Electronic Band Structure Engineering and Enhanced Thermoelectric

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Electronic band structure engineering and enhanced thermoelectric transport properties in Pb-doped BiCuOS oxysulfide Jean-Baptiste Labégorre, Rabih Al Rahal Al Orabi, Agathe Virfeu, Jacinthe Gamon, Philippe Barboux, Lauriane Pautrot-d'Alençon, Thierry Le Mercier, David Berthebaud, Antoine Maignan, and Emmanuel Guilmeau Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b04989 • Publication Date (Web): 08 Jan 2018 Downloaded from http://pubs.acs.org on January 8, 2018

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Chemistry of Materials

Electronic band structure engineering and enhanced thermoelectric transport properties in Pb-doped BiCuOS oxysulfide

Jean-Baptiste Labégorre,1 Rabih Al Rahal Al Orabi,2,3* Agathe Virfeu,2 Jacinthe Gamon,4,5 Philippe Barboux,5 Lauriane Pautrot-d’Alençon,4 Thierry Le Mercier,4 David Berthebaud,1 Antoine Maignan,1 Emmanuel Guilmeau1,*

1

Laboratoire CRISMAT, UMR-CNRS 6508, ENSICAEN, UNICAEN, Normandie

Université, 6 Boulevard du Maréchal Juin, 14050 Caen Cedex 04, France 2

Solvay, Design and Development of Functional Materials Department, Axel’One, 87 avenue

des Frères Perret, 69192 Saint Fons, Cedex, France 3

Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48879, United

States 4

Solvay, Centre de Recherches d’Aubervilliers, 52 rue de la Haie-Coq, 93308 Aubervilliers

Cedex, France 5

Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie de

Paris, , 11 rue Pierre et Marie Curie, 75005 Paris, France *Email : [email protected], Tel : +33 231 45 13 67 *Email : [email protected], Tel : +33 428 27 10 80

ACS Paragon Plus Environment

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Abstract In this paper, Bi1-xPbxCuOS samples (0 ≤ x ≤ 0.05) have been synthesized with a simple and scalable ball-milling process, followed by a reactive Spark Plasma Sintering. Our results highlight that, Pb for Bi substitution increases the charge carriers concentration by more than two orders of magnitude from 1.4 × 1017 cm-3 to 2.6 × 1019 cm-3 for x = 0 and x = 0.05 respectively. As a result, the electrical resistivity is divided by more than 50 at room temperature and the Seebeck coefficient drops from 707 µV K-1 to 265 µV K-1 where our experimental results are supported with Density Functional Theory (DFT) calculations. Electronic structure calculations show that, just below the top of the valence band, several other bands are present and may contribute to the transport properties with appropriate tuning of the heavy-light valence band and the position of the Fermi level. Pb doping increases the number of holes pockets and several band degeneracies appear around the Fermi level, leading to a drastic enhancement of the power factor up to 0.2 mW m-1 K-2 at 700 K. This is 5 times higher than the value of the pristine compound. The intrinsically low thermal conductivity of 0.7 W m-1 K-1 at 700 K is interpreted on the basis of vibrational properties calculations within the Density Functional Perturbation Theory (DFPT) approach. It indicates that soft acoustic modes along Γ-Z direction suggest weak interatomic bonding between the layers and possible strong anharmonicity. The power factor being enhanced with a minimal impact on the thermal conductivity, the figure of merit ZT reaches 0.2 at 700 K for x = 0.05. To the best of our knowledge, it is considered the best reported value among the family of oxysulfides


