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Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics

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Science  03 Apr 2015:
Vol. 348, Issue 6230, pp. 109-114
DOI: 10.1126/science.aaa4166

Squeezing out efficient thermoelectrics

Thermoelectric materials hold the promise of converting waste heat into electricity. The challenge is to develop high-efficiency materials that are not too expensive. Kim et al. suggest a pathway for developing inexpensive thermoelectrics. They show a dramatic improvement of efficiency in bismuth telluride samples by quickly squeezing out excess liquid during compaction. This method introduces grain boundary dislocations in a way that avoids degrading electrical conductivity, which makes a better thermoelectric material. With the potential for scale-up and application to cheaper materials, this discovery presents an attractive path forward for thermoelectrics.

Science, this issue p. 109

Abstract

The widespread use of thermoelectric technology is constrained by a relatively low conversion efficiency of the bulk alloys, which is evaluated in terms of a dimensionless figure of merit (zT). The zT of bulk alloys can be improved by reducing lattice thermal conductivity through grain boundary and point-defect scattering, which target low- and high-frequency phonons. Dense dislocation arrays formed at low-energy grain boundaries by liquid-phase compaction in Bi0.5Sb1.5Te3 (bismuth antimony telluride) effectively scatter midfrequency phonons, leading to a substantially lower lattice thermal conductivity. Full-spectrum phonon scattering with minimal charge-carrier scattering dramatically improved the zT to 1.86 ± 0.15 at 320 kelvin (K). Further, a thermoelectric cooler confirmed the performance with a maximum temperature difference of 81 K, which is much higher than current commercial Peltier cooling devices.

Thermoelectric (TE) Peltier devices enable solid-state cooling to replace cumbersome vapor-compression cycle technologies as well as electricity generation from a variety of waste heat sources such as industries and vehicles. Next-generation distributed cooling systems enabled by small Peltier devices promise zonal and personal temperature control to provide enhanced comfort with reduced overall energy use (1). Widespread use of TE devices requires improvements in performance of TE materials but also the realization of improved performance in actual devices (1). The performance of TE materials is evaluated with a dimensionless figure of merit [zT = S2 × σ ×T/(κele + κlat)] dependent on the Seebeck coefficient (S), electrical conductivity (σ), electronic (κele) and lattice (phonon, κlat) thermal conductivity, and absolute temperature (T). Introducing dislocation arrays at grain boundaries has the potential to improve zT by decreasing thermal conductivity, but dislocation arrays formed by traditional sintering techniques also decrease electrical conductivity. By modifying a traditional liquid-phase sintering technique, we avoid this pitfall and provide a different pathway for fabricating bulk alloys with high zT.

Bismuth antimony telluride alloys are the most widely used TE bulk material developed in the 1960s for Peltier cooling with p-type composition close to Bi0.5Sb1.5Te3 and peak zT of 1.1 near 300 K (2). The Bi-Sb atomic disorder in Bi0.5Sb1.5Te3 scatters the heat-carrying phonons, reducing κlat that permits such high zT values. Matched with Bi2Te3–based n-type alloys, devices are commercially produced that provide a maximum temperature drop (ΔTmax) of 64 to 72 K with 300 K hot side (Th) (3, 4). Recent measured improvements in zT of Bi0.5Sb1.5Te3 bulk alloys have been reported using strategies primarily based on nanometer-scale microstructures to add boundary scattering of phonons at the composite interface or grain boundaries (58). However, improvements in the performance (ΔTmax) of Peltier cooling devices have not been realized since the development of bismuth antimony telluride (4).

Heat-carrying phonons cover a broad spectrum of frequencies (ω), and the lattice thermal conductivity (κlat) can be expressed as a sum of contributions from different frequencies (4, 9): Embedded Image. The spectral lattice thermal conductivity κs(ω) can be expressed as arising from the spectral heat capacity of phonons Cp(ω), their velocity v(ω), and their scattering time τ(ω), such that κs(ω) = Cp(ω) × v2(ω) × τ(ω). Phonons in all crystalline materials are scattered by other phonons by Umklapp scattering, which generally has a τU−1 ∼ ω2 dependence. Combining this with the Debye approximation for heat-carrying phonons [Cp(ω) ∼ ω2] gives κs(ω) = constant. This leaves a wide range of phonon frequencies where all frequencies contribute to the thermal conductivity (Fig. 1A).

