbTe ingot. Aminimum lattice thermal conductivity of 0.64Wm−1 K−1 at 473K is achieved in the sample synthesized by aqueous chemical routewhich is significantly smaller than the thermal conductivity of bulk PbTe∼1.50 at 450K.
2. Experimental section
Analytically pure lead acetate [Pb(CH3COO)2], Telluriummetal powder (Te), Sodiumborohydride (NaBH4), and sodiumhydroxide (NaOH) have been procured fromSigmaAldrich.
2.1. Preparation of PbTe Aqueous chemical route:Approximately 5 gNaOHpowderwas dissolved in double-distilledwater at 323K. WhenNaOH is completely dissolved, 2 gNaBH4 and 0.01mol Temetal powderwere added to the aqueous NaOH solutionwith constantmagnetic stirring. After the change in the color of the solution to dark purple, 0.01mol lead acetate aqueous solutionwas added to the beaker drop-by-drop. Once the reaction is completed, the beakerwas allowed to cool to room temperature, and the obtained black powderwas filtered out andwashed with distilledwater, acetone, and ethanol. At last, the powder samplewas dried in air ambient for 3 h at 323K.
Hydrothermal synthesis route:The stoichiometric amount of lead acetate and telluriumpowderwere added to a beaker containing an aqueous solution ofNaBH4with constantmagnetic stirring. After some time, 20ml aqueousNaOH solutionwas added to the beaker, and the resulting solutionwas transferred to a Teflon- lined stainless-steel autoclave. Finally, the autoclave wasfilled to 80%of the total capacitywith distilledwater andmaintained at 433K for 14 h in a furnace. After the reactionwas over, the autoclave was cooled to room
Figure 1. Schematic of Synthesis process (a) aqueous chemical route, (b) hydrothermal route. From [18]. Reprintedwith permission fromElsevier.
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temperatures. The obtained black powderwasfiltered out andwashedwith distilledwater, acetone, and ethanol. Lastly, the powder samplewas dried in air ambient for 3 h at 323K, as in the former route.
2.2. Sintering The as-synthesized PbTe nanopowders were loaded in graphite die and consolidated using spark plasma sintering (SPS)using Syntex, Japanmake furnace at a temperature of 773K for 8 min under a pressure of 20MPa.
A schematic of the synthesis process is shown infigure 1.
2.3. Characterization TheXRDmeasurements on as-synthesized Lead telluride samples were performed by employing a diffractometer (Philips Xpert Pro) usingCu-Kα radiation from20° to 80°with a step size of 0.02°. Microstructure of both the as-synthesized samples and the SPS’ed (Spark Plasma Sintered)PbTe samples have been investigated by FESEM (field emission scanning electronmicroscope) (Jeol JSM-7800F) and (EDS) energy dispersive patterns. Themorphology of nanostructured PbTe samples was determined by using TEM (Transmission electronmicroscopy) andHR-TEM (high-resolution transmission electronmicroscopy (JEM 2100F JEOL).
2.4.Measurements The thermoelectric properties of the SPS’ed lead telluride samples have been investigated from room temperature to 700K. The thermal conductivity of the bulk nanostructured samples was calculated using the expression k r= C D,p whereρ, Cp andD are the density, specific heat and thermal diffusivity of the sample, respectively. The density of the samples wasmeasured using Archimedesmethod, and the thermal diffusivity (D) was determined by employing Laser Flash Apparatus ((LFA 1000), LinseisMessgeraete GmbH,GermanyNPL). Specific heat capacity value has been adapted fromdata reported byQuin B et al, (2019) [19]. After the measurement of thermal diffusivity on the samples, rectangular pellets were cut out from the SPS’ed discs for the simultaneousmeasurements of Seebeck coefficient and electrical conductivity by employingULVACZEM3 in a Helium atmosphere.
3. Results and discussions
3.1. Structural analysis TheXRDdiffractograms of the as-synthesized lead telluride samples fromboth the routes have been demonstrated infigure 1, alongwith the Rietveld refinement profiles.
As can be observed from figure 2, all the prominent diffraction peaks can be indexed to the FCCPbTe structure with space group Fm-3m (225) JCPDS#78-1905. There are no diffraction peaks from any impurity in the XRDdiffractogram (See figure 2(b)), confirming that single phase PbTe has been successfully synthesized by using a simple hydrothermal reactionThe intensity of the XRDpeaks observed in the lead telluride sample synthesized by the hydrothermalmethod is relatively higher in contrast to the sample synthesized by aqueous chemical route (Seefigure 2). It indicates that the sample synthesized by the hydrothermal route ismore
Figure 2.X-ray diffractogram andRietveld refinement profiles of the lead telluride prepared by (a) aqueous chemical route, and (b) Hydrothermal routes.
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crystalline in comparison to the sample synthesized by the aqueous chemical route. Further, the sharp peaks indicate that the crystallite size of the lead telluride sample synthesized by hydrothermalmethod is larger in comparison to the sample synthesized by aqueous chemical route which is also consistent with theHR-TEM observations (See figure 3).On the contrary, the sample synthesized by the aqueous chemical precipitation method results in PbTe product having relatively small-sized nanoparticles (broad peaks)with a few additional peaks corresponding to traces of unreacted Te in the sample (See figure 2(a)). Further, two peaks of very low intensity (marked by *) couldn’t be identified as the Braggs position due to both the phase lies very close and hence peaks possibly. The calculated lattice constant using Rietveld refinement for the sample synthesized by hydrothermal route is 0.64556 nmand that synthesized using aqueous chemical route is 0.64590 nm; both values are in close agreement with the literature value (0.64540 nm) [20].
The value of various parameters obtained by the Rietveld refinement has been shown in table 1.
Table 1.The value of various parameters obtained by the Rietveld refinement.
Refined parameters Sample A (Aq)
Sample B (Hy) PbTe Te PbTe
a(nm) 0.64590 0.44546 0.64556
b(nm) 0.64590 0.44546 0.64556
c(nm) 0.64590 0.59229 0.64556
α (°) 90 90 90
β (°) 90 90 90
γ (°) 90 120 90
Rp (%) 21.1 12.2
Rwp (%) 29.9 18.2
Rexp (%) 28.41 16.0
Chi square (χ2) 1.10 1.17
Figure 3.TEM/HR-TEM image of the as- synthesized lead telluride sample by (a), (b) aqueous chemical route, (c), (d) hydrothermal route (inset infigure 3(c) shows the size distribution histogramof lead telluride nanoparticles synthesized using hydrothermal route as calculated using the corresponding TEM image).
