Bonding Hierarchy Gives Rise to High Thermoelectric Performance in

Subscriber access provided by REGIS UNIV

Article

Bonding Hierarchy Gives Rise to High Thermoelectric Performance in Layered Zintl Compound BaAuP 2

4

Koushik Pal, Jiangang He, and C. Wolverton Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b03130 • Publication Date (Web): 12 Oct 2018 Downloaded from http://pubs.acs.org on October 15, 2018

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 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 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.

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 17 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

Chemistry of Materials

Bonding Hierarchy Gives Rise to High Thermoelectric Performance in Layered Zintl Compound BaAu2P4 Koushik Pal, Jiangang He, and C. Wolverton∗ Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA E-mail: [email protected].

Abstract

tice thermal conductivity, which results in a high thermoelectric figure of merit (zT). Thus, our findings should encourage the exploration of new thermoelectric materials in the family of layered compounds with small band gaps and crystallographic heterogeneity.

The search for new thermoelectric materials has gained rapid progress in recent years as thermoelectric technology offers the potential for environmentally friendly and sustainable energy conversion methods from waste heat to electricity. In this work, we use first-principles calculations based on density functional theory to predict high thermoelectric performance in BaAu2 P4 , a layered Zintl compound with a small band gap. BaAu2 P4 exhibits crystallographic heterogeneity in which rigid [Au2 P4 ]2− units are separated by layers of Ba2+ cations which are bonded relatively weakly to the lattice through electrostatic interactions. The phosphorus atoms are covalently bonded to each other and form infinite chains within the crystal. While the phosphorus chains facilitate large electrical conductivity, the presence of multiple bands near the Fermi level gives rise to an enhanced Seebeck coefficient. On the other hand, the loosely bound Ba along with Au strongly scatter the heat carrying acoustic phonons, significantly reducing the lattice thermal conduction along the stacking direction. As a consequence of this bonding hierarchy (i.e., coexisting rigid and fluctuating sublattices), BaAu2 P4 exhibits a large power factor and low lat-

INTRODUCTION Thermoelectric materials, being able to convert waste thermal energy into electricity via a solid state technology, offer significant compactness, reliability and scalability over alternative energy conversion methods such as those which rely heavily on fossil fuels. 1–6 Despite being potentially sustainable and environmentally friendly source of energy generation and conservation, thermoelectric materials suffer from low conversion efficiency. Efforts are therefore underway to explore new materials with high thermoelectric performance 7,8 and to optimize the efficiency of the existing ones. 9–12 The efficiency of thermoelectric materials is quantified by figure of merit (zT ), which depends on conflicting material properties like Seebeck coefficient (S ), electrical conductivity (σ) and thermal conductivity 2 (κ) through the relation zT = S κσT with T being the absolute temperature. The thermal conductivity (κ = κe + κl ) consists of electronic (κel ) and lattice (κl ) contributions. Therefore a high zT requires a simultaneous presence of large S

ACS Paragon Plus Environment

1

Chemistry of Materials 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 2 of 17

and σ together with low κ in a single material. The thermoelectric efficiency of a material can be improved synergistically by enhancing the electronic transport properties coupled with the suppression of the lattice thermal conductivity. Band engineering which can increase the valley and orbital degeneracies of the electronic bands near the Fermi level through tuning the composition and doping in materials, has been shown to be an effective tool to enhance the bulk thermoelectric figure of merit by simultaneously increasing the Seebeck coefficient as well as the electrical conductivity. 8,9,12–14 Compounds with multi-valley bands close to the Fermi level, which facilitate in band convergence, were also shown to exhibit superior thermoelectric properties in SnSe, 11,15 CoSb3 , 16 PbTe. 9 Moreover, it was shown 7,17,18 that combination of flat (possessing large effective mass) and dispersive (light effective mass) bands gives rise to simultaneous enhancement of electrical conductivity and Seebeck coefficient respectively, yielding in high thermoelectric power factor (S 2 σ). On the other hand, suppression of lattice thermal conductivity has been achieved through extrinsic routes such as all-scale hierarchical architectures or nano-structuring that leads to a degradation of thermal transport properties due to increased phonon-scattering. 19–22 Thus, solids with intrinsically low thermal conductivity are desirable as they offer independent control over the electronic transport properties (Seebeck coefficient and electrical conductivity) through modifications of their electronic bands. Unconventional phonon-scattering mechanism are shown to be responsible for the low κl in filledskutterudites, 23 clathrates 24 with rattling guest filler compounds. A common characteristic of these materials is that they exhibits crystallographic heterogeneity consisting of co-existing rigid and fluctuating sub-lattices. While lone pair induced bond-anharmonicity leads to ultralow lattice thermal conductivity in I-IV-VI2 semiconductors, 25,26 anharmonic rattling-like vibrations of the cations also engender ultralow κl in Cu3 SbSe3 , 27,28 InTe, 29 TlInTe2 30 compounds.

Figure 1: (a) Conventional unit cell (outlined with black line) of BaAu2 P4 in which [Au2 P4 ]2− layers are separated by layers of Ba2+ cations which are stacked along the crystallographic y-axis. Connectivity of the P atoms denotes infinite chains of P atoms in the crystal structure. (b) Total charge density plot showing strong overlap of charge clouds between P atoms implying the presence of covalent bonding, and a relatively weak overlap of charges between Au and P atoms within the [Au2 P4 ]2− layers. Nonoverlapping charge density of Ba atoms suggests that they are relatively weakly bonded to the lattice. (c) Calculated electron localization function (ELF, visualized at an iso-surface value of 0.9) reveals presence of lone pairs around P atoms. (d) Potential energy well of the constituent atoms calculated as a function of displacements along the in-plane (x) and out-ofplane (y) directions of the crystal.

