Optimization of Thermoelectric Properties of MgAgSb-Based Materials

Subscriber access provided by UNIV OF CALIFORNIA SAN DIEGO LIBRARIES

Article

Optimization of Thermoelectric Properties of MgAgSbBased Materials: A First-Principles Investigation Naihua Miao, and Philippe Ghosez J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 02 Jun 2015 Downloaded from http://pubs.acs.org on June 2, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 16

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

The Journal of Physical Chemistry

Optimization of Thermoelectric Properties of MgAgSb-Based Materials: A First-Principles Investigation Naihua Miao and Philippe Ghosez∗ Theoretical Materials Physics, Institut de Physique, Universit´ e de Li` ege, Li` ege, B-4000, Belgium. E-mail: [email protected]

∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment


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

Abstract Recently, MgAgSb-based materials (MAS) have been proposed as promising candidates for room-temperature thermoelectric applications with a ZT larger than unity. In this work, we present a comprehensive theoretical study of the structural, electronic and thermoelectric properties of MAS by combining first-principles calculations and Boltzmann transport theory. The predicted Seebeck coefficients are compared with available experimental data. The effects of crystal structure and volume on the electronic and thermoelectric properties of MAS are discussed. The thermoelectric quantities are optimized with respect to the chemical potential tuned by doping carriers. It is suggested that the thermoelectric performance of the α phase of MAS can be enhanced by hole doping and strain engineering. Our work intends to provide a theoretical support for the future improvement on the thermoelectric performance of the MAS and related materials.

Keywords MgAgSb; Thermoelectric Properties; Electronic Structure; First-principles Calculation

Introduction With the increase of world’s energy demands, it is essential to explore desirable alternative energy sources. Thermoelectric materials have been the focus of attention due to their potential application in waste heat harvesting, solar-thermal electrical-energy production, radioisotope thermoelectric generators and also Peltier cooling devices. 1,2 The efficiency of thermoelectric materials is evaluated by a dimensionless figure of merit: ZT = S 2 σT /κ, where S, σ, T and κ (κ = κl + κe ) are the Seebeck coefficient, the electrical conductivity, the absolute temperature and the thermal conductivity from lattice and electronic contributions, respectively. To achieve the best performance of the thermoelectric materials, the


Page 2 of 16

Page 3 of 16

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


power factor (PF = S 2 σ) should be maximized, while the thermal conductivity should be minimized. Materials with ZT ≥ 1 are of particular interest for practical applications. Bi2 Te3 -based alloys with a ZT larger than unity have been the only thermoelectric materials for room-temperature device applications since 1950. 2–5 Unfortunately large-scale commercial applications were limited by the scarcity and high-cost of Te element. Recently, the α phase of MgAgSb-based materials (MAS) with a high ZT ∼1 near room-temperature has been reported and continuous effort has been devoted to improve the thermoelectric performance for low temperature power generation by various doping or nano-structuring. 6–8 As the constituent elements in MAS are relatively abundant on the earth, these materials are much promising for large scale commercial applications. Actually, there are three phases in MAS materials, i.e., the low-temperature (300-600 K) α phase (SPG. NO. 120), the medium-temperature (600-700 K) β phase (SPG. NO. 129) and the high-temperature (700 K-) γ phase (SPG. NO. 216). 9 So far, most of the works were experimental and focused mainly on the α phase. The measured resistivity 6 of α phase is of the order of 10−5 Ωm which is in the limit of conductors, suggesting that α phase might be metallic. A very recent theoretical study of the electronic structure of MAS reported that the α phase might also be a semiconductor with a very small electronic band gap of 0.1 eV. 8 The purpose of present work is to provide a comprehensive description of the structural, electronic and thermoelectric properties of the different phases of MAS materials, which is very useful for the improvement of their thermoelectric performance. In this work, the crystal structure, electronic structure and thermoelectric properties of the three phases of MAS are investigated using the first-principles calculations and semi-classical Boltzmann transport theory. Our study will provide a clue to optimize the power factor of MAS. We will start from the structural properties firstly and then access the electronic structures of MAS. Moreover, the effect of volume change on the thermoelectric quantities of MAS will be discussed. With the calculated electronic eigenvalues, the optimal power factor of different MAS phases will be estimated.