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Wehave calculated the crystallite size for the (200) peak using theDebye–Scherrer equation,
l b q
=D K
Cos 2XRD ( )
WhereK,λ,β, and θ are Scherrer constant, wavelength of copper Kα radiation, FWHM (full width of the peak at halfmaximum) andBragg’s angle, respectively. The value of Scherrer constant lies between 0.89 to 0.94. The (200)-diffraction peak yields a crystallite size of 23.5 nm for the sample synthesized by the aqueous chemical route and 29.0 nm for the sample synthesized by the hydrothermal route. It is to be noted that crystallite size is not necessarily the same as that of particle size. Further, the broadening of the XRDpeak can also be due to the internal stress and defects induced during the synthesis process. Hence, the crystallite size as estimated using Scherrer equation is expected to be smaller than the actual value [20]. The calculated crystallite size for both the synthesized samples is far lesser thanBohr’s excitonic radius of lead telluride (∼152 nm) [21]. It is noteworthy that the Seebeck coefficient could be remarkably enhanced in the nanostructured systems due to carrier filtering and quantum confinement effects [22].
3.2.Morphological analysis Figure 3(a) shows the TEM image of as-synthesized lead telluride nanoparticles synthesized by aqueous chemical route. It can be observed from the figure that the nanoparticles exhibitmixedmorphologywith particle size<50 nm (See figure 3(a). TheHR-TEM image of the lead telluride sample synthesized by aqueous chemical route has been depicted infigure 3(b). The clear lattice fringes as evident inHR-TEM image have the interplanar spacing of 0.323 nmand 0.228 nm,which corresponds to (200) and (220) plane of lead telluride. Figure 3(c) presents the TEM image of the lead telluride sample synthesized by hydrothermal route. It is evident from the figure that the as-synthesized nanoparticles have cubicmorphologywith edge length∼50 nm. The inset in figure 3(c) shows the size distribution histogram for PbTe nanoparticles synthesized using the hydrothermal route. Figure 3(d)presents theHR-TEM image of the single particle of lead telluride sample synthesized by hydrothermal route. The lattice fringes observed infigure 3(d) have an interplanar spacing of 0.323 nmwhich corresponds to (200) plane of lead telluride crystal.
Figure 4. FESEM-EDS Images of sintered pellets of lead telluride synthesized by aqueous chemical route (a)–(c) and hydrothermal route (d)–(f).
Figure 5. FESEM images of the spark plasma sintered samples of lead telluride, synthesized by (a) aqueous chemical route and (b)hydrothermal route.
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The clear lattice fringes observed inHR-TEM images (See figure 3(b) and d)), indicates that lead telluride nanoparticles synthesized fromboth the routes are perfectly crystalline. The FESEM-EDS images of SPS’ed PbTe samples are shown infigures 4(a)–(c) for aqueous chemical route and figures 4(d)–(f) for hydrothermal route. It was revealed from the elementalmapping images (b), (c), and (e), (f) that both the elements (Pb, Te) are uniformly distributed in thewholematrix, confirming that homogeneous composition has been achieved in both the samples.
The FESEM images of the sintered pellets are shown infigure 5. The images reveal the porous nature of the samples synthesized by the aqueous chemical route, while the
sample synthesized by the hydrothermal route appears relatively compact and distinctly dense. The existence of pores in the former is also consistent with themeasurement of density in them. The density of the sample synthesized by the aqueous chemical route is close to 78%, and that of the sample synthesized by the hydrothermal route is 88%of the theoretical density. The relatively smaller density in our SPS’ed samples in comparison to the samples synthesized by the top-down approach (ballmilling) [23] confirms the presence of porosity in the SPS’ed samples. In order to achieve higher densities, remarkably excessive sintering temperatures and prolonged durations are required, whichmay result in inevitable grain growth. The relationship between thermal conductivity and volume of pores inside amaterial is given by,
k k= - P10 2 3( )/
Where,κ is the coefficient of thermal conductivity with porosity, k0 is the coefficient of thermal conductivity with 100% total density, and P is the porosity. As per the equation, an increase in porosity has a detrimental effect on the thermal conductivity due to additional scattering of phonons across the pores in the porous material [24, 25].
It was reported that a nearly 100% enhancement in zT could be achieved by porous architecture engineering [26]. However, therewill always be a tradeoff between the beneficial effect of reduction in thermal conductivity and the detrimental impact on the electrical conductivity.
3.3. Thermoelectric properties In this section, the impact ofmicrostructure on the transport properties of synthesized nanostructured lead telluride samples will be addressed. The temperature dependent Seebeck coefficient and electrical conductivity are presented infigures 6(a) and (c), respectively. Furthermore, the thermoelectric properties of raw ingot of the
Figure 6. (a)Temperature dependent Seebeck coefficient, (b) variation of ln (σT1/2)with 1/kT, (c)Temperature dependent electrical conductivity, and (d)Temperature dependent Power factor.
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PbTe and also of the PbTe-nanowires synthesized by another chemical route retrieved from [27] and [28], respectively, will be used for the sake of comparisonwith the results of the present study.
The SPS’ed discs of PbTe synthesized fromboth the aqueous chemical (aq) and hydrothermal (Hy) routes exhibited a p-type Seebeck coefficient fromRT to∼500K as shown in figure 6(a), suggesting that thematrix is Te rich in both the samples. A conversion from p-type to n-type has been observed at∼550K for sample A (aq) and at∼500K for sample B (Hy). Such a behavior is also consistent with the PbTe raw ingot synthesized by conventionalmelting and quenching or chemical route [27, 28]. The total Seebeck coefficient of a semiconductor with bipolar conduction involving two different types charge carriers is given by,
s s s s
( )
Where Se, and Sh are the Seebeck coefficients of the two types of carriers, andσe andσh are the contributions of the two charge carriers to electrical conductivity. At temperatures below 500K, the second term in the numerator of equation (2), i.e., (Shσh) dominates over thefirst term leading to a positive Seebeck coefficient in this temperature range. As PbTe is a narrow band gap semiconductor, the number of charge carriers in the conduction band increases progressively with the increase in temperature due to thermal excitation leading to an increase in Se and thefirst termof equation (1). Consequently, the overall Seebeck coefficient decreases at T>500K. The dominance of intrinsic charge carriers at high temperatures is also consistent with the enhanced electrical conductivity at temperatures>500K, as evidenced in the lead telluride sample synthesized by hydrothermalmethod (See figure 6(c). The Seebeck coefficient exhibits amaximumvalue of 426 μV K−1 at 375K (Sample B) and 420 μV K−1 at 425K (Sample A). The values are comparable to the reported values in PbTe synthesized by chemical route (i.e., 322 μV K−1 at∼373K [28]). It is to be noted thatwe obtained a significantly enhanced Seebeck coefficient in both types of samples (i.e., Aq&Hy types) compared to the bulk ingot 243 μV K−1 at∼320K.