Bulk materials with two-dimensional strucACS Paragon Plus Environment

2

Page 3 of 17 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


tures exhibit outstanding thermoelectric properties due to their strong anisotropic features. 31 Recently, layered Zintl compounds such as Mg3 Sb2 32,33 and CaMg2 Sb2 34 have been shown to exhibit promising thermoelectric properties which originate from the presence of multivalley bands 33 in their electronic band structures. While the presence of multiple bands near the Fermi level in the above compounds facilitates band convergence, and hence an improved thermoelectric power factor, low κl can be achieved by introducing heavy atoms in the crystal with weak bonding. In this regard, compounds containing weakly bonded Ba atoms tend to exhibit low κl . 26,35 For example, Ba8 Au16 P30 , a clathrate compound, exhibits κl of 0.18 W/mK at room temperature. 35 BaBiTe3 , 36 on the other hand, shows multiband electronic transport properties as well as low κl (0.28 W/mK at 300 K) due to heavy Ba atoms. Moreover, electrostatic repulsion between the lone pairs of the cations and anions introduce anharmonicity in the lattice of BaBiTe3 , which gives rise to enhanced phonon scattering, leading to low κl . 25,26 In another recent work, the metal phosphides have been shown to exhibit good thermoelectric properties. 37

phosphorus atom has a coordination number of three (two P and one Au atoms), each Au atom is almost linearly coordinated by two P atoms. Ba atoms, on the other hand, are coordinated by six gold and eight phosphorus atoms forming a distorted bicapped hexagonal antiprism. 38 One interesting feature of the crystal structure is the presence of infinite chains of P atoms (see the connectivity of P atoms in Figure 1a) within each [Au2 P4 ]2− layer that run parallel to one another and are linked together by Au atoms. The corrugated Au-P layers resemble the creased anisotropic layers of SnSe which exhibits very low lattice thermal conductivity, 10 and the layers of black phosphorus that possesses very high electrical mobility. 39 Thus we see in the compound the possibility that, on one hand, anisotropic layered structure in BaAu2 P4 could induce low lattice thermal conductivity, and on the other hand, the infinite chains of P atoms could facilitate large electronic conductivity.

METHODS We performed first-principles calculations based on density functional theory (DFT) using the Vienna Ab-initio Simulation Package (VASP). 40,41 We replaced the potential arising from the interaction between nucleus and core electrons of an atom with a pseudopotentials derived within the projected augmented wave (PAW) method, 40,42 treating the exchange and correlation energy of the electrons with a generalized gradient approximated (GGA) 43 functional. The expansions of electronic wave functions in plane wave basis were truncated with a cut-off energy of 520 eV. Brillouin Zone (BZ) integrations were sampled on uniform mesh of 10×10×5. The discontinuity in occupations numbers of electronic states near the gap was smeared with Fermi-Dirac distribution functions. We first optimized the crystal structure using PBE 43 parametrization of the GGA functional which overestimated by the the lattice constant along the stacking direction by more than 3%. On the other hand, the lattice constants optimized (aopt = 8.7343 ˚ A, bopt = 21.6261 ˚ A, copt = 6.5705 ˚ A) using 44 PBEsol method of the GGA functional agree well (error < 1.5%) with the experimentally re-

Motivated by these recent findings, and in an effort to discover new materials that possess multi-valley bands and bonding hierarchy, we focus on the layered Zintl compounds, using BaAu2 P4 as an example. 38 The crystal structure of BaAu2 P4 consists of covalently bonded chains of P atoms that facilitate large σ. On the other hand, relatively weakly bonded Ba2+ and Au1+ cations scatter phonons, leading to low κl . Our first-principles calculations based on density functional theory show that BaAu2 P4 is a promising p-type material with large power factor and intrinsically low κl , resulting in a high thermoelectric figure of merit (zT). BaAu2 P4 crystallizes in the orthorhombic Fddd space group (No. 70). 38 The crystal structure (Figure 1a) consists of [Au2 P4 ]2− layers stacked alternatively with the layers of Ba2+ cations along the crystallographic y-direction. The coordination environments of the constituent atoms are quite interesting. While each


3


ported values 38 (aexp = 8.8670 ˚ A, bexp = 21.8440 ˚ A, cexp = 6.5171 ˚ A). Hence, we used PBEsol for further calculations. The conventional unit cell contains 56 atoms, while the primitive unit cell has 14 atoms in it. We used the optimized primitive unit cell for further calculations and analysis. Calculations with hybrid density functional were performed with the HSE06 45,46 functional, where the many body exchange correlation functional is constructed by mixing 25% exact Hartree-Fock exchange and 75% PBE, and the long range Coulomb interaction is suitably screened according to µ parameter (with µ = 0.207 ˚ A−1 ).

Page 4 of 17

The electronic transport properties i.e., electrical conductivity (σ), electronic contribution to the thermal conductivity (κe ) and Seebeck coefficient (S) were calculated using the Boltzmann transport equation within the constant relaxation time approximation as implemented in the BoltzTraP code. 47 Electronic relaxation times at different temperatures were obtained from first-principles calculations. We obtained converged values of σ, κe and S based on the electronic energies calculated at a dense mesh of 30×30×15 k-points. xx, yy and zz components of the calculated transport coefficients (σ, S) are denoted with x, y and z subscripts respectively. We have used a combination of Quantum Espresso 48 and EPW 49,50 codes to calculate the relaxation times of the electrons. The dynamical matrices and the phonon frequencies were first calculated in 2×2×1 coarse grid of phonon wavevectors using the PH 51 module of the Quantum Espresso code which were subsequently used to compute the matrix elements of the electron-phonon coupling using the EPW code. Finally, the electronic self-energy (whose imaginary part gives the electronic relaxation time) was computed in a dense grid of 40×40×20 phonon wavevectors. we have calculated the distribution of electronic relaxation times (τ ) of BaAu2 P4 as a function of electronic energy at three different temperatures (300 K, 600 K and 900 K). As electron-phonon coupling is the dominant mechanism which affects the electronic transport properties, 52 we have determined τ from the imaginary part of the calculated electronic self energy that depends on the electronphonon coupling matrix elements. 50,53 Our calculations reveal that BaAu2 P4 possesses relatively large τ at 300 K which varies from 25 fs to 108 fs for the electronic bands that lie within 0.6 eV of the either side of the Fermi level (see Figure 6). As expected, the calculated relaxation time decreases as a function of increasing temperature. For example, τ varies from 12 fs to 67 fs at 600 K, which is further reduced at 900 K where it varies from 6 fs to 44 fs. Phonon dispersion of BaAu2 P4 was calculated using the finite-displacement method using Phonopy 54 and VASP taking a 2×2×1 supercell containing 56 atoms. Gruneisen parame-

