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Defect Engineering for Realizing High Thermoelectric Performance in n-Type Mg3Sb2-Based Materials Jun Mao, Yixuan Wu, Shaowei Song, Qing Zhu, Jing Shuai, Zihang Liu, Yanzhong Pei, and Zhifeng Ren ACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 05 Sep 2017 Downloaded from http://pubs.acs.org on September 5, 2017

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ACS Energy Letters

Defect Engineering for Realizing High Thermoelectric Performance in n-Type Mg3Sb2-Based Materials

Jun Maoa, b, Yixuan Wuc, Shaowei Songa, Qing Zhua, Jing Shuaia, Zihang Liua, Yanzhong Peic, and Zhifeng Rena*

a

Department of Physics and Texas Center for Superconductivity, University of

Houston, Houston, TX 77204, USA b

Department of Mechanical Engineering, University of Houston, Houston, TX 77204,

USA c

School of Materials Science and Engineering, Tongji University, Shanghai 201804,

China

*Corresponding author, email address: [email protected]

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ABSTRACT Point defects, which scatter the electronic carriers as well as phonons, play a vital role in the transport properties of thermoelectric materials. Therefore, the defect engineering can be utilized for tuning the thermoelectric properties. Mg vacancies, as the dominant defects in the n-type Mg3Sb2-based materials, can greatly impact the transport properties of this compound. Here we demonstrate that the Mg vacancies in the n-type Mg3Sb2-based materials can be successfully manipulated by simply tuning the preparation conditions. A substantial enhancement in the Hall mobility is obtained, from ~39 cm2 V-1 s-2 to ~128 cm2 V-1 s-2, an increase of ~228%. The significantly improved Hall mobility noticeably boosts the power factor from ~6 µW cm-1 K-2 to ~20 µW cm-1 K-2 and effectively enhances the thermoelectric figure of merit. Our results demonstrate that defect engineering could be very effective in improving the thermoelectric performance of n-type Mg3Sb2-based materials.

TOC Graph 150 -0.98 120 T

1073 K 30 min 973 K 2 min 923 K 2 min

90 60

T

0.08

T

1.09

2

-1

-1

µH (cm V s )

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30

Mg Sb

Tamaki et al.

Mg vacancy electron

Electron scattering by Mg vacancy

300

450

600

750 900

T (K)


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The rising global energy consumption and aggravated environmental impact from utilizing the fossil fuel greatly stimulate the exploring of green energy and novel energy conversion technique. As one of the competitive candidates, the thermoelectric energy conversion technique is capable of converting heat into electricity and vice versa, therefore enabling promising applications like generating electricity from the waste heat as well as cooling the electronics1-3. The efficiency of the thermoelectric energy conversion is governed by the Carnot efficiency and the material’s performance measured by ZT that defines as ZT = (S2σ/κ)T, where S, σ, κ, and T are the Seebeck coefficient, the electrical conductivity, the thermal conductivity (κ = κele + κlat, where κele is the electronic thermal conductivity and κlat is the lattice thermal conductivity), and the absolute temperature, respectively4-13. The enhancement in ZT relies on the synergistic optimization of the transport properties S, σ, and κ. Since the thermoelectric parameters are heavily interdependent via the carrier concentration, optimization of the carrier concentration by introducing the impurities (i.e., dopants) has been regarded as one of the most traditional methods in thermoelectrics4, 14. On the other hand, reducing the lattice thermal conductivity via the phonon scattering by defects (e.g., point defects15-22, dislocations23-26, grain boundaries27-30, and nanoprecipiates31-37) has also been proven effective in enhancing the ZT. Therefore, the manipulation of the thermoelectric properties essentially depends upon the controlling of defects. Among the various defects, point defects, which are widely present in various materials and can greatly impact the transport properties38-45. In this regard, the defect engineering could be utilized to manipulate 3 ACS Paragon Plus Environment

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the transport properties. Recently, n-type Mg3Sb2-based materials with promising thermoelectric performance were reported46-49. Actually, this material was usually regarded as a strong p-type compound50-52. According to the calculation by Tamaki et al.46, Mg vacancies are the dominant defects in Mg3Sb2-based materials. The existence of Mg vacancies explained the persistent p-type characteristic of Mg3Sb2 and justified the importance of extra Mg for the n-type compound. In addition, the neutral Mg vacancies will easily become negatively charged in the n-type Mg3Sb2-based materials46 and are the most likely reason for the ionized impurity scattering in Mg3.2Sb1.5Bi0.49Te0.01 at lower temperature range46,

48

. In addition, anomalous

temperature dependences of electrical conductivity are observed in the Te-doped n-type Mg3Sb2-based materials53. The reason for such anomalies also closely relates to the presence of Mg vacancies. Therefore, the Mg vacancies play a critical role in the thermoelectric performance of n-type Mg3Sb2-based materials. In this scenario, further enhancement in the thermoelectric performance of this compound is possible if the Mg vacancies can be effectively controlled. It is well-understood that point defects are sensitive to the preparation conditions. Therefore, the manipulation of the point defects via optimizing the preparation conditions is feasible. In this work, Mg vacancies are effectively controlled by tuning the preparation conditions (e.g., hot-pressing temperature and holding time). A significant Hall mobility enhancement is achieved from ~39 cm2 V-1 s-2 to ~128 cm2 V-1 s-2, hence lead to a dramatic increase in the power factor, from ~6 µW cm-1 K-2 to 4 ACS Paragon Plus Environment