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

Computational Methodology Our calculations were performed within Density Functional Theory (DFT), using a projectoraugmented wave method 10 as implemented in the Vienna ab initio Simulation Package (VASP). 11 The 2p3s levels of Mg, 4d 5s levels of Ag, and 5s5p levels for Sb were treated as valence electrons. The Generalized Gradient Approximation (GGA-PBE 12 ) has been used for exchange-correlation functional. The cut-off energy for the plane-wave basis set was set to 400 eV, which was checked to provide results sufficiently converged to support our conclusions. The relaxation convergence for ions and electrons were 1×10−5 eV and 1×10−6 eV, respectively. Γ-centered k-point meshes of 5×5×4 for α phase, 10×10×8 for β phase and 8×8×8 for γ phase were used in the geometry optimization, respectively. For the computation of electronic properties, denser k-point meshes (twice as large as for the geometry optimization) were adopted for Brillouin zone integration to ensure the convergence and accuracy of eigenvalues. The conventional unit cells of different phases were built from the crystal structures determined by Kirkham and co-workers. 9 The thermoelectric properties were computed from the semi-classical Boltzmann transport theory within the constant relaxation time approximation and a rigid band approach using the BoltzTraP code, which has been used to investigate many thermoelectric materials successfully. 13

Results and discussion The lattice parameters and atomic positions of the different phases of MAS have been fully relaxed following the approach described in the previous section. The calculated structural properties are given in Table 1 and compared with available experimental data. 9 In Table 1, it is observed that the calculated lattice constants of the α and β phases are only slightly overestimated by ∼1% compared with experiments. The discrepancy is slightly larger for the high-temperature γ phase (∼2%), which can be justified by the fact that our structural relaxations are performed at 0 K and neglect the lattice thermal expansion. 9 The atomic 4 ACS Paragon Plus Environment

Page 4 of 16

Page 5 of 16

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


positions in all the three phases are also in reasonable agreement with the experimental data, supporting the validity of our approach. Table 1 The calculated lattice constants a and c, atomic Wyckoff positions and volumes of various phases of MAS compared with available experimental results. 9

a (˚ A) ˚ c (A) V (˚ A3 ) Mg x Mg y Mg z Sb x Sb y Sb z Ag (1) x Ag (1) y Ag (1) z Ag (2) x Ag (2) y Ag (2) z Ag (3) x Ag (3) y Ag (3) z

α Phase Calc. Expt. 9.268 9.176 12.762 12.696 1096.3 1069.0 -0.026 -0.036 0.276 0.296 0.115 0.096 0.231 0.236 0.476 0.475 0.116 0.120 0 0 0 0 0.25 0.25 0 0 0 0 0 0 0.222 0.224 0.222 0.224 0.25 0.25

β Phase Calc. Expt. 4.454 4.420 6.844 6.890 135.8 134.6 0.25 0.25 0.25 0.25 0.295 0.333 0.25 0.25 0.25 0.25 0.719 0.729 0.75 0.75 0.25 0.25 0 0 -

γ Phase Calc. Expt. 6.564 6.700 6.564 6.700 282.8 300.8 0.5 0.5 0.5 0.5 0.5 0.5 0 0 0 0 0 0 0.25 0.25 0.25 0.25 0.25 0.25 -

The electronic density of states (DOS) are plotted in Figure 1a for the three phases of MAS, both within the fully relaxed theoretical structure and the experimental structure from Kirkham et.al . 9 In our calculations, all three phases exhibit a finite DOS at the Fermi energy, attesting a metallic character. There is also no substantial difference between the DOS of the relaxed and experimental structures around the Fermi energy (Ef ). Inspection of the electronic band structure in Figure 1b reveals that the α phase has to be better classified as a “semimetal”, with highly-dispersive conduction and valence bands overlapping slightly and crossing the Fermi level at distinct k-points. This Fermi surface, plotted in Figure 1c, includes an electron pocket centred around Γ and hole pockets closer to the corners of the Brillouin zone of the conventional cell. These hole pockets do not include any high-symmetry point and only touch the ZA line, as also apparent from the electronic 5 ACS Paragon Plus Environment