(a)

(b)

Figure 2: (a) Crystal orbital Hamilton population (COHP) and (b) integrated COHP (iCOHP) for the nearest neighbor atomic pairs of BaAu2 P4 . Subscript for each atom pair indicates whether they are in the xz-plane (i.e., in-plane) or along y-direction (i.e., out-of-plane) within the unit cell of BaAu2 P4 . The black arrow in (a) indicates that the nearest neighbor P-P interaction gives rise to the largest peak in COHP near the Fermi level. The dashed vertical line denotes the position of the Fermi level.


4

Page 5 of 17 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


ter (γ) measures the degree of anharmonicity of phonons in a material. We estimated mode Gruneisen parameters (γqν ) of this compound using a central difference formula taking phonon frequencies calculated at two different volumes (1.02V0 and 0.98V0 , V0 being the optimized unit cell volume). Temperature dependent atomic displacement parameter (ADP) has been calculated using Phonopy. The third-order force constant matrix was calculated for BaAu2 P4 using a 2×2×1 supercell using thirdorder.py 55 utility avail within ShengBTE code, 56 which was then used in conjunction with the second-order force constant matrix within the ShengBTE code 56 to calculate the phonon life time and lattice thermal conductivity (κl ). A linearized Boltzmann transport equation was solved within ShengBTE using a 10×10×8 q-point mesh to obtain converged values of κl . xx, yy and zz components of κl are denoted with x, y and z subscripts respectively.

different from solids with crystallographic homogeneity. We have investigated and analyzed the chemical bonding of BaAu2 P4 with the help of real space descriptors such as charge density analysis and the electron localization function (ELF) 64 calculated within density functional theory. The electronic charge density plot (see Figure 1b) shows (a) a strong overlap of charge density of P atoms in the chain, showing strong covalent bonding between them and (b) relatively weaker overlap of charges between Au and P atoms within the [Au2 P4 ]2− layers. On the other hand, non-overlapping charge spheres around Ba2+ cations suggests the fact that they are weakly bonded to the lattice, which interact with other atoms through electrostatic interactions. As expected, the ELF reveals lone-pairs around the P atoms (Figure 1c). These lone pairs induce lattice anharmonicity, which is manifested in large DFT calculated mode Gruneisen parameters (γqν ) of the acoustic phonon branches. To get more insight into the bonding hierarchy and atomic-level dynamics in BaAu2 P4 , we have calculated the potential energy curves of each atom by displacing them along different crystallographic directions from their equilibrium positions (see Figure 1d). The calculated energy curves show that Ba and Au atoms are located in shallow potential wells, whereas P atoms are confined in a relatively deep energy well. This suggests that Ba and Au atoms are relatively loosely bound and can vibrate more easily, leading to an enhanced scattering of the heat carrying phonons. The crystal orbital Hamilton population (COHP) method allows the partitioning of the band energies of a solid into pairs of orbital interactions, enabling identification of different chemical bonds. 65,66 More importantly, the integrated COHP (iCOHP) provides the contribution of a chemical bond to the one particle band energies and indicates its total bond strength 67,68 Here, we have performed COHP analysis for different pairs of atoms of BaAu2 P4 (Figure 2) using the LOBSTER code 66 Our calculations show that nearest neighbor P-P interaction results in the largest peak (indicated with a black arrow in Figure 2a) in the COHP near the Fermi level, indicating a stronger P-P bonding. The integrated

RESULTS AND DISCUSSION According to the Zintl concept, BaAu2 P4 is a valance balanced compound 38 which has coexisting ionic and covalent sublattices. In BaAu2 P4 , electrons are transferred from electropositive Ba and Au cations to the anionic substructure of P atoms which form two P-P bonds in which each P has oxidation state 38 of -1. Hence, the formal valence charges of the atoms are (Ba2+ )(Au+ )2 (P− )4 , making it a valence balanced compound which possesses a finite band gap. First-principles calculations based on density functional theory (DFT) have been applied successfully to predict novel thermoelectric materials 37,57–60 and analyze their properties. 28,61–63 Here, we study the thermoelectric properties of BaAu2 P4 using DFT. As PBEsol functional gave good estimation of the lattice constants of BaAu2 P4 , we performed all calculations (electronic structure, phonon, thermal conductivity) using the PBEsol functional in this work. As BaAu2 P4 consists of rigid and weakly bound substructures, we expect the chemical bonding environments in this compound to be


5


Page 6 of 17

(b)

(a) z

T Y

K2 X1

A1

L

A L

x

K1

(d)

(c)

Figure 3: (a) Phonon dispersion and (b) atom projected phonon density of states of BaAu2 P4 . (c) Mode Gruneisen parameter (γqv ) of the longitudinal (LA) and two transverse acoustic (TA1 and TA2) phonon branches calculated along the high symmetry directions in the Brillouin zone. (d) Atomic displacement parameter (ADP) of the constituent atoms of BaAu2 P4 calculated as a function of temperature along the crystallographic x, y and z-directions. High symmetry points in the first Brillouin zone are shown in the inset of (a).