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~20 µW cm-1 K-2. Our work highlights the importance of controlling the Mg vacancies for obtaining higher thermoelectric performance in the n-type Mg3Sb2-based materials. Importantly, the strategy of defect engineering should be widely applicable to various material systems. The optimized composition of Mg3.2Sb1.5Bi0.49Te0.01 in Tamaki et al.’s report is chosen for our study. The effects of different hot-pressing temperature and holding time (Fig. S1, Supporting Information) on the thermoelectric properties of Mg3.2Sb1.5Bi0.49Te0.01 are investigated. Fig. 1a shows the temperature-dependent electrical conductivity for the samples prepared at different hot-pressing temperatures. A significant difference in the electrical conductivity (mainly at lower temperature range) is noted, where the room temperature electrical conductivity is ~1.5×104 S m-1 for the sample prepared at 923 K for 2 min but ~5.9×104 S m-1 for the sample hot-pressed at 1073 K for 30 min. This substantial enhancement mainly originates from the notably improved Hall mobility as shown in Fig. 1b. The Hall mobility for the sample prepared at 923 K for 2 min shows two distinctly different temperature dependences, where it first increases with temperature at lower temperature range (dominated by the ionized impurity scattering) and then decreases at higher temperature range (dominated by the acoustic phonon scattering)46, 48. A noticeable difference in the temperature dependence of Hall mobility is observed for the samples hot-pressed at higher temperature, where the carrier scatter mechanism at lower temperature changes from the ionized impurity scattering to the mixed scattering by ionized impurities and acoustic phonons. The variation in the carrier scattering 5 ACS Paragon Plus Environment

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mechanism significantly improves the Hall mobility. The room temperature Hall mobility for the sample hot-pressed at 1073 K for 30 min is ~128 cm2 V-1 s-1, but only ~39 cm2 V-1 s-1 for the sample prepared at 923 K for 2 min, a dramatic increase of ~228%. Temperature exponents of the Hall mobility are extracted and the relationship between the preparation conditions and the temperature exponent is shown in Fig. 1c. At the lower temperature range, the ionized impurity scattering clearly shifts to the mixed scattering when the hot-pressing temperature increases. On the contrary, the carrier scattering mechanism at higher temperature range remains close to the acoustic phonon scattering for all of the samples. The temperature exponent dependent Hall mobility is plotted in Fig. 1d, where the Hall mobility substantially increases from the ionized impurity scattering dominated condition toward the acoustic phonon scattering dominated condition. Fig. 2a shows the temperature-dependent Seebeck coefficient for the samples prepared at different conditions. The Seebeck coefficient remains similar for all of the samples and only slight reduction in Seebeck coefficient for the samples prepared at higher temperature is noted. For the n-type Mg3Sb2-based materials, the Seebeck coefficient depends upon the carrier concentration as well as the carrier scattering mechanism. Relationship among the Seebeck coefficient, Hall carrier concentration, and carrier scattering mechanisms can be well-described by the Pisarenko plot as shown in Fig. 2b. The samples prepared at 923 K is much closer to the blue dash line of ionized impurity scattering (r = 0, r is the scattering factor). In a contrast, all the samples prepared at higher temperature are located in between the black dash lines of 6 ACS Paragon Plus Environment

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mixed scattering (r between 1 and 0.5). Owing to the significantly improved electrical conductivity and the similar Seebeck coefficient, the power factors are substantially improved for the samples prepared at higher temperatures (Fig. 3a). The room temperature power factor is ~6 µW cm-1 K-2 for the sample prepared at 923 K for 2 min, but ~20 µW cm-1 K-2 for the sample hot-pressed at 1073 K for 30 min. Comparison of average power factors (calculated by the integration method from 300 to 773 K) among the specimens is shown in Fig. 3b, where an effective enhancement in the average power factor is achieved. It is ~14.7 µW cm-1 K-2 for the sample prepared at 923 K for 2 min but more than 18 µW cm-1 K-2 for all of the samples prepared at higher temperature. The sample prepared at 973 K shows the highest average power factor of ~18.9 W cm-1 K-2, an enhancement of ~29% comparing to the one prepared at 923 K. The substantially increased power factor should be mainly ascribed to the drastically improved Hall mobility. The relationship between power factor and mobility is clearly demonstrated in Fig. 3c, where the power factor increases monotonically with the Hall mobility. The temperature exponent dependent power factor is further shown in Fig. 3d. The power factor increases from the ionized impurity scattering dominated condition towards the acoustic phonon scattering dominated condition. The material’s power factor plays a decisive role in the maximum output power density (ωmax) of the thermoelectric device: 2

1 (TH − TC ) ωmax = PF 4 Lleg

(1)


