Dislocation-induced ultra-low lattice thermal conductivity in rare earth doped β-Zn4Sb3

Scripta Materialia 174 (2020) 95–101

Contents lists available at ScienceDirect

Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat

Dislocation-induced ultra-low lattice thermal conductivity in rare earth doped β-Zn4Sb3 Vaithinathan Karthikeyan a,b, Clement Manohar Arava a,b, May Zin Hlaing a,b, Baojie Chen a,c, Chi Hou Chan a,c, Kwok-Ho Lam d, Vellaisamy A.L. Roy a,b,⁎ a

State Key Laboratory for Terahertz and Millimeter Waves, City University of Hong Kong, Kowloon Tong, Hong Kong Special Administrative Region Department of Materials Science & Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong Special Administrative Region Department of Electronic Engineering, City University of Hong Kong, Kowloon Tong, Hong Kong Special Administrative Region d Department of Electrical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong Special Administrative Region b c

a r t i c l e

i n f o

Article history: Received 22 March 2019 Received in revised form 16 August 2019 Accepted 28 August 2019 Available online xxxx Keywords: Thermal conductivity Impurity-doping Defect engineering Thermoelectrics Lattice dislocations Anharmonicity

a b s t r a c t Defect engineering in thermoelectric materials leads to the formation of exotic transport properties. Specifically, reduction in lattice thermal conductivity (кL) can be realized through scattering of low and high-frequency phonons by interfacial and point defects respectively. Herein we explore such phenomena by inducing dense dislocations through doping of rare earth (RE) impurities in β-(Zn1−xREx)4Sb3 [x = 0.3–0.5 at.%] as phonon scattering source of all frequencies. Lattice anharmonicity created results in an ultra-low кL of ~0.15 W/mK for β-(Zn0.997 Yb0.003)4Sb3. Vibrational properties and phonon scattering altered by the lattice anharmonicity are studied in detail through terahertz and infrared spectroscopies. © 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.

Thermoelectric materials have gained a lot of attention, focused by the demand for clean energy resources. By the process of Seebeck and Peltier effect, the thermoelectric materials can be utilized for power generation and space cooling respectively. Inheriting properties like emission-free and vibration-free conversion of heat to electricity, thermoelectric materials aided by their transport properties, add a lot of advantages [1–4]. The challenge lies in improving the power conversion efficiency, which is limited by the interdependency of the parameters in the dimensionless figure of merit zT = S2σ/(кE + кL), where S is Seebeck coefficient, σ is electrical conductivity, кE and кL are the electronic and lattice thermal conductivity and temperature T [5,6]. Difficulties in decoupling the interdependency between S, σ and кE led to a clear-cut strategy of improving the figure of merit through the power factor enhancement and Lattice thermal conductivity кL reduction [8]. These strategies were assimilated and showcased by various groups through band structure engineering, nanoinclusions and creating superlattice structures [9–12]. To achieve a low lattice thermal conductivity, effective phonon scattering is required in particular [13,14]. Enhancing phonon scattering at the grain boundaries through nanostructuring [15,16] and point defect scattering through

⁎ Corresponding authors at: State Key Laboratory for Terahertz and Millimeter Waves, City University of Hong Kong, Kowloon Tong, Hong Kong Special Administrative Region. E-mail address: [email protected] (V.A.L. Roy).

https://doi.org/10.1016/j.scriptamat.2019.08.037 1359-6462/© 2019 Published by Elsevier Ltd on behalf of Acta Materialia Inc.