6

Page 7 of 17

COHP for P-P interaction is the largest (see Figure 2b) which confirms that P atoms have the strongest chemical bonding in the lattice. 3.4

x,z

the longitudinal acoustic (LA) and two transverse acoustic (TA1 and TA2) phonon branches of BaAu2 P4 along high symmetry directions e.g., Γ-X (LA: 18 cm −1 , TA1: 28 cm−1 , TA2: 15 cm−1 ), Γ-Y (LA: 17 cm−1 , TA1: 31 cm−1 , TA2: 24 cm−1 ), Γ-Z (LA: 36 cm −1 , TA1: 8 cm−1 , TA2: 9 cm−1 ) are also below 40 cm−1 , indicating low sound velocities in these directions. The lattice thermal conductivity of a material can be written as 26 κl = 13 Cv v`, where Cv is the heat capacity, v is the speed of sound and ` is the phonon mean free path. The velocity of sound along the above high symmetry directions i.e., Γ-X (vLA : 3 km/s, vT A1 : 1.36 km/s, vT A2 : 2.25 km/s), Γ-Y (vLA : 2.5 km/s, vT A1 : 2.37 km/s, vT A2 : 2.24 km/s) and Γ-Z (vLA : 2.88 km/s, vT A1 : 0.54 km/s, vT A2 : 0.79 km/s) are comparable to the sound velocities of SnSe which possesses ultralow thermal conductivity. 10 These low sound velocities particularly along the stacking direction is consistent with a low lattice thermal conductivity in BaAu2 P4 . As expected from the bonding and potential energy wells of the atoms, it is clearly seen from Figure 3b that low frequency phonon modes are largely dominated by the vibrations of the heavier Au and Ba atoms (see also supplementary Figure S1).

y

3.0 2.6 κl (Wm−1K−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


2.2 1.8 1.4 1.0 0.6 0.2 300

500 700 Temperature (K)

900

Figure 4: Lattice thermal conductivity (κl ) of BaAu2 P4 as a function of temperature along the in-plane (i.e., x and z), and stacking (i.e., y) directions of the crystal. Acoustic phonon modes are primarily responsible for the transport of heat in a material. The heat conduction depends on the phonon group velocities which are given by the slope of the linear region of the acoustic phonon branches. The maximum phonon frequency in the linear part of an acoustic phonon branch defines the cut-off frequency which determines the group velocity for that phonon branch. The dispersion of an acoustic branch deviates from linearity beyond this cut-off frequency. The calculated phonon dispersion in Figure 3a exhibits very low cut-off frequencies (∼ 8 cm−1 and 9 cm−1 ) for the two transverse acoustic branches along the Γ-Z direction (which is the crystallographic stacking direction i.e., the y-axis in the unit cell of Figure 1a), indicating a low velocity of sound along that direction. Weak bonding between the adjacent layers along the stacking direction gives rise to weaker force constants, hence the low phonon cutoff frequencies. Such low cutoff frequency (e.g., 4 cm −1 ) in the acoustic phonon branch has also been observed along the stacking direction in layered BiSe compound 69 which possesses a very low lattice thermal conductivity (0.6 w/mK at 300 K). The cutoff frequencies for

The Gruneisen parameter (γ) is a measure of the degree of anharmonicity in a solid. We have determined the mode Gruneisen parameter (γqν ) of BaAu2 P4 for the three acoustic phonon branches (see Figure 3c) along the high symmetry directions of the Brillouin zone. While the LA mode along the Γ-Y direction (which is perpendicular to the stacking direction in the unit cell) shows very large anharmonicity due to the electrostatic repulsion originating from the lone pairs of the phosphorus atoms, the acoustic modes along the stacking direction (i.e. Γ-Z) show anomalously large γqν (∼ 50) due to weaker bonding along the y-axis of the unit cell. In the high temperature regime where Umklapp phonon scattering is dominant, the lattice thermal conductivity decreases 26 as γ12 . Therefore, qν such a large value of γqν reflects the large anharmonicity and strong phonon-phonon scattering, giving another indication that BaAu2 P4 possesses low lattice thermal conductivity. Such


7


(a)

Page 8 of 17

(b)

Figure 5: (a) Electronic structure of BaAu2 P4 calculated within PBEsol exchange correlation functional. (b) Projected density of states shows that phosphorus atoms primarily contributes to the valence bands, facilitating large electrical conductivity for p-type doping. components. On the other hand, as each Au atom is linearly coordinated by two phosphorous atoms along each chain in the xz-plane of the crystal, the opposing electrostatic forces on Au atoms coming from either side of the chain restrict their movements along the xz-plane. As a result, the x and z-components of the ADPs of Au become smaller than its y-component, bringing them closer to the ADPs of the P atoms.

anomalously large mode Gruneisen parameters were also observed in the transverse acoustic mode (γqν ∼ 100) 25 of AgBiSe2 which possesses very low lattice thermal conductivity (κl ∼ 0.7 W/mK at 300 K). 26 Figure 3d shows the atomic displacement parameter (ADP) of the Ba, Au, and P atoms as a function of temperature. ADP measures the mean-square displacement of an atom around its equilibrium position. As Ba atoms have a relatively weaker bonding to the lattice, the ADPs of the Ba atoms are much higher compared to the ADPs of Au and P atoms. Thus Ba atoms play an important role in the scattering of the heat carrying phonons, which helps in inducing the low lattice thermal conductivity in BaAu2 P4 . The subtle variation of the ADPs of the constituent atoms in the crystal structure of BaAu2 P4 can be explained on the basis of (a) how strongly the atoms are connected to the lattice and (b) the electrostatic repulsions originating from the lone pairs of P atoms and (c) the competition between these two factors. Ba atoms being weakly bonded to the lattice have the largest ADPs along x (or z) directions. As the lone pairs of the phosphorous atoms (which are sitting in one layer above and below the layers of Ba atoms along the ydirection) exert electrostatic forces on Ba atoms from opposite directions, it strongly restricts the motion of Ba atoms along the y-direction. As a consequence, the y-component of the ADP of Ba is suppressed compared to its x and z-