Fig. 1 Full-spectrum phonon scattering in high-performance bulk thermoelectrics.

(A) The inclusion of dislocation scattering (DC + DS) is effective across the full frequency spectrum. Boundary (B) and point defect (PD) are effective only at low and high frequencies. The acoustic mode Debye frequency is fa. (B) Lattice thermal conductivity (κlat) for Bi0.5Sb1.5Te3 alloys produced by melt-solidification (ingot), solid-phase compaction (BM and S-MS), and liquid-phase compaction (Te-MS). The lowest κlat of Te-MS can be explained by the midfrequency phonon scattering due to dislocation arrays embedded in grain boundaries (inset, fig. S15C) (17). (C) The figure of merit (zT) as a function of temperature for Bi0.5Sb1.5Te3 alloys. The data points (red) give the average (±SD) of all 30 Te-MS samples (inset, fig. S9F) (17), which shows excellent reproducibility. (D) A Peltier cooling module (bottom) with 127 couples made from p-type Bi0.5Sb1.5Te3 Te-MS pellet (top) and n-type 1 weight percent (wt %) SbI3 doped Bi2Te2.7Se0.3 ingot. (E) The maximum coefficient of performance (COPmax) measured on modules of (D) where the high performance is confirmed with notably high ∆Tmax of 81 K with 300 K hot side (17).

The κlat can be further reduced with additional scattering mechanisms. Traditional mechanisms are only effective at the high- or low-frequency ends (4). Point-defect scattering of phonons from the Bi-Sb disorder in Bi0.5Sb1.5Te3 targets high-frequency phonons with a scattering time depending on frequency as τPD−1 ∼ ω4 (4), similar to Rayleigh scattering. However, boundary scattering of phonons targets low-frequency phonons, as it is frequency independent (τB−1 ~ constant) (10). Even the scattering of nanometer-sized particles can be well described with these two models as the small-size Rayleigh regime rapidly crosses over to the boundary regime as the particle size increases (11). A full-spectrum strategy targeting the wide spectrum of phonons, including midfrequency phonon scattering, is necessary for further reduction in κlat. However, at the same time the high carrier mobility (μ) must be maintained because the maximum zT of a material is determined by the ratio μ/κlat (quality factor) (4). Thus, any reduction in κlat by phonon scattering must not be compensated by a similar reduction in μ due to electron scattering for there to be a net benefit (12).

Liquid-phase sintering produces low-energy, semicoherent grain boundaries that one can expect to have a minimal effect on electron scattering. The techniques to engineer and characterize grain boundaries have been well established in materials science due to their importance in engineering the mechanical strength (13), magnetism (14), and other material properties (15). Most importantly, the periodic dislocations that can arise from such low-energy grain boundaries add a new mechanism that targets the midfrequency phonons with both τ −1 ∼ ω and τ −1 ∼ ω3 dependence that is between those for point-defect and boundary scattering (4, 9). To produce the periodic dislocations at low-energy grain boundaries in Bi0.5Sb1.5Te3 alloys, we applied a simple liquid-phase compacting process. The process differed from typical liquid-phase sintering because it included applied pressure and transient flow of the liquid phase during compaction. The process greatly reduced κlat to 0.33 W m−1 K−1 at 320 K (Figs. 1B and 2D) and resulted in an exceptionally high zT of 1.86 ± 0.15 at 320 K for dozens of independently measured Bi0.5Sb1.5Te3 samples (Fig. 1C) used to make a Peltier cooling module with 127 couples (Fig. 1D). The module outperforms all known single-stage Peltier cooling modules (4, 16), demonstrating a ΔTmax of 81 K with Th of 300 K (Fig. 1E). We compare ingot, ball-milled (BM), and stoichiometric melt-spun (S-MS) Bi0.5Sb1.5Te3 materials (Figs. 1 and 2) (17). The latter two types of samples were fabricated by using spark plasma sintering (SPS). Two different melt-spun materials were synthesized, stoichiometric (S-MS) and with excess Te (Te-MS) (Fig. 3A, red arrow).