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where Lleg is length of leg, TH is the hot-side temperature and TC is the cold-side temperature. According to eq. 1, the noticeably improved power factor will effectively increase the output power density. Fig. 3e shows the relationship between the applied electric current and output power density at the hot-side temperature of 573 K and cold-side temperature of 298 K. Clearly, the sample hot-pressed at 1073 K for 30 min shows considerably higher output power density than that of the sample prepared at 923 K for 2 min. Hot-side temperature dependent maximum output power density is shown in Fig. 3f and the experimental results are in a reasonable agreement with the theoretical predictions. The measured peak maximum output power density is ~0.29 W cm-2 for the sample prepared at 923 K for 2 min but ~0.62 W cm-2 for the sample hot-pressed at 1073 K for 30 min, an increase of ~114%. Owing to the enhanced electrical conductivity, a slight increase in the thermal conductivity (mainly at lower temperature range) is noted for the samples prepared at higher temperatures compared to the one prepared at 923 K (as shown in Fig. 4a). Finally, benefiting from the significantly enhanced power factor, ZTs at lower temperatures have been considerably improved. The room temperature ZT is ~0.16 for the sample prepared at 923 K but ~0.5 for the sample prepared at 1073 K for 30 min. The energy conversion efficiency can be well described by the (ZT)eng54. Calculation of (ZT)eng at the cold side temperature of 323 K is shown in Fig. 4c, where the peak (ZT)eng is ~0.72 for the sample prepared at 923 K but ~0.92 for the sample prepared at 973 K, an increase of ~28%. The average ZT is also calculated (by the integration method between 298 and 773 K) and shown in Fig. 4d. Samples prepared at higher 8 ACS Paragon Plus Environment

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temperatures show a noticeable enhancement in (ZT)avg compared to the one prepared at 923 K for 2 min. It is ~0.93 for the sample prepared at 923 K for 2 min but ~1.13 for the sample prepared at 973 K, an enhancement of ~22%. As pointed out in the previous reports53, the presence of charged Mg vacancies can

directly

impact

the

Hall

carrier

concentration.

Therefore,

the

temperature-dependent Hall carrier concentration can be used to understand the defect chemistry in the n-type Mg3Sb2-based materials. Similar to the previous results53, the Hall carrier concentration of the sample prepared at 923 K for 2 min shows an anomalous temperature dependence (as shown in Fig. 5). The Hall carrier concentration decreases with the temperature in the range of 300 - 400 K (the dash line circled region). In the n-type Mg3Sb2-based materials, the neutral Mg vacancies easily become negatively charged (i.e., neutral Mg vacancies obtain electrons from the matrix)46. This reduced Hall carrier concentration should be mainly ascribed to the increased thermodynamically equilibrium concentration of the negatively charged Mg vacancies when the temperature increases53. In other words, the presence of such anomalous temperature dependence of Hall carrier concentration indicates the existence of a noticeable amount of Mg vacancies. Contrary to the sample prepared at 923 K, all of the all the samples prepared at higher temperatures do not show such anomalous temperature dependence of Hall carrier concentration. This indicates that the samples prepared at higher temperatures should have much lower concentration of Mg vacancies. Usually, it is understood that the concentration of vacancies increases with 9 ACS Paragon Plus Environment

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temperature55, 56. This is indeed the case for the vacancies in thermodynamically equilibrium.

In

addition,

supersaturated

vacancies

(non-thermodynamically

equilibrium) will also appear in the samples when certain preparation method (e.g., ball-milling)57, 58 or treatments (e.g., quench, plastic deformation, and irradiation by fast particles or Gamma-rays)59 is applied. Currently, n-type Mg3Sb2-based materials have been prepared by arc-melting47 and ball-milling46, 48, 53 methods. By carefully comparing the electrical conductivity between the different reports, the ionized impurity scattering seems only occurs in the samples prepared by ball-milling method46, 48, 53 (as shown in Fig. S2, Supporting Information). This indicates that, in addition to the intrinsic Mg vacancies (thermodynamically equilibrium vacancies), the ball-milling method introduces an appreciable amount of supersaturated Mg vacancies into the n-type Mg3Sb2-based materials. These supersaturated Mg vacancies will inevitably diffuse in the crystal structure during the hot-pressing process, and will disappear when they diffuse into the grain boundaries or the surfaces of the specimens. Since the temperature and time are the two most important extrinsic parameters for diffusion60, it justifies the manipulation of supersaturated Mg vacancies by controlling the preparation conditions. Due to the reduced concentration of Mg vacancies when the hot-pressing temperature is increased and holding time is elongated, it explains the carrier mobility enhancement via optimizing the preparation conditions. In addition, the manipulation of supersaturated Mg vacancies by the long-time annealing treatment at elevated temperatures should also be possible. However, the reaction between Mg3Sb2 and the quartz tube will appear at high temperature. Therefore, in 10 ACS Paragon Plus Environment

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order to apply the high temperature annealing method, it is needed to avoid such reaction first. In this work, Mg vacancies in the n-type Mg3Sb2-based materials are effectively controlled by tuning the preparation conditions. Significant enhancement in Hall mobility is observed, which substantially enhances the power factor and finally improves the average ZT. Our results clearly show that Mg vacancies play a dominant role in the thermoelectric properties in the n-type Mg3Sb2-based materials, and effective enhancement in thermoelectric properties can be achieved by controlling the Mg vacancies. Our work demonstrates that defect engineering should also be applicable to various materials for obtaining better thermoelectric performance.