The accurate calculation of lattice thermal conductivity (κl ) requires determination of third order interatomic force constant (IFC) matrix. 7,70–72 We have obtained the 3rd order IFC matrix through a supercell approach (see Methods for details), and used a linearized Boltzmann transport equation as implemented in ShengBTE 56 to calculate the lattice thermal conductivity (see Figure 4). Our results reveal that κl is much lower along the stacking direction (i.e., κl y < κl x(z) ) of the unit cell, as expected from bonding and analysis of atomic-level dynamics. At 300 K, the lattice thermal conductivities along x(z) and y directions are κl x(z) = 3.1 W/mK and κl y = 0.9 Wm/K, respectively, which are comparable to that of PbTe. 73 As expected from the chemistry of a valence balanced compound, the calculated (PBEsol) electronic structure (Figure 5a) of BaAu2 P4 reveals that it is a semiconductor with a band gap of 0.18 eV. Like SnSe, 11 the anisotropic two dimensional Au-P layers gives rise to multiple


8

Page 9 of 17 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


(a)

pockets in the valence and conduction bands near the Fermi level. The presence of multiple band extrema near the Fermi level in the electronic structure usually gives rise to a high Seebeck coefficient. In BaAu2 P4 , nearly degenerate valence band maxima appear at L point and along the Γ-K1 directions in the Brillouin zone. Another band extremum appears at the K1 point and lies 40 meV below the degenerate band maxima. Multiple bands near the Fermi level results in band convergence which in turn enhances the electrical conductivity and Seebeck coefficient, resulting in a high thermoelectric power factor (S2 σ). Analysis of atom-projected density of states (Figure 5b) and electronic structure (see supplementary Figure S2) reveal that while P atoms primarily contribute to the valence bands just below the Fermi level as expected from the bonding chemistry, the low energy conduction bands have contributions from Ba, Au and P atoms.

(b)

(c)

GGA exchange-correlation functionals are well know to underestimate the band gaps of materials. In order to obtain a good estimation of the band gap, we turn to more accurate hybrid functional (HSE06) 45,46 calculations. The electronic structure calculated within HSE06 (see supplementary Figure S3) reveals a band gap 0.74 eV of BaAu2 P4 . As the band gap (Eg ) strongly influences the electronic transport properties of a material, it was necessary to correct the PBEsol calculated band gap to a more accurate value obtained using HSE06 functional. We applied a simple scissor correction to the band energies obtained using PBEsol, and determined the electronic transport coefficients (see Figure 7) using the Boltzmann transport equation within the constant relaxation time approximation as a function of temperature. Our calculation shows that electronic conductivity (σ) is much higher along the in-plane directions (x and z) compared to the stacking direction (y) of the unit cell. On the other hand, the Seebeck coefficient is higher along the stacking direction. This is expected from that fact that the bonding is much weaker along the stacking direction than along x and z-directions. The calculated directional average Seebeck coefficient (Sav = 13

Figure 6: Phonon limited distributions of electronic relaxation times (τ ) of BaAu2 P4 as a function of electronic energy calculated at three different temperatures (a) 300 K, (b) 600 K and (c) 900K. At 300 K, BaAu2 P4 possesses relatively large τ that varies from 25 fs to 108 fs. Relaxation times decrease with increasing temperature. For example, τ varies from 12 fs to 67 fs at 600 K, which is further reduced at 900 K where it varies from 6 fs to 44 fs. The position of the Fermi level is denoted with a vertical dotted line.


9


S(μVK−1)

800

300K 600K 900K

600 400

Sy

Sx, z

(a)

(b)

200 0

σ/t

(10,12Scm,1)

20

S2σ/t (10,14μWcm,1K,2)

15 10

σx, z

(c)

σy

(d)

5 0 80 60 40

(e)

PFx, z

PFy

(f)

20 0 3 2

(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 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 17

1

300K(t=25fs)

300K(t=108fs)

(g)

600K(t=12fs) 600K(t=67fs)

(Tx, z

900K(t=6fs) 900K(t=44fs)

(Ty

( )

0 ,1μ0 ,0μ5 0μ0 0μ5 1μ0 ,1μ0 ,0μ5 0μ0 0μ5 1μ0 20 ,3 20 ,3 Carrier concentration (10 cm ) Carrier concentration (10 cm ) Figure 7: (a,b) Seebeck coefficient (S), (c,d) electrical conductivity (σ/t) and (e,f) power factor (S2 σ/t) as a function of temperature and carrier concentrations along the in-plane (i.e., x and z), 2 and stacking (i.e., y) directions of the crystal. (g,h) Thermoelectric figure of merit (zT= S κσT ) has been evaluated based on these transport coefficients and relaxation times obtained from our first-principles calculations. Here, κ (= κe + κl ) is the total thermal conductivity that consists of electronic (κe ) and lattice (κl ) contributions. Positive and negative signs of the carrier concentrations denote p- and n-type doping, respectively.


10

Page 11 of 17 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


(Sxx + Syy + Szz )) of BaAu2 P4 (S = 207 µV/K−1 for hole concentration of 4×1019 cm−3 at 300 K) is slightly higher than the Seebeck coefficient of SnSe 11 (S = 160 µV/K−1 for the same hole concentration and temperature). Finally, we estimate the thermoelectric figure of merit (zT) using he relaxation times (Figure 6) calculated from first-principles calculations at three different temperatures (300K, 600K and 900K). Our calculation shows that BaAu2 P4 exhibits zT > 1.0 (at a small relaxation time of 6 fs) at 900 K for p-type doping at carrier concentration ≥ 3 × 1019 cm−3 . It is interesting to note that although the stacking direction of SnSe has the lowest κl , it possesses the highest zT along the in-plane (i.e., perpendicular to the stacking) direction. 10 However in BaAu2 P4 , a combination of large S and a low κl results in a higher zT along the stacking direction.

high zT in BaAu2 P4 .

