Dislocation Evolution and Migration at Grain Boundaries in

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Dislocation Evolution and Migration at Grain Boundaries in Thermoelectric SnTe Di Wu, Xiang Chen, Fengshan Zheng, Hongchu Du, Lei Jin, and Rafal E Dunin-Borkowski ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.9b00061 • Publication Date (Web): 02 Apr 2019 Downloaded from http://pubs.acs.org on April 3, 2019

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ACS Applied Energy Materials

Dislocation Evolution and Migration at Grain Boundaries in Thermoelectric SnTe Di Wu†, Xiang Chen‡, Fengshan Zheng§,*, Hongchu Du§,||, Lei Jin§,*, Rafal E. Dunin-Borkowski§ †Key

Laboratory for Macromolecular Science of Shaanxi Province, Shaanxi Key Laboratory for Advanced Energy Devices, School of Materials Science and Engineering, Shaanxi Normal University, Xi’an 710119, China ‡Materials Chemistry, RWTH Aachen University, 52074 Aachen, Germany §Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany ||Central Facility for Electron Microscopy, RWTH Aachen University, 52074 Aachen, Germany ABSTRACT: The close relationship between sample preparation processes and microstructure can lead to significant variations in the electrical and thermal transport properties of materials. Here, we use (scanning) transmission electron microscopy to study differences in microstructure between Sn0.995In0.005Te samples that were synthesized by three different methods: water quenched ingot as cast (IAC); hand milled + spark plasma sintered pellet (HMS); and ball milled + spark plasma sintered pellet (BMS). We find that dislocations are relocated from within the grains in the IAC sample to form arrays of dislocations at grain boundaries in the HMS and BMS samples. We suggest that the locations and types of the dislocations affect the scattering of charge carriers and heat-carrying phonons and are responsible for the different thermoelectric behaviors of the samples. Our results may shed light on the relationship between sample synthesis, microstructure and thermoelectric properties in such materials. KEYWORDS: thermoelectric materials, SnTe, in-grain dislocations, grain boundary dislocations, charge carrier scattering, phonon scattering INTRODUCTION Thermoelectric materials can be used to realize direct conversion between heat and electricity. The efficiency of a thermoelectric device is determined by the intrinsic figure of merit of the constituent material ZT=S2σT/(κe+κl) , where S, σ, T, κe and κl are the Seebeck coefficient, electrical conductivity, absolute temperature and electrical and lattice thermal conductivities, respectively. In order to achieve a high thermoelectric figure of merit, a high electrical power factor (PF=S2σ) and a low lattice thermal conductivity κl are necessary1. Strategies that can be used to influence the electrical properties of thermoelectric materials include carrier concentration optimization, band convergence2-4, resonant states5,6 and modulation doping7, while strategies that can be used to reduce lattice thermal conductivity include phase compositing8-13, nanostructuring1,14,15 and the use of all-scale hierarchical architectures16,17. Little attention has been paid to the influence of different synthesis process on thermoelectric performance. SnTe is a well-studied thermoelectric material system with high crystal symmetry and good thermoelectric performance6,18-21. Here, we study Sn0.995In0.005Te samples that were prepared using three different methods: water quenched ingot as cast (IAC); hand milled + spark plasma sintered pellet (HMS); and ball milled + spark plasma sintered pellet (BMS). The three samples have very different thermal/electrical transport behaviors. The microstructural origin of these differences in performance are investigated using spherical aberration corrected (scanning) transmission electron microscopy ((S)TEM). Sn0.995In0.005Te was selected for this study because of its relatively simple composition and thermoelectric performance. We find that dislocations are initially located inside grains in the IAC sample. They subsequently migrate to form arrays of dislocations at grain boundaries in the HMS and BMS samples. Lattice thermal conductivity simulations and charge carrier mobility analyses are used to conclude that the evolution and migration of dislocations are responsible for the different thermoelectric behaviors of the three samples. RESULTS AND DISCUSSION The electrical transport properties (Figures 1a,b), calculated power factor and figure of merit (Figures 1e,f) of the investigated samples are discussed in a later section. Figures 1c,d show the measured thermal conductivities and inferred lattice thermal conductivities (obtained by subtracting the electrical contribution κe = LσT from the total thermal conductivity) for the Sn0.995In0.005Te IAC, HMS and BMS samples. In particular, Figure 1d shows that the lattice thermal conductivities of the three samples exhibit large differences. The room temperature lattice thermal conductivity is reduced from ~4.7 W/mK in the IAC sample to ~3.7 W/mK in the HMS sample and ~2.8 W/mK in the BMS sample. Given that the samples have the same nominal composition, the observed differences in lattice thermal conductivity are unexpected.