Density of States (states eV -1 f.u.-1)

1.6 (a)

1.4 1.2 1 0.8 0.6 0.4 0.2 0

-0.5

0

0.5

Energy-Ef (eV)

0.8

(b)

0.6 0.4

Energy (eV)

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 6 of 16

0.2 Ef 0 -0.2 -0.4 -0.6 -0.8 Z

A

(c)

M

Γ

Z

R

Γ

X

g3 R Z

A

X �

g1

M

g2

Figure 1 Calculated (a) total density of states around the Fermi level for the α (blue), β (green) and γ (red) phases of MAS at the fully relaxed (dashed line) and experimental (solid line) atomic structures; (b) electronic band structure of the α phase along a path within the Brillouin zone of the conventional cell; (c) Fermi surface of the semi-metallic α phase highlighting an electron pocket around Γ and hole pockets around the corners of the Brillouin zone of the conventional cell.


Page 7 of 16

band structure in Figure 1b. The semi-metallic character of the α phase is consistent with experimental measurements of the resistivity, 6 which is in the range between metals and semiconductors. Our conclusion contrasts however with the recent proposal by Ying et.al 8 that the α phase might be semiconducting, with a small indirect bandgap of 0.1 eV between Γ and X. In fact, their calculated electronic band structure does not show any qualitative difference with ours. Similarly to them, we do not see any overlap between the valence band at X and the conduction band at Γ. Their mis-interpretation originates in the fact that they restricted their investigations to a limited path within the primitive Brillouin zone that does not cross the hole pockets. As ours, their DOS shows a finite value at Ef , which is incompatible with a semi-conducting behavior. We recalculated the electronic properties independently with the LDA 14 and GGA-PBEsol 15 functionals and confirmed a semi-metal character, consistently with our initial calculation within the GGA-PBE. 250 Alpha

Seebeck Coefficient (µVK-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 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Beta

Gamma

600

700

200

150

100

50

0 200

300

400

500

800

T (K)

Figure 2 Evolution of the Seebeck coefficients Sxx (triangle) and Szz (circle) of an intrinsic MAS crystal with the temperature in the α (blue), β (green) and γ (red) phases for the fully relaxed (empty symbols) and experimental structures (filled symbols). The x and z directions are aligned with the lattice vectors a and c as described in Ref. 9. Experimental measurements (black) from NanoE-2014 6 (inverse triangle) and PRB-2012 9 (diamond) are reported for comparison. Vertical lines show the limit of stability of the three phases.

Figure 2 shows the evolution of the computed Seebeck coefficient (S ) of an intrinsic MAS 7 ACS Paragon Plus Environment


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 8 of 16

Table 2 Electron and hole contributions to the carrier density (n), electrical conductivity (σ/τ ) and Seebeck coefficient (S) of the α phase of MAS, along different directions, at 550K. The upper part of the Table corresponds to an intrinsic crystal for which the chemical potential (µ) adjusts at finite temperature so that the density of electrons and holes remains equal (relevant for comparison with Figure 2). The lower part of the Table corresponds to a case where the chemical potential is kept aligning with the Fermi energy (Ef ), which requires, at finite temperature, a finite doping (relevant for comparison with Figure 4).

Holes Electrons Total Holes Electrons Total

µ-Ef n (eV) (1019 cm−3 ) 0.034 5.9 0.034 -5.9 0.034 0.0 0.000 10.8 0.000 -3.9 0.000 6.9

σxx /τ = σyy /τ (1018 Sm−1 s−1 ) 4.5 4.9 9.5 8.1 3.4 11.5

σzz /τ Sxx = Syy (1018 Sm−1 s−1 ) µVK−1 5.0 274 3.0 -138 8.0 59 9.1 226 2.0 -165 11.1 111

