The effects of transition element doping on the thermoelectric properties of β-Zn4Sb3

Journal of Alloys and Compounds 793 (2019) 179e184

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The effects of transition element doping on the thermoelectric properties of b-Zn4Sb3 Mian Liu a, b, Kun Xu a, Xiaoying Qin b, **, Changsong Liu b, Zhe Li a, * a

Center for Magnetic Materials and Devices and Key Laboratory for Advanced Functional and Low Dimensional Materials of Yunnan Higher Education Institute, Qujing Normal University, Qujing, 655011, China b Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, P.O. Box 1129, Hefei, 230031, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 January 2019 Received in revised form 12 April 2019 Accepted 15 April 2019 Available online 16 April 2019

The effects of transition elements Fe, Co, and Ni on the electronic structure and thermoelectric properties of b-Zn4Sb3 were investigated by performing self-consistent ab initio electronic structure calculations within density functional theory and solving the Boltzmann transport equations within the relaxation time approximation. The results demonstrate that these transition elements with 3d orbitals could introduce giant sharp resonant peaks in the electronic density of states (DOS) near the host valence band maximum or conduction band minimum in energy. And these deliberately engineered DOS peaks result in a sharp increase of the room-temperature Seebeck coefficient of b-Zn4Sb3 by a factor of nearly 60, 80 and 130, respectively. Additionally, with the simultaneous decline of carrier thermal conductivity upon Co/Ni doping, potentially, at least, 1.21/1.13-fold increase in thermoelectric figure of merit of b-Zn4Sb3 at room temperature are achieved, indicating that the substitution of Co and Ni for Zn can effectively elevate thermoelectric performance of b-Zn4Sb3. © 2019 Elsevier B.V. All rights reserved.

Keywords: Thermoelectric materials b-Zn4Sb3 Thermoelectric properties Electron density of states resonance

1. Introduction Currently, there has been a renewed interest toward thermoelectric materials for energy conversion and power generation driven by energy crisis and the environment issues [1e6]. The thermoelectric potential of a material at an operating temperature T is assessed with the figure of merit of ZT defined as ZT ¼ S2 sT=l (here S is the Seebeck coefficient, s is the electrical conductivity, lð¼ lC þ lL Þ is thermal conductivity with both the carrier (lC ) and lattice (lL ) contributions, and T is the absolute temperature). Among the good thermoelectric materials known, b-Zn4Sb3 emerged as a prospective thermoelectric material for commercial application in the moderate temperature range because of the prominent high thermoelectric performance, ZT ¼ 1.3 at 670 K, which primarily arises from its extraordinarily low thermal conductivity (~0.7 Wm1 K1 at 650 K) [7]. Such extraordinarily low thermal conductivity can be likened to a “phonon glass-electron crystal” thermoelectric property [8], characteristic of an ideal thermoelectric material, and was recognized originating at least in

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (X. Qin), [email protected] (Z. Li). https://doi.org/10.1016/j.jallcom.2019.04.156 0925-8388/© 2019 Elsevier B.V. All rights reserved.

part from the complex and substantially disordered crystal structure with vacancies and interstitial Zn atoms [9,10], or due to the low frequency rattling motion of the Sb dimers in the crystal structure [11]. The ZT value of b-Zn4Sb3 has been elevated through many approaches, such as developing new synthesis methods [12], elemental doping and nano-structuring [13,14]. The traditional strategy for boosting ZT of b-Zn4Sb3 is to adjust the carrier concentration and lower thermal conductivity simultaneously by doping. For instance, dopants such as Pb, Bi, Mg, Cu, Sn, In, Cd, Al, Ga, Nb, Hg, Co, Te, I, Se, Fe and Ag have been investigated so far [15e33]. However, the results showed that although the individual parameters were affected by doping, there was a little or no overall improvement of its thermoelectric performance. The main reasons lie in the following factors: (i) thermal conductivity of b-Zn4Sb3 is very low (<1 W m1K1) [7,24,34] which is close to the practical lower limit for the thermal conductivity in solids [9]; this means that there is no much room in lowering its thermal conductivity; (ii) the hole concentration of pristine b-Zn4Sb3 is in the order of 1024~1025 m3 [7,35,36], which indicates that its carrier concentration has already been close to the optimum. These characters of b-Zn4Sb3 mentioned here suggest that it is difficult to enhance its thermoelectric performance remarkably through doping, unless