EXPERIMENTAL METHODS Synthesis. Magnesium turnings (Mg, 99.98%; Alfa Aesar), bismuth pieces (Bi, 99.99%; Alfa Aesar), antimony shots (Sb, 99.8%; Alfa Aesar), tellurium pieces (Te, 99.999%;

Alfa

Aesar)

were

weighed

according

to

the

composition

of

Mg3.2Sb1.5Bi0.49Te0.01. The elements were loaded into stainless-steel ball-milling jar in the glove box under an argon atmosphere with an oxygen level below 0.1 ppm. The materials were ball-milled for 10 hours and then loaded into a graphite die with an inner diameter of 12.7 mm in glove box. Then, the graphite die with loaded powder was removed from glove box and immediately sintered by alternative current hot-pressing at different temperatures (923, 973, 1023, and 1073 K) with the pressure of ~80 MPa for different holding time (2, 20, 30, and 60 min). The hot-pressed disks 11 ACS Paragon Plus Environment

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are about 2-3 mm thick. It should be pointed out that there are some minor differences in the thermoelectric properties of the sample prepared at 923 K to that of our previous report48. This is mainly due to the reason that we prepared a much larger batch of powders in this work but without optimizing the ball-milling time. The larger batch of powders is needed in order to prepare all the samples in this study and to ensure the results are consistent.

Thermoelectric property characterizations. All the samples were cut into pieces with the dimension about 2 mm × 2 mm × 12 mm for simultaneous electrical resistivity and Seebeck coefficient characterizations under Helium atmosphere (ZEM-3; ULVAC Riko). Thermal conductivity κ = dDCp was calculated using the measured density (d) by the Archimedean method, specific heat (Cp) by the differential scanning calorimetry (DSC 404 C; Netzsch) and thermal diffusivity (D) by the laser flash method (LFA 457; Netzsch). Hall coefficient RH was measured at room temperature on a commercial system (PPMS; Quantum Design) using a four-probe configuration, with the magnetic field sweeping between +3 and -3 T and an electrical current between 10 and 20 mA. Temperature-dependent Hall measurement was conducted under a reversible magnetic field of 1.5 T using the Van der Pauw technique from 300 to 773 K. Hall carrier concentration nH and carrier mobility µ were calculated via the relations nH = 1/(e RH) and µ = RH/ρ.

Structure and composition. The phase composition of the samples was characterized 12 ACS Paragon Plus Environment

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by X-ray diffraction (PANalytical X’pert PRO diffractometer). All the specimens do not show any impurity phases within the detection limit of the machine (Fig. S3, Supporting Information).

ASSOCIATED CONTENTS Supporting Information: XRD patterns, thermoelectric properties of the samples prepared at 673 K with different holding time, comparison of electrical conductivity between different reports.

AUTHOR INFORMATION Corresponding author *Email: [email protected] ORCID Zhifeng Ren: 0000-0001-8233-3332 Notes

The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The work performed at the University of Houston is funded by the US Department of Energy under Contract DE-SC0010831, and that at Tongji University is funded by the 13 ACS Paragon Plus Environment

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National Natural Science Foundation of China (Grant No. 51422208 and 11474219).