Szz µVK−1 279 -154 120 230 -180 158

crystal (i.e. without doping) in the three phases in comparison to available experimental data from PRB-2012 9 and NanoE-2014. 6 In all three phases, S is positive attesting from the dominant hole carrier contribution. In the α phase, S appears to be rather large and highly anisotropic, Szz being almost twice as large as Sxx . This anisotropy of the Seebeck coefficient is compatible with the crystal symmetry of the α phase, where the lattice parameters along the x and y directions are significantly different from that along the z direction. Further insight on the origin of this anisotropy is provided in Table 2, where the individual hole and electron contributions to the electrical conductivity (σh /τ and σe /τ ) and Seebeck coefficients (Sh and Se ) are reported (at 550 K). Surprisingly, Sh and Se are quite isotropic. The strong anisotropy of the total Seebeck coefficient, S = (Sh σh + Se σe )/(σh + σe ), has to be mainly assigned to the anisoptropy of σe , which is significantly smaller along z than along x and y. This lower conductivity of the electrons along z can, in turn, be related to a larger effective mass along z, as apparent from the electronic band structure and Fermi surface in Figure 1. The results are strongly sensitive to the structures (experimental or relaxed). The amplitude and temperature evolution (peak around 400-450 K) of Szz for the experimental structure are compatible with experimental data. A better agreement could even be obtained assuming


Page 9 of 16

that the materials is naturally hole-doped (curve shifted up with a maximum around 150 µV/K). We notice also the wide dispersion of experimental data, which certainly call for further experiments. In the β phase, S appears to be isotropic and very low, consistently with the abrupt jump observed experimentally at the phase transition. Here again the amplitude calculated is compatible with that reported experimentally. In the γ phase, S is again isotropic but keeps a very low value comparable to that of the β phase. This result is independent of the use of the relaxed or experimental structure and contrasts with what is observed experimentally: it cannot explain the sudden increase of S observed in the high-temperature regime. 200


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


150

100

50

0 200

300

400

500

600

T (K)

Figure 3 Evolution of the temperature dependence of Sxx (filled symbols) and Szz (empty symbols) of MAS with temperature in the α phase of an intrinsic MAS crystal at experimental volume 9 V0 (orange triangles), 99% V0 (purple circles) and 98% V0 (green squares), respectively.

The strong sensitivity of S with the atomic structure in the α phase suggests the possibility to perform strain engineering of the thermoelectric properties in MAS. As an illustration of that, we report in Figure 3 the evolution of S under isotopic compressive strain. For similarity, the atomic positions were kept fixed. We observe that a small volume compression of 2% produces an increase of Sxx and Szz of around 15% and 30% at 300 K, respectively. 9 ACS Paragon Plus Environment



200

PF/τ (10-3W*fs-1m-1K-2)

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 10 of 16

150

(a) Alpha

(b) Beta

300 K 400 K 500 K 600 K 700 K 800 K

(c) Gamma

100 50 0 -50

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.5

0

0.5

Chemical potential (eV)

-0.5

0

0.5


-0.5

0

0.5


Figure 4 Evolution of the xx (filled line) and zz (dashed line) components of Seebeck coefficients S and power factor over relaxation time (PF/τ ) with the chemical potential in the three phases of MAS. Different temperatures are considered, compatible wit the range of stability of each phase.


Page 11 of 16

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


As the Seebeck coefficient of the α phase of MAS is more strongly dependent on the crystal structure, in the following, we will report the results calculated at the fixed experimental structures for all the phases. The evolution of the Seebeck coefficients Sxx and Szz with the chemical potential are given in the upper panel of Figure 4a, 4b and 4c for the α, β and γ phases of MAS, respectively. For each phase, we consider different temperatures compatible with its range of stability. In the α phase, S can be maximized under slight p-type doping with a carrier concentration of 9.73×1019 cm−3 at 300 K and in the whole range of stability from 300 to 600 K. This is consistent with recent experimental works considering Na, In and Cu doping (Mg1−x Nax AgSb, MgAgSb1−x Inx and MgAg1−x Cux Sb0.99 ). 6,8,16 The Seebeck coefficients of β and γ phases are relatively small in comparison to the α phase. The optimal S can be also achieved under p-type doping but keeping a modest value always below 50 µV/K. This attests that the experimentally observed increase of S in the γ phase previously discussed cannot be explained by self-doping. The lower panel of Figure 4 also reports the evolution of power factor (PF) over relaxation time τ with the chemical potential for the three phases of MAS. Again, different temperatures are considered compatible with the range of stability of each phase. For all three phases, the maximum value of PF/τ is achieved at chemical potentials comparable to those maximising the Seebeck coefficients. In the α phase this corresponds to slight hole-doping with a carrier concentration of 3.35×1020 cm−3 at 300 K. As for S, the PF/τ along z is larger than along x and y, the anisotropy of S being only marginally compensated by that of σ/τ (see Table 2 for a quantitative comparison at µ = 0 and T = 550 K). We notice that PF/τ can also be achieved in the β and γ phases under electron-doping but at much larger carrier concentrations (5.44×1021 cm−3 at 700 K for β phase and 5.57×1021 cm−3 at 800 K for γ phase, respectively), which are likely more difficult to access experimentally. With a relaxation time of ∼5.6×10−14 s fitted from the calculated resistivity to experimental value 8 at 400 K, we get a power factor of ∼1.4×10−3 Wm−1 K−2 for undoped crystal and ∼2.18×10−3 Wm−1 K−2 at optimal doping along zz direction, which is close to the previ-



