Enhancement of High-Temperature Thermoelectric Properties in Pd-decorated Bi-Sb-Te System

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Abstract

1. INTRODUCTION

In the ongoing fight against global warming, research on diverse sustainable energy harvesting technologies continues to be a crucial focus[1]. Among environmentally friendly approaches, thermoelectric technology stands out for its ability to directly convert waste heat into electricity, eliminating the need for fossil fuel combustion[2]. The effectiveness of thermoelectric devices hinges on the thermoelectric figure-of-merit (zT) of the materials used[3,4]. As a result, a significant research effort has been directed towards enhancing the zT of thermoelectric materials. zT (=S²σT/κ) relies on the Seebeck coefficient (S), electrical conductivity (σ), temperature (T in Kelvin), and thermal conductivity (κ). The κ comprises both electronic contribution to thermal conductivity (κ_e) and lattice thermal conductivity (κ_l)[5,6]. The term S² σ in the zT equation is referred to as the power factor (PF), which determines the electron transport properties of the material[7]. As illustrated in the zT equation, the optimization of zT occurs when the PF is high, and κ is low.

Bismuth telluride (Bi₂Te₃)-alloy-based systems have been extensively investigated as thermoelectric materials for near-room-temperature applications, and are predominant in the thermoelectric cooling industry[8-10]. Notably, recent advancements in processing techniques, particularly nanostructuring, have significantly enhanced the thermoelectric performance of p-type Bi-Te-based materials, especially within the Bi-Sb-Te alloy system[1,11-12]. The use of high-energy ball milling and spark plasma sintering (SPS) to synthesize nanocomposites has led to a remarkable increase in the zT of p-type Bi-Sb-Te alloys. The zT value has risen from 1.0, which is typically observed in ingots of the pristine material, to a range of 1.4-1.5[13, 14]. This enhancement is attributed to the reduction in lattice thermal conductivity (κ_l) achieved by introducing phonon scattering centers with varying size scales, including nanosized inclusions and grain boundaries.

The concept of ‘nanoparticle-in-alloy’, which involves the dispersion of nanoparticles into the alloy matrix, has been explored as a straightforward and scalable nano-structuring method for bulk thermoelectric materials[15]. Many studies have employed the method of adding metal acetate powders to alloys and then generating metal nanoparticles through reduction pyrolysis. The metal nanoparticles produced by this method are several tens of nanometers in size. For instance, Lee et al. incorporated 50 nm Ag and Cu acetate powders into Bi_0.5Sb_1.5Te₃ and achieved Ag and Cu nanoparticles of around 40 nm after reduction heat treatment[16,17]. Similarly, Hwang et al. employed reduction heat treatment with Co acetate powder to obtain Co particles ranging from 20 to 80 nm[18].

This study investigates the impact of incorporating metal nanoparticles into a Bi_0.5Sb_1.5Te₃ matrix. Previous studies have utilized acetate precursors to obtain particles with sizes in the tens of nanometers[16-18]. This study explores the thermoelectric properties of 500-1000 nm Pd nanoparticles obtained through the pyrolysis of Pd acetate. Samples were sintered with 0.02, 0.04, 0.08, and 2.00 wt.% of Pd acetate, respectively. In addition, we analyzed data obtained from the experiment using an Effective Mass (EM) model. We calculated key band parameters like density-of-states effective mass (m_d^*), non-degenerate mobility (μ₀), and weighted mobility (μ_W) using the EM model. Specifically, it was determined that the m_d^* of all samples increased and exceeded that of pristine Bi_0.5Sb_1.5Te₃, and the μ₀ of all samples decreased compared with pristine Bi_0.5Sb_1.5Te₃. In the low-temperature range (T < 423 K), no improvement in thermoelectric properties was observed with the addition of Pd acetate. However, at high temperatures (T ≥ 423 K), an improvement in thermoelectric properties was noted with the addition of 0.02 wt.% Pd acetate, due to both μ_W improvement and κ_l suppression.

2. EXPERIMENTAL

Bi_0.5Sb_1.5Te₃ was synthesized using a conventional solid-state process with high purity (99.999%) Bi, Sb, and Te shots. The raw materials were stoichiometrically weighed and placed in a 15 mm-diameter quartz tube and the quartz tube was vacuum sealed at 10^-4 torr. The quartz tubes were melted in a furnace for 12 h at 1073 K and then water quenched. The ingots were crushed into powder using a high-energy ball mill (SPEX 8000D, SPEX). For the Pd acetate samples, Pd acetate powder was mixed with Bi_0.5Sb_1.5Te₃ powder and the mixed powder was transferred to an alumina crucible and heated at 573 K for 3 h in an N2 atmosphere. The powders mixed with Pd acetate were sintered by spark plasma sintering (SPS) at 730 K for 5 min at a pressure of 60MPa in a vacuum (SPS-1030, Sumitomo Coal Mining Co., Ltd.).