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the Seebeck coefficient S can be extra elevated upon doping. This is extremely important to the material system since the Seebeck coefficient of b-Zn4Sb3 is relatively small (around 100 mV/K at room temperature [7,8,24e26,35,37e39]), and only when large S is achieved can the thermoelectric performance of b-Zn4Sb3 be improved substantially. Recently, Heremans and his coworkers [40] demonstrated experimentally that ZT of Tl-doped PbTe doubled, which results from an increase in S and is caused by additional Tl-induced peaks in the electronic density of states (DOS). Similar phenomenon was also observed in Bi2Te3 doped with Sn [41]. The key issue to be settled here is whether there exits analogous elements that can cause a resonance-like peak in DOS of b-Zn4Sb3, just as Tl acts in PbTe. As we know, the valence electrons of transition elements are filled in 3d orbitals of the sub-outer layer in turn. If the 3d levels of these elements overlap or hybridize with the host band and to form resonate peaks close to the Femi level in DOS, great enhancement in Seebeck coefficient can be expected in such doped material systems as predicted theoretically by Mahan and Sofo [42]. It is thus particularly interesting to understand and explore possibilities of transition-dopant-induced resonance-like distortion peaks in the DOS with a view of improving thermoelectric efficiency, which could provide us a promising avenue for designing highperformance thermoelectric materials. Based on our preliminary investigation on the structural and thermoelectric properties of b-Zn4Sb3, in the present work we focused our attention on the change behavior of the electronic states and thermoelectric properties after doping of transition elements (here Fe, Co and Ni) in b-Zn4Sb3. Through combinations of ab initio calculations with analytic calculations we tried to extract some important information which would help us to understand the effects of transition-element doping on the thermoelectric properties of b-Zn4Sb exploring a possible path to enhancing its thermoelectric performance ultimately.

2. Computational methods

Fig. 1. Crystal structures of Zn36Sb30. Sb(1)3- atoms (red); Sb(2)2- atoms (purple); Zn atoms (cyan). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Cargnoni's model [9]. Please refer to our earlier work [46] for more details on this model. Then ab initio electrical structure calculations were carried out for the Zn-substituted compounds MZn35Sb30 (M ¼ Fe/Co/Ni). In order to understand the effects of transition element doping on the thermoelectric properties, s, S and lC were computed according to the ab initio calculation results, from the solution of the Boltzmann transport equation within the relaxation time approximation with the following expressions [47]:

s ¼ e2 Lð0Þ

(1a)

.  eTLð0Þ

(1b)

lC ¼ 1=TLð2Þ  S2 sT

(1c)

S ¼ Lð1Þ

where e is the electron charge, and the integrals L(a) is defined as: ðaÞ

L



þ∞ ð

¼

dE ∞

Our calculations are performed within the framework of the density-functional theory, with the PBE generalized gradient approximation to the exchange correlation energy, and the valence electron-ion interaction was modeled by the projector augmented wave potential, as implemented in the Vienna ab initio simulation package (VASP) [43e45]. The atoms of system were put in a unit cell with periodical boundary condition. The plane wave cutoff and k-point density, obtained using the Monkhorst-Pack method, were both checked for convergence for each system to be within 0.001 eV per atom. Following a series of test calculations, a plane wave cutoff of 350 eV was adopted. The structural optimization is truncated when the forces converge to less than 0.001 eV/Å. Structural re-

where

f0



 a  vf0 gðEÞvðEÞ2 tðEÞ E  Ef vE is

Fermi

distribution

(1d)

function

(¼

1

f 1 þ expð½E  Ef =kB TÞg ), Ef is the Fermi energy, y(E) is the electron velocity ( ¼ 1=Z  Vk EðkÞ), k is the electron wave vector, g(E) is the density of states, and t is the total relaxation time with three dominant contributions considered here: scattering by the deformation potential of acoustic and optical phonons, and polar scattering by optical phonons. The expressions for these scattering mechanisms [48,49] were listed below in Eqs. (2a)e(2d). Then the total relaxation time t was determined using the Matthiessen's rule 1 1 (t1 ¼ t1 po þto þta ),