Figure 6(c) presents the temperature dependent electrical conductivity of both the samples in comparison with the literature. One can observe the temperature-activated electrical conductivity in both sampleswhich is more intense in the lead telluride sample synthesized hydrothermalmethod. It was reported byNolas et al, (2009) that the electrical transport properties of PbTe synthesized bywet chemical route depends upon the surface oxygen adsorption, stoichiometry, and density [29]. The density of our synthesized samples has been measured using theArchimedesmethod.We hypothesize that the lower density of sample synthesized by the aqueous chemical route is responsible for lower electrical conductivity relative to the sample synthesized by the hydrothermal route. The electrical conductivity of PbTe synthesized by hydrothermal route can be further improved by optimizing the sintering conditions (temperature, time, and pressure). Similar electrical behavior is observed in the nanostructured lead telluride samples synthesized fromother wet chemical routes [29, 30]. Such temperature dependence of electrical conductivity can be ascribed to the charge carriers scattering from the potential barriers at crystal interfaces and grain boundaries. The charge carriers with low energies are trapped at grain boundaries, and those having sufficient energy are allowed to pass. The trapping of low-energy charge carriers by grain boundaries is also favorable for improving the Seebeck coefficient. Themeasurement of room temperature Seebeck coefficient is also in accordancewith the hypothesis. The room temperature Seebeck coefficient of sample synthesized by aqueous chemical route is 347 μV K−1, and that of sample synthesized by hydrothermal route is 380 μV K−1, which are significantly enhanced as compared to Seebeck coefficient of bulk PbTe ingot 243 μV K−1 at 320K [22]. The remarkably enhanced Seebeck coefficient values observed in the present case could be a signature of the carrierfiltering effect in our nanostructured samples [31]. The height of the potential energy barrier at crystal interfaces/grain boundaries can be estimated according to the following equation,
s = --T Exp E
( )/
Whereσeff is the effective electrical conductivity, k is the Boltzmann constant,T is the absolute temperature, and EB is the height of the grain boundary potential energy barrier. In order to justify this assumption, we have plotted ln(σT1/2) versus 1/kT infigure 6(b). The linear fit of the data sets confirms the applicability of the carrier filteringmodel. The height of the potential energy barrier comes out to be∼210meV in the sample synthesized by the aqueous chemical route and∼201meV in the sample synthesized by the hydrothermal route. The calculated height of the potential energy barrier is relatively large in contrast to the energy barrier reported by Scheele et al,EB=140meV [32]. These higher values of potential energy barrier are also consistent with the lower electrical conductivity observed in our synthesized samples.
Figure 6(d)presents the temperature-dependent power factor (=S 2σof the synthesized samples. It can be observed from thefigure that the power factor of synthesized samples is significantly lower than the bulk ingot. The power factor of the sample synthesized by hydrothermal route reaches a value of 201 μWm−1 K−2 at a temperature∼376K, and 188 μWm−1 K−2 at 673K.However, the power factor of sample synthesized by
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Table 2.The comparative values of thermoelectric parameters S,σ andκ at three different temperatures i.e., 303K, 473K and 673K.
Seebeck coefficient S
(μV K−1)
ductivityσ
(S m−1) Power factor (S2σ) (μW m−1 K−2)
Thermal con-
Figure of
S2 T)
Temp. (K) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy)
303K 346.5 379.3 501 775 60 111 0.96 1.43 0.015 0.025
473K 352.7 141.3 231 875 23 15 0.65 0.96 0.007 0.003
673K −135.7 −266.9 480 2800 9 188 0.66 0.76 0.003 0.176
Figure 8.Temperature dependent (a)Electronic component of thermal conductivity, (b)Bipolar component of thermal conductivity, (c) difference of total thermal conductivity and electronic thermal conductivity, and (d) plot of ln (κBipolar) versus 1/2kT.
Figure 7.Temperature dependence of the (a)Total thermal conductivity, and (b) Lattice thermal conductivity contribution in the PbTe samples synthesized using two routes (Aq&Hy). A comparison is alsomadewith the data reported on bulk ingot sample of PbTe [27].
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aqueous chemical route remains low∼60 μWm−1 K−2 at room temperature. The lower power factor in our samplesmay be attributed to lower values of electrical conductivity due to the scattering of the charge carriers at numerous interfaces.We propose that the decreased electrical conductivity in our samples is not fully compensated by the enhanced Seebeck coefficient. The comparative values of thermoelectric parameters S,σ andκ at three different temperatures i.e., 303K, 473K and 673Khas been shown in table 2.
The principal benefit of nanostructuredmaterials in comparison to bulkmaterials is the significant decrease in lattice thermal conductivity. The temperature dependent total and lattice thermal conductivity has been presented infigures 7(a) and (b), respectively.
It can be readily observed fromfigure 7, that the thermal conductivity of samples synthesized fromboth the routes is remarkably reduced in comparison to the thermal conductivity of bulk ingot [27] in the entire measurement temperature range. This result demonstrate successful reduction in the thermal conductivity to ∼38% in the sample synthesized by hydrothermal route and to∼58% in the sample synthesized by aqueous chemical route when compared to the thermal conductivity of bulk ingot. Furthermore, figure 7 reveals that the total thermal conductivity is close to the lattice thermal conductivity, and itmight be attributed to the inferior electrical conductivity of our synthesized samples.
The total thermal conductivity of amaterial is comprised of two components, i.e., the electronic component (κEl) and the lattice component (κL). Further, the electronic component of thermal conductivity is directly proportional to electrical conductivity throughWiedemann–Franz law (κEl=LσT), where L,σ, andT are the Lorentz number, electrical conductivity, and absolute temperature, respectively. The value of Lorentz number can be estimated from the absolute values of Seebeck coefficient according to the following equation [33],
= + -L Exp S
( )
In the above equation, S is in the units ofμV K−1, and L is in 10−8WΩK−2. The value of the electronic thermal conductivity is computed from the estimated values of Lorentz number
and experimentallymeasured electrical conductivity values (figure 8(a)). It is directly observed from figure 8(a) that the electronic thermal conductivity increases with the increase in temperature and displays the same behavior as that of electrical conductivity.
The electrical band gap of lead telluride is∼0.3 eV at room temperature [34, 35]. In such a narrow band gap semiconductor, a notable contribution to thermal conductivity comes frombipolar diffusion of charge carriers. This contribution is termed as bipolar thermal conductivity and is found to increase with temperature. Besides an additional contribution to thermal conductivity, such as bipolar effects also lowers the Seebeck coefficient’s absolute value and hence are responsible for inferior thermoelectric performance.
The total thermal conductivity is given by,
k k k k= + + 6Tot Latt Elec Bipolar ( )
To estimate the bipolar thermal conductivity, we have used a simplemethod proposed by Zhao et al, [9].
Figure 9.Temperature dependent figure ofmerit of PbTe sample synthesized by aqueous chemical route (black curve), hydrothermal route (red curve) in comparison to the PbTe bulk ingot (green curve).