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

ous independent experimental work of ∼1.5×10−3 Wm−1 K−2 obtained by Ying and Kirkham et.al. 8,9 and ∼1.8×10−3 Wm−1 K−2 measured by Zhao et.al 6 in the undoped case. It seems that the thermal conductivity of the α phase can be well tuned by the sample synthesis process and composition optimization as suggested by recent experiments. 6,8 Assuming a κ value of 1.0 W/mK, Figure 4 also can be a indicator for the optimization of ZT with respect to the chemical potential. Assuming this value, we estimate ZT of ∼0.64 for undoped crystal at 400 K and ∼0.87 at optimal hole doping along the zz direction of the α phase, which is in good agreement with the experimental results. 6,8,9 Moreover, with the proper synthesis process and nano-grain-size control, the thermal conductivity of the α phase can be further reduced to ∼0.7 W/mK, 6 which could greatly improve its figure of merit. With this low κ, we obtained a ZT of ∼0.8 for pure crystal at 400 K and ∼1.25 at optimal doping along the zz direction of the α phase. The volume-dependence of the Seebeck coefficient and PF/τ of the α phase of MAS are illustrated in Figure 5a and 5b, respectively. At the chemical potential optimal Szz , a volume compression of 2% produces and increase of both Sxx and Szz of ∼25%. Similarly, at the chemical potential of -0.1 eV optimizing PF/τ , a volume compression of 2% enhances the value of PF/τ along both xx and zz directions by ∼10%, indicating that the figure of merit can also be improved significantly by strain engineering.

Conclusions In this work, we have studied theoretically the structural, electronic and thermoelectric properties of the three phases of MAS using first-principles simulations and Boltzmann transport theory within the constant relaxation time approximation. The calculated lattice constants and atomic positions are consistent with the experiments. The electronic DOS show that all the three phases of MAS have a metallic character, with the α phase behaving more precisely as a semi-metal. The computed Seebeck coefficients are compatible with


Page 12 of 16

Page 13 of 16


200

(a) Seebeck coefficient

150

100

50

0

-50

(b) PF/τ 0.7

PF/τ (10-3W*fs-1m-1K-2)

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


0.6 0.5 0.4 0.3 0.2 0.1 0 -0.5

0

0.5


Figure 5 Evolution of the xx (filled line) and zz (dashed line) components of S (top panels) and PF/τ (bottom panels) with the chemical potential in the α phase of MAS at volumes V0 (orange) and 98% V0 (green). Calculations have been performed at 550 K.

the experimental measurements for the α and β phases, but do not reproduce the large value observed in the γ phase. We have highlighted that, the Seebeck coefficient and power factor of the α phase are very anisotropic and quite sensitive to the crystal structures. We have shown their maximum values can be reached under very small hole-doping. From our calculations, we suggest that further significant improvement of the thermoelectric properties in the α phase could be obtained from strain engineering.