A phase analysis of the samples was performed using X-ray diffraction (XRD) (Bruker D8 Discover with Cu Kα, λ = 1.54059 Å). The samples were examined using scanning electron microscopy (SEM) (HITACHI (SU8010)). Energy-dispersive spectrometry (EDS) (Bruker Quantax Xflash 6/60) was utilized for elemental mapping.

The S and σ were measured in a temperature range of 300–520 K using a ZEM-3 (Advanced RIKO Inc., Yokohama, Japan) under a He atmosphere. The Hall measurement was made using the van der Pauw method at 300 K (HMS5300, Ecopia, Anyang, South Korea). The temperature dependence of the thermal diffusivity, λ, was measured in both directions using a laser flash method (LFA457, Netzsch, Selb, Germany) and converted to a κ value using a combination of heat capacity, C_p, and density, ρ_s, (κ = ρ_sC_pλ).

We also calculated the band parameters like density-of-states effective mass (m_d^*), non-degenerate mobility (μ₀), and weighted mobility (μ_W) using the EM model[19,20].

According to the EM model, the S is defined as Equation (1).

where k_B, e, η, and F_j(η) are the Boltzmann constant, electric charge, reduced Fermi level, and the Fermi integral of order j (Equation (2)), respectively.

The n_H can be described in terms of the η (within the Fermi integral) and the density-of-states effective mass (m_d^*) as shown below in Equation (3).

The T and h in Equation (3) are the absolute temperature and the Planck constant, respectively.

The μ_H and μ₀ can be defined with Equations (4, 5).

where C_l, N_v and E_def are the elastic constant, valley degeneracy and deformation potential.

The μ_W is defined with Equations (6,7) below, the μ_W at 300 K is calculated using the m_d^* and μ₀ from Equations (3, 4). Equation (7) is an expression that approximates μ_W within 3% accuracy for |S|≥20 even in the absence of n_H [19]. At high temperatures, Hall measurements are not conducted, so μ_W was calculated using Equation (7).

where m₀ is the electron rest mass.

And the B-factor is defined with Equation (8).

While the theoretical maximum zT at 473 K requires measuring n_H using the SPB model, the absence of n_H data at this temperature necessitated the calculation of intrinsic conductivity (σ₀) as proposed by Hu et al. The relationship between σ₀ and the experimental conductivity σ is described by the Fermi integral of order 0, F₀, as follows[21].

where F₀ can be defined as Equation (11).

In Equation (11), S_r represents the ratio of the experimental S, to the constant S₀ (=k_B/e). The optimal S_r for the theoretical maximum zT (S_r,opt) is directly linked to the B-factor and is given by Equation (12).

The theoretical maximum zT (zT_max)can be calculated using Equation (13), which involves S_r,opt, L, and the B-factor.

3. RESULTS AND DISCUSSION

Fig 1 shows the XRD analysis pattern of the sintered Pd-decorated samples (pristine Bi_0.5Sb_1.5Te₃, and Bi_0.5Sb_1.5Te₃ decorated with 0.02, 0.04, 0.08, and 2.00 wt.% of Pd acetate). It can be seen that rhombohedral crystal structured Bi_0.5Sb_1.5Te₃ was synthesized without impurities in all the samples, as their peaks coincide with the peaks of Bi_0.5Sb_1.5Te₃ (JCPDs # 491713), without secondary phase peaks. There was an observable peak shift in all samples.

Fig. 1.

X-ray diffraction (XRD) patten of Bi_0.5Sb_1.5Te₃ with varying amounts of added Pd acetate (0, 0.02, 0.04, 0.08, and 2.00 wt.%).

Figs 2(a-c) show TEM images of the Bi_0.5Sb_1.5Te₃ powders mixed with 0.08 wt.% Pd acetate after pyrolysis. The protruding parts in Figs 2(a-c) can be identified as Pd from the lattice spacing. At this point, the lattice spacing of Pd metal particles is 0.31 nm, closer to the value of Pd(111)[22]. Pd metal particles of various sizes co-existed, including those in the tens of nanometers range and larger particles approaching 1 micrometer. However, when the amount of Pd acetate mixed with Bi_0.5Sb_1.5Te₃ powder increased, the size of the Pd particles after pyrolysis also increased.