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Introduction Thermoelectric devices are promising candidates to reduce the CO2 emissions and fight against the energy crisis due to their ability to achieve direct and reversible energy conversion between heat and electricity. The conversion efficiency of a thermoelectric material is commonly described by the dimensionless figure of merit ZT (ZT = S2T/ρκ), where T is the absolute temperature (K), S is the Seebeck coefficient (µV K-1), ρ is the electrical resistivity (Ω m) and κ is the thermal conductivity (W m-1 K-1).1 However, current thermoelectric modules are confined to niche markets due to elements scarcity, high costs, toxicity and low thermal stability under air. During the last two decades, efforts have been devoted to develop thermoelectric oxides that are capable of addressing the aforementioned issues.2–5 A significant step has been especially crossed with the discovery of relatively low thermal conductivity and high electrical performances (p-type), that exists inside the natural superlattices of NaxCoO26 and Ca3Co4O9.7,8 Nevertheless, these oxides are still not considered to have good performance compared to other thermoelectric materials because of their relatively high electrical resistivity and large thermal conductivity. In 2010, another layered material BiCuOSe attracted tremendous attention due to its promising ZT in the medium temperature range (0.32 at 673 K).9 This oxychalcogenide superlattice crystallizes in the tetragonal P4/nmm space group and is built of two different layers that are stacked along the c axis alternately (Figure 1).10 The covalent anti-fluorite-like layer (Cu2Se2)2-, build up from edge-sharing CuSe4 tetrahedra, is the conductive pathway for charge carriers transport. The ionic (Bi2O2)2+ block is insulating and acts as a charge reservoir. The succession of these two weakly bonded layers behave like phonon scattering interfaces and give it a very low lattice thermal conductivity (~ 0.5 W m-1 K-1 at 773 K).11 On the other hand, the high electrical resistivity problem should be solved in order to enhance the merit figure of this material further. This has been achieved by increasing the carrier concentration with monovalent or


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divalent cations (Na+, K+, Mg2+, Ca2+, Sr2+, Ba2+ or Pb2+)9,12–18 substitution inside the insulating (Bi2O2)2+ layer. Furthermore, other strategies have been used, such as the creation of copper vacancies in the conductive (Cu2Se2)2- layer,

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as well as limiting the decrease of

the charge carriers mobility via modulation doping.20 Electronic band structure engineering through the isoelectronic substitution of Se by Te has also been developed successfully.21 These studies led to a substantial improvement of the thermoelectric performances to record ZT values of 1.4 (at 923 K) and 1.5 (at 873 K) for doped and textured samples22 and for dually doped samples respectively.23 Thus, this material became a viable alternative to the use of PbTe and nearly competes with the high performance of multiple-filled skutterudites (ZT = 1.7 at 850 K).24 Despite the achievements reached in the BiCuOSe system in the past years, there is a lack of studies on the isostructural sulfur counterpart due to its lower thermoelectric performances, i.e. a ZT ∼0.07 at 650 K.25 The low value of ZT is mainly attributed to (1) a lower carrier concentration (1017 cm-3 against ∼1019 cm-3 in BiCuOSe), (2) a wider band gap (1.1 eV

against 0.75 eV in BiCuOSe) which is much higher than the optimal value predicted by the Goldsmid-Sharp formula Eg = 2eSmaxTmax of 0.35 eV for thermoelectric materials,26 and (3) a higher thermal conductivity in BiCuOS than in BiCuOSe (S is much lighter than Se). Nevertheless, sulfur being significantly less toxic and more abundant than selenium, there would be undeniable benefits in replacing Se by S, while maintaining relatively thermoelectric performances. Pb doping has been well investigated in p-type BiCuOSe for its role in the significant improvement of the power factor compared to those of pristine BiCuOSe. However, to the best of our knowledge, electrical transport properties were solely investigated for Pb-doped BiCuOS.27–29 The similarities of the band and crystal structure between BiCuOS and BiCuOSe gave a hint that Pb-doping could modify the electronic properties and enhance the ACS Paragon Plus Environment

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power factor. In this paper, we present the effect of Pb doping on the band structure and electronic properties of BiCuOS, using both theoretical and experimental studies for the first time. We prove that Pb doping in BiCuOS improves the electronic properties by activating several hole-pockets with high effective masses, resulting in an enhanced power factor. This yields to a high figure of merit ZT of 0.2 at 700 K for a Pb concentration of 5%. To the best of our knowledge, it is the best ever achieved figure of merit value for an oxysulfide compound.