!  1=2  2EE þ E  h i 1   E þ E 2 Eg g 1 2 1  ¼     1  d ln 1 þ d 2 1  2d þ 2d ln 1 þ d 1=2 1 1 þ 2E E e2 ð2m* Þ kB T ε1 2E þ Eg g ∞  ε0 

tpo

laxations have been performed by using the conjugate gradient algorithm. The ionic coordinates and the unit cell's size and shape were optimized simultaneously to eliminate structures with internal stress. For simplicity, in the present work we utilized the crystal structure of a hypothetical disorder-free b-Zn4Sb3 with a framework of Zn36Sb30 as shown in Fig. 1, one of basic structures in

to ¼

  1=2 2Z2 a2 rðZu0 Þ2 E þ E2 Eg   3=2  pE2oc kB Tð2m* Þ 1 þ 2E Eg Q

(2a)

(2b)

M. Liu et al. / Journal of Alloys and Compounds 793 (2019) 179e184

ta ¼

  1=2 2pZ4 Cl E þ E2 Eg   3=2  E2ac kB Tð2m* Þ 1 þ 2E Eg Q

Q¼1

181

(2c)

    8E Eg 1 þ E Eg   2 3 1 þ 2E Eg

(2d)

In these equations, m* is the density-of-states effective mass, ε∞ and ε0 are the high-frequency and static permittivity values, respectively, Eg is the band gap, a is the lattice constant, r is the material density, u0 is the optical phonon frequency, Cl is the average elastic constant, Eac and Eoc are the acoustic and optical deformation potential constants, respectively. In addition,

d ¼ ð2kr∞ Þ2 , where r∞ is the screening length given by r2 ∞ ¼ e2 ε∞

R∞ 0







vf vE

gðEÞdE. Values for material constants used in these

equations are given in Table 1. These values were obtained by fitting the curves of experimentally measured transport properties of pristine b-Zn4Sb3 as a function of temperature [7] with a two-band Kane energy dispersion relation [48], except for the values of r, Eg, a, and ε∞ that were taken directly from the literature [7,15]. 3. Results and discussions According to our calculation, as presented in Fig. 2, the DOS of Zn36Sb30 system is partitioned into Sb-s and Zn-d bands, which are bonding inactive, and the valence band (VB) and conduction band (CB) primarily composed of Zn-s, p and Sb-p states; The Fermi energy is ~0.35 eV below the VB top with a band gap of about 0.52 eV, which are consistent with the earlier model calculations [47]. The energy origin is chosen to be the top of the valence band of Zn36Sb30. And for the sake of comparison, the DOS of MZn35Sb30 (M ¼ Fe/Co/Ni) was shifted by a small amount (~0.4/0.27/0.3 eV) so that the core bands at the lower edge of the valence band DOS of the systems with and without Fe/Co/Ni can match perfectly. It was found that Fe affects the host band greatly and introduce high double resonant peaks in the DOS near the valence band maximum (VBM), as expected, which can be seen clearly in Fig. 2 (a); the two sharp peaks appear at 0.012 eV and 0.269 eV above the VBM. From the calculated total energies one can deduce the formation energies Eform of the Fe point defects is ~ 3.58 eV/atom which is defined as [26]:

Eform ¼ Edoped þ mZn  Eundoped  mFe=Co=Ni

(3)

here Edoped is the total free energy for the supercell containing the dopant (Fe/Co/Ni), Eundoped the total free energy for the undoped supercell, andm is the chemical potentials of the constituent elements. The partial DOS as shown in Fig. 2 (b) further reveals that the two sharp peaks are both caused mainly by the unique d levels of the Fe atoms which are located at the DOS peaks in energy. In contrast, Co doping, which corresponds to formation energy 3.53 eV/atom, has a little increased density of states near

Fig. 2. The total ((a), (c), and (d)) and partial (b) DOS of Zn36Sb30 with and without M (M ¼ Fe/Co/Ni). The energy is in respect to the host valence band maximum.