Fig. 2 Comparison of thermoelectric properties of Bi0.5Sb1.5Te3 between different fabrication methods.

Introduction of dislocation arrays has a large effect on thermal conductivity but a small effect on electronic conductivity. (A) Temperature dependence of electrical conductivity (σ). Charge-carrier mobilities of S-MS (190 cm2 V−1 s−1) are lower than for Te-MS (280 cm2 V−1 s−1) materials (inset). (B) Temperature dependence of Seebeck coefficient (S) and power factor (σS2) (inset). Temperature dependences of total (C) and lattice (D) thermal conductivity (κtot and κlat) for all samples. The error bars of Te-MS in all panels are the standard deviations from the measurements of 30 samples (fig. S9).

Fig. 3 Generation of dislocation arrays at grain boundaries in Bi0.5Sb1.5Te3.

(A) Phase diagram of Bi0.5Sb1.5Te3–Te system showing an eutectic composition at 92.6 at % Te. Blue and red arrows indicate the nominal composition of melt-spun stoichiometric Bi0.5Sb1.5Te3 (S-MS) and 25 wt % Te excess Bi0.5Sb1.5Te3 (Te-MS) material. (B) The scanning electron microscope (SEM) image of melt-spun ribbon of Te-MS material showing the Bi0.5Sb1.5Te3 platelets surrounded by the eutectic phase of Bi0.5Sb1.5Te3–Te mixture, in which the Bi0.5Sb1.5Te3 particles (white spots) have the size of 10 to 20 nm. The SEM image of melt-spun ribbons of S-MS is shown in fig. S1B. (C) Schematic illustration showing the generation of dislocation arrays during the liquid-phase compaction process. The Te liquid (red) between the Bi0.5Sb1.5Te3 grains flows out during the compacting process and facilitates the formation of dislocation arrays embedded in low-energy grain boundaries.

Melt-spun samples have plate-like microstructure of S-MS and Te-MS ribbons with platelets several micrometers wide and several hundred nanometers thick (Fig. 3B and fig. S1, B to D) (17). The Te excess composition has an eutectic microstructure over the entire ribbon that forms between the Bi0.5Sb1.5Te3 platelets (Fig. 3B and fig. S1, C and D) (17). The eutectic phase consists mostly of elemental Te and a small amount of Bi0.5Sb1.5Te3 nanoparticles. During the high temperature (480°C) and pressure (70 MPa) process of SPS, above the melting point of Te (450°C), the excess Te in the eutectic phase was liquidified and expelled to the outer surface of the graphite die (Fig. 3C and fig. S3) (17).

The morphology of the grain boundary structure in the Te-MS material is remarkably different than the typical grain boundaries as found in the S-MS material. Transmission electron microscopy (TEM) images (Fig. 4, B to J) reveal a Moiré pattern (up to 50 nm wide) at the grain boundaries between the Bi0.5Sb1.5Te3 grains in the Te-MS material (Fig. 4B), compared to the few nanometer width as observed in the S-MS material (Fig. 4A). Moiré patterns can be observed when the grain boundary plane is oblique to the TEM zone axis, so the two crystals overlap along the viewing direction. The Moiré patterns indicate that the grains are highly crystalline with clean grain boundaries in which the obscured dislocations exist. From the elemental mapping (TEM-energy-dispersive x-ray spectroscopy) in the Te-MS material, we confirmed no presence of excess Te at the grain boundaries (fig. S19), suggesting that the abnormal contrast is not due to a secondary phase.

Fig. 4 Dislocation arrays embedded in grain boundaries.