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The lattice thermal conductivity can be approximated as
k q
2
( ) /
WhereM,V are the averagemass and average atomic volume per atom, θD is theDebye temperature, and γ the Gruneisen parameter [10]. At low temperatures, we can approximate the acoustic phonon scattering as the governingmechanism and hence k k- ,Tot Elec which is k .Latt The latter is found to be inversely proportional to temperature (see figures 7(b), 8(c)). As the temperature is increased, kLatt begins to diverge from the linear correspondence between kLatt and inverse temperature. The value of bipolar thermal conductivity can be computed by extrapolating the linear correspondence between kLatt and inverse temperature as specified by the solid linemarked by blue color (Sample A) and green color (Sample B). The variation of bipolar thermal conductivity with temperature is presented infigure 8(b). It is evident from the figure that the bipolar thermal conductivity becomes considerable at temperaturesmore than 450K.
The energy barrier for bipolar diffusion is computed using the relationship between kBipolar and temperature,
k = -AExp E
( )
WhereEB is the energy barrier for bipolar diffusion andA is a pre-exponential coefficient. To estimate the energy barrier for bipolar diffusion, we have plotted ln(κBipolar) versus 1/2kT for the synthesized samples (figure 8(d)). The linearfitting of the datasets yields an energy barrier value of 0.73 eV for sample B, and 0.53 eV for sample A.
The temperature dependent dimensionless figure ofmerit has been depicted infigure 9. Thefigure ofmerit of PbTe bulk ingot has been retrieved from [27]. Although the power factor of the sample synthesized by the hydrothermal route is relatively smaller than the bulk ingot, the figure ofmerit is distinctly on the higher side.
The large value offigure ofmerit in case of PbTe synthesized using hydrothermal route is due to significantly smaller thermal conductivity in the nanostructured sample. Thefigure ofmerit reaches to amaximumvalue of 0.18 at 673K in the sample synthesized by the hydrothermal route. On the other side, the dimensionless figure of merit of the sample synthesized by the aqueous chemical route remains low in the entiremeasurement temperature range owing to its poor electrical properties.
4. Conclusions
In summary, we have reported the structure and thermoelectric transport properties of nanostructured lead telluride samples synthesized by an aqueous chemicalmethod and a hydrothermalmethod. The as-synthesized nanoparticles were consolidated by using spark plasma sintering. Thermoelectric properties have been measured on the bulk nanostructured samples from room temperature to 700K. The large values of room temperature Seebeck coefficient in both the samples in contrast to the bulk ingot have been attributed to the carrier energy filtering effect. However, it was found that the enhancement in the Seebeck coefficient could not fully compensate for the decrease in electrical conductivity due to scattering of charge carriers at numerous interfaces. Thermal conductivity is significantly decreased in the nanostructured samples over the entire measurement temperature range leading to amaximum figure ofmerit of 0.18 at 673K in the sample synthesized by the hydrothermal route. On the other hand, the sample synthesized by aqueous chemical route shows low crystallinity, higher porosity and the presence of unreacted Te as secondary phase thus leading to relatively lower values of zT. It is to be noted that the present workmainly focusses on the synthesis and thermoelectric properties of undoped lead telluride. It is expected that zTmaxvalues of the nanostructured lead telluride synthesized as in the present work can be further enhanced by process optimization and controlled doping.
Acknowledgments
Data availability statement
The data that support thefindings of this study are available upon reasonable request from the authors.
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[19] QinB,HuX, Zhang Y,WuH, Pennycook S J andZhao LD 2019Comprehensive Investigation on the Thermoelectric Properties of p-Type PbTe-PbSe-PbSAlloysAdv. Electron.Mater. 5 1–8
[20] SaleemiM,ToprakMS, Li S, JohnssonMandMuhammedM2012 Synthesis, processing, and thermoelectric properties of bulk nanostructured bismuth telluride (Bi2Te3) J.Mater. Chem. 22 725–30
[21] IbrahimEMM,AhmedGA, KhavrusV,HadiaNMA,Mohamed SH,Hampel S andAdamAM2021 Effect of surfactant concentration on themorphology and thermoelectric power factor of PbTe nanostructures prepared by a hydrothermal routePhysica E 125 114396
[22] Martin J, NolasG S, ZhangWandChen L 2007PbTe nanocomposites synthesized fromPbTe nanocrystalsAppl. Phys. Lett. 90 67–70 [23] Zhang J,WuD,HeD, FengD, YinM,QinX andHe J 2017 Extraordinary thermoelectric performance realized in n-Type PbTe through
multiphaseNanostructure engineeringAdv.Mater. 29 1–7 [24] Yoon S, KwonO J, Ahn S, Kim J Y, KooH, Bae SH, Cho J Y, Kim J S andPark C2013The effect of grain size and density on the
thermoelectric properties of Bi2Te3-PbTe compounds J. Electron.Mater. 42 3390–6 [25] Bulat L P, Pshenay-severinDAandOsvenskii VB 2016 Effect of porosity on the thermoelectric efficiency of PbTe Semiconductors 58
1532–8 [26] KhanAU et al 2017Nano-micro-porous skutterudites with 100%enhancement in ZT for high performance thermoelectricityNano
Energy 31 152–9 [27] He J, Girard SN,KanatzidisMGandDravid VP 2010Microstructure-lattice thermal conductivity correlation in nanostructured
PbTe0.7S0.3 thermoelectricmaterialsAdv. Funct.Mater. 20 764–72 [28] WangQ,ChenG andYinH2013New insights into the growthmechanism of hierarchical architectures of PbTe synthesized through a
triethanolamine-assisted solvothermalmethod and their shape-dependent electrical transport properties J.Mater. Chem. A 1 15355–69 [29] Martin J,Wang L, Chen L andNolas G S 2009 Enhanced Seebeck coefficient through energy-barrier scattering in PbTe nanocomposites
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PAPER • OPEN ACCESS
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This content was downloaded from IP address 65.21.228.167 on 08/04/2022 at 07:03
PAPER
Thermoelectric properties of Spark plasma sintered PbTe synthesized without any surfactant and organic solvent
PradeepKumar Sharma1,2, TDSenguttuvan3, VK Sharma2, NKGupta1,M Saravanan3 and Sujeet Chaudhary1,∗
1 Thin Film Laboratory, Department of Physics, Indian Institute of TechnologyDelhi, NewDelhi 110 016, India 2 ShyamLal College, University ofDelhi, Delhi 110 032, India 3 CSIR-National Physical Laboratory, DrK. S. KrishnanMarg, NewDelhi 110 012, India ∗ Author towhomany correspondence should be addressed.