Fig. 1 Crystal structure of 2×2×2 supercells of BiCuOS (left) and Bi0.937Pb0.063CuOS (right) used for the computations.

Experimental details Bi1-xPbxCuOS (x = 0, 0.025, 0.0375, 0.05) powders were synthesized from stoichiometric mixtures of Bi2O3 (> 99.5 %, Alfa Aesar), Bi (> 99.99 %, Alfa-Aesar), PbO (> 99 %, Merck), Cu (> 99 %, < 625 mesh, Alfa Aesar) and S (> 99 %, < 325 mesh, Alfa Aesar). The precursors were weighed and 5.5 g of each composition were set inside a 45 mL tungsten carbide jar with 7 tungsten carbide balls (Ø 10 mm). The jar was closed in argon-filled glove box to ensure an inert atmosphere during the process. The mechanosynthesis was held in a planetary


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ball mill (Fritsch Pulverisette 7 Premium line) during 6 cycles of 30 min at 600 rpm. Finally, the resulting powder were ground, placed in 10 mm graphite dies and densified by Spark Plasma Sintering (SPS) under a uniaxial pressure of 64 MPa under vacuum at 748 K for 25 min (heating and cooling rates of 100 K/min). The relative densities of the samples were respectively 90.6 % (x = 0), 94.5 % (x =0.025), 94.9 % (x = 0.0375) and 94.1 % (x = 0.05) of the theoretical values. Powder X-Ray diffraction (PXRD) patterns were collected at room temperature using a PANalytical X-Pert Pro diffractometer equipped with a Cu Kα X-ray tube. The scanning angle 2θ was varied between 20° and 100°. PXRD patterns were refined by the Rietveld method with FullProf and WinPLOTR software packages.30,31 Details of the refinements are listed in Table S1. Microstructures and grain sizes of sintered samples were examined by scanning electron microscopy (SEM) on a ZEISS Supra 55. The electrical resistivity (ρ) and the Seebeck coefficient (S) were simultaneously measured on bar-shaped samples with typical size of 3.0 × 3.0 × 8.0 mm3 using the standard four-probe method (ULVAC-RIKO ZEM-3). The measurements were performed from room temperature to 673 K under partial helium pressure. Heating and cooling cycles were carried out to assess the thermal stability during the measurement and gave repeatable data. The thermal conductivity (κ) was calculated from the product of the geometrical density, heat capacity (Dulong-Petit) and thermal diffusivity obtained by laser flash diffusivity method on a Netzsch LFA 457 (with 6.0 × 6.0 × 1.0 mm3 samples) measured between 300 K and 673 K. Finally, Hall effect measurements by Van der Pauw method were carried out in a PPMS (Physical Properties Measurement System) system from Quantum Design to determine the carrier concentrations (nH = 1/eRH where e is the electronic charge) and mobilities at room temperature. Samples with dimensions of 3.0 × 3.0

× 0.3 mm3 were used with indium as contacts. The Hall coefficients were calculated from the linear fits of the Hall resistivities versus magnetic fields between -7 T and 7 T. It is


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noteworthy that the electrical and thermal properties were measured along the direction perpendicular to the compression applied during the sintering process. The estimated measurements uncertainties are 6% for the Seebeck coefficient, 8% for the electrical resistivity, 11% for the thermal conductivity and 16% for the final figure of merit, ZT.32