(A) Low-magnification TEM image of S-MS material. (B) Low-magnification TEM image of a Te-MS material. (C) Enlarged view of boxed region in (B). The grain boundary indicated by the red arrow is aligned along the zone axis showing only strain effects, whereas the two grain boundaries in the upper part show Moiré patterns. The high-magnification TEM image of circled area is shown in fig. S15. (D) Enlarged view of boxed region in (C). The insets are FFT images of adjacent grains crossing a twist-type grain boundary (GB). (E) IFFT image of (0 1 5) and (0 1 Embedded Image) atomic planes of left and right grains in the inset (D). Along the boundary, edge dislocations, indicated as red symbols, are clearly shown. Burgers vectors of each dislocation is BD = <0 1 5>, parallel to the boundary. The misfit between the two planes is ~0.15 Å (~ 4.5%), which compensates the misfit spacing of ~6 nm and is identical to the periodic patterns (~6 nm spacing) in (F) and (G). (F) Enlarged view of boxed region in (B). A view of tilted zone axis from (C), showing periodic Moiré patterns along GBs. (G) Enlarged views of boxed region in (F). (H) Enlarged view of boxed region in (B). (I) Enlarged view of boxed region in (H). The insets are FFT images of adjacent grains crossing a tilt-type GB. Enlarged high-resolution TEM image of boxed region dislocation arrays is shown in fig. S18C. (J) FFT image of (0 1 5) atomic planes in the inset of (I). Burgers vectors of the each dislocation is BD=<Embedded Image 1 0>, perpendicular to the boundary. The misfit spacing of ~2.5 nm was obtained. Insets of (E) and (J) are the IFFT images of boxed areas, respectively, clearly identifying the dislocations. Other arrays of dislocations embedded in the low-angle grain boundary are shown in figs. S17 and S18.

The clean grain boundary structure observed in Te-MS material requires the presence of periodic arrays of dislocations that form at low-energy grain boundaries. Figure 4C shows a grain boundary (indicated by red arrow) aligned along the zone axis showing only strain effects. The indexing of fast Fourier transform (FFT) images confirmed the coincidence of (0 1 Embedded Image) and (0 1 5) atomic planes along the two adjacent grains at the twist-type grain boundary with lattice spacing of 3.30 and 3.15 Å, respectively. Edge dislocation arrays are found in inverse FFT (IFFT) images of Fig. 4D (Fig. 4E, red symbols). The dislocations compensate for the d-spacing mismatch between the crystallographic planes of adjacent grains, which is ~0.15 Å (4.5%) between (0 1 5) and (0 1 Embedded Image) atomic planes, introducing misfit spacing of ~6 nm. This mismatch is identical, as expected (18) to the periodicity in the translational Moiré patterns of the grain boundary observed in Figs. 4, F and G, which were taken by slightly tilting the zone axis from that of Figs. 4, C and D. Dislocation arrays with the periodic spacing of ~2 nm were observed together with Moiré fringes at the circled area of the upper grain boundary in Fig. 4C (fig. S15). Another array of dislocations was observed in tilt-type boundary in Fig. 4H. The FFT images in the inset of Fig. 4I revealed the 5° misorientation between two adjacent grains and an inverse IFFT image of (0 1 5) atomic planes in Fig. 4J and dislocation arrays with the misfit spacing of ~2.5 nm (fig. S16C). Such dislocation arrays are expected to be present in low-angle grain boundaries or between grains with small d-spacing mismatch to lower the interfacial energy (19). The dislocation arrays observed here have a close spacing between cores of ∼2.5 and 6 nm, which, considering the size of the grains, corresponds to an areal dislocation density of ∼2 × 1011 cm−2 that is 100 times higher than that observed in grains of Bi2Te3 (20).

In a typical solid-phase sintering, the grain boundaries have random alignment due to a limited diffusion length of atoms/dislocations, and so the chance of low-angle boundary (<11°) is very low (19). In contrast, in liquid-phase sintering, the wetting liquid penetrates into the grain boundaries (21). Atoms in a liquid have much higher diffusivities and also dislocations at the grain boundaries have much higher diffusion lengths (22). The high solubility of Bi and Sb in the Te liquid and insignificant solubility of Te in the solid phase contributes to the very rapid mass transport (over 100 times faster than in solids) and rapid rearrangement of the grains (21). In addition, the capillary force of the liquid at the grain boundary exerts a force facilitating grain rearrangement (21, 23).