extrinsic doping [17] creates a strong phonon-umklapp scattering by inducing lattice anharmonicity [18–22]. All these scattering mechanisms together decrease the total phonon relaxation time (τtot) with a characteristic frequency ω, thereby leading to a reduced lattice thermal conductivity [23–26]. Grain boundaries effectively scatter the lower frequency phonons with relaxation time τB α ω0 and the introduction of point defects induces scattering with a relaxation time τPD α ω−4 while the anharmonicity induced lattice vibrations scatters all other frequencies of phonons through Umklapp process possessing a relaxation time τU,N α ω−2 [27,28]. Lattice dislocation strain fields (τDS α ω−1) and cores (τDC α ω−3) dependent phonon scattering contributes towards the mid-frequency range phonon scattering which is not included by other phonon scattering mechanisms [16,26,29]. Lattice vibrations induced phonons are primarily determined by atomic mass and interatomic forces of the lattice vibrators. Accordingly manipulating interaction forces of atoms through lattice strains or grain boundary dislocation based scattering is an effective approach for advanced thermal transport optimization in thermoelectrics [30]. Recently, dislocations induced scattering is observed to have reduced a large percentage of lattice thermal conductivity. Hence, to attain lower lattice thermal conductivity for thermoelectric materials, an estimated dislocation density of 1012/cm2 is required, which is far higher than the intrinsic dislocation density found in semiconductors [31]. Plastic deformation, nanoprecipitates and vacancy defects create a higher density of dislocations in the material which is required for

96

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

optimizing the lattice thermal conductivity [32,33]. Vacancy defect engineering in thermoelectric materials easily increases dislocation density by the formation of vacancy defect clusters and the migration of these clusters act as Bardeen- Herring sources [31,34]. This mechanism is easily realized in an ionic crystal through the predominant Frenkel and Schottky defects, whereas the vacancy defects introduced by charge compensation reactions through cationic dopants are more complicated [35]. Alternatively, introducing highly dense dislocation extensively reduces the carrier mobility, thus it is very important to design the defect structure by considering the mean free path (MFP) of electrons and phonons with maximum mobility to кL ratio [36]. For a compound with smaller cation to anion ratio is very likely to have a low cationic vacancy defect formation energy compared to other anionic interstitial defects, which causes activation of Bardeen-Herring sources [37]. Thus the density of dislocation can be controlled by adjusting the dopant levels and the material's compositions. In this work, we demonstrate the above-mentioned strategy of reducing lattice thermal conductivity by rare earth element doping in β-Zn4Sb3. β-Zn4Sb3 is the best known thermoelectric material operating at an intermediate temperature range of 450–650 K [38,39]. Indeed, this material naturally possesses lower thermal conductivity compared with that of the vitreous materials because of its structural complexity [40]. Herein we have induced Zinc vacancy clusters through the extrinsic doping with different rare earth elements (Ce, Er, Eu, Lu and Yb) which produced uniform scattering due to the high density of dislocations. These dislocations together with the point defect scattering aided by the rare-earth dopants led to an ultra-low value of lattice thermal conductivity of ~0.15 W/m/K creating an improved the midfrequency phonon scattering in the material ultimately resulting in a better figure of merit. This concept of cationic vacancy induced dislocations concerning lattice thermal conductivity reduction could be implemented to other materials in order to improve their figure of merit. Experimentally, polycrystalline rare-earth doped β-Zn4Sb3 was prepared by the conventional melting and hot-pressing method. Seebeck Coefficient (S) and Electrical conductivity (σ) were measured by SBA 458 Nemesis (Netzsch). Thermal conductivity (к) was determined from the relation к = α Cp ρ, where α is the thermal diffusivity measured by laser flash method using Netzsch LFA 457 analyzer, Cp is the specific heat measured through Differential Scanning Calorimetry