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(32) He, J. Q.; Sootsman, J. R.; Girard, S. N.; Zheng, J. C.; Wen, J. G.; Zhu, Y. M.; Kanatzidis, M. G.; Dravid, V. P. On the origin of increased phonon scattering in nanostructured PbTe based thermoelectric materials. J. Am. Chem. Soc. 2010, 132, 8669-8675. (33) He, J. Q.; Girard, S. N.; Kanatzidis, M. G.; Dravid, V. P. Microstructure-lattice thermal conductivity correlation in nanostructured PbTe0.7S0.3 thermoelectric materials. Adv. Funct. Mater. 2010, 20, 764-772. (34) Xie, W. J.; He, J.; Kang, H. J.; Tang, X. F.; Zhu, S.; Laver, M.; Wang, S. Y.; Copley, J. R. D.; Brown, C. M.; Zhang, Q. J.; Tritt, T. M. Identifying the specific nanostructures responsible for the high thermoelectric performance of (Bi,Sb)2Te3 nanocomposites. Nano Lett. 2010, 10, 3283-3289. (35) Zhao, L. D.; Lo, S.-H.; He, J. Q.; Li, H.; Biswas, K.; Androulakis, J.; Wu, C. I.; Hogan, T. P.; Chung, D. Y.; Dravid, V. P. High performance thermoelectrics from earth-abundant materials: enhanced figure of merit in PbS by second phase nanostructures. J. Am. Chem. Soc. 2011, 133, 20476-20487. (36) Zhao, L. D.; He, J. Q.; Wu, C.-I.; Hogan, T. P.; Zhou, X. Y.; Uher, C.; Dravid, V. P.; Kanatzidis, M. G. Thermoelectrics with earth abundant elements: High performance p-type PbS nanostructured with SrS and CaS. J. Am. Chem. Soc 2012, 134, 7902-7912. (37) Zhao, L. D.; Zhang, X.; Wu, H. J.; Tan, G. J.; Pei, Y. L.; Xiao, Y.; Chang, C.; Wu, D.; Chi, H.; Zheng, L.; Gong, S. K.; Uher, C.; He, J. Q.; Kanatzidis, M. G. Enhanced thermoelectric properties in the counter-doped SnTe system with strained endotaxial SrTe. J. Am. Chem. Soc. 2016, 138, 2366-2373. (38) Brebrick, R. Deviations from stoichiometry and electrical properties in SnTe. J. Phys. Chem. Solids 1963, 24, 27-36. (39) Snyder, G. J.; Christensen, M.; Nishibori, E.; Caillat, T.; Iversen, B. B. Disordered zinc in Zn4Sb3 with phonon-glass and electron-crystal thermoelectric properties. Nat. Mater. 2004, 3, 458-463. (40) Kurosaki, K.; Matsumoto, H.; Charoenphakdee, A.; Yamanaka, S.; Ishimaru, M.; Hirotsu, Y. Unexpectedly low thermal conductivity in natural nanostructured bulk Ga2Te3. Appl. Phys. Lett. 2008, 93, 012101. (41) May, A. F.; Fleurial, J.-P.; Snyder, G. J. Thermoelectric performance of lanthanum telluride produced via mechanical alloying. Phys. Rev. B 2008, 78, 125205. (42) Qiu, P. F.; Yang, J.; Huang, X. Y.; Chen, X. H.; Chen, L. D. Effect of antisite defects on band structure and thermoelectric performance of ZrNiSn half-Heusler alloys. Appl. Phys. Lett. 2010, 96, 152105. (43) Hu, L. P.; Zhu, T. J.; Liu, X. H.; Zhao, X. B. Point defect engineering of high-performance bismuth-telluride-based thermoelectric materials. Adv. Funct. Mater. 2014, 24, 5211-5218. (44) Jiang, G. Y.; He, J.; Zhu, T. J.; Fu, C. G.; Liu, X. H.; Hu, L. P.; Zhao, X. B. High performance Mg2(Si,Sn) solid solutions: a point defect chemistry approach to enhancing thermoelectric properties. Adv. Funct. Mater. 2014, 24, 3776-3781. (45) Liu, Z. H.; Geng, H. Y.; Mao, J.; Shuai, J.; He, R.; Wang, C.; Cai, W.; Sui, J. H.; Ren, Z. F. Understanding and manipulating the intrinsic point defect in α-MgAgSb for 16 ACS Paragon Plus Environment

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ACS Energy Letters

higher thermoelectric performance. J. Mater. Chem. A 2016, 4, 16834-16840. (46) Tamaki, H.; Sato, H. K.; Kanno, T. Isotropic conduction network and defect chemistry in Mg3+δSb2-based layered Zintl compounds with high thermoelectric performance. Adv. Mater. 2016, 28, 10182-10187. (47) Zhang, J.; Song, L.; Pedersen, S. H.; Yin, H.; Hung, L. T.; Iversen, B. B. Discovery of high-performance low-cost n-type Mg3Sb2-based thermoelectric materials with multi-valley conduction bands. Nat. Commun. 2017, 8, 13901. (48) Shuai, J.; Mao, J.; Song, S. W.; Zhu, Q.; Sun, J. F.; Wang, Y. M.; He, R.; Zhou, J. W.; Chen, G.; Singh, D. J.; Ren, Z. F. Tuning the carrier scattering mechanism to effectively improve the thermoelectric properties. Energy Environ. Sci. 2017, 10, 799-807. (49) Zhang, J. W.; Song, L. R.; Mamakhel, A.; Jørgensen, M. R. V.; Iversen, B. B. High-performance low-cost n-type Se-doped Mg3Sb2-based Zintl compounds for thermoelectric application. Chem. Mater. 2017, 29, 5371-5383. (50) Condron, C. L.; Kauzlarich, S. M.; Gascoin, F.; Snyder, G. J. Thermoelectric properties and microstructure of Mg3Sb2. J. Solid State Chem. 2006, 179, 2252-2257. (51) Ahmadpour, F.; Kolodiazhnyi, T.; Mozharivskyj, Y. Structural and physical properties of Mg3-xZnxSb2 (x = 0-1.34). J. Solid State Chem. 2007, 180, 2420-2428. (52)Shuai, J.; Wang, Y. M.; Kim, H. S.; Liu, Z. H.; Sun, J. Y.; Chen, S.; Sui, J. H.; Ren, Z. F. Thermoelectric properties of Na-doped Zintl compound: Mg3-xNaxSb2. Acta Mater. 2015, 93, 187-193. (53) Mao, J.; Wu, Y. X.; Song, S. W.; Shuai, J.; Liu, Z. H.; Pei, Y. Z.; Ren, Z. F. Anomalous electrical conductivity of n-type Te-doped Mg3Sb2-based materials. Mater. Today Phys. 2017, 3, 1-6. (54) Kim, H. S.; Liu, W. S.; Chen, G.; Chu, C. W.; Ren, Z. F. Relationship between thermoelectric figure of merit and energy conversion efficiency. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 8205-8210. (55) Tan, T. Y. Point defect thermal equilibria in GaAs. Mater. Sci. Eng. B 1991, 10, 227-239. (56) Tan, T. Y.; You, H. M.; Gösele, U. M. Thermal equilibrium concentrations and effects of negatively charged Ga vacancies in n-type GaAs. Appl. Phys. A 1993, 56, 249-258. (57) Suryanarayana, C. Mechanical alloying and milling. Prog. Mater. Sci. 2001, 46, 1-184. (58) Suryanarayana, C.; Ivanov, E.; Boldyrev, V. The science and technology of mechanical alloying. Mater. Sci. Eng. A 2001, 304, 151-158. (59) Seeger, A.; Chik, K. Diffusion mechanisms and point defects in silicon and germanium. Phys. Status Solidi 1968, 29, 455-542. (60) Reed-Hill, R. E.; Abbaschian, R.; Abbaschian, R. Physical metallurgy principles. Van Nostrand New York: 1973; Vol. 17.