Fig. 2.

(a-c) Transmission electron microscopy (TEM) images of Bi_0.5Sb_1.5Te₃ with 0.08 wt.% Pd acetate before sintering, (d) scanning electron microscopy (SEM) image of Bi_0.5Sb_1.5Te₃ with 2.00 wt.% Pd acetate before sintering, and (e) SEM-EDS (Energy dispersive spectroscopy) Pd mapping of the sample shown in (d).

Fig 2(d) shows an SEM image of the Bi_0.5Sb_1.5Te₃ powders mixed with 2.00 wt.% Pd acetate after pyrolysis. We observed two different kinds of particles: brighter particles of a few micrometers size, and darker particles with a much larger size. Among the brighter particles, some of them were identified as Pd particles by Pd elemental mapping via SEM-EDS (Fig 2(e)). When a significantly higher amount of Pd acetate (approximately 25 times more) was added to the sample shown in Figs 2(d,e), compared to those in Figs 2(a-c), large agglomerated Pd particles measuring approximately 1 µm were observed. This indicates that the addition of excessive Pd acetate hinders effective dispersion, leading to the formation of larger particle clusters rather than well-dispersed smaller particles.

Fig 3(a) presents a SEM image of the Pd acetate 0.08 wt.% sample after sintering. It reveals brighter regions, some appearing as spots, while others exhibit elongated shapes, with dimensions approximately a few micrometers in size. To identify the elemental composition of these regions, we performed EDS mapping on the area shown in Fig 3(a). The EDS spectra (Fig 3(b)) and elemental mapping for Bi (Fig 3(c)), Sb (Fig 3(d)), Te (Fig 3(e)), and Pd (Fig 3(f)) provide insight into the sample’s composition. Figs 3(c-e) demonstrate that the brighter regions correspond to clustered Pd, while the darker regions represent the Bi_0.5Sb_1.5Te₃ matrix. The EDS analysis, as shown in Table 1, detected Pd at 1.06 wt.% in the mapped area, significantly higher than the nominal 0.08 wt.% in the initial sample. This discrepancy suggests that Pd may have agglomerated in this specific region during the sintering process.

Fig. 3.

(a) SEM image of the 0.08 wt.% Pd acetate sample after sintering, (b) EDS spectra, SEM-EDS elemental mapping of the same sample for (c) Bi, (d) Sb, (e) Te, and (f) Pd.

Table 1.

EDS spectra of the Fig. 3(a) region of the 0.08 wt.% Pd acetate sample after sintering.

Fig 4 shows the electronic properties of samples with varying Pd acetate content. Fig 4(a) specifically presents the electrical conductivity (σ) as a function of temperature and Pd acetate concentration. Generally, σ decreases as temperature rises across all samples. The addition of 0.02 wt.% Pd acetate enhanced σ at temperatures below 400 K, compared to pristine Bi_0.5Sb_1.5Te₃. Above 400 K, however, the pristine sample exhibited higher σ. The 0.02 wt.% Pd acetate sample reached a peak σ of 463.2 S cm^-1 at 300 K. Samples with 0.04 and 0.08 wt.% Pd acetate showed lower σ than the pristine material across all tested temperatures. In contrast, the 2.00 wt.% Pd acetate sample displayed the highest σ throughout the temperature range. This anomalous behavior of the 2.00 wt.% sample likely stems from the presence of heavily agglomerated Pd particles, observed even before sintering (as shown in Fig 2(e)).

Fig. 4.

(a) σ (T), (b) S (T), and (c) PF (T) of the Bi_0.5Sb_1.5Te₃ + x wt.% Pd acetate samples (x = 0, 0.02, 0.04, 0.08, and 2.00) in a T range of 300-523 K.

Fig 4(b) shows the S as a function of temperature and Pd acetate content. S peaks near 375 K for all samples, then decreases with temperature due to increasing bipolar conduction. Pristine Bi_0.5Sb_1.5Te₃ exhibited the highest S below 423 K, reaching 276.2 μV K^-1 at 373 K. As temperature rises, Pd-included samples showed a higher S than pristine Bi_0.5Sb_1.5Te₃. At 473 K, the 0.02 wt.% Pd acetate sample achieved the highest S (212.3 μV K^-1). This suggests Pd inclusion may suppress bipolar conduction, as evidenced by a slower S decrease at higher temperatures. However, the 2.00 wt.% Pd sample showed significantly lower S compared to samples with less Pd content. At 300 K, increasing Pd content decreased the PF compared to the pristine sample. Above 400 K, the PF of the 0.02 wt.% Pd sample was comparable to that of the pristine sample, likely due to suppressed bipolar conduction from Pd inclusion.