(DSC 404, Netzsch) and ρ is the sample's density measured by Archimedes' method. Lattice thermal conductivity was determined by deducing the electronic thermal conductivity (кE = LσT) from total thermal conductivity (к = кL + кE). Lorenz number (L) was found by using the method proposed by Kim et al. [41]. Fig. 1(a), X-ray diffraction studies show the formation of the high purity poly-crystalline β-Zn4Sb3 phases [42]. The formation of rare earth doped β-Zn4Sb3 solid solution and the induced vacancy defects is evidenced from the decreasing lattice parameter with an increase in dopant concentration which obeys Vegard's rule as shown in Fig. 1 (b) [43]. Doping-induced cationic vacancy defects are explained through various mechanisms in semiconductor materials [44–46]. Here the rare earth dopants acted as the Bardeen-Herring sources which assisted the dislocation climb through vacancy defect migration [47]. These rare earth dopant elements act as multiplication sites for dislocation and are migration-limited processes. According to impurity diffusion theory, the dominance of vacancies will control the migration of impurities by columbic attraction, which prevents aggregation of dopant impurities. However, the migration of vacancies will be largely activated, leading to increase in dislocation density. This phenomenon of cationic vacancies induced dislocation in β-Zn4 Sb 3 is confirmed by our STEM observations as shown in Fig. 2. Fig. 2(c) shows the uniformly distributed dopant induced lattice dislocation which stands as strong evidence for the change in lattice parameter a. Fig. 2(f) shows the observed dislocation induced stress moire like fringes [38]. Microscopically, the density of dislocations is estimated through the Williamson-Hall model for the rare earth doped βZn4Sb3 which can be compared with the TEM observed dislocations. Analysis of Williamson-Hall plot explains the strong relation between the dislocation density and crystal size through the peak broadening effect as shown in Fig. 1(c) where the slope and the intercept correspond to dislocation density and crystal size respectively [26]. Relating this with normal XRD results, quantitatively, the density of dislocations increases with a corresponding increase in the dopant concentration. In a β-Zn4Sb3 crystal structure there are 78 negatively Sb charged ions (18Sb3− and 12Sb2−) which require 39Zn2− charged ions to be balanced. But there are only 36 sites available for Zn atoms which leave three zinc ions in interstitial sites attributing to Zn ion migration in

Fig. 1. (a) Powder XRD pattern of rare-earth doped β-Zn4Sb3 (x = 0.3 at.%) (b) shows the decreasing lattice parameter with different dopant % (c) Williamson-Hall plot for peak broadening analysis where the slope (×10−2) and intercept (×10−2) reveals dislocation density and crystal size respectively.

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

97

Fig. 2. (a) and (b) are the FESEM images of the hot-pressed β-Zn4Sb3. STEM images of β-Zn3.997Yb0.003Sb3 (c) and (d) uniformly distributed dense dislocation induced by Zn vacancy defect and their migration (e) HRTEM image with arrow mark showing the dislocation area (f) Moires like fringe developed shows the stress induced in the crystal.

the crystal [40,48]. Additionally, the rare earth dopant induced more Zn ion migration leading to the creation of a high density of dislocation in the structure as shown in the STEM-HAADF image. To investigate the lattice anharmonicity induced by these dislocations, micro-Raman scattering and Infrared scattering experiments were performed and analyzed. Addition of impurities to the host crystal with different atomic mass gave rise to additional vibrational modes with higher frequencies than that of host crystal's vibrational modes. The potential energy function generated for a defect is anharmonicity which causes the vibrational frequency to be lower than the harmonic frequency [49]. Impurity-induced anharmonic vibrational modes also affect their vibrational lifetime through the coupling of low-frequency modes and impurity modes which are spatially localized or delocalized. The phonon active modes in β-Zn4Sb3 were determined by the

correlation method: Infrared and Raman selection rules for lattice vibrations. Based on the space group, the number of atoms per unit cell and their degree of freedom, the lattice vibration and phonon active modes for each crystallographic site in β-Zn4Sb3 are: Гvib ð36f Þ ¼ 3A1g þ 3A2g þ 6Eg þ 3A1u þ 3A2u þ 6Eu Гvib ð18eÞ ¼ A1g þ 2A2g þ 3Eg þ A1u þ 2A2u þ 3Eu Гvib ð12cÞ ¼ A1g þ A2g þ 2Eg þ A1u þ A2u þ 2Eu

Totally, for β-Zn4Sb3: Гvib ðβ−Zn4 Sb3 Þ ¼ 5A1g þ 6A2g þ 11Eg þ 5A1u þ 6A2u þ 11Eu