E-mail: [email protected]
Keywords: thermoelectrics, bulk nanostructuredmaterials, lead telluride, hydrothermal synthesis,figure ofmerit
Abstract We report a systematic investigation on structural and thermoelectric properties of Spark plasma sintered Lead telluride synthesized by hydrothermal route and a low temperature aqueous chemical routewithout using any organic solvent and surfactant. The as-synthesized powder samples obtained from these two different synthesis routes were identically subjected to spark plasma sintering. The size of nanocubes formed by the hydrothermalmethod, as evident fromTEM-HRTEM images, is 50 nm; however, the samples synthesized by aqueous chemical route showsmixedmorphologywith particle size<50 nm. The thermoelectric properties of spark plasma sintered bulk nanostructured samples have beenmeasured fromRT to 700K.Notably, large Seebeck coefficient and small electrical resistivity values are observed in the sample synthesized by the hydrothermal route, which is ascribed to the charge carrier energy filtering effect. Amaximum reduction of∼38%and∼58%has been observed in the sample synthesized by the hydrothermal route and aqueous chemical route, respectively, compared to the bulk ingot. Themaximumfigure ofmerit attained is 0.18 at 673K in the lead telluride sample synthesized by the hydrothermal route.
1. Introduction
Thermoelectric energy conversion technology utilizes the Seebeck and Peltier effect for the interconversion between thermal and electrical energy. There has been a renewed interest in thermoelectric technology due to a large interest in harvesting thewaste heat and solid-state refrigeration-based devices [1]. This technique ismore significant in the areas where there is ample quantity of waste heat and is likely to play a crucial part in clean and renewable energy [2]. The conversion efficiency of a thermoelectricmaterial is determined by the dimensionless figure ofmerit zT, which is, in turn, the function of the intrinsicmaterial parameters,
s k
=zT S
Where S,σ, andκ represent the Seebeck coefficient, electrical conductivity, and coefficient of thermal conductivity at the temperatureT [3]. Hence, to boost the thermoelectric performance of amaterial, the Seebeck coefficient and electrical conductivity need to be enhancedwhile simultaneouslymaintaining small values of thermal conductivity. However, the complicated relationship between thesematerial parameters impedes the efforts in obtaining highTE performance and thewidespread use of thermoelectric technology [4]. Nanostructured thermoelectricmaterials are of great interest as they offer a uniqueway to independently tune thesematerial parameters and hence enhance the zT value [5]. Recent advances show that it is possible to improve the zT values in nanostructuredmaterial by reducing the lattice component of thermal conductivity through the intensive scattering of the phonons at grain boundaries/crystal interfaces and enhancing the thermoelectric power factor by carrier energyfiltering and quantum confinement effects [6].
OPEN ACCESS
7 July 2021
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In the present work, we report the synthesis of lead telluride by two different routes, a low-temperature aqueous chemical route and a hydrothermal route without using any organic surfactant or organic precursors, and the thermoelectric properties. The nanoparticles synthesized through both themethods are in sufficiently large quantities and are easily further processed through spark plasma sintering. The present study aims to investigate the outcome of nano-structuration on the thermoelectric properties of PbTe.We have systematically investigated the thermoelectric properties (S,σ andκ) across a broad temperature range 300–700K.One of the main outcomes of this study is that the total thermal conductivity of samples at room temperature synthesized by hydrothermal route and aqueous chemical route, respectively, are∼38%and 58% less than the thermal conductivity of bulk PbTe ingot. Aminimum lattice thermal conductivity of 0.64Wm−1 K−1 at 473K is achieved in the sample synthesized by aqueous chemical routewhich is significantly smaller than the thermal conductivity of bulk PbTe∼1.50 at 450K.
2. Experimental section
Analytically pure lead acetate [Pb(CH3COO)2], Telluriummetal powder (Te), Sodiumborohydride (NaBH4), and sodiumhydroxide (NaOH) have been procured fromSigmaAldrich.
2.1. Preparation of PbTe Aqueous chemical route:Approximately 5 gNaOHpowderwas dissolved in double-distilledwater at 323K. WhenNaOH is completely dissolved, 2 gNaBH4 and 0.01mol Temetal powderwere added to the aqueous NaOH solutionwith constantmagnetic stirring. After the change in the color of the solution to dark purple, 0.01mol lead acetate aqueous solutionwas added to the beaker drop-by-drop. Once the reaction is completed, the beakerwas allowed to cool to room temperature, and the obtained black powderwas filtered out andwashed with distilledwater, acetone, and ethanol. At last, the powder samplewas dried in air ambient for 3 h at 323K.
Hydrothermal synthesis route:The stoichiometric amount of lead acetate and telluriumpowderwere added to a beaker containing an aqueous solution ofNaBH4with constantmagnetic stirring. After some time, 20ml aqueousNaOH solutionwas added to the beaker, and the resulting solutionwas transferred to a Teflon- lined stainless-steel autoclave. Finally, the autoclave wasfilled to 80%of the total capacitywith distilledwater andmaintained at 433K for 14 h in a furnace. After the reactionwas over, the autoclave was cooled to room
Figure 1. Schematic of Synthesis process (a) aqueous chemical route, (b) hydrothermal route. From [18]. Reprintedwith permission fromElsevier.
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temperatures. The obtained black powderwasfiltered out andwashedwith distilledwater, acetone, and ethanol. Lastly, the powder samplewas dried in air ambient for 3 h at 323K, as in the former route.
2.2. Sintering The as-synthesized PbTe nanopowders were loaded in graphite die and consolidated using spark plasma sintering (SPS)using Syntex, Japanmake furnace at a temperature of 773K for 8 min under a pressure of 20MPa.
A schematic of the synthesis process is shown infigure 1.
2.3. Characterization TheXRDmeasurements on as-synthesized Lead telluride samples were performed by employing a diffractometer (Philips Xpert Pro) usingCu-Kα radiation from20° to 80°with a step size of 0.02°. Microstructure of both the as-synthesized samples and the SPS’ed (Spark Plasma Sintered)PbTe samples have been investigated by FESEM (field emission scanning electronmicroscope) (Jeol JSM-7800F) and (EDS) energy dispersive patterns. Themorphology of nanostructured PbTe samples was determined by using TEM (Transmission electronmicroscopy) andHR-TEM (high-resolution transmission electronmicroscopy (JEM 2100F JEOL).
2.4.Measurements The thermoelectric properties of the SPS’ed lead telluride samples have been investigated from room temperature to 700K. The thermal conductivity of the bulk nanostructured samples was calculated using the expression k r= C D,p whereρ, Cp andD are the density, specific heat and thermal diffusivity of the sample, respectively. The density of the samples wasmeasured using Archimedesmethod, and the thermal diffusivity (D) was determined by employing Laser Flash Apparatus ((LFA 1000), LinseisMessgeraete GmbH,GermanyNPL). Specific heat capacity value has been adapted fromdata reported byQuin B et al, (2019) [19]. After the measurement of thermal diffusivity on the samples, rectangular pellets were cut out from the SPS’ed discs for the simultaneousmeasurements of Seebeck coefficient and electrical conductivity by employingULVACZEM3 in a Helium atmosphere.