Supporting Information Available: The Supporting Information is available free of charge on the ACS Publications website at DOI:. Atom-projected phonon dispersion, atomprojected electronic structure, HSE06 functional calculated electronic structure. This material is available free of charge via the Internet at http://pubs.acs.org/.

ACKNOWLEDGMENTS K.P. (DFT and thermoelectric calculations) and C.W. (overall leadership of project) acknowledge support from the U. S. Department of Energy under Contract No. DE-SC0015106. J.H. (data analysis and interpretation of results) acknowledges support from the U.S. Department of Energy, Office of Science and Office of Basic Energy Sciences, under Award No. DE-SC0014520. The authors acknowledge computing resources provided by (a) the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC0205CH11231 and (b) the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

CONCLUSIONS In conclusion, using first-principles calculations based on density functional theory we show that BaAu2 P4 is a good p-type thermoelectric material with high power factor and intrinsically low lattice thermal conductivity. Our analysis revealed that BaAu2 P4 possesses an anisotropic bonding hierarchy in which rigid Au-P layers coexist with relatively loosely bound Ba2+ cations. While the rigid sublattice gives rise to an enhanced electronic transport properties due to multiple bands extrema in its electronic structure, the loosely bound sublattice helps in suppressing the lattice thermal transport effectively. Although Ba2+ shows larger atomic displacement parameter, both Ba and Au atoms contribute to the low energy phonon frequencies and hence are active in scattering the heat carrying phonons, leading to a very low lattice thermal conductivity along the stacking direction of the crystal. Lone pairs around the phosphorus atoms induce lattice anharmonicity which is revealed by the large values of the mode Gruneisen parameters. Thus, our findings should engender further exploration of thermoelectric materials in layered compounds with crystallographic heterogeneity and small band gaps, and warrants experimental verification of our prediction of

References (1) Snyder, G. J.; Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 2008, 7, 105. (2) Bell, L. E. Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 2008, 321, 1457–1461. (3) DiSalvo, F. J. Thermoelectric cooling and power generation. Science 1999, 285, 703– 706. (4) Vineis, C. J.; Shakouri, A.; Majumdar, A.;


11


Kanatzidis, M. G. Nanostructured thermoelectrics: big efficiency gains from small features. Adv. Mater. 2010, 22, 3970–3980.

Page 12 of 17

trivial electronic topology. J. Mater. Chem. C 2015, 3, 12130–12139. (13) Pei, Y.; Wang, H.; Snyder, G. J. Band engineering of thermoelectric materials. Adv. Mater. 2012, 24, 6125–6135.

(5) Zeier, W. G.; Zevalkink, A.; Gibbs, Z. M.; Hautier, G.; Kanatzidis, M. G.; Snyder, G. J. Thinking like a chemist: intuition in thermoelectric materials. Angew. Chem., Int. Ed. 2016, 55, 6826–6841.

(14) Zhao, L.; Wu, H.; Hao, S.; Wu, C.I.; Zhou, X.; Biswas, K.; He, J.; Hogan, T. P.; Uher, C.; Wolverton, C.; Kanatzidis, M. G. All-scale hierarchical thermoelectrics: MgTe in PbTe facilitates valence band convergence and suppresses bipolar thermal transport for high performance. Energy Environ. Sci. 2013, 6, 3346– 3355.

(6) May, A. F.; Fleurial, J.-P.; Snyder, G. J. Thermoelectric performance of lanthanum telluride produced via mechanical alloying. Phys. Rev. B 2008, 78, 125205. (7) He, J.; Amsler, M.; Xia, Y.; Naghavi, S. S.; Hegde, V. I.; Hao, S.; Goedecker, S.; Ozoli¸nˇs, V.; Wolverton, C. Ultralow thermal conductivity in full Heusler semiconductors. Phys. Rev. Lett. 2016, 117, 046602.

(15) others,, et al. 3D charge and 2D phonon transports leading to high out-of-plane ZT in n-type SnSe crystals. Science 2018, 360, 778–783.

(8) He, J.; Hao, S.; Xia, Y.; Naghavi, S. S.; Ozolins, V.; Wolverton, C. Bi2PdO4: A Promising Thermoelectric Oxide with High Power Factor and Low Lattice Thermal Conductivity. Chem. Mater. 2017, 29, 2529–2534.

(16) Tang, Y.; Gibbs, Z. M.; Agapito, L. A.; Li, G.; Kim, H.-S.; Nardelli, M. B.; Curtarolo, S.; Snyder, G. J. Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb 3 skutterudites. Nat. Mater. 2015, 14, 1223.

(9) Pei, Y.; Shi, X.; LaLonde, A.; Wang, H.; Chen, L.; Snyder, G. J. Convergence of electronic bands for high performance bulk thermoelectrics. Nature 2011, 473, 66.

(17) Bilc, D. I.; Hautier, G.; Waroquiers, D.; Rignanese, G.-M.; Ghosez, P. Lowdimensional transport and large thermoelectric power factors in bulk semiconductors by band engineering of highly directional electronic states. Phys. Rev. Lett. 2015, 114, 136601.

(10) Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 2014, 508, 373.

(18) Isaacs, E. B.; Wolverton, C. Inverse Band Structure Design via Materials Database Screening: Application to Square Planar Thermoelectrics. Chem. Mater. 2018, 30, 1540–1546.

(11) Zhao, L.-D.; Tan, G.; Hao, S.; He, J.; Pei, Y.; Chi, H.; Wang, H.; Gong, S.; Xu, H.; Dravid, V. P.; Uher, C.; Snyder, J. G.; Wolverton, C.; Kanatzidis, M. G. Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal SnSe. Science 2015, aad3749.

(19) Biswas, K.; He, J.; Blum, I. D.; Wu, C.I.; Hogan, T. P.; Seidman, D. N.; Dravid, V. P.; Kanatzidis, M. G. Highperformance bulk thermoelectrics with allscale hierarchical architectures. Nature 2012, 489, 414.