ACS Energy Letters

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

FIGURE CAPTIONS Figure 1. (a) Temperature-dependent electrical conductivity of the specimens, (b) temperature-dependent Hall mobility, (c) relationship between the preparation conditions and the temperature exponents of Hall mobility, and (d) relationship between the exponent at lower temperature range and the room temperature Hall mobility.

Figure 2. (a) Temperature-dependent Seebeck coefficient of the specimens hot-pressed at different conditions, and (b) relationship among Hall carrier concentration nH, carrier scattering mechanism, and Seebeck coefficient.

Figure 3. (a) Temperature-dependent power factor for the specimens hot-pressed at different conditions, (b) comparison of the average power factor among the specimens, (c) the relationship between room temperature Hall mobility and power factor, and (d) the relationship between the exponent of lower temperature range and room temperature power factor, (e) applied current dependent maximum output power density measured with the hot-side temperature of 573 K and cold side temperature of 298 K, and (f) hot-side temperature dependent maximum output power density measured with the cold-side temperature of 298 K.

Figure 4. Temperature-dependent thermal conductivity (a) and ZT (b) of the specimens, (c) calculated (ZT)eng at TC = 323 K, and (d) comparison of (ZT)avg among 18 ACS Paragon Plus Environment

Page 18 of 30

Page 19 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

the samples

Figure 5. Temperature-dependent Hall carrier concentration for the specimens prepared at different conditions.


ACS Energy Letters

FIGURES Figure 1

4

(b) 150 -0.98 120 T -0.67 T

-1

-1

µH (cm V s )

4

3x10

-0.24 90 T

60

T

0.08

T

1.09

2

-1

σ (S m )

(a) 7x104 6x10 4 5x10 4 4x10

4

2x10

Tamaki et al. Ref [46] 4

10

300

400

923 K 2 min 973 K 2 min 1023 K 2 min 1073 K 2 min 1073 K 30 min

500

923 K 2 min 973 K 2 min 1023 K 2 min 1073 K 2 min 1073 K 30 min Tamaki et al. Ref [46]

30

600 700 800

300

450

T (K)

Lower temperature range Higher temperature range Mixed scattering (r = 0)

-1

Acoustic phonon scattering

2

0 Acoustic phonon scattering (r = -1.5)

750 900

(d) 150 -1

1

Ionized impurity scattering (r = 1.5)

1073 K 30 min

120

-1

2

600

-2.14

T -2.31 T -2.22 T -1.85 T -1.93 T

T (K)

µH (cm V s )

(c)

Exponent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 30

1073 K 2 min

90

1023 K 2 min

Mixed scattering

973 K 2 min

60

Ionized impurity scattering

-2

923 K 2 min

30 -2

923 K 973 K 1023 K 1073 K 1073 K 2 min 2 min 2 min 2 min 30 min

-1

0

1

Temperature exponent

Condition


2

Page 21 of 30

Figure 2 (b) -250

(a) -300

-225 -1

-1

-250 -225


-200 -175

S (µV K )

-275

S (µV K )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

300

400

500

600

700

Ionized impurity scattering (r = 1.5) 973 K 2 min

-200 -175

1073 K 30 min

-100

1073 K 2 min

Mixed scattering (r = 1.0)

-150

Mixed scattering (r = 0.5)

-125

800

923 K 2 min

1023 K 2 min

Acoustic phonon scattering (r = -0.5)

1

2

3

4 19

5 -3

nH (10 cm )

T (K)


6

ACS Energy Letters

Tamaki et al. Ref [46]

15 14.7 973 K 2 min

8

12

300 400 500 600 700 800

1023 K 2 min

16

1073 K 2 min 973 K 2 min

12 8 4 30

Ionized impurity scattering 923 K 2 min

60

90 2

0.9

0.6

20

16 1073 K 2 min 12

150

973 K 2 min 1023 K 2 min Mixed scattering

8

-1

Ionized impurity scattering 923 K 2 min

-1

0

1

2

Temperature exponent

µH (cm V s ) 923 K 2 min 1073 K 30 min

Leg: ~7 mm

Acoustic phonon scattering 1073 K 30 min

4 -2

(f)