98

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

At Г point, the vibrational modes are expressed as Гvibrational = Гacoustic + Гoptical [50]. The irreducible acoustic vibrational modes are A2u + Eu. Infrared and Raman active mode are 5A2u + 10Eu and 5A1g + 11Eg respectively [51]. With 16 Raman active modes, two peaks and one shoulder peak are clearly observed in the micro-Raman spectrum of β-Zn4Sb3 as shown in Fig. 3(a). Fig. 3(b) shows the Raman peak shift associated with rare earth dopant, here the peaks at 148 cm−1 and 172 cm−1 correspond to Zn\\Sb and Sb\\Sb bonds in β-Zn4Sb3 phase respectively [51]. With the rare earth impurity added to the β-Zn4Sb3, clear change in A1g peak positions was observed, which stands as clear evidence of the increased defect or dislocation density induced by stress in the crystal lattice which resulted in the peak broadening of Eg. The change in the charge states of these induced defects causes change in the charge localized in Zn\\Sb bond leading to a shift in their vibrational frequencies [52]. Here the shift in the peak indicates the formation of deep-level defects in the material. This generated lattice anharmonicity stands as first-order scattering of phonons decreasing their relaxation time τ [53,54]. The decrease in relaxation time is found to be directly related to the peak width expressed as:

τ¼

1 2πcγ

ð1Þ

where γ the peak width and τ is the relaxation time or phonon lifetime. In IR reflectance experiments, the reflectance with frequency for the sample with defect of interest is obtained. The infrared vibrational absorption band area is proportionate to the defect concentration, N specified by: Z

    α ðϑÞdϑ ¼ πq2 N = μnc2

ð2Þ

where α is the absorption coefficient, ϑ is frequency, n is the refractive index of the material, c is the speed of light and q is effective oscillating charge [55]. Fig. 3(c) compares the infrared reflectance spectrum of rare earth doped β-Zn4Sb3 where the peak shift and reduction in peak intensity corresponds to the induced lattice anharmonicity. The intensity and broadening effect observed, corresponds to the phonon scattering with an increase in Zn vacancy and their induced dislocation density. Additionally, to evaluate the phonon scattering, we measured the time domain terahertz reflection spectrum (THz-TDS) which presents the anharmonicity created through rare earth impurities [56]. Terahertz spectroscopy has the capability to reveal the lattice and carrier dynamics in semiconductors. For a material with strong electron-phonon coupling, these carrier-lattice interaction causes local lattice deformations which causes anharmonic frequencies as shown in the Fig. 3(d). We

Fig. 3. (a) Raman spectra of β-Zn4Sb3 with Lorentzian fitted peak (b) shows the Raman spectra for different rare earth doped β-Zn4Sb3 showing peak shift and broadening (c) FT-IR reflectance spectra explains the dampening of lattice vibrations (d) Resonance peak of THz-TDS indicating the Lattice anharmonicity developed for different rare earth doped β-Zn4Sb3 where x = 0.3 at.%.

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

measured our samples in the frequency range of 0.2–1.2 THz which is exactly in the range of vibrational frequency of phonons [7]. The shift in the terahertz frequency resonance curve shows the lattice deformations induced by each dopant compared to the pristine βZn4Sb3. For pristine β-Zn4Sb3, the THz reflectance spectrum shows harmonic phonon vibration signifying absence of scattering points. Whereas, for samples with rare earth dopant, THz reflectance spectrum exhibits anharmonic behaviour caused by the introduced lattice strain and dislocations as scattering points. The change in the reflectance intensity and the change in the resonance peak articulates the anharmonicity caused by the dislocation induced by the dopants [57]. Seebeck coefficient of these rare earth doped samples do not show much variation compared to the pristine β-Zn4Sb3 which implies that the induced dislocation in the material does not damage the electronic properties. On the other hand, electrical resistivity is rapidly decreased due to increase in the carrier concentration and positively charged Zn vacancy defects. Lattice thermal conductivity is determined from total thermal conductivity by deducting electronic thermal conductivity found through Wiedermann-Franz law. From the measured thermal conductivity, we observed the rapid decrease in the lattice thermal conductivity for the rare earth doped β-Zn4Sb3. The temperature dependent lattice thermal conductivity dependence on the relation:

кL ¼

 3 Z θD =T kB kB T x4 ex τtot ðxÞ dx 2 2π υ ħ ðex −1Þ2 0

ð3Þ

where kB the Boltzmann is constant, υ is the average speed of sound, ħ is reduced Planck constant, θD is debye temperature, total phonon lifetime or total relaxation time is τtot where x = ħω/kBT. This total relaxation time is the sum of the scattering caused by Umklapp, phonon-phonon, point defect and the lattice dislocations [27]. −1 −1 −1 −1 τtot ¼ τ−1 U þ τ N þ τ PD þ τ DC þ τ DS

