Design of Advanced Thermoelectric Materials
Shaabani, Laaya
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Chapter
5
Thermoelectric performance of
Ce-doped PbSe
Abstract
Lead chalcogenide systems have been shown to be promising materials for thermoelectric applications. Here, we report on the synthesis and thermoelectric
properties of Pb1-xCexSe (x = 0.00, 0.01, 0.03 and 0,05) alloys. All of the samples
are n-type semiconductors and the Seebeck coefficient at 300 K increases from
196 μVK-1 for undoped PbSe to 290 μVK-1 for Ce doping of x = 0.01. The maximum
zT value of 0.27 is obtained for the sample with x = 0.01 at 775 K due to enhanced
5
5.1
Introduction
Thermoelectric (TE) materials and devices have drawn great interest for several
decades due to their potential in the conversion of waste heat into electricity.1-3 The
efficiency of any thermoelectric material in this conversion process depends on the
dimensionless figure of merit: zT = (S2σT)/κ, where S, σ, κ and T are the Seebeck
coefficient, electrical conductivity, thermal conductivity, and absolute temperature,
respectively.1,4,5 The electrical properties are determined by the power factor
(PF), defined as S2σ or S2/ρ, where ρ is the electrical resistivity. Maximizing the
thermoelectric figure of merit can be achieved by improving the PF or reducing the thermal conductivity.
One of the best thermoelectric materials in the intermediate temperature range (400-800K) is considered to be lead telluride (PbTe), which is the most widely
studied lead chalcogenide compound.6 A significant enhancement of zT has been
achieved in PbTe-based compounds by employing a wide range of dopants,7-12
nanostructuring,13-18 or modifying the band structure.10,12,19-23 For example, a figure of
merit of 1.5 at 773K was obtained in Tl-doped PbTe due to the introduction of resonant states near the Fermi level.12 However, it is desirable to replace Te for practical
applications because this element is scarce in the Earth’s crust and, therefore, would be too costly if used on a large scale. The cheaper and more abundant selenide analog, PbSe, is remarkably similar to PbTe in terms of its electronic and structural
properties, and could be a good alternative for thermoelectric applications.20-21,24-26 A
theoretical calculation on PbSe by Parker and Singh predicted a figure of merit as high
as 2.0 at 1000 K if it is heavily doped with holes [24]. The effect of doping PbSe with
group IIIA elements,20, 25, 27,28 Bi,29 Na,21 Cd,30 Mn,30 Cr,31 Br32 and rare earth elements
(Ce, Pr, Nd, Eu, Gd, and Yb)33 and La34 have previously been reported. Recently, high
zT values has been reported in PbSe materials, such as Cr-doped PbSe (~1 at 573 K),31
Br-doped PbSe (~1.2 at 850 K),32 Al-doped PbSe (~1.3 at 850 K).17 However, PbSe has
been less studied than PbTe in this context and there has been no systematic study of the thermoelectric properties of PbSe doped with Ce. Following the predictions
of Mahan and Sofo,24 the 4f levels of rare-earth elements have rather heavy effective
the thermoelectric figure of merit. It is concluded from the Pisarenko plot,33 Seebeck
coefficient as a function of carrier concentration, that Ce can be considered as a promising rare-earth dopant for PbSe.
The aim of this study is to investigate the influence of cerium doping on the
thermoelectric properties of Pb1-xCexSe (x = 0.00, 0.01, 0.02 and 0,03) alloys and to
optimize the doping level to obtain the best performance of this compound as a thermoelectric material.
5.2
Experimental section
5.2.1 Sample fabrication
Synthesis. Polycrystalline Pb1-xCexSe (x = 0.00, 0.002, 0.01, 0.02, 0.03) samples were synthesized by the solid state reaction method. Stoichiometric amounts of high purity starting materials - Pb chunks (99.999%, Alfa Aesar), Se granules (99.999%, Alfa Aesar), and Ce metal pieces (99.9%, Aldrich) - were weighed in an argon atmosphere glove box. A total mass of 10 g was loaded into carbon-coated quartz tubes and the tubes were sealed under vacuum. The tubes were slowly heated to 1323 K, kept at that temperature for 10 hours, and then quenched in cold water followed by annealing at 823 K for 72 hours.
Sintering. The ingots obtained were pulverized into fine powder using an agate
mortar and pestle, which was subsequently sintered into 12 mm diameter disk-shaped pellets by spark plasma sintering (SPS) at 793 K for 1 hour at an axial pressure of 40 MPa under vacuum.