0.8 0.6

Solid line: calculation Symbol: Experimental results

2

ωmax (W cm )

2

(e)

120 -1

(d) -2

1073 K 30 min

-1

-1

Mixed scattering

24

PF (µW cm K )

PF (µW cm K )

20

-2

(c)

18.8

Sample

T (K) 24

18.5

18

923 K 2 min

-1


12

18.6

1073 K 30 min

PFavg (µW cm K )

-1

16

4

18.9

1073 K 2 min

20

21

1023 K 2 min

(b) -2

24

-2

(a) PF (µW cm K )

Figure 3

ωmax (W cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 30

0.3

0.4 1073 K 30 min

0.2 923 K 2 min

0.0 0.0

0.3

0.6

0.9

1.2

1.5

0.0 300 350 400 450 500 550 600

1.8

I (A)

TH (K)


Page 23 of 30

Figure 4

1.2 923 K 2 min 973 K 2 min 1023 K 2 min 1073 K 2 min 1073 K 30 min

1.0

1.6 1.2

ZT

0.8

0.9 0.4

0.8

300

400

500

600

700

0.0

800

300

400

T (K)

700

800

(d) 1.2 923 K 2 min 973 K 2 min 1023 K 2 min 1073 K 2 min 1073 K 30 min

0.2

400

500

600

700

0.7

800

1.09

1.07

0.93 0.9 0.8

300

1.09

1.0 973 K 2 min

TC = 323 K

923 K 2 min

0.6

1.13 1.1

(ZT)avg

0.8

0.0

600

T (K)

(c) 1.0

0.4

500

Sample

TH (K)


1073 K 30 min

0.7


1073 K 2 min

-1

-1

κ (W m K )

1.1

(b)

1023 K 2 min

(a)

(ZT)eng

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Energy Letters

ACS Energy Letters

Figure 5 4.5 4.0

Dominated by Mg vacancies

-3

nH (10 cm )

3.5

19

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 30

3.0 923 K 2 min 973 K 2 min 1023 K 2 min 1073 K 2 min 1073 K 30 min

2.5 2.0

300

400

500

600

700

T (K)


800

Page 25 of 30

(a ) 7 x 6 x 5 x 4 x

4

(b ) 1 5 0 1 2 0

1 0 1 0

4

1 0

4

3 x 1 0

4

2 x 1 0

4

9 0

-0 .9 8

T

-0 .6 7

T

-0 .2 4

T

-1

V

-1

)

s

-1

)

1 0

4

6 0

0 .0 8

T

T a m a k i e t a l. R e f [4 6 ] 4

1 0

3 0 0

4 0 0

5 0 0

6 0 0

T

1 .0 9

H

K 2 m in K 2 m in 3 K 2 m in 3 K 2 m in 3 K 3 0 m in



9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

(c m

2

m  (S

3 0

7 0 0 8 0 0

3 0 0

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7 T a m

K 2 m in K 2 m in 3 K 2 m in 3 K 2 m in 3 K 3 0 m in a k i e t a l. R e f [4 6 ]

4 5 0

6 0 0

T (K )

T

-2 .2 2

T

-1 .8 5 -1 .9 3

T

9 0 0

1 0 7 3 K 3 0 m in

1 2 0 1 0 7 3 K 2 m in

1 0 2 3 K 2 m in

V

M ix e d s c a tte r in g ( r = 0 )

A c o u s tic p h o n o n s c a tte r in g

)

L o w e r te m p e ra tu re ra n g e H ig h e r te m p e r a tu r e r a n g e

(d ) 1 5 0

-1

Io n iz e d im p u r ity s c a tte r in g ( r = 1 .5 )

1

-2 .3 1

T

s

2

7 5 0

-2 .1 4

T

T (K )

-1

(c )

E x p o n e n t

9 0

(c m

2

0

H

-1

A c o u s tic p h o n o n s c a tte r in g ( r = - 1 .5 )



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

ACS Energy Letters

M ix e d s c a tte r in g

9 7 3 K 2 m in

6 0

Io n iz e d im p u r ity s c a tte r in g

-2

9 2 3 K 2 m in

9 2 3 K 2 m in

9 7 3 K 2 m in

1 0 2 3 K 2 m in

C o n d itio n

1 0 7 3 K 2 m in

3 0 1 0 7 3 K -2 3 Paragon 0 m i n Plus Environment ACS

-1

0

1

T e m p e ra tu re e x p o n e n t

2

ACS Energy Letters

(b ) -2 5 0

(a ) -3 0 0

-2 2 5

-2 2 5

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

-2 0 0 -1 7 5

Io n iz e d im p u r ity s c a tte r in g ( r = 1 .5 ) 9 7 3 K 2 m in

-2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

T (K )


7 0 0

8 0 0

9 2 3 K 2 m in

1 0 2 3 K 2 m in

-1

-2 5 0

S ( µV K

S ( µV K

)

)

-2 7 5

-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Page 26 of 30

-1 7 5

1 0 7 3 K 3 0 m in

M ix e d s c a tte r in g ( r = 1 .0 )

-1 5 0

M ix e d s c a tte r in g ( r = 0 .5 )