However, the liquid phase becomes absorbed in the matrix of the grain in a typical transient liquid-phase sintering, leading to compositional variation of the matrix. This prohibits the application of traditional liquid-phase sintering for thermoelectric Bi-Sb-Te because compositional variation will degrade the TE properties. In contrast, the liquidified excess Te in the eutectic phase is expelled during the high-pressure–assisted liquid-phase compacting processing. Any slight amount of Te remaining is nearly insoluble in Bi0.5Sb1.5Te3 and does not as dramatically affect the carrier concentration. Furthermore, the applied pressure induces additional stresses, which helps create dislocations (23) and accelerate grain rearrangement (21). As a result, the grain interfaces rearrange to allow low-energy grain boundaries, which results in dislocation arrays within much of the grain boundary.

From the thermal and electrical transport properties, it appears that the semicoherent grain boundaries of Te-MS material do maintain high charge-carrier mobility (17) but provide sufficient atomic strain to scatter heat-carrying phonons. The small increase in the Seebeck coefficient is due to a slight decrease in carrier concentration for S-MS and Te-MS materials compared with the ingot material (Fig. 2B). The reduced grain size of the S-MS and Te-MS materials leads to lower carrier mobility. This decrease is less dramatic for Te-MS indicating that the semicoherent grain boundaries in Te-MS are less disruptive to charge carriers than those in the S-MS material (Fig. 2A). Low-energy grain boundaries in Bi-Sb-Te are likely formed when atomic displacements are primarily in the Te-Te van der Waals layer, which have been observed experimentally (24). Displacements in this layer are also likely to be least disruptive to the charge carriers and maintain high mobility.

Although the dense dislocation arrays embedded in grain boundaries do little to scatter charge carriers, they are remarkably efficient at scattering phonons and greatly reducing thermal conductivity in the Te-MS material (Fig. 2D). The κlat values were extracted from κtot by subtracting the electronic thermal conductivity (κele), which was estimated using the Wiedemann-Franz relation. We calculated the Lorenz number (L0) using the reduced Fermi energy obtained from measured S values at different temperatures (17). The calculations indicate that dislocation arrays embedded in grain boundaries cause the reduction of κlat. The κlat value at 320 K (0.33 W m−1 K−1) of the Te-MS sample is comparable to the reported value (0.29 W m−1 K−1) in highly deformed Bi0.2Sb1.8Te3 with high-density lattice defects (25), indicating that dense dislocation arrays at grain boundaries are effective to reduce the κlat.

We have modeled the temperature-dependent κlat of BM, S-MS and Te-MS materials based on the Debye-Callaway model (26) using parameters derived from independently measured physical properties (Fig. 1B) (17). The total phonon relaxation time (τtot) was estimated by including scattering from Umklapp processes (τU) and point defects (τPD) using parameters based on bulk alloys (9, 27, 28). We used microscopy to determine the parameter of average grain size (d) for the grain boundary scattering (τB) (17, 18). The calculated κlat (0.66 W m−1 K−1 at 300 K) for BM matches the measured data well, verifying the values used for Umklapp processes (τU) and point defects (τPD) of Bi0.5Sb1.5Te3 alloys. The 18% reduction in κlat observed in S-MS material relative to BM material at 300 K is explained by a grain size reduction from 50 μm to 300 nm. The additional 29% reduction in κlat for Te-MS material is explained by introducing phonon relaxation times associated with additional scattering from dislocation cores (τDC) and strain (τDS) (2931), using the experimentally determined dislocation density (~2 × 1011 cm−2) and the effective Burgers vector (BD of ~12.7 Å).