the VBM; while a sharp peak appears near conduction band minimum (CBM), which leads to a considerable enhancement in DOS at 0.658 eV near the CBM. Similarly, after Ni-doping, the DOS has a slightly increased density of states near the VBM and a sharp peak at 0.465 eV appears near the CBM, which shows a very similar behavior to the case with Co doping. Fig. 3 shows the calculated Seebeck coefficient S and electrical conductivity s of Zn36Sb30 at T ¼ 300 K as a function of carrier concentration n. It can be clearly seen that the calculated S and s agree well with experimentally measured values for pristine bZn4Sb3 [7,26,49], which indicates that the model applied in the theoretical simulation is reasonable and the predicted transport properties can reflect the reality with enough reliability. Fig. 4 shows the calculated Seebeck coefficient S, electrical

Table 1 Material parameters used to calculate the relaxation times for bulk b-Zn4Sb3. me is the free electron mass. Parameter

Value

Parameter

Value

Eac Eoc Cl m* Eg

30 eV 30 eV 8.1968  1010 N/m2 0.9 me 1.2 eV

ε0 ε∞

25.6410  8.85  1012 F/m 21  8.85  1012 F/m 2.06  1013 s1 12.231 Å 6077 kg/m3

u0 a

r

Fig. 3. Carrier concentration dependence of the calculated Seebeck coefficient and electrical conductivity for Zn36Sb30 at T ¼ 300 K; therein the experimental data (solid squares) for b-Zn4Sb3 reported in literature [7,23,45] are compared with our calculated results.

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M. Liu et al. / Journal of Alloys and Compounds 793 (2019) 179e184

Fig. 4. The variation of thermoelectric properties with carrier concentration at room temperature for b-Zn4Sb3 doped with Fe/Co/Ni. (a) Seebeck coefficient, (b) electrical conductivity, and (c) power factor.

conductivity s, and power factor S2 s of MZn35Sb30 (M ¼ Fe/Co/Ni) as a function of carrier concentration n. One can see from Fig. 4 (a) that Seebeck coefficient S for all the compounds increase as carrier concentration decreases, except for the three Fe/Co/Ni-doped cases whose S change their signs as n < 1.23  1027 m3, n < 0.32  1027 m3, and n < 0.003  1027 m3 respectively. However, S of Fe/Co/Ni-doped systems is significantly larger than that of undoped b-Zn4Sb3 in the interesting carrier concentration range. Especially for the three Fe/Co/Ni-doped cases, the maximum S is nearly 60/80/130 times as large as that of b-Zn4Sb3 at n z 1.3  1027 m3, n z 0.36  1027 m3, and n z 0.004  1027 m3 respectively. Certainly, it might be rather difficult and even impossible to obtain so great enhancement in the actual experiments due to the small solubility limit of impurities in b-Zn4Sb3. However, it is not completely impossible because the peaks induced by Fe/Co/Ni doping would be more and more d-functionlike in the DOS as Fe/Co/Ni concentration decreases which could lead to a sharper increase in S according to Mott formula [50]. Anyhow, these results suggest that modifying electronic structure via doping transition elements with d electrons could be an important direction to design new materials with substantially improved thermoelectric performance. Roughly speaking, electrical conductivity s for four cases all increase as carrier concentration increases as shown in Fig. 4 (b). It was found that electrical conductivity of three doped systems degrades greatly compared with that of undoped b-Zn4Sb3 in the interesting carrier concentration range. Especially for the Fe-doped case, s is nearly less than half that of b-Zn4Sb3 at n z 4  1027 m3. Just because of this, Fe doping system achieves a roughly equal optimizing power factor with undoped system as shown in Fig. 4

(c). While for two other Co/Ni doping cases, their optimizing power factors, both enhanced by a factor of almost 1.18/1.12 compared to that of undoped system, occur at n z 1.03  1027 m3, and n z 0.33  1027 m3, respectively. The calculated carrier thermal conductivity lC of MZn35Sb30 (M ¼ Fe/Co/Ni) is shown in Fig. 5(a). One can see that lC of MZn35Sb30 (M ¼ Fe/Co/Ni) has similar change behavior with carrier concentration to that of the electrical conductivity: (a) lC for three doped compounds all increase with carrier concentration increasing; (b) lC of Fe-doped system degrades greatly compared with that of undoped b-Zn4Sb3. Just relying on this point, Fe doping system achieves a roughly equal and high maximum ZT with undoped system as shown in Fig. 5 (b). Giant peaks in the DOS of Co/Ni-doped compounds bring great enhancement of the Seebeck coefficient and power factor which consequently would result in a sharp increase in the ZT. As shown in Fig. 5(b), it is true that the ZT assuming lL ¼ 0:6 Wm1 K1 (an average experimental value for pristine b-Zn4Sb3) of Co/Ni-doped systems are improved greatly as expected. The maximum ZT for the Co-doped case, appears at n z 1.03  1027 m3 near the optimal value of n for maximum power factor, owing to the raising of power factor and the simultaneous declining of carrier thermal conductivity. While the peak of ZT for Ni doping has a large shift to a smaller carrier concentration 3.3  1026 m3, which locates just in the range of increased power factor and degraded carrier thermal conductivity. However, the largest room temperature ZT values for Co and Ni doping are still encouraging, which can reach up to 0.18 and 0.17 at n z 1.03  1027 m3 or 3.3  1026 m3, about 1.21 and 1.13 times larger than the maximum ZT value of undoped system (ZT z 0.15 at n z 4.5  1025 m3), respectively. Therefore, it is