ð4Þ

From the room temperature values of β-Zn4Sb3, к = 17.1 mW/cm/K, υ = 9.89 × 105 cm/s, specific heat C = 0.29 J/g/K, we calculated the mean free path of phonon as 11.6 Å and even lower for rare earth doped β-Zn4Sb3 as shown in Fig. 5. Mean free path of phonons are lower than the unit cell lattice parameter which indicates the transmission of heat through lattice vibration is by hopping from one atom to another [58]. The spacing of lattice defects is in the order of one-unit cell, which significantly reduces the mean free path of phonon and thus the кL. These lattice defects will locally influence the phonon frequencies and induce anharmonicity, leading to lattice softening. The effect of lattice softening can be seen from the change in speed of sound in the materials as tabulated in Table 1. Though, the lattice softening and phonondefect scattering are distinguishable in the temperature dependence of кL. Phonon-defect scattering is more effective at lower temperature than higher temperature, whereas lattice softening is effective in all temperature range. The reduction in the speed of sound directly corresponds to the rise in internal strain of the material.

99

In order to verify the obtained minimum thermal conductivity theoretically, we have used the Cahill's model for minimum thermal conductivity as simplified by Agne et al. [59]:

кmin

2 kB υ 2 1 kB ð2V T þ V L Þ ¼ 1:21n3 ¼ 1:21n3 3

ð5Þ

where n is the number density of atoms, kB is Boltzmann constant and υ is the velocity of sound. The кmin is used as a predictor for experimental minimum thermal conductivity of amorphous and disordered materials. The obtained theoretical thermal conductivity (кmin) of β-Zn4Sb3 calculated from Cahill model [59] is 15 mW/cm/K, this is in good estimation with the measured value 17.13 mW/cm/K at room temperature, similarly for rare earth doped samples the measured thermal conductivity values are close to the estimated theoretical minimum of thermal conductivity as shown in inset of Fig. 4(c). Fig. 4(d) shows the measured lattice thermal conductivity for the rare earth doped β-Zn4Sb3 samples where it shows a drastic decrease in the lower and mid-range of temperature. This decrease in the lower and mid-range temperature is attributed from the scattering induced by the point defects and the dislocation density respectively. Such a fall in the lattice thermal conductivity is also observed previously in other materials [30]. The phonon scattering by point defect generated by rare-earth dopant affecting the relaxation time of phonon with respect to their concentration is derived as: τ−1 PD ¼ V a C i

  mi −mave 2 ω4 mave 4πv3

ð6Þ

where mi and mave are mass of defect and average mass of the atoms, Va is atomic volume, Ci is the defect concentration created [38]. However, due to the change in defect concentration with temperature causes a slight increase in the lattice thermal conductivity at higher temperature. Increase in the concentration of Zn vacancy defects significantly decreases the low frequency phonon scattering relaxation which is clearly observed from our measured values. On the other hand, the high density of dislocation created by the migration of Zn vacancies contributes for major anharmonicity and scattering of mid frequency phonons thereby deeply reducing their relaxation time. The effect of dislocation density on the phonon relaxation time is explained by: τ−1 DS ¼

23=2 37=2

2

N d b γ2 ω

ð7Þ

where Nd is the density of dislocation created, b is burgers vector, ω is the characteristic phonon frequency and γ is Grűreisen respectively. As a result of phonon-umklapp process, point defects and dislocation scattering of phonon has significantly minimised in the lower and mid frequency range phonon with respect to temperature. Here in our case, we claim that the dislocation induced scattering as the main reason for the reduction in lattice thermal conductivity. Moreover, the Zn

Table 1 Calculated and Experimental parameters for undoped and rare earth doped β-Zn4Sb3. Sample (x = 0.3%)

Density (g/cm3)

Speed of sound (×105 cm/s)

Grain size (nm)

Internal strain ԑ (×10−4)