-1 2 5 -1 0 0

ACS Paragon Plus Environment

1 0 7 3 K 2 m in

1

A c o u s tic p h o n o n s c a tte r in g ( r = - 0 .5 )

2

n

3 H

4

(1 0

1 9

c m

5 -3

)

6

)

2 0

2 1

(b )

ACS Energy Letters -2

1 8 .6

1 8 .5

1 8 .8

1 8

3 0 0

4 0 0

5 0 0

1 4 .7

1 2

6 0 0

7 0 0

8 0 0

S a m p le

T (K ) 2 4

(d )

1 0 7 3 K 3 0 m in

9 7 3 K 2 m in

8 3 0

6 0

9 0

(e )

0 .9

)

0 .6

H

(c m

1 2 0 2

V

-1

s

-1

8 4

1 5 0

Io n iz e d im p u r ity s c a tte r in g 9 2 3 K 2 m in

-2

-1

0

1

2

T e m p e ra tu re e x p o n e n t )

9 2 3 K 2 m in 1 0 7 3 K 3 0 m in

0 .8

(f)

0 .6

S o lid lin e : c a lc u la tio n S y m b o l: E x p e r im e n t a l r e s u lts

0 .4 1 0 7 3 K 3 0 m in

(W

c m

c m

2

)

L e g : ~ 7 m m

1 0 7 3 K 2 m in 9 7 3 K 2 m in 1 0 2 3 K 2 m in M ix e d s c a tte r in g

1 2

Io n iz e d im p u r it y s c a t te r in g 9 2 3 K 2 m in



4

1 6

P F ( µW

P F ( µW

1 2

0 .2



m a x

0 .3



m a x

2 0

c m

1 0 7 3 K 2 m in

c m

-1

1 6

2

A c o u s t ic p h o n o n s c a tt e r in g 1 0 7 3 K 3 0 m in

K

K

1 0 2 3 K 2 m in

(W

2 4

-2

)

2 0

-2

)

M ix e d s c a tt e r in g

-1

(c )

1 0 7 3 K 3 0 m in

c m

T a m a k i e t a l. R e f [4 6 ]

4

1 5

9 7 3 K 2 m in

8

a v g

1 2


( µW

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

P F

P F ( µW

c m

1 6

9 2 3 K 2 m in

-1

-1

K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

K

-2

)

1 8 .9

1 0 7 3 K 2 m in

2 4

1 0 2 3 K 2 m in

(a )

Page 27 of 30

9 2 3 K 2 m in

0 .0

0 .0

0 .3

0 .6

0 .9

I (A )

0 .0 3 0 0 3 5 0 1 . 2 ACS1 Paragon .5 1 . 8 Plus Environment

4 0 0

T

4 5 0 H

5 0 0

(K )

5 5 0

6 0 0

ACS Energy Letters

1 .2

(a )

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

1 .0


1 .6

(b )

1 .2 0 .8

0 .9

 (

0 .4

0 .8

4 0 0

5 0 0

6 0 0

7 0 0

0 .0

8 0 0

3 0 0

4 0 0

5 0 0

T (K ) 1 .0

(d )

T

0 .4

C

1 .1 3 1 .1

= 3 2 3 K

0 .2 0 .0

4 0 0

5 0 0

T H

6 0 0

(K )

7 0 0

8 0 0

1 .0 9

1 .0 7

0 .9 3 0 .9 0 .8

3 0 0

1 .0 9

1 .0

0 .7


9 7 3 K 2 m in

0 .6

8 0 0

1 .2

9 2 3 K 2 m in

e n g

0 .8


a v g

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

7 0 0

T (K )

(Z T )

(c )

6 0 0

S a m p le

1 0 7 3 K 3 0 m in

3 0 0


1 0 7 3 K 2 m in

0 .7

9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

1 0 2 3 K 2 m in

W

m

Z T

-1

K

-1

)

1 .1

(Z T )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 28 of 30

Page 29 of 30

4 .5

c m

-3

)

4 .0

D o m in a te d b y M g v a c a n c ie s

3 .5 3 .0 9 2 3 9 7 3 1 0 2 1 0 7 1 0 7

n

H

(1 0

1 9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ACS Energy Letters

2 .5 2 .0

3 0 0

4 0 0

5 0 0

6 0 0

T (K )


7 0 0


8 0 0

s

-1

)

1 5 0 1 2 0 9 0

- 0 .9 8 Energy Letters Page 30 of 30 T -ACS 0 .6 7

T

- 0 .2 4

T

T

0 .0 8



H

(c m

2

V

-1

1 6 0 2 1 .0 9 - 2 .1 4 T 3 T - 2 .2 2 1 0 7 3 K 3 0 m in T a m a k i e t a l. T 4 3 0 - 2 .3 1 1 0 7 3 K 2 m in T - 1 .8 5 1 0 2 3 K 2 m in 5 T - 1 .9 3 9 7 3 K 2 m in T 6 ACS Paragon Plus 9 2 3 K Environment 2 m in 7 3 0 0 4 5 0 6 0 0 7 5 0 9 0 0 8 T (K )

Defect Engineering for Realizing High ... - ACS Publications

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