M. Liu et al. / Journal of Alloys and Compounds 793 (2019) 179e184

183

Fig. 5. Carrier concentration dependence of room temperature thermoelectric parameters for b-Zn4Sb3 doped with Fe/Co/Ni. (a) electronic thermal conductivity, (b) ZT with lL ¼ 0:6 Wm1 K1 .

reasonable to believe that one can further obtain systems with significant ZT enhancement when combining with other mechanisms (such as alloy scattering or nanostructure [51]) that reduce lattice thermal conductivity. Taken together, these results suggest that Co-doping is most helpful to enhance the thermoelectric performance of b-Zn4Sb3. To further clarify the details of thermoelectric performance evolution during Fe/Co/Ni doping, the Fermi energy dependence of room temperature carrier concentration n(EF) for MZn35Sb30 (M ¼ Fe/ Co/Ni) are shown in Fig. 6. As the carrier concentration is given by R nðEÞ ¼ gðEÞf ðEÞdE, where gðEÞ and f ðEÞ are the carrier density of states (DOS) and the Fermi distribution function, respectively. Thus, carrier concentration n increase with the upward shift of EF into the valence bands normally originating from an increased DOS of the deeper lying valence bands. In the energy range studied, carrier concentration n(Fe)>n(Co)>n(Ni) for a same EF. From which we can derive DOS(Fe)>DOS(Co)>DOS(Ni) for a same E, in good agreement with those obtained in the above-mentioned DOS calculation (Fig. 2). When room temperature ZT of three compounds MZn35Sb30 (M ¼ Fe/Co/Ni) reach their highest values at n z 1.3  1027 m3, n z 1.03  1027 m3 and 3.3  1026 m3, respectively, it is found that their corresponding EF sites are as follows: EF(Fe) ¼ 0.02eV, EF(Co) ¼ 0.01eV and EF(Ni) ¼ 0 eV. Their optimal EF are all located near the host valence band maximum. This condition is consistent with that found to maximize the ZT through introducing resonant states as mentioned in recent research articles [52,53].

4. Conclusions In summary, we have investigated the electronic structure and thermoelectric properties of b-Zn4Sb3 system doped with transition impurities Fe, Co and Ni through self-consistent ab initio electronic structure calculations within density functional theory and the Boltzmann transport equation within the relaxation time approximation. The calculations for Fe/Co/Ni-doped systems indicated that these atoms with d-electrons could introduce high sharp resonant peaks in the DOS near the valence band maximum or conduction band minimum, which could result in a boost Seebeck coefficient and a significantly suppressed conductivity. And consequently, significant reduction in carrier thermal conductivity leads to the enhancement of thermoelectric performance for bZn4Sb3 system. Moreover, the corresponding EF of the maximal ZT are all located near the host valence band maximum. We expect that further enhancement would be achieved by combining with other mechanisms (such as double-element-doping) that can further increase the conductivity. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grants No. 11674322, No. 51672278), Program for Innovative Research Team (in Science and Technology) in University of Yunnan Province, and the Center for Computational Science, Hefei Institutes of Physical Sciences. References

Fig. 6. The dependence of Fermi energy on carrier concentration at room temperature for MZn35Sb30 (M ¼ Fe/Co/Ni). The energy is in respect to the host valence band maximum. Arrows indicate where the best thermoelectric performance is achieved.

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