β-Zn4Sb3 β-(Zn1−xCex)4Sb3 β-(Zn1−xErx)4Sb3 β-(Zn1−xEux)4Sb3 β-(Zn1−xLux)4Sb3 β-(Zn1−xYbx)4Sb3

5.4511 5.5111 5.5647 5.1490 5.2132 5.3462

5.042 5.014 4.89 5.088 4.94 4.77

54.16 45.98 30.7 50.6 25 40.3

5.75 7.85 12.42 6.55 20.45 17.45

100

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

Fig. 4. (a) and (b) are Seebeck coefficient and electrical resistivity for rare earth doped β-Zn4Sb3 where x = 0.3 at.% respectively (c) shows the total thermal conductivity (insight image shows the calculated theoretical minimum thermal conductivity [59]) and (d) dislocation and defect-induced decrease in Lattice thermal conductivity кL through different scattering mechanism.

Fig. 5. Mean free Path of phonons calculated using experimental values of к for rare earth doped β-Zn4Sb3 (x = 0.3 at.%).

vacancy clusters inducing the lattice dislocation and migration of these clusters act as Bardeen-Herring sources. Hence it is not possible for the dislocations to be annealed out at high temperature. The vibrational spectroscopic study of each dopant also corresponds to the decrease in lattice thermal conductivity, which also shows the optimization needed for attaining perfect кL. Totally, the effect of reduction in thermal conductivity of the material improves their thermoelectric performance. In summary, our work incorporates a method of modifying lattice thermal conductivity of thermoelectric materials by inducing regulated defects and uniform lattice dislocations through external impurity doping. The rare earth f- orbital elements exhibited a significant role in β-Zn4Sb3 by creating excessive Zn vacancies owing to their size effect, high electronegativity and their interaction force between atoms, these migrating Zn vacancies generates a uniformly distributed lattice dislocations throughout the crystal. The created Zn vacancies and dislocations contributed towards the scattering of low and mid frequency range phonons which ultimately leading to ultra-low lattice thermal conductivity. We have presented the effect of lattice anharmonicity created by the rare earth f- orbital dopants through the vibrational spectroscopy studies. Hence, by optimizing the defect dislocation density, we have recognized a whole new dimension in thermoelectric materials which can offer new insights in the coming years.