5.2.2 Transport properties measurements
Seebeck coefficient and resistivity measurements. The Seebeck coefficient (S)
and electrical conductivity (σ) were simultaneously measured using a Linseis LSR-3 instrument. Measurements were done under a helium atmosphere and data
5
were collected from room temperature to 823 K. The typical samples for these measurements had a parallelepiped shape and were obtained from the disk-shaped SPS samples by cutting and polishing.
Thermal conductivity measurements. The thermal diffusivity (D) was measured on
samples with ∼12 mm diameter and ∼2 mm thickness by the laser flash diffusivity method (Linseis LFA 1000) in the temperature range 300-773 K. The density (ρ) of the pellets was calculated by measuring the mass and dimensions, and the densities of the measured samples were around ∼97% of the theoretical values. The specific
heat capacity (Cp) was taken from the equation Cp (KB per atom) = (3.07+4.7 ×10-4
(T/K-300)).35 The total thermal conductivity (κ) was calculated using κ = ρDC
p.
5.2.3 Materials Characterization
X-Ray diffraction. The crystal structure and phase purity were studied using a GBC
Scientific X-ray diffractometer with Cu Kα radiation at room temperature.
5.3
Results and Discussion
Powder X-ray diffraction patterns of the investigated samples are shown in Figure
5.1 for the Pb1-xCexSe (x = 0, 0.01, 0.02 and 0.03) compositions. All of the peaks were
indexed in terms of the face-centered cubic rocksalt (NaCl) structure and no impurity
peaks were observed. The lattice parameters of the Pb1-xCexSe (x = 0, 0.01, 0.02 and
0.03) samples are 6.1300(2), 6.1315(1), 6.1307(1) and 6.1288(1) respectively (Table 5.1). There is no clear variation of lattice parameter with dopant concentration. The
electrical resistivity and Seebeck coefficients of the Pb1-xCexSe (x = 0, 0.01, 0.02 and
Figure 5.1: Room temperature X-ray diffraction patterns of the Pb1-xCexSe (x = 0, 0.01, 0.02 and 0.03) compounds.
Table 5.1: Lattice parameters of Pb1-xCexSe (x = 0, 0.01, 0.02, and 0.03) compounds
Sample name Lattice parameter(Å)
a
PbSe 6.1300(2)
Pb0.99Ce0.01Se 6.1315(1)
Pb0.98Ce0.02Se 6.1307(1)
Pb0.97Ce0.03Se 6.1288(1)
For the heavily doped samples, the electrical resistivity increases with temperature over the entire temperature range. However, for the undoped and x = 0.01 samples, deviation from this trend occurs in that the electrical resistivity reaches a maximum value and then decreases. This is indicative of the bipolar effect, where the minority carriers begin to contribute to the transport properties of narrow bandgap semiconductor materials with increasing temperature. In the case of the more highly doped samples, there is no sign of any bipolar effect, which can be attributed to
5
the fact that by increasing the electron concentration via Ce doping, the Fermi level moves deeper to the conduction band, and thus hinder minority carriers (holes) from jumping across the band gap, which results in the suppression of the bipolar effect. As shown in Figure 5.2b, the Seebeck coefficients of the doped compounds are negative over the entire temperature range measured, which indicates that all the doped samples are n-type semiconductors. The Seebeck coefficient decreases with increasing Ce content, which is consistent with the trend in electrical resistivity.
The Seebeck coefficient at 300 K increases from 196 μVK-1 for the undoped sample
to 290 μVK-1 upon Ce doping for x = 0.01. The room temperature thermoelectric
properties of Ce-doped polycrystalline PbSe in our study compared to other reported values (Table 5.2). The thermoelectric properties of the undoped samples are similar, but the Seebeck coefficient and electrical resistivity of our sample with x = 0.03 is
higher compared with the reported values for sample with the same composition33
and La-doped PbSe.34
300 400 500 600 700 800 900 -400 -200 0 200 400 (b) Temperature (K ) Seeb ec k c oef fic ien t ( mV /K ) x = 0 x = 0.01 x = 0.02 x = 0.03 300 400 500 600 700 800 900 0 5 10 15 20 25 30 (a) x = 0 x = 0.01 x = 0.02 x = 0.03 R es is tiv ity (mO hm. cm) Temperature (K )
Figure 5.2: (a) Temperature dependence of the electrical resistivity of Pb1-xCexSe (x = 0, 0.01, 0.02 and 0.03) samples in the temperature range 300-823 K. (b) Temperature dependence of the Seebeck coefficient of Pb1-xCexSe (x = 0, 0.01, 0.02 and 0.03) samples in the temperature range 300-823 K.