Fig 5(a) shows the temperature-dependent κ for varying Pd contents in Bi_0.5Sb_1.5Te₃. The pristine sample exhibited the highest κ across most temperature ranges, except for the 2.00 wt.% Pd sample. Lightly Pd-decorated samples (x ≤ 0.08) showed significantly lower κ than the pristine sample as temperature increases. For narrow band gap materials like Bi_0.5Sb_1.5Te₃ (~0.2 eV), κ comprises lattice thermal conductivity (κ_l), electronic thermal conductivity (κ_e), and bipolar thermal conductivity (κ_bp): κ = κ_l + κ_e + κ_bp. Fig 5(b) demonstrates that Pd inclusion effectively suppresses κ_l + κ_bp across all temperatures, particularly for the 0.02 wt.% Pd sample. The κ_e is calculated using κ_e = LσT, where L is the Lorenz number. L is estimated using Equation (9)[23]:

Fig. 5.

(a) κ (T), (b) κ_l + κ_bp (T) (inset: κ_l (x) at 300 K), (c) κ_l + κ_bp (T^-1) (dashed line: κ_l), (d) κ_bp (T) (inset: κ_bp (x) at 300 K), and (e) zT (T) (inset: average zT (x) (423-523 K) of the Bi_0.5Sb_1.5Te₃ + x wt.% Pd acetate samples (x = 0, 0.02, 0.04, 0.08, and 2.00) in a T range of 300-523 K.

The inset in Fig 5(b) shows the Pd content (x) dependence of κ_l at 300 K, where κ_bp is negligible. The 0.02 wt.% Pd sample exhibited the lowest κ_l (0.69 W m^-1K^-1), approximately 10% lower than the pristine sample. Fig 5(d) presents the estimated κ_bp, obtained by subtracting the extrapolated ~T^-1 trend of κ_l from κ_l + κ_bp. As shown in Fig 5(c), we identified the region where κ_l + κ_bp decreases as T^-1 increases by plotting T^-1 on the x-axis. Assuming a linear relationship between κ_l and T^-1, we extrapolated a line (dashed line) from the slope of the decreasing region to determine the κ_l values corresponding to different T^-1 values.

For this analysis, we assume κ_bp is negligible at room temperature. The κ_bp increases substantially with temperature for all samples, with the x = 0.02 sample showing a significantly lower κ_bp than the pristine sample at 523 K. The inset in Fig 5(d) shows that at 473 K, the κ_bp of the x = 0.02 sample decreased by 30% compared to the pristine sample (from 0.44 to 0.31 W m^-1 K^-1). Fig 5(e) shows the temperature-dependent zT. At 473 K, the zT of the pristine sample increased by 32% (from 0.41 to 0.54) when x = 0.08. While the Pd-containing samples had a lower zT than pristine Bi_0.5Sb_1.5Te₃ below 373 K, they surpassed the pristine sample at higher temperatures, primarily due to κ_l and κ_bp suppression.

The inset in Fig 5(e) presents the average zT for temperatures above 423 K, demonstrating the improvement due to Pd addition. The average zT increased from 0.44 in pristine Bi_0.5Sb_1.5Te₃ (20% increase) with 0.02 wt.% Pd acetate, and to 0.47 (7% increase) with 0.04 wt.% Pd. This enhancement in average zT at high temperatures is attributed to the simultaneous reduction of κ_l and κ_bp by the Pd acetate addition.

Fig 6(a) shows the measured Hall carrier concentration (n_H) as a function of Pd acetate content (x). While n_H increases with x, the changes are not substantial. In Fig 6(b), Seebeck-Pisarenko plots, calculated using the effective mass (EM) model, are fitted to the measured n_H and S for different x values. This fitting allows the determination of the density-of-states effective mass (m_d^*) using Equations (1) and (3). At 300 K, m_d^* shows a gradual increase with increasing x. The increase in m_d^* with x is primarily attributed to an increase in the single band mass (m_b^*). Consequently, as shown in Fig 6(c), the corresponding non-degenerate mobility (μ₀) decreases with increasing x at 300 K, as calculated using Equations (3) and (4). From μ₀, which is inversely proportional to both m_b^* and the deformation potential (E_def), we can derive the change in E_def with increasing x (shown in the inset of Fig 6(c)). For these calculations, a valley degeneracy (N_v) of 6 and an elastic constant of 68 GPa were used (Equation (5))[24]. Generally, E_def increases with increasing x, indicating that the carrier-phonon interaction becomes stronger as x increases. This stronger interaction hinders carrier transport[25-27].