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Figure 1 Temperature-dependent (a) S, (b) σ, (c) κ, (d) κl, (e) PFs and (f) ZTs of the IAC, HMS and BMS Sn0.995In0.005Te samples. The inset to (b) shows the corresponding room temperature Hall carrier concentrations and mobilities. In order to establish the microstructural origin of the different lattice thermal conductivities, we performed (S)TEM experiments together with electron back scattered diffraction (EBSD) investigations on the three samples. Figures 2a-l show conventional bright-field TEM images of the IAC (red framed), HMS (green framed) and BMS (purple framed) samples, with the objective aperture chosen to enhance the image contrast. The IAC sample shows a large grain structure over the field of view of several micrometers (Figures 2a-c and Supplemental Figures S2a,b). A high density of dislocations is visible inside each grain, with a Burgers vector that is identified to be of type a on the basis of the g·b = 0 criterion (where g is a reciprocal lattice vector and b is the Burgers vector), as shown in Supplemental Figure S3. The grain size is reduced after both hand milling (Figures 2d-h and Supplemental Figure S2c) and ball milling (Figures 2i-l), down to a size of ~680 nm in the latter case (Supplemental Figure S2d).


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Figure 2 Low-magnification bright-field TEM images of the (a-c) IAC, (d-h) HMS and (i-l) BMS Sn0.995In0.005Te samples.

In addition to the change in grain size and grain boundary density, a redistribution of dislocations is observed in both milled samples, resulting in a striking difference in the morphology of the grain boundary structure (Figures 2d-l) from the typical (sharp) boundaries that are found in the IAC ingot (Figures 2a,b). In Supplemental Figures S4 and S5, we provide more images of the IAC and HMS samples. Examination of the orientations of adjacent grains in the BMS sample (as well as the HMS sample) reveals an abundant presence of low-angle grain boundaries. This observation was confirmed using high-resolution STEM imaging, together with strain quantification using geometric phase analysis (GPA)22, 23. Figure 3a shows a low-angle annular dark-field (LAADF) STEM overview image of the BMS sample, including a grain boundary, which is marked using a purple arrow in Figure 2i. In comparison to the high-angle annular dark-field (HAADF) signal, the LAADF signal is more sensitive to effects that lead to dechanneling of the incident electron probe, including strain fields associated with defects. It can therefore be interpreted approximately in term of strain contrast24. In Figure 3a and its inset, the contrast in both grains is homogenous and similar, suggesting that the channeling condition is almost the same, i.e., i) the crystallographic axis is similar, and ii) the dislocation density in the grains is reduced significantly. In contrast, dashed-line-shaped contrast is observed at the boundary, as a result of the presence of dislocation arrays25. The atomic details of the boundary area are shown in Figure 3b, while a corresponding rotation map created using GPA is shown in Figure 3c. The electron beam direction is and the rotation angles for the left and right grains (Figure 3c) are 0º and -1.1º (standard deviation for both grains: 0.1º), respectively. In Figure 3b, segments that show strong strain contrast are outlined by dotted ellipses, as derived from the LAADF image (inset to Figure 3a). Two dislocations are indicated by circles, with a spacing between the cores of ~20 nm (denoted by the white symbol “T” and also marked in Figure 3c). Figure 3d shows a magnified version of the top left area of Figure 3b, illustrating the dislocation core structure. A Burgers circuit analysis marked in Figure 3d reveals that both dislocations in Figure 3b possess vectors of bproj = a/4, where a = 0.6318 nm for SnTe. The complete Burgers vectors are therefore b = a/4 + a/n = a/4 or a/4 = a/2 or a/2 (n = 4 or -4), which is energetically favorable for face centered cubic structures. Since this is not a full dislocation, it must connect with another partial dislocation through the mediation of a stacking fault, thereby forming an extended defect configuration. We note that positions marked by the yellow symbol “T” exhibit strong strain contrast in Figure 3a, whereas they do not show lattice disruption in Figure 3b. This observation suggests that the area marked by an ellipse contains only one inclined dislocation line, leading to intersections with the top and bottom surfaces of the sample (or entrance and exit planes with respect to the path of