Figure 5.3 shows the total thermal conductivity, κ, and the lattice thermal conductivity, κL, of the Pb1-xCexSe (x = 0.00, 0.01, 0.02 and 0.03) compounds as a function of temperature in the range of 300-773 K. The lattice thermal conductivity,
κL, was calculated by subtracting the electronic contribution, κe, from the measured
total thermal conductivity such that κL = κtotal-κe, where the value of κe can be
estimated by employing the Wiedemann-Franz law, κe = LσT, where σ is the electrical
conductivity, T is the temperature, and L is the Lorenz number calculated by using
a single parabolic band model with the acoustic phonon scattering assumption.36
The thermal conductivity of the undoped sample is 1.91 W m-1 K-1 at 300 K which
is reduced to 1.26 W m-1 K-1 at 773 K, which is lower compared with the previously
reported result (2.52 at 300 K),33 but comparable to the values of 1.7 W m-1 K-1and 1.3
W m-1 K-1 reported for undoped PbSe at the same temperatures.34 It is observed that
at high temperature with increasing doping level, the thermal conductivity increases and the sample with x = 0.03 possess much higher thermal conductivity than lightly-doped samples. This can be attributed to the significant contribution of electronic thermal conductivity in this compound. The thermal conductivity of this sample
is 3.24 W m-1 K-1 at 300 K which is significantly lower than the previously reported
value in sample with the same composition, 7.86 W m-1 K-1 at 300 K,33 (Table 5.2).
The thermal conductivity of the undoped sample goes through a minimum and then increases, which is consistent with the variation of the Seebeck coefficient and can be attributed to the bipolar effect.
Table 5.2: Comparison of transport properties of PbSe doped with Ce and La at 300 K
Composition S (μVK-1) ρ (mΩcm) κ t (Wm-1 K-1) zT Pb0.97Ce0.03Se33 -21 0.22 7.86 0.008 PbSe33 212 2.57 2.52 0.21 Pb0.98La0.02Se34 -140 1.1 - 0.05 Pb0.97Ce0.03Se (our work) -44 0.353 3.24 0.056
5
300 400 500 600 700 800 0,8 1,2 1,6 2,0 2,4 2,8 3,2 3,6 k L x = 0 x = 0.01 x = 0.02 x = 0.03 Temperature (K ) k, kL (W /m .K ) kFigure 5.3: Total thermal conductivity, κ, and calculated lattice thermal conductivity, κL, of the Pb1-xCexSe (x = 0, 0.01, 0.02 and 0.03) compounds in the temperature range 300-773 K. Figure 5.4b shows the temperature dependence of the figure of merit, zT, for the
Pb1-xCexSe (x = 0.00, 0.01 and 0.03) samples in the temperature range of 300-773 K. It
is observed that the zT value is enhanced at high temperature by doping with Ce. An effective increase in power factor of the sample with x = 0.01 compared to undoped sample (Figure 5.4a), in combination with lower thermal conductivity compared to highly doped samples leads to the largest zT value of 0.27 at 775 K for this sample. According to the Table 5.2, the room temperature zT value of the sample with x = 0.03 is higher than the reported value for sample with the same composition in
Ref. 33, and very similar to the La doped sample.34 The very different transport
properties of La-doped PbSe and lower zT values compared with regular n-type PbSe was attributed to much lower mobility for this compound even though the carrier
300 400 500 600 700 800 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 x = 0 x = 0.01 x = 0.02 x = 0.03 (b) Temperature (K ) Fi gu re o f M er it 300 400 500 600 700 800 0 5 10 15 (a) x = 0 x = 0.01 x = 0.02 x = 0.03 Temperature (K ) PF (* 10 -4 W /m K ^2 )
Figure 5.4: (a) Temperature dependence of the thermoelectric power factor, PF, for Pb
1-xCexSe (x = 0, 0.01, 0.02 and 0.03) samples 300-800 K (b) Temperature dependence of the thermoelectric figure of merit, zT, for Pb1-xCexSe (x = 0, 0.01 and 0.02) samples in the temperature range of 300-773 K.
5.4 Conclusions
In summary, we have synthesized a series of polycrystalline compounds Pb1-xCexSe (x =
0, 0.01, 0.02 and 0.03) and investigated the effect of Ce doping on the thermoelectric properties. The substitution of Ce for Pb in PbSe results in an enhanced Seebeck coefficient for x = 0.01. The highest zT value of 0.27 was achieved for x = 0.01 at 775 K due to the enhanced electrical transport properties, which is rather low compared to other high performance thermoelectric materials. Nevertheless, given the small number of compositions considered here, further research will be required to
synthesize Pb1-xCexSe compounds with lower doping levels of Ce to fully understand
5
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