This analysis shows that the periodic spacing of dislocation arrays plays a vital role for reducing κlat. When the spacing between dislocation cores is small, as observed in Te-MS material, the scattering from dislocation strain is reinforced (32). This effect was experimentally observed in Ag-Cd alloys with the large scattering effect as due to the dislocation pile-up (10). When dislocations are closely spaced, the effective Burgers vector (BD) is the sum of the individual Burgers vectors involved (33). As the scattering rate is proportional to BD2 (17), this pile-up of dislocation strain leads to a nonlinear increase in scattering. The exact amount of reinforcement is not precisely specified in the theory and leads to the only adjustable parameter in the model. Nevertheless, the Burgers vector that precisely fits the data is well within the range observed experimentally (24).

The dislocation scattering mechanism is particularly effective because it targets phonons not scattered sufficiently by the other mechanisms providing a full-spectrum solution to scatter phonons. Compared with Umklapp scattering (Fig. 1A), boundary scattering from grain boundaries (τB−1 ∼ ω0) is efficient at scattering low-frequency phonons but quickly becomes ineffective at higher frequencies. Conversely, point defects scatter mostly high-frequency phonons (τPD−1 ∼ ω4). However, most of the remaining heat-carrying phonons have intermediate frequency around 0.63 THz (Fig. 1A) and avoid scattering from boundaries and point defects. The 0.63 THz phonons still carry 74% of the heat that they would have carried without any scattering from boundaries or point defects in the S-MS material. Including the dislocation scattering as found in the Te-MS material, the κs of 0.63 THz phonons drops to less than 45% of the heat that they would have carried with only Umklapp scattering (Fig. 1A).

The low thermal conductivity while maintaining high mobility results in a dimensionless figure of merit (zT) for Te-MS that reaches a maximum value of 2.01 at 320 K within the range of 1.86 ± 0.15 at 320 K for 30 samples (Fig. 1C and fig. S9F), a much higher value than for S-MS or ingot materials. Most importantly, for cooling applications, the zT at 300 K is high (1.72 ± 0.12), suggesting that it should provide superior refrigeration than other materials. For example, the zT is higher than that of nanograined Bi0.5Sb1.5Te3 alloy (dotted line in Fig. 1C) (7) near room temperature. This results from the ability of dislocation arrays to enable a full-spectrum scattering of phonons due to a compounding effect not found in randomly dispersed dislocations inside grains. The present liquid-phase compaction method assisted with a transient liquid flow is highly scalable for commercial use and generally applicable to other thermoelectric systems such as PbTe, CoSb3, and Si-Ge alloys, and even engineer thermal properties of other thermal materials such as thermal barrier coatings (34). This may accelerate practical applications of thermoelectric systems in refrigeration and beyond to waste heat recovery and power generation.

The ultimate verification of the exceptional zT comes from testing the performance of a Peltier cooler (Fig. 1D) made using Te-MS materials. A state-of-the-art Peltier device using the Te-MS as the p-type material and an n-type ingot material made cutting-edge commercial methods (17). The device not only greatly outperforms a similar device made with the p- and n-type ingot materials (Fig. 1E) but also outperforms all commercial Peltier devices (16). We determined the coefficient of performance (COP) (cooling power divided by input power) to assess the cooling performance of both Peltier devices. A key characteristic performance metric of a Peltier cooler is ΔTmax, which is directly related to the zT of materials. The ΔTmax values are easily extracted from the COP measurements as the temperature difference reached when the cooling power vanishes. Although the ΔTmax of the Peltier cooler made from the ingot materials falls within the range of current commercial devices, 64 K < ΔTmax < 72 K for Th of 300 K, the Peltier cooler made with the Te-MS p-type material exhibits a ΔTmax of 81 K for Th of 300 K (Fig. 1E) (17).

Supplementary Materials

www.sciencemag.org/content/348/6230/109/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S21

Tables S1 to S4

References (3556)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: This work was supported by IBS-R011-D1, the National Research Foundation of Korea (2013R1A1A1008025), the Human Resources Development program (no. 20124010203270) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry, and Energy, and AFOSR MURI FA9550-10-1-0533.
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