3. Results and discussions
3.1. Structural analysis TheXRDdiffractograms of the as-synthesized lead telluride samples fromboth the routes have been demonstrated infigure 1, alongwith the Rietveld refinement profiles.
As can be observed from figure 2, all the prominent diffraction peaks can be indexed to the FCCPbTe structure with space group Fm-3m (225) JCPDS#78-1905. There are no diffraction peaks from any impurity in the XRDdiffractogram (See figure 2(b)), confirming that single phase PbTe has been successfully synthesized by using a simple hydrothermal reactionThe intensity of the XRDpeaks observed in the lead telluride sample synthesized by the hydrothermalmethod is relatively higher in contrast to the sample synthesized by aqueous chemical route (Seefigure 2). It indicates that the sample synthesized by the hydrothermal route ismore
Figure 2.X-ray diffractogram andRietveld refinement profiles of the lead telluride prepared by (a) aqueous chemical route, and (b) Hydrothermal routes.
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crystalline in comparison to the sample synthesized by the aqueous chemical route. Further, the sharp peaks indicate that the crystallite size of the lead telluride sample synthesized by hydrothermalmethod is larger in comparison to the sample synthesized by aqueous chemical route which is also consistent with theHR-TEM observations (See figure 3).On the contrary, the sample synthesized by the aqueous chemical precipitation method results in PbTe product having relatively small-sized nanoparticles (broad peaks)with a few additional peaks corresponding to traces of unreacted Te in the sample (See figure 2(a)). Further, two peaks of very low intensity (marked by *) couldn’t be identified as the Braggs position due to both the phase lies very close and hence peaks possibly. The calculated lattice constant using Rietveld refinement for the sample synthesized by hydrothermal route is 0.64556 nmand that synthesized using aqueous chemical route is 0.64590 nm; both values are in close agreement with the literature value (0.64540 nm) [20].
The value of various parameters obtained by the Rietveld refinement has been shown in table 1.
Table 1.The value of various parameters obtained by the Rietveld refinement.
Refined parameters Sample A (Aq)
Sample B (Hy) PbTe Te PbTe
a(nm) 0.64590 0.44546 0.64556
b(nm) 0.64590 0.44546 0.64556
c(nm) 0.64590 0.59229 0.64556
α (°) 90 90 90
β (°) 90 90 90
γ (°) 90 120 90
Rp (%) 21.1 12.2
Rwp (%) 29.9 18.2
Rexp (%) 28.41 16.0
Chi square (χ2) 1.10 1.17
Figure 3.TEM/HR-TEM image of the as- synthesized lead telluride sample by (a), (b) aqueous chemical route, (c), (d) hydrothermal route (inset infigure 3(c) shows the size distribution histogramof lead telluride nanoparticles synthesized using hydrothermal route as calculated using the corresponding TEM image).
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Wehave calculated the crystallite size for the (200) peak using theDebye–Scherrer equation,
l b q
=D K
Cos 2XRD ( )
WhereK,λ,β, and θ are Scherrer constant, wavelength of copper Kα radiation, FWHM (full width of the peak at halfmaximum) andBragg’s angle, respectively. The value of Scherrer constant lies between 0.89 to 0.94. The (200)-diffraction peak yields a crystallite size of 23.5 nm for the sample synthesized by the aqueous chemical route and 29.0 nm for the sample synthesized by the hydrothermal route. It is to be noted that crystallite size is not necessarily the same as that of particle size. Further, the broadening of the XRDpeak can also be due to the internal stress and defects induced during the synthesis process. Hence, the crystallite size as estimated using Scherrer equation is expected to be smaller than the actual value [20]. The calculated crystallite size for both the synthesized samples is far lesser thanBohr’s excitonic radius of lead telluride (∼152 nm) [21]. It is noteworthy that the Seebeck coefficient could be remarkably enhanced in the nanostructured systems due to carrier filtering and quantum confinement effects [22].
3.2.Morphological analysis Figure 3(a) shows the TEM image of as-synthesized lead telluride nanoparticles synthesized by aqueous chemical route. It can be observed from the figure that the nanoparticles exhibitmixedmorphologywith particle size<50 nm (See figure 3(a). TheHR-TEM image of the lead telluride sample synthesized by aqueous chemical route has been depicted infigure 3(b). The clear lattice fringes as evident inHR-TEM image have the interplanar spacing of 0.323 nmand 0.228 nm,which corresponds to (200) and (220) plane of lead telluride. Figure 3(c) presents the TEM image of the lead telluride sample synthesized by hydrothermal route. It is evident from the figure that the as-synthesized nanoparticles have cubicmorphologywith edge length∼50 nm. The inset in figure 3(c) shows the size distribution histogram for PbTe nanoparticles synthesized using the hydrothermal route. Figure 3(d)presents theHR-TEM image of the single particle of lead telluride sample synthesized by hydrothermal route. The lattice fringes observed infigure 3(d) have an interplanar spacing of 0.323 nmwhich corresponds to (200) plane of lead telluride crystal.
Figure 4. FESEM-EDS Images of sintered pellets of lead telluride synthesized by aqueous chemical route (a)–(c) and hydrothermal route (d)–(f).
Figure 5. FESEM images of the spark plasma sintered samples of lead telluride, synthesized by (a) aqueous chemical route and (b)hydrothermal route.
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The clear lattice fringes observed inHR-TEM images (See figure 3(b) and d)), indicates that lead telluride nanoparticles synthesized fromboth the routes are perfectly crystalline. The FESEM-EDS images of SPS’ed PbTe samples are shown infigures 4(a)–(c) for aqueous chemical route and figures 4(d)–(f) for hydrothermal route. It was revealed from the elementalmapping images (b), (c), and (e), (f) that both the elements (Pb, Te) are uniformly distributed in thewholematrix, confirming that homogeneous composition has been achieved in both the samples.
The FESEM images of the sintered pellets are shown infigure 5. The images reveal the porous nature of the samples synthesized by the aqueous chemical route, while the
sample synthesized by the hydrothermal route appears relatively compact and distinctly dense. The existence of pores in the former is also consistent with themeasurement of density in them. The density of the sample synthesized by the aqueous chemical route is close to 78%, and that of the sample synthesized by the hydrothermal route is 88%of the theoretical density. The relatively smaller density in our SPS’ed samples in comparison to the samples synthesized by the top-down approach (ballmilling) [23] confirms the presence of porosity in the SPS’ed samples. In order to achieve higher densities, remarkably excessive sintering temperatures and prolonged durations are required, whichmay result in inevitable grain growth. The relationship between thermal conductivity and volume of pores inside amaterial is given by,
k k= - P10 2 3( )/
Where,κ is the coefficient of thermal conductivity with porosity, k0 is the coefficient of thermal conductivity with 100% total density, and P is the porosity. As per the equation, an increase in porosity has a detrimental effect on the thermal conductivity due to additional scattering of phonons across the pores in the porous material [24, 25].