First-Principle Calculations Density Functional Theory (DFT) geometry optimizations were carried out with the CASTEP8.0 code33 using a set of ultrasoft pseudopotentials34,35 with the PBEsol exchange– correlation functional.36 Cell parameters and atomic positions were both relaxed. During the geometry optimizations, a convergence threshold of 0.02 eV Å−1 was used for the residual forces and 0.1 kbar for the pressure. The cut-off energy for plane-waves was set to 700 eV. For the electronic band structures we used the full-potential linearized augmented plane wave (FLAPW) approach, as implemented in the WIEN2K code.37 A plane-wave cutoff corresponding to RMTKmax= 7 was used in all calculations. The radial wave functions inside the non-overlapping muffin-tin spheres were expanded up to lmax=12. The charge density was Fourier expanded up to Gmax=16 Å-1. Total energy convergence was achieved with respect to the Brillouin zone (BZ) integration mesh with 500k-points. Because GGA exchangecorrelation functionals are known to underestimate experimental band gaps, we used the modified Becke-Johnson (mBJ) functional which leads to excellent agreement with the experimental values for the energy separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).38 Since the Bi atoms in oxychalcogenide compounds have fairly high atomic number and mass, the relativistic effect can not be neglected, and we have included the effect of spin-orbit coupling to elucidate realistic electronic structure. We used 5000 k-points in the BZ to compute the band derivatives and the density of states. The doping effect was examined by constructing a ACS Paragon Plus Environment

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2×2×2 (64 atoms) supercell in which one of the Bi atoms was replaced by a Pb atom and the corresponding Pb doping concentration is 6.3 at.%. The band structure of both undoped and Bi0.937Pb0.063CuOS was calculated using the 2×2×2 supercell under the same calculation conditions. Vibrational properties have been obtained by using Density Functional Perturbation Theory (DFPT)39 as implemented in the Quantum ESPRESSO (QE) package.40 The calculation has been performed by using a set of ultrasoft pseudopotentials35 with the PBEsol exchangecorrelation functional.36 The kinetic energy cutoff and the charge density cutoff are set to be 40 Ry and 480 Ry, respectively. An 8 x 8 x 4 k-point mesh is used to sample the Brillouin zone. The Grüneisen’ parameter can be defined as = −

and

characterizes the relationship between phonon frequency and volume change. In the quasiharmonic DFT phonon calculations, the system volume is isotropically expanded by +4% from the DFT relaxed volume.

Results and discussion Crystal structure Figure 2a displays the PXRD patterns of Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) sintered samples. All the major Bragg peaks can be indexed in the ZrSiCuAs structure with the tetragonal P4/nmm space group.41 The samples with x ≤ 0.025 are single phase, whereas the main peak (012) of metallic bismuth (Bi) is discernible at ~ 27.1° for the two highest lead contents, indicating < 1 wt.% (x = 0.0375) and ~ 1 wt.% (x = 0.05) of bismuth metal in the samples, respectively. The increase of the bismuth content as secondary phase probably originates from the decrease of Bi vacancies formation energy when Pb fraction rises, as discussed in Bi1-xPbxCuOTe samples


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by Tae-Ho An et al.42 It is noteworthy that minor amounts of unreacted Bi and Bi2O3 are found after the ball-milling process, as highlighted in Figure S1. During SPS, the assynthesized powders react and high purity bulk polycristalline samples are formed when x ≤ 0.025. This short process enables a reduction of the synthesis time as compared to sealed tube (> 10 h)27 or hydrothermal (> 55 h)43 synthesis.

Fig. 2 (a) PXRD patterns of the Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) samples processed by SPS. The green stars indicate the main diffraction peak (012) of metallic bismuth (R-3m) observed in


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the samples x = 0.0375 and x = 0.05. Rietveld refinements of PXRD patterns of (b) x = 0 and (c) x = 0.025 sintered samples.