Fig. 6.

(a) Hall carrier concentration (n_H) (x), (b) m_d^* (x), (c) μ₀ (x), and inset of (c) deformation potential (E_def) (x) of the Bi_0.5Sb_1.5Te₃ + x wt.% Pd acetate samples (x = 0, 0.02, 0.04, 0.08, and 2.00) at 300 K.

Fig 7 presents the theoretical maximum PF and zT estimated using the EM model. At 300 K, Fig 7(a) shows the calculated μ_W for different Pd content. The μ_W, which is comprised of band parameters like m_d^* and μ₀, is related to the maximum PF of a sample. The pristine sample exhibited the highest μ_W (403 cm² s^-1 V^-1) among all samples at 300 K, suggesting it will have the highest theoretical maximum PF at this temperature.

Fig. 7.

(a) μ_W (x), (b) B-factor (x), (c) PF (x), (d) zT (n_H) at 300 K, (e) μ_W (x), and (f) B-factor (x) at 473 K of the Bi_0.5Sb_1.5Te₃ + x wt.% Pd acetate samples (x = 0, 0.02, 0.04, 0.08, and 2.00).

Fig 7(b) shows the calculated B-factor at 300 K, which is a function of μ_W, T, and ĸ_l (as shown in Equation (8)). While μ_W relates to the theoretical maximum PF, the B-factor corresponds to the theoretical maximum zT. At 300 K, the B-factor decreased with increasing Pd content, with the highest value (0.354) observed in the pristine sample. This indicates that increasing Pd content (x) did not help improve the theoretical maximum zT at 300 K. Based on the 300 K μ_W obtained in Fig 7(a), Fig 7(c) presents the theoretical Hall carrier concentration (n_H)-dependent PF calculations (shown as lines) alongside experimental PF values (indicated as symbols). Comparing these reveals that further doping to increase n_H could improve the PF of all samples. For instance, the experimental PF of the pristine sample (2.97 mW cm^-1 K^-2) could potentially be improved by 22 % (to 3.61 mW cm^-1 K^-2) according to the EM model calculation. Fig 7(d) presents the calculated n_H-dependent zT curves (lines) together with the experimental values (symbols). Unlike the PF, the experimental zT of all samples are positioned near the optimum n_H for the highest predicted zT. The theoretical maximum zT and PF calculated using the EM model represent the upper limits achievable when the n_H is tuned to its optimal value. Since the experimental value is not optimized for n_H, a discrepancy between this theoretical value and the experimental results is commonly observed.

At higher temperatures, such as 473 K, both the μ_W and B-factor peak at x = 0.02, unlike the pristine sample, as shown in Figs 7(e,f). This shift is attributed to the suppression of bipolar conduction and ĸ_l. The B-factor improvement in the x = 0.02 sample (0.177) compared to the pristine sample (0.125) amounts to a 42 % increase. This suggests a comparable improvement in the theoretical maximum zT could be achieved if the n_H is optimally tuned. Using Equations (10-13), the zT_max of the x = 0 and 0.02 sample are 0.41 and 0.55, respectively. The zT_max of the x = 0.02 sample is about 34 % higher than that of the pristine sample.

4. CONCLUSIONS

This study examined the effects of sintering Bi_0.5Sb_1.5Te₃ powders decorated with nanoscale Pd particles. Despite post-sintering aggregation into micron-sized clusters, the Pd particles had a significant influence on their thermoelectric properties. At 300 K, Pd-decorated samples exhibited lower weighted mobilities but enhanced phonon scattering compared to the pristine sample. As the temperature increased, both weighted mobility and thermoelectric quality factor improved in the Pd-decorated samples, indicating a higher theoretical maximum power factor and zT. At 473 K, the Bi_0.5Sb_1.5Te₃ + 0.02 wt.% Pd sample demonstrated a remarkable 40 % improvement in theoretical maximum zT over the pristine sample, primarily due to effective suppression of bipolar conduction. These findings highlight that Pd decoration, even with particle aggregation, can substantially enhance the thermoelectric properties of Bi_0.5Sb_1.5Te₃, especially at elevated temperatures.

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