It was reported that a nearly 100% enhancement in zT could be achieved by porous architecture engineering [26]. However, therewill always be a tradeoff between the beneficial effect of reduction in thermal conductivity and the detrimental impact on the electrical conductivity.
3.3. Thermoelectric properties In this section, the impact ofmicrostructure on the transport properties of synthesized nanostructured lead telluride samples will be addressed. The temperature dependent Seebeck coefficient and electrical conductivity are presented infigures 6(a) and (c), respectively. Furthermore, the thermoelectric properties of raw ingot of the
Figure 6. (a)Temperature dependent Seebeck coefficient, (b) variation of ln (σT1/2)with 1/kT, (c)Temperature dependent electrical conductivity, and (d)Temperature dependent Power factor.
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PbTe and also of the PbTe-nanowires synthesized by another chemical route retrieved from [27] and [28], respectively, will be used for the sake of comparisonwith the results of the present study.
The SPS’ed discs of PbTe synthesized fromboth the aqueous chemical (aq) and hydrothermal (Hy) routes exhibited a p-type Seebeck coefficient fromRT to∼500K as shown in figure 6(a), suggesting that thematrix is Te rich in both the samples. A conversion from p-type to n-type has been observed at∼550K for sample A (aq) and at∼500K for sample B (Hy). Such a behavior is also consistent with the PbTe raw ingot synthesized by conventionalmelting and quenching or chemical route [27, 28]. The total Seebeck coefficient of a semiconductor with bipolar conduction involving two different types charge carriers is given by,
s s s s
( )
Where Se, and Sh are the Seebeck coefficients of the two types of carriers, andσe andσh are the contributions of the two charge carriers to electrical conductivity. At temperatures below 500K, the second term in the numerator of equation (2), i.e., (Shσh) dominates over thefirst term leading to a positive Seebeck coefficient in this temperature range. As PbTe is a narrow band gap semiconductor, the number of charge carriers in the conduction band increases progressively with the increase in temperature due to thermal excitation leading to an increase in Se and thefirst termof equation (1). Consequently, the overall Seebeck coefficient decreases at T>500K. The dominance of intrinsic charge carriers at high temperatures is also consistent with the enhanced electrical conductivity at temperatures>500K, as evidenced in the lead telluride sample synthesized by hydrothermalmethod (See figure 6(c). The Seebeck coefficient exhibits amaximumvalue of 426 μV K−1 at 375K (Sample B) and 420 μV K−1 at 425K (Sample A). The values are comparable to the reported values in PbTe synthesized by chemical route (i.e., 322 μV K−1 at∼373K [28]). It is to be noted thatwe obtained a significantly enhanced Seebeck coefficient in both types of samples (i.e., Aq&Hy types) compared to the bulk ingot 243 μV K−1 at∼320K.
Figure 6(c) presents the temperature dependent electrical conductivity of both the samples in comparison with the literature. One can observe the temperature-activated electrical conductivity in both sampleswhich is more intense in the lead telluride sample synthesized hydrothermalmethod. It was reported byNolas et al, (2009) that the electrical transport properties of PbTe synthesized bywet chemical route depends upon the surface oxygen adsorption, stoichiometry, and density [29]. The density of our synthesized samples has been measured using theArchimedesmethod.We hypothesize that the lower density of sample synthesized by the aqueous chemical route is responsible for lower electrical conductivity relative to the sample synthesized by the hydrothermal route. The electrical conductivity of PbTe synthesized by hydrothermal route can be further improved by optimizing the sintering conditions (temperature, time, and pressure). Similar electrical behavior is observed in the nanostructured lead telluride samples synthesized fromother wet chemical routes [29, 30]. Such temperature dependence of electrical conductivity can be ascribed to the charge carriers scattering from the potential barriers at crystal interfaces and grain boundaries. The charge carriers with low energies are trapped at grain boundaries, and those having sufficient energy are allowed to pass. The trapping of low-energy charge carriers by grain boundaries is also favorable for improving the Seebeck coefficient. Themeasurement of room temperature Seebeck coefficient is also in accordancewith the hypothesis. The room temperature Seebeck coefficient of sample synthesized by aqueous chemical route is 347 μV K−1, and that of sample synthesized by hydrothermal route is 380 μV K−1, which are significantly enhanced as compared to Seebeck coefficient of bulk PbTe ingot 243 μV K−1 at 320K [22]. The remarkably enhanced Seebeck coefficient values observed in the present case could be a signature of the carrierfiltering effect in our nanostructured samples [31]. The height of the potential energy barrier at crystal interfaces/grain boundaries can be estimated according to the following equation,
s = --T Exp E
( )/
Whereσeff is the effective electrical conductivity, k is the Boltzmann constant,T is the absolute temperature, and EB is the height of the grain boundary potential energy barrier. In order to justify this assumption, we have plotted ln(σT1/2) versus 1/kT infigure 6(b). The linear fit of the data sets confirms the applicability of the carrier filteringmodel. The height of the potential energy barrier comes out to be∼210meV in the sample synthesized by the aqueous chemical route and∼201meV in the sample synthesized by the hydrothermal route. The calculated height of the potential energy barrier is relatively large in contrast to the energy barrier reported by Scheele et al,EB=140meV [32]. These higher values of potential energy barrier are also consistent with the lower electrical conductivity observed in our synthesized samples.
Figure 6(d)presents the temperature-dependent power factor (=S 2σof the synthesized samples. It can be observed from thefigure that the power factor of synthesized samples is significantly lower than the bulk ingot. The power factor of the sample synthesized by hydrothermal route reaches a value of 201 μWm−1 K−2 at a temperature∼376K, and 188 μWm−1 K−2 at 673K.However, the power factor of sample synthesized by
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Table 2.The comparative values of thermoelectric parameters S,σ andκ at three different temperatures i.e., 303K, 473K and 673K.
Seebeck coefficient S
(μV K−1)
ductivityσ
(S m−1) Power factor (S2σ) (μW m−1 K−2)
Thermal con-
Figure of
S2 T)
Temp. (K) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy) A (Aq) B (Hy)
303K 346.5 379.3 501 775 60 111 0.96 1.43 0.015 0.025
473K 352.7 141.3 231 875 23 15 0.65 0.96 0.007 0.003
673K −135.7 −266.9 480 2800 9 188 0.66 0.76 0.003 0.176
Figure 8.Temperature dependent (a)Electronic component of thermal conductivity, (b)Bipolar component of thermal conductivity, (c) difference of total thermal conductivity and electronic thermal conductivity, and (d) plot of ln (κBipolar) versus 1/2kT.