The refined unit cell parameters of BiCuOS, a = 3.870(1) Å and c = 8.561(1) Å are in good agreement with the values reported for single crystals, i.e. a = 3.8705(5) Å and c = 8.561(1) Å.10 Moreover, the Rietveld refinements of PXRD patterns (See for Figures 2b and 2c, for x = 0 and x = 0.025 respectively; refinement parameters are reported in Table S1) evidenced a copper site occupancy ranging between 0.95 and 0.99 for all the samples. This is considered consistent with the ability of MCuOCh (M = La, Bi ; Ch = S, Se, Te) system to easily form copper vacancies, leading to non-intentional p-type doping in pristine samples.27,29,44,45 As shown in Figure 3, the cell parameters a and c, which are determined from Rietveld refinements, increase monotonically with the Pb fraction from x = 0 to 0.0375. The linear increase of both lattice parameters follows Vegard’s law and is consistent with the substitution of lead on bismuth site because Pb2+ (129 pm) has a larger ionic radius than Bi3+ (117 pm).46 However, c axis expands faster than a axis when lead content is raised. This behavior reveals the weakness of Coulombic attraction between the layers due to substitution. Indeed, the holes transferred to the conductive layer decrease the difference of electronic charge between the two blocks [(Bi1-xPbx)2O2](2-2x)+ and [Cu2S2](2-2x)-. Thus the Coulombic attraction decreases with x which leads to a larger increase of c axis when the lead amount rises.47 The decrease of the lattice constants between x = 0.0375 and x = 0.05 could be due to Bi vacancies as evidenced by the increase of the Bi metal secondary phase. Such decrease of lattice parameters is due to Bi deficiencies which is already noted for BiCuOSe samples.48 It seems that the intrinsic nature of BiCuOS to form Cu and Bi vacancies hinders the synthesis of highly pure samples when the Pb fraction is high. This low doping level is in sharp contrast


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with the selenide-derivative, firstly reported with a Pb2+ solubility lower than 7 at.% before being synthesized until 20 at.%.18,49 Finally, a typical SEM micrograph of the fractured cross-section of the densified Bi1xPbxCuOS

sample is displayed in Figure 4. It reveals a fine and dense microstructure with an

average grain size between 100-200 nm. Such small grain size is mostly explained by the combination of mechanosynthesis and SPS processes. Indeed, as showed in Figure S1, the wide width of the diffraction peaks suggest that the crystallites are in a nanometric scale after the mechanosynthesis process. The subsequent grain growth during SPS is also limited due to the short time process (25 min) and the low sintering temperature to prevent from sulfur volatilization.

Fig. 3 Lattice parameters of the Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) series after sintering, obtained by Rietveld refinements of the PXRD patterns.


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Fig. 4 Typical SEM micrograph of Bi0.95Pb0.05CuOS sintered sample. The microstructure is representative of all the samples.

Thermoelectric properties The temperature dependences of the electrical resistivity (ρ) in the Bi1-xPbxCuOS series are illustrated in Figure 5a. The electrical resistivity of all the samples decreases upon heating, indicating a semiconducting behavior. Pristine BiCuOS exhibits high resistivity over the whole temperature range, from 5.3×104 mΩ cm at 300 K to 5.7×102 mΩ cm at 700 K. The electrical resistivity is decreased gradually by the Pb for Bi substitution, and reached minimum values of 1.0×103 mΩ cm at 300 K and 5.6×101 mΩ cm at 700 K for Bi0.95Pb0.05CuOS sample. Aiming to prove the impact of lead doping over the carrier concentration, Hall effect measurements were performed. The Hall coefficients obtained by the Van der Pauw method are all positive at 300 K, demonstrating that holes are the dominant carriers in the samples. The room temperature Hall carrier concentration (nH) of BiCuOS is approximately 1.4×1017 cm-3 (Figure 6). As discussed earlier in the structural part, the copper vacancies are considered to be the source of hole carriers in the undoped sample.27,29,44,45 The carrier concentration increases by more than two orders of magnitude and reaches 2.6×1019 cm-3 for x = 0.05. The simultaneous increase of the lattice parameters and of the charge ACS Paragon Plus Environment

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carriers concentration demonstrates that Pb2+ was successfully incorporated into the BiCuOS lattice. Thus, assuming that Pb substitution adopts the one carrier model, the decrease of the electrical resistivity originates from the holes generated according to the equation:

× + ℎ

The charge carriers mobility (µH) depicted in Figure 6 unveil a very low value, close to 1 cm2 V-1 s-1 in the undoped sample. This one is decreased further to 0.3 cm2 V-1 s-1 for x = 0.05. The drop of the mobility can be attributed to the increase of the ionized impurity scattering, to the rise of the charge carriers concentration and hole effective mass, as discussed below.50 By comparison, the mobility of the undoped selenide analogue is close to ~20 cm2 V-1 s-1.47 This significant contrast originates from a lower hybridization of Cu 3d and S 3p orbitals due to more localized 3p orbitals compared to Se 4p. Furthermore, the small grain size produced by the mechanical alloying process increases the grain boundaries density and the number of charge barriers. This is confirmed by mobilities as low as 2.8 cm2 V-1 s-1 in ball-milled BiCuOSe samples with 1-2 µm grains.11