V. Karthikeyan et al. / Scripta Materialia 174 (2020) 95–101

Acknowledgment We acknowledge grants from the Environmental Conservation Fund project no: ECF 44/2014 and Research Grants Council of Hong Kong Special Administrative Region Project no: T42-103/16N. We thank Dr. Abhijit Pramanick for helpful discussions during the preparation of this manuscript. References [1] S. Twaha, J. Zhu, Y. Yan, B. Li, Renew. Sust. Energ. Rev. 65 (2016) 698–728. [2] M.S. Dresselhaus, G. Dresselhaus, J.-P. Fleurial, T. Caillat, Int. Mater. Rev. 48 (2003) 45–66. [3] C. Xiao, Z. Li, K. Li, P. Huang, Y. Xie, Acc. Chem. Res. 47 (2014) 1287–1295. [4] D.K. Aswal, R. Basu, A. Singh, Energy Convers. Manag. Energy Convers. Manag. 114 (2016) 50–67. [5] X. Shi, L. Chen, C. Uher, Int. Mater. Rev. 61 (2016) 379. [6] K. Biswas, J. He, I.D. Blum, C.-I. Wu, T.P. Hogan, D.N. Seidman, V.P. Dravid, M.G. Kanatzidis, Nature 489 (2012) 414–418. [7] Z. Chen, Z. Jian, W. Li, Y. Chang, B. Ge, R. Hanus, J. Yang, Y. Chen, M. Huang, G.J. Snyder, Y. Pei, Adv. Mater. 29 (2017) 1–8. [8] S. Wang, F. Fu, X. She, G. Zheng, H. Li, X. Tang, Intermetallics 19 (2011) 1823–1830. [9] Y. Liu, M. Zhou, J. He, Scr. Mater. 111 (2016) 39–43. [10] G. Tan, L.D. Zhao, F. Shi, J.W. Doak, S.H. Lo, H. Sun, C. Wolverton, V.P. Dravid, C. Uher, M.G. Kanatzidis, J. Am. Chem. Soc. 136 (2014) 7006–7017. [11] K. Termentzidis, O. Pokropyvnyy, M. Woda, S. Xiong, Y. Chumakov, P. Cortona, S. Volz, J. Appl. Phys. 113 (2013). [12] B.-L. Huang, M. Kaviany, Phys. Rev. B 77 (2008) 125209. [13] W.H. Shin, K. Ahn, M. Jeong, J.S. Yoon, J.M. Song, S. Lee, W.S. Seo, Y.S. Lim, J. Alloys Compd. 718 (2017) 342–348. [14] J. Shuai, J. Mao, S. Song, Q. Zhu, J. Sun, Y. Wang, R. He, J. Zhou, G. Chen, D.J. Singh, Z. Ren, C.W. Chu, G. Chen, Z. Ren, Energy Environ. Sci. 10 (2017) 799–807. [15] S. Lin, W. Li, X. Zhang, J. Lin, Z. Chen, Y. Pei, Inorg. Chem. Front. 4 (2017) 1066–1072. [16] S. Il Kim, K.H. Lee, H.A. Mun, H.S. Kim, S.W. Hwang, J.W. Roh, D.J. Yang, W.H. Shin, X.S. Li, Y.H. Lee, G.J. Snyder, S.W. Kim, Science 348 (109) (2015) 114. [17] H.J. Queisser, E.E. Haller, Science 281 (1998) (945 LP–950). [18] H. Wang, Y. Pei, A.D. LaLonde, G.J. Snyder, Proc. Natl. Acad. Sci. 109 (2012) 9705–9709. [19] D. Bansal, C.W. Li, A.H. Said, D.L. Abernathy, J. Yan, O. Delaire, Phys. Rev. B 92 (2015) 214301. [20] Z. Wang, C. Fan, Z. Shen, C. Hua, Q. Hu, F. Sheng, Y. Lu, H. Fang, Z. Qiu, J. Lu, Z. Liu, W. Liu, Y. Huang, Z.A. Xu, D.W. Shen, Y. Zheng, Nat. Commun. 9 (2018) 47. [21] J.G. Park, Y.H. Lee, Curr. Appl. Phys. 16 (2016) 1202–1215. [22] X. Meng, Z. Liu, B. Cui, D. Qin, H. Geng, W. Cai, L. Fu, J. He, Z. Ren, J. Sui, Adv. Energy Mater. 7 (2017), 1602582. [23] Y. Pei, H. Wang, G.J. Snyder, Adv. Mater. 24 (2012) 6125–6135. [24] L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Nature 508 (2014) 373–377. [25] M. Hong, T.C. Chasapis, Z.G. Chen, L. Yang, M.G. Kanatzidis, G.J. Snyder, J. Zou, ACS Nano 10 (2016) 4719–4727. [26] Z. Chen, B. Ge, W. Li, S. Lin, J. Shen, Y. Chang, R. Hanus, G.J. Snyder, Y. Pei, Nat. Commun. 8 (2017), 13828.

[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]