the electron beam). Since HAADF STEM is more sensitive to features that are located at the (top) entrance plane, only intersections at this plane are evident (i.e., dislocations marked by the white symbol “T”). The intersections at the (bottom) exit plane are invisible (i.e., dislocations marked by the yellow symbol “T”). We do not exclude the possibility that positions marked by the yellow symbol “T” may be pure screw dislocations. Nevertheless, they do not contribute to the rotation of the grains. According to Frank’s formula sin(θ/2) = |b| / 2d, 26 where |b| is the magnitude of the Burgers vector of the edge component (i.e., |bproj|) and d is their separation (~20 nm), the misorientation angle θ is ~1.1º, which is consistent with our quantitative GPA measurement, as shown in Figure 3c.

Figure 3 (a) LAADF STEM image of the grain boundary in the BMS sample, marked by a purple arrow in Figure 2i. The inset shows a magnified image of the dislocation array; (b) atomic-resolution HAADF STEM image of dislocations at the grain boundary in (a); (c) corresponding rotation map generated using GPA. The angles for the left and right grains are 0º and -1.1º (standard deviation: 0.1º), respectively; (d) Magnification of the top left corner of (b) showing the detail of dislocation core. A Burgers circuit analysis is shown. (e) Atomic model of SnTe showing the determination of bproj.

We performed a statistical analysis of the lattice misorientations in the HMS and BMS samples by tilting the grains to the zone axis and determining that the misorientation is in the range of 2~6º (e.g., Figure 3c and Supplemental Figure S5b). By using an average misorientation angle of 4º, the distance between the dislocations is determined to be ~6.5 nm. In the BMS sample, the dislocation density at the grain boundary is approximately three times that in the HMS sample and is estimated to be ~3.46 × 1010 cm-2. We note that in both milled samples large-angle grain boundaries are also present. However, due to the difficulty of determining such grain boundary dislocations, here we assume that a similar ratio of three between HMS and BMS samples is maintained. Figures 2 and 3, together with Supplemental Figures S2-S5, provide an understanding of dislocation evolution from the IAC sample to the HMS and BMS samples. A high density of dislocations is initially present in the grains of the IAC sample (Figures 2a-c and Supplemental Figures S3 and S4). The grain size is large and the grain boundary density is low. Milling then results in the formation of small crystal grains. The in-grain dislocations are expected to be unchanged (or their density should be even higher due to the milling process). Subsequent sintering causes the migration of in-grain dislocations. Two possibilities can be deduced: i) For small grains, the in-grain dislocations move directly towards the surface and interact with dislocations coming from adjacent grains, thereby forming randomly tilted grain boundaries;


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ii) For relatively large grains, the in-grain dislocations may meet and interact within an individual grain, leading to the formation of low-angle grain boundaries, i.e., an individual grain breaks into two or more grains. If the in-grain dislocations are insufficient, then this situation will result in the formation of incomplete boundaries, as evidenced by the residual neck connections (black arrows) in Figures 2d,e and Figures 2i,j. In order to evaluate the efficacy of the individual dislocation morphology on phonon scattering, we adopted the classical Debye-Callaway model26 in the relaxation time approximation to perform related simulations. Three extrinsic microstructure-related scattering processes, i.e., Sn vacancy scattering, grain boundary scattering and dislocation scattering, were considered to contribute to thermal transport. In(Sn) substitutional point defect scattering is ignored, considering that its extremely low molar ratio limits scattering efficacy. Since the distributions and detailed parameters of the dislocations are complicated27-29, their contribution to phonon scattering can only be deduced by comparing simulations (involveing vacancy scattering and grain boundary scattering) with experimental results. Simulated lattice thermal conductivities based on the parameters shown in Table S3 are shown in Figure 4a. By comparing the simulated values and experimental lattice thermal conductivities for the IAC, HMS and BMS samples, it is possible to deduce the phonon scattering efficacy for the different dislocation morphologies that were observed using (S)TEM, i.e., in-grain dislocations in the IAC sample and arrays of dislocations at grain boundaries in the HMS and BMS samples. Simulated values of κL for the IAC sample are close to the experimental measurements (Figure 4b), suggesting that grain boundaries and Sn vacancies contribute to almost all of the extrinsic phonon scattering, while in-grain dislocation scattering is nearly negligible. Simulated values that consider dense grain boundaries and Sn vacancies are consistently higher than experimental measurements for the HMS and BMS samples (Figures 4c,d). As no other phonon scatterers (other than vacancies, grain boundaries and dislocations) were visible using (S)TEM, it is likely that dislocation arrays at the grain boundaries alone are responsible for the differences between the simulations and experimental measurements. The aggregation of dislocations into arrays at grain boundaries was also found to be effective in reducing lattice thermal conductivity in other thermoelectric systems30.