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Fig. 5 Temperature dependences of (a) electrical resistivity (b) Seebeck coefficient (c) power factor (d) thermal conductivity; blue dashed line is the calculated lattice thermal conductivity (for x = 0) and (e) ZT in the Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) series.


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Fig. 6 Temperature dependences of the charge carriers concentration (nH) and mobility (µH) in the Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) samples at 300 K.

As shown in Figure 5b, the temperature dependence of the Seebeck coefficient is positive for all samples over all the temperature range and corroborates p-type transport behavior. The pristine sample shows a large Seebeck coefficient close to 707 µV K-1 at 300 K. This value decreases to 545 µV K-1 when the temperature is raised to 700 K as expected for insulating or semiconductor materials. The Seebeck values of all the Pb substituted samples adopt a degenerated semiconductor behavior and increases with the temperature. The value reaches 339 µV K-1 at 700 K for the highest lead content. The magnitude of the Seebeck coefficient decreases with the increasing of Pb fraction and drops to 265 µV K-1 at 300 K for x = 0.05, which is consistent with the increase in carrier concentration. It must be noted that the Seebeck coefficient and the carrier concentration tend to saturate above x = 0.0375, when the secondary phase (Bi) appears. Nonetheless, the carrier concentration being governed by different structural features, such as cationic vacancies (Bi, Cu), Pb/Bi substitution, sulfur vacancies, it makes difficult to establish clearly the role of Bi metal on the TE properties.


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Using our experimental Seebeck coefficient at 300 K, the chemical potential ( ! ) can be

estimated using equation 1 where kB is the Boltzmann constant, " is the acoustic phonon scattering (" = 0) and Fj(!) are the Fermi integrals given in equation 2. The hole effective mass can then be determined from equation 3 using the measured carrier concentration (Np) : $=

%& ) + *+, * - ( − -. 1 ' , + *+* - 5

+0 - = 1

6

Ϛ0 3Ϛ 2 , + 'Ϛ4- )D C

=> :) 8 = < B )%& ; ?@+,⁄) - ∗

3

As shown in Table 1, the large Seebeck coefficient is related to the significant effective mass of BiCuOS (1.71 me), which is higher than the value reported in BiCuOSe sample (1.1 me).13 Furthermore m* progressively increases from 1.71 me to 2.1 me (me being the free electronic mass) with increasing Pb content from 0 to 0.05, which is probably resulting from the increasing contribution of several hole pockets in the multi-valley valence band of BiCuOS.

Table 1 Calculated effective mass from experimental Seebeck coefficient values for the different compounds of Bi1-xPbxCuOS (0 ≤ x ≤ 0.05) series. Compounds m*/me

x=0 1.71

x = 0.025 1.81

x = 0.0375 1.85

x = 0.05 2.2

As shown in Figure 5c, the maximum power factor (PF = S2/ρ) is obtained for the Bi0.95Pb0.05CuOS sample at 700 K (0.2 mW m-1 K-2) and is 5 times higher than the undoped sample value (4.0 × 10-2 mW m-1 K-2). However, the limited carrier concentration and the low ACS Paragon Plus Environment

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electronic mobility restrain this enhancement and better values could probably be reached with higher effective doping. Aiming to clarify the improved electronic properties, we performed DFT calculations to determine the electronic structure of BiCuOS and 6.3 at.% Pb-doped BiCuOS (Figure 1). As mentioned in the introduction, the band structure of pristine BiCuOS exhibits features that do not favor high electronic properties for thermoelectric applications. This limit is related to the large band gap of the pristine BiCuOS (1.1 eV), which is much higher than the optimal values predicted by Goldsmid-Sharp formula