Thermoelectric properties of Spark plasma sintered PbTe synthesized
without any surfactant and organic solventMaterials Research
Express
PAPER • OPEN ACCESS
-
-
-
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
Original content from this workmay be used under the terms of the
Creative CommonsAttribution 4.0 licence.
Any further distribution of this workmustmaintain attribution to
the author(s) and the title of thework, journal citation
andDOI.
© 2021TheAuthor(s). Published by IOPPublishing Ltd
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.
2
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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.
3
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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).
4
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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.
5
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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.
6
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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
7
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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].
8
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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).
9
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
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.
10
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
ORCID iDs
[1] EnescuD2019Thermoelectric energy harvesting: basic principles
and applicationsGreen Energy Advances 1–2 [2] Andrei V, Bethke K
andRademannK 2016Thermoelectricity in the context of renewable
energy sources: joining forces instead of
competingEnergy Environ. Sci. 9 1528–32 [3] SnyderG J andToberer E
S 2008Complex thermoelectricmaterials. Complex
thermoelectricmaterialsNatureMater 7 105–14 [4] ZhuT, Liu Y,
FuC,Heremans J P, Snyder J G andZhaoX 2017Compromise and synergy in
high-efficiency thermoelectricmaterials
Adv.Mater. 29 1605884 [5] NeophytouN et al 2020Hierarchically
nanostructured thermoelectricmaterials: Challenges and
opportunities for improved power
factorsEur. Phys. J. B 93 213 [6] LanY,MinnichA J, ChenG andRenZ
2010 Enhancement of thermoelectric figure-of-merit by a bulk
nanostructuring approachAdv.
Funct.Mater. 20 357–76 [7] Heremans J P, Jovovic V, Toberer E S,
Saramat A, Kurosaki K, Charoenphakdee A, Yamanaka S and SnyderG J
2008 Enhancement of
thermoelectric of the electronic density of states Science 321
1457–61 [8] XiaoY,WuH,Cui J,WangD, Fu L, ZhangY, ChenY,He J,
Pennycook S J andZhao LD 2018Realizing high performance n-type
PbTe
by synergistically optimizing effectivemass and carriermobility and
suppressing bipolar thermal conductivity Energy Environ. Sci. 11
2486–95
[9] Pei Y,WangH,Gibbs ZM, LaLonde ADand Snyder J G 2012Thermopower
enhancement in Pb1-xMnxTe alloys and its effect on thermoelectric
efficiencyNPGAsiaMater. 4 1–6
[10] Zhao LD et al 2013All-scale hierarchical thermoelectrics:MgTe
in PbTe facilitates valence band convergence and suppresses bipolar
thermal transport for high performance Energy Environ. Sci. 6
3346–55
[11] TanG, Shi F,Hao S, Zhao LD,ChiH, ZhangX,Uher
C,WolvetronC,Dravid PV andKanatzidisMD2016Non-equilibrium
processing leads to record high thermoelectric figure ofmerit in
PbTe–SrTeKang, C. Nature Communication 7 12167
[12] Biswas K,He J, Blum ID,WuC I,HoganTP, SeidmanDN,DravidV P
andKanatzidisMG2012High-performance bulk thermoelectrics with
all-scale hierarchical architecturesNature 489 414–8
[13] Kadel K, Kumari L,WangX, LiW,Huang J Y and Provencio P P 2014
Synthesis and structure of undoped and indium-doped thermoelectric
lead telluride nanoparticlesNanoscale Res. Lett. 9 227
[14] YangH, Finefrock SW,Caballero JDA andWuY2014 Environmentally
benign synthesis of ultrathinmetal tellurideNanowires J. Am. Chem.
Soc. 136 10242–5
[15] Fard-Fini S A,Niasari SM andMohandes F 2014 Synthesis and
characterization of PbTe nanostructures in the presence of novel
surfactantsAdv. Powder Technol. 25 301–9
[16] NithiyananthamU,OzaydinMF, TazebayA S andKundu S 2016 Low
temperature formation of rectangular PbTe nanocrystals and their
thermoelectric propertiesNew J. Chem. 40 265–77
[17] Kungumadevi L and Sathyamoorthy R 2013 Structural, optical and
electrical properties of solvothermally synthesized PbTe nanodisks
Adv. Powder Technol. 24 218–23
[18] RamanathanA,Krishnan PK andMuraliraja R 2019A review on the
production ofmetalmatrix composites through stir casting— Furnace
design, properties, challenges, and research opportunities J.Manuf.
Processes 42 213–45
[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
Phys. Rev. B 79 115311 [30] PopescuA,Woods LM,Martin J andNolas G S
2009Model of transport properties of thermoelectric
nanocompositematerials
Physical ReviewB -CondensedMatter andMaterials Physics 79 1–7 [31]
Heremans J P, ThrushCMandMorelli DT 2004Thermopower enhancement in
lead telluride nanostructures Physical Review B -
CondensedMatter andMaterials Phys. Rev.B 70 115334 [32]
ScheeleM,OeschlerN, Veremchuk I, Peters SO, Littig A, Kornowski A,
Klinke C andWellerH 2011Thermoelectric properties of Lead
chalcogenides core–shell nanostructuresACSNano 5 8541–51
11
Mater. Res. Express 8 (2021) 075004 PK Sharma et al
[34] RavindraNM,Auluck S and Srivastava VK 1979Temperature
dependence of the energyGap in PbS, PbSe, and PbTePhysica Status
Solidi (A) 52K151–5
[35] Gelmont B L,Globus TR andMatveenkoAV1981Optical absorption and
band structure of PbTe Solid State Commun. 38 931–4
12
Mater. Res. Express 8 (2021) 075004 PK Sharma et al