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

Acknowledgement We thank Matthieu Verstraete, Bin Xu and Daniel Bilc for helpful discussions.This work is supported by the ARC project TheMoTherm (Grant No. 10/15-03). N.M. thanks Prof. Zhifeng Ren from the University of Houston for valuable discussions on their experimental work. Ph.G. thanks the Francqui Foundation for a Research Professorship. Calculations have been performed on C´ eci-HPC facilities funded by F.R.S.-FNRS (Grant No 2.5020.1) and the Tier-1 supercomputer of the Fed´ eration Wallonie-Bruxelles funded by the Walloon Region (grant no 1117545). They also took advantage of the PRACE projects TheoMoMuLaM and TheDeNoMo.

References (1) DiSalvo, F. J. Thermoelectric Cooling and Power Generation. Science 1999, 285, 703– 706. (2) Snyder, G. J.; Toberer, E. S. Complex Thermoelectric Materials. Nature Mater. 2008, 7, 105–114. (3) Yim, W.; Rosi, F. Compound Tellurides and Their Alloys for Peltier Cooling-A Review. Solid-State Electron. 1972, 15, 1121–1140. (4) Venkatasubramanian, R.; Siivola, E.; Colpitts, T.; O’quinn, B. Thin-film Thermoelectric Devices with High Room-temperature Figures of Merit. Nature 2001, 413, 597–602. (5) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y.; Minnich, A.; Yu, B.; Yan, X.; Wang, D.; Muto, A.; Vashaee, D. et al. High-thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys. Science 2008, 320, 634–638. (6) Zhao, H.; Sui, J.; Tang, Z.; Lan, Y.; Jie, Q.; Kraemer, D.; McEnaney, K.; Guloy, A.; Chen, G.; Ren, Z. High Thermoelectric Performance of MgAgSb-based Materials. Nano Energy 2014, 7, 97–103. 14 ACS Paragon Plus Environment

Page 14 of 16

Page 15 of 16

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


(7) Shuai, J.; Kim, H. S.; Lan, Y.; Chen, S.; Liu, Y.; Zhao, H.; Sui, J.; Ren, Z. Study on Thermoelectric Performance by Na Doping in Nanostructured Mg1−x Nax Ag0.97 Sb0.99 . Nano Energy 2015, 11, 640–646. (8) Ying, P.; Liu, X.; Fu, C.; Yue, X.; Xie, H.; Zhao, X.; Zhang, W.; Zhu, T.-J. High Performance α-MgAgSb Thermoelectric Materials for Low Temperature Power Generation. Chem. Mater. 2015, 27, 909–913. (9) Kirkham, M. J.; dos Santos, A. M.; Rawn, C. J.; Lara-Curzio, E.; Sharp, J. W.; Thompson, A. J. Ab Initio Determination of Crystal Structures of the Thermoelectric Material MgAgSb. Phys. Rev. B 2012, 85, 144120. (10) Blochl, P. E. Projector Augmented-wave Method. Phys. Rev. B 1994, 50, 17953. (11) Hafner, J. Ab-initio Simulations of Materials Using VASP: Density-functional Theory and Beyond. J. Comput. Chem. 2008, 29, 2044–2078. (12) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (13) Madsen, G. K.; Singh, D. J. BoltzTraP. A Code for Calculating Band-structure Dependent Quantities. Comput. Phys. Commun. 2006, 175, 67–71. (14) Perdew, J. P.; Zunger, A. Self-interaction Correction to Density-functional Approximations for Many-electron Systems. Phys. Rev. B 1981, 23, 5048. (15) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (16) Sui, J.; Shuai, J.; Lan, Y.; Liu, Y.; He, R.; Wang, D.; Jie, Q.; Ren, Z. Effect of Cu Concentration on Thermoelectric Properties of Nanostructured p-type MgAg0.97−x Cux Sb0.99 . Acta Mater. 2015, 87, 266–272. 15 ACS Paragon Plus Environment


Graphical TOC Entry 1

PF/τ (10-3W*fs-1m-1K-2)

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 16 of 16

(a) Alpha

(b) Beta

300 K 400 K 500 K 600 K 700 K 800 K

(c) Gamma

0.8 0.6 0.4 0.2 0 -0.5

0

0.5


-0.5

0

0.5


-0.5

0

0.5



Optimization of Thermoelectric Properties of MgAgSb-Based Materials

Recommend Documents