Figure 4 (a) Simulated lattice thermal conductivities for the IAC, HMS and BMS Sn0.995In0.005Te samples, according to the Callaway model in the relaxation time approximation, considering Umklapp processes (U), Normal processes (N), grain boundary scattering (GB) and Sn vacancy scattering (VSn). The scattering effects of the dislocations can be assessed by comparing the simulated results with experimental values for the (b) IAC, (c) HMS and (d) BMS samples. Other than the very distinct thermal transport properties, the different preparation processes also result in different electrical transport properties, as shown in Figures 1a,b for the IAC, HMS and BMS Sn0.995In0.005Te samples. The HMS sample has the highest Seebeck coefficient, resulting from the fact that it has the lowest hole concentration of the three samples (see Table S4). Figure 1b shows that the BMS sample has the highest electrical conductivity, primarily due to its high hole mobility of ~56.4 cm2/Vs. The IAC sample has the lowest electrical conductivity, as a result of its unusually low carrier mobility of ~7.1 cm2/Vs. Considering the relatively large grain size of the IAC sample and its intermediate hole concentration (~6.4×1020/cm3), its low carrier mobility can only originate from strong scattering by the high density of dislocations in the grains. When the dislocations migrate and aggregate in arrays at the grain boundaries in the HMS and BMS samples, their scattering effect on charge carriers weakens. The hole mobilities of the HMS and BMS samples are 47.0 and 56.4 cm2/Vs, respectively. The calculated power factors and figures of merit are given in Figures 1e,f., respectively. The milled samples have similar power factors despite the large difference in their carrier concentrations. The IAC sample has much lower values of power factor over the entire temperature range,



as a result of its lower electrical conductivity. When combined with the measured values of thermal conductivity shown in Figure 1, the HMS and BMS samples both exhibit peak ZT values of ~0.7 at 823 K, which is ~ 11% higher than the value of ~0.6 for the IAC sample at the same temperature. CONCLUSIONS In summary, dislocation evolution has been studied systematically in Sn0.995In0.005Te samples that were prepared in three different ways: water quenched ingot as cast; hand milled + spark plasma sintered; and ball milled + spark plasma sintered. Dislocations are observed to migrate from the interiors of the grains in the IAC sample to form arrays at grain boundaries in the HMS and BMS samples. Characterization of the thermoelectric properties of the three samples reveals that in-grain dislocations and dislocation arrays at grain boundaries have distinct effects on thermal and electrical transport. In-grain dislocations are inferred to deteriorate charge carrier transport but with little effect on thermal conduction, while dislocation arrays at grain boundaries are inferred to strongly scatter heat-carrying phonons but not reduce charge carrier mobility. The results demonstrate that synthesis processes can have profound effects on dislocation morphology and thereby on thermoelectric performance. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publication website at xxx Experimental details, EBSD mapping, additional STEM images and Debye-Callaway model simulation details. AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected]; * E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the Natural Science Foundation of China (No. 11504160), the Fundamental Research Funds for the Central Universities (GK201802007). H.D. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) under Grant SFB 917 Nanoswitches. Doris Meertens and Maximilian Kruth are acknowledged for (S)TEM specimen preparation using focused ion beam milling. REFERENCES

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