Figure 7.Temperature dependence of the (a)Total thermal conductivity, and (b) Lattice thermal conductivity contribution in the PbTe samples synthesized using two routes (Aq&Hy). A comparison is alsomadewith the data reported on bulk ingot sample of PbTe [27].
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aqueous chemical route remains low∼60 μWm−1 K−2 at room temperature. The lower power factor in our samplesmay be attributed to lower values of electrical conductivity due to the scattering of the charge carriers at numerous interfaces.We propose that the decreased electrical conductivity in our samples is not fully compensated by the enhanced Seebeck coefficient. The comparative values of thermoelectric parameters S,σ andκ at three different temperatures i.e., 303K, 473K and 673Khas been shown in table 2.
The principal benefit of nanostructuredmaterials in comparison to bulkmaterials is the significant decrease in lattice thermal conductivity. The temperature dependent total and lattice thermal conductivity has been presented infigures 7(a) and (b), respectively.
It can be readily observed fromfigure 7, that the thermal conductivity of samples synthesized fromboth the routes is remarkably reduced in comparison to the thermal conductivity of bulk ingot [27] in the entire measurement temperature range. This result demonstrate successful reduction in the thermal conductivity to ∼38% in the sample synthesized by hydrothermal route and to∼58% in the sample synthesized by aqueous chemical route when compared to the thermal conductivity of bulk ingot. Furthermore, figure 7 reveals that the total thermal conductivity is close to the lattice thermal conductivity, and itmight be attributed to the inferior electrical conductivity of our synthesized samples.
The total thermal conductivity of amaterial is comprised of two components, i.e., the electronic component (κEl) and the lattice component (κL). Further, the electronic component of thermal conductivity is directly proportional to electrical conductivity throughWiedemann–Franz law (κEl=LσT), where L,σ, andT are the Lorentz number, electrical conductivity, and absolute temperature, respectively. The value of Lorentz number can be estimated from the absolute values of Seebeck coefficient according to the following equation [33],
= + -L Exp S
( )
In the above equation, S is in the units ofμV K−1, and L is in 10−8WΩK−2. The value of the electronic thermal conductivity is computed from the estimated values of Lorentz number
and experimentallymeasured electrical conductivity values (figure 8(a)). It is directly observed from figure 8(a) that the electronic thermal conductivity increases with the increase in temperature and displays the same behavior as that of electrical conductivity.
The electrical band gap of lead telluride is∼0.3 eV at room temperature [34, 35]. In such a narrow band gap semiconductor, a notable contribution to thermal conductivity comes frombipolar diffusion of charge carriers. This contribution is termed as bipolar thermal conductivity and is found to increase with temperature. Besides an additional contribution to thermal conductivity, such as bipolar effects also lowers the Seebeck coefficient’s absolute value and hence are responsible for inferior thermoelectric performance.
The total thermal conductivity is given by,
k k k k= + + 6Tot Latt Elec Bipolar ( )
To estimate the bipolar thermal conductivity, we have used a simplemethod proposed by Zhao et al, [9].
Figure 9.Temperature dependent figure ofmerit of PbTe sample synthesized by aqueous chemical route (black curve), hydrothermal route (red curve) in comparison to the PbTe bulk ingot (green curve).
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The lattice thermal conductivity can be approximated as
k q
2
( ) /
WhereM,V are the averagemass and average atomic volume per atom, θD is theDebye temperature, and γ the Gruneisen parameter [10]. At low temperatures, we can approximate the acoustic phonon scattering as the governingmechanism and hence k k- ,Tot Elec which is k .Latt The latter is found to be inversely proportional to temperature (see figures 7(b), 8(c)). As the temperature is increased, kLatt begins to diverge from the linear correspondence between kLatt and inverse temperature. The value of bipolar thermal conductivity can be computed by extrapolating the linear correspondence between kLatt and inverse temperature as specified by the solid linemarked by blue color (Sample A) and green color (Sample B). The variation of bipolar thermal conductivity with temperature is presented infigure 8(b). It is evident from the figure that the bipolar thermal conductivity becomes considerable at temperaturesmore than 450K.
The energy barrier for bipolar diffusion is computed using the relationship between kBipolar and temperature,
k = -AExp E
( )
WhereEB is the energy barrier for bipolar diffusion andA is a pre-exponential coefficient. To estimate the energy barrier for bipolar diffusion, we have plotted ln(κBipolar) versus 1/2kT for the synthesized samples (figure 8(d)). The linearfitting of the datasets yields an energy barrier value of 0.73 eV for sample B, and 0.53 eV for sample A.
The temperature dependent dimensionless figure ofmerit has been depicted infigure 9. Thefigure ofmerit of PbTe bulk ingot has been retrieved from [27]. Although the power factor of the sample synthesized by the hydrothermal route is relatively smaller than the bulk ingot, the figure ofmerit is distinctly on the higher side.
The large value offigure ofmerit in case of PbTe synthesized using hydrothermal route is due to significantly smaller thermal conductivity in the nanostructured sample. Thefigure ofmerit reaches to amaximumvalue of 0.18 at 673K in the sample synthesized by the hydrothermal route. On the other side, the dimensionless figure of merit of the sample synthesized by the aqueous chemical route remains low in the entiremeasurement temperature range owing to its poor electrical properties.
4. Conclusions
In summary, we have reported the structure and thermoelectric transport properties of nanostructured lead telluride samples synthesized by an aqueous chemicalmethod and a hydrothermalmethod. The as-synthesized nanoparticles were consolidated by using spark plasma sintering. Thermoelectric properties have been measured on the bulk nanostructured samples from room temperature to 700K. The large values of room temperature Seebeck coefficient in both the samples in contrast to the bulk ingot have been attributed to the carrier energy filtering effect. However, it was found that the enhancement in the Seebeck coefficient could not fully compensate for the decrease in electrical conductivity due to scattering of charge carriers at numerous interfaces. Thermal conductivity is significantly decreased in the nanostructured samples over the entire measurement temperature range leading to amaximum figure ofmerit of 0.18 at 673K in the sample synthesized by the hydrothermal route. On the other hand, the sample synthesized by aqueous chemical route shows low crystallinity, higher porosity and the presence of unreacted Te as secondary phase thus leading to relatively lower values of zT. It is to be noted that the present workmainly focusses on the synthesis and thermoelectric properties of undoped lead telluride. It is expected that zTmaxvalues of the nanostructured lead telluride synthesized as in the present work can be further enhanced by process optimization and controlled doping.
Acknowledgments
Data availability statement
The data that support thefindings of this study are available upon reasonable request from the authors.
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ORCID iDs
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Mater. Res. Express 8 (2021) 075004 PK Sharma et al