101

P.G. Klemens, Proc. Phys. Soc. Sect. A 68 (1955) 1113. A.J. Millis, P.A. Lee, Phys. Rev. B 35 (7) (1987) 3394–3414. J. Xin, H. Wu, X. Liu, T. Zhu, G. Yu, X. Zhao, Nano Energy 34 (2017) 428–436. Y. Wu, Z. Chen, P. Nan, F. Xiong, S. Lin, X. Zhang, Y. Chen, L. Chen, B. Ge, Y. Pei, Joule (2019) 1–13. D.L. Dexter, F. Seitz, Phys. Rev. 86 (1952) 964–965. S. Das, R. Chetty, K. Wojciechowski, S. Suwas, R.C. Mallik, Appl. Surf. Sci. 418 (2017) 238–245. N. Wang, D. West, J. Liu, J. Li, Q. Yan, B.L. Gu, S.B. Zhang, W. Duan, Phys. Rev. B Condens. Matter Mater. Phys. 89 (2014) 1–6. F.C. Frank, Discuss. Faraday Soc. 23 (1957) 122–127. R.W. Whitworth, Adv. Phys. 24 (1975) 203–304. C. Zhou, Y.K. Lee, J. Cha, B. Yoo, S.-P. Cho, T. Hyeon, I. Chung, J. Am. Chem. Soc. 140 (2018) 9282–9290. A. Faghaninia, C.S. Lo, J. Phys. Condens. Matter 27 (2015) 125502. D.-T. Ngo, L.T. Hung, N. Van Nong, ChemPhysChem 19 (2018) 108–115. E.S. Toberer, P. Rauwel, S. Gariel, J. Taftø, G. Jeffrey Snyder, J. Mater. Chem. 20 (2010) 9877–9885. G.J. Snyder, M. Christensen, E. Nishibori, T. Caillat, B.B. Iversen, Nat. Mater. 3 (2004) 458–463. H.S. Kim, Z.M. Gibbs, Y. Tang, H. Wang, G.J. Snyder, APL Mater. 3 (2015). B. Gault, E.A. Marquis, D.W. Saxey, G.M. Hughes, D. Mangelinck, E.S. Toberer, G.J. Snyder, Scr. Mater. 63 (2010) 784–787. M.H. Lee, D.-G. Byeon, J.-S. Rhyee, B. Ryu, J. Mater. Chem. A 5 (2017) (2017) 2235–2242. D.M. Sim, M. Kim, S. Yim, M.J. Choi, J. Choi, S. Yoo, Y.S. Jung, ACS Nano 9 (2015) 12115–12123. N.K. Singh, S. Bathula, B. Gahtori, K. Tyagi, D. Haranath, A. Dhar, J. Alloys Compd. 668 (2016) 152–158. X. Du, Y. Wang, R. Shi, Z. Mao, Z. Yuan, J. Eur. Ceram. Soc. 38 (2018) 3512–3517. P. Zhai, G. Li, P. Wen, Y. Li, Q. Zhang, L. Liu, J. Solid State Chem. 193 (2012) 76–82. C.S. Birkel, E. Mugnaioli, T. Gorelik, U. Kolb, M. Panthöfer, W. Tremel, J. Am. Chem. Soc. 132 (2010) 9881–9889. A. Alkauskas, M.D. McCluskey, C.G. Van De Walle, J. Appl. Phys. 119 (2016) 181101. Z. Zhao, J. Elwood, M.A. Carpenter, J. Phys. Chem. C 119 (2015) 23094–23102. R. Viennois, M.C. Record, V. Izard, J.C. Tedenac, J. Alloys Compd. 440 (2007) 22–25. M. Sabarinathan, M. Omprakash, S. Harish, M. Navaneethan, J. Archana, S. Ponnusamy, H. Ikeda, T. Takeuchi, C. Muthamizhchelvan, Y. Hayakawa, Appl. Surf. Sci. 418 (2017) 246–251. O. Delaire, J. Ma, K. Marty, A.F. May, M.A. McGuire, M. Du, D.J. Singh, A. Podlesnyak, G. Ehlers, M.D. Lumsden, B.C. Sales, Nat. Mater. 10 (2011) 614. C.W. Li, J. Hong, A.F. May, D. Bansal, S. Chi, T. Hong, G. Ehlers, O. Delaire, Nat. Phys. 11 (2015) 1063–1069. M. Stavola, W.B. Fowler, J. Appl. Phys. 123 (2018) 161561. T. Yang, Y. Li, R. Stantchev, Y. Zhu, Y. Qin, X. Zhou, W. Huang, Appl. Opt. 55 (2016) 4139. G. Choi, Y.M. Bahk, T. Kang, Y. Lee, B.H. Son, Y.H. Ahn, M. Seo, D.S. Kim, Nano Lett. 17 (2017) 6397–6401. T. Caillat, J.-P. Fleurial, A. Borshchevsky, J. Phys. Chem. Solids 58 (1997) 1119–1125. M.T. Agne, R. Hanus, G.J. Snyder, Energy Environ. Sci. 11 (2018) 609–616.