(12) Pal, K.; Anand, S.; Waghmare, U. V. Thermoelectric properties of materials with non-


12

Page 13 of 17 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


(20) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y.; Minnich, A.; Yu, B.; Yan, X.; Wang, D.; Muto, A.; Vashaee, D.; Chen, X.; Liu, J.; Dresselhaus, M. S.; Chen, G. C.; Ren, Z. High-thermoelectric performance of nanostructured bismuth antimony telluride bulk alloys. Science 2008, 320, 634–638.

(28) Zhang, Y.; Skoug, E.; Cain, J.; Ozoli¸nˇs, V.; Morelli, D.; Wolverton, C. First-principles description of anomalously low lattice thermal conductivity in thermoelectric Cu-SbSe ternary semiconductors. Phys. Rev. B 2012, 85, 054306. (29) Jana, M. K.; Pal, K.; Waghmare, U. V.; Biswas, K. The Origin of Ultralow Thermal Conductivity in InTe: Lone-Pair-Induced Anharmonic Rattling. Angew. Chem., Int. Ed. 2016, 55, 7792–7796.

(21) Zhao, L.-D.; Hao, S.; Lo, S.-H.; Wu, C.I.; Zhou, X.; Lee, Y.; Li, H.; Biswas, K.; Hogan, T. P.; Uher, C.; Kanatzidis, M. G. High thermoelectric performance via hierarchical compositionally alloyed nanostructures. J. Am. Chem. Soc. 2013, 135, 7364–7370.

(30) Jana, M. K.; Pal, K.; Warankar, A.; Mandal, P.; Waghmare, U. V.; Biswas, K. Intrinsic rattler-induced low thermal conductivity in Zintl type TlInTe2. J. Am. Chem. Soc. 2017, 139, 4350–4353.

(22) Barabash, S.; Ozolins, V.; Wolverton, C. First-principles theory of competing order types, phase separation, and phonon spectra in thermoelectric AgPb m SbTe m+ 2 alloys. Phys. Rev. Lett. 2008, 101, 155704.

(31) Zhou, Y.; Zhao, L.-D. Promising thermoelectric bulk materials with 2D structures. Adv. Mater. 2017, 29, 1702676.

(23) Shi, X.; Yang, J.; Salvador, J. R.; Chi, M.; Cho, J. Y.; Wang, H.; Bai, S.; Yang, J.; Zhang, W.; Chen, L. Multiple-filled skutterudites: high thermoelectric figure of merit through separately optimizing electrical and thermal transports. J. Am. Chem. Soc. 2011, 133, 7837–7846.

(32) Imasato, K.; Kang, S. D.; Ohno, S.; Snyder, G. J. Band engineering in Mg 3 Sb 2 by alloying with Mg 3 Bi 2 for enhanced thermoelectric performance. Mater. Horiz. 2018, (33) Zhang, J.; Song, L.; Pedersen, S. H.; Yin, H.; Hung, L. T.; Iversen, B. B. Discovery of high-performance low-cost n-type Mg 3 Sb 2-based thermoelectric materials with multi-valley conduction bands. Nat. commun. 2017, 8, 13901.

(24) Takabatake, T.; Suekuni, K.; Nakayama, T.; Kaneshita, E. Phonon-glass electron-crystal thermoelectric clathrates: Experiments and theory. Rev. Mod. Phys. 2014, 86, 669.

(34) Wood, M.; Aydemir, U.; Ohno, S.; Snyder, G. J. Observation of Valence Band Crossing: The Thermoelectric Properties of CaZn2Sb2-CaMg2Sb2 Solid Solution. J. Mater. Chem. A 2018,

(25) Nielsen, M. D.; Ozolins, V.; Heremans, J. P. Lone pair electrons minimize lattice thermal conductivity. Energy Environ. Sci. 2013, 6, 570–578. (26) Morelli, D.; Jovovic, V.; Heremans, J. Intrinsically minimal thermal conductivity in cubic I- V- VI 2 Semiconductors. Phys. Rev. Lett. 2008, 101, 035901.

(35) Fulmer, J.; Lebedev, O. I.; Roddatis, V. V.; Kaseman, D. C.; Sen, S.; Dolyniuk, J.A.; Lee, K.; Olenev, A. V.; Kovnir, K. Clathrate Ba8Au16P30: The gold standard for lattice thermal conductivity. J. Am. Chem. Soc. 2013, 135, 12313–12323.

(27) Qiu, W.; Xi, L.; Wei, P.; Ke, X.; Yang, J.; Zhang, W. Part-crystalline part-liquid state and rattling-like thermal damping in materials with chemical-bond hierarchy. Proc. Natl. Acad. Sci. 2014, 111, 15031– 15035.

(36) Maier, S.; Ohno, S.; Yu, G.; Kang, S.; Chasapis, T.; Ha, V. A.; Miller, S.; Berthebaud, D.; Kanatzidis, M.; Rignanese, G.-


13


Page 14 of 17

(45) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 2003, 118, 8207–8215.

M.; Hautier, G.; Snyder, G. J.; Gascoin, F. Resonant Bonding, Multiband Thermoelectric Transport, and Native Defects in nType BaBiTe3–x Se x (x= 0, 0.05, and 0.1). Chem. Mater. 2017, 30, 174–184.

(46) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum: Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 2006, 124, 219906.

(37) Pöhls, J.-H.; Faghaninia, A.; Petretto, G.; Aydemir, U.; Ricci, F.; Li, G.; Wood, M.; Ohno, S.; Hautier, G.; Snyder, G. J.; Rignanese, G.-M.; Jain, A.; White, M. A. Metal phosphides as potential thermoelectric materials. J. Mater. Chem. C 2017, 5, 12441–12456.

(47) Madsen, G. K.; Singh, D. J. BoltzTraP. A code for calculating band-structure dependent quantities. Comput. Phys. Commun. 2006, 175, 67–71.

(38) Fulmer, J.; Kaseman, D. C.; Dolyniuk, J.A.; Lee, K.; Sen, S.; Kovnir, K. BaAu2P4: Layered Zintl Polyphosphide with Infinite 1 (P–) Chains. Inorg. Chem. 2013, 52, 7061– 7067.

(48) Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502.

(39) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Black phosphorus field-effect transistors. Nat. Nanotechnol. 2014, 9, 372.

(49) Noffsinger, J.; Giustino, F.; Malone, B. D.; Park, C.-H.; Louie, S. G.; Cohen, M. L. EPW: A program for calculating the electron–phonon coupling using maximally localized Wannier functions. Comput. Phys. Commun. 2010, 181, 2140–2148.

(40) Kresse, G.; Furthm¨ uller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15–50.

(50) Poncé, S.; Margine, E. R.; Verdi, C.; Giustino, F. EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions. Comput. Phys. Commun. 2016, 209, 116–133.

(41) Kresse, G.; Furthm¨ uller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169.

(51) Baroni, S.; De Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 2001, 73, 515.

(42) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. (43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865.

(52) Xu, B.; Verstraete, M. J. First principles explanation of the positive seebeck coefficient of lithium. Phys. Rev. Lett. 2014, 112, 196603.

(44) 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.

(53) Poncé, S.; Margine, E. R.; Giustino, F. Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors. Phys. Rev. B 2018, 97, 121201.


14

Page 15 of 17 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


(54) Togo, A.; Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 2015, 108, 1–5.

(63) Zhang, Y. First-principles Debye–Callaway approach to lattice thermal conductivity. J. Materiomics 2016, 2, 237–247.

(55) Li, W.; Lindsay, L.; Broido, D.; Stewart, D. A.; Mingo, N. Thermal conductivity of bulk and nanowire Mg 2 Si x Sn 1- x alloys from first principles. Phys. Rev. B 2012, 86, 174307.

(64) Savin, A.; Nesper, R.; Wengert, S.; Fässler, T. F. ELF: The electron localization function. Angew. Chem., Int. Ed. Engl. 1997, 36, 1808–1832.

(56) Li, W.; Carrete, J.; Katcho, N. A.; Mingo, N. ShengBTE: A solver of the Boltzmann transport equation for phonons. Comput. Phys. Commun. 2014, 185, 1747– 1758.

(65) Dronskowski, R.; Blöchl, P. E. Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on densityfunctional calculations. J. Phys. Chem. 1993, 97, 8617–8624.

(57) Zhang, Y.; Ozolins, V.; Morelli, D.; Wolverton, C. Prediction of new stable compounds and promising thermoelectrics in the Cu–Sb–Se system. Chem. Mater. 2014, 26, 3427–3435.

(66) Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R. Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets. J. Phys. Chem. A 2011, 115, 5461–5466.

(58) Yan, J.; Gorai, P.; Ortiz, B.; Miller, S.; Barnett, S. A.; Mason, T.; Stevanović, V.; Toberer, E. S. Material descriptors for predicting thermoelectric performance. Energy Environ. Sci. 2015, 8, 983–994.

S.; Deringer, V. L.; (67) Maintz, Tchougréeff, A. L.; Dronskowski, R. Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids. J. Comput. Chem. 2013, 34, 2557–2567.

(59) Bhattacharya, S.; Madsen, G. K. Highthroughput exploration of alloying as design strategy for thermoelectrics. Phys. Rev. B 2015, 92, 085205.

(68) L¨ ucke, A.; Gerstmann, U.; K¨ uhne, T. D.; Schmidt, W. G. Efficient PAW-based bond strength analysis for understanding the In/Si (111)(8× 2)–(4× 1) phase transition. J. Comput. Chem. 2017, 38, 2276–2282.

(60) Liu, T.-H.; Zhou, J.; Li, M.; Ding, Z.; Song, Q.; Liao, B.; Fu, L.; Chen, G. Electron mean-free-path filtering in Dirac material for improved thermoelectric performance. Proc. Natl. Acad. Sci. 2018, 201715477.

(69) Samanta, M.; Pal, K.; Pal, P.; Waghmare, U. V.; Biswas, K. Localized vibrations of Bi bilayer leading to ultralow lattice thermal conductivity and high thermoelectric performance in weak topological insulator n-type BiSe. J. Am. Chem. Soc. 2018,

(61) Xing, G.; Sun, J.; Li, Y.; Fan, X.; Zheng, W.; Singh, D. J. Electronic fitness function for screening semiconductors as thermoelectric materials. Phys. Rev. Mater. 2017, 1, 065405.

(70) Chaput, L.; Togo, A.; Tanaka, I.; Hug, G. Phonon-phonon interactions in transition metals. Phys. Rev. B 2011, 84, 094302.

(62) Vo, T. T.; Williamson, A. J.; Lordi, V.; Galli, G. Atomistic design of thermoelectric properties of silicon nanowires. Nano Lett. 2008, 8, 1111–1114.

(71) Togo, A.; Chaput, L.; Tanaka, I. Distributions of phonon lifetimes in Brillouin zones. Phys. Rev. B 2015, 91, 094306.


15


(72) Zhou, F.; Nielson, W.; Xia, Y.; Ozoli¸nˇs, V. Lattice anharmonicity and thermal conductivity from compressive sensing of firstprinciples calculations. Phys. Rev. Lett. 2014, 113, 185501. (73) Heremans, J. P.; Jovovic, V.; Toberer, E. S.; Saramat, A.; Kurosaki, K.; Charoenphakdee, A.; Yamanaka, S.; Snyder, G. J. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 2008, 321, 554–557.


16

Page 16 of 17

Page 17 of 17 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


le ltip mu nd ba ema r ext

low t la conhermttice du al cti vit y

TOC graphic.


17

Bonding Hierarchy Gives Rise to High Thermoelectric Performance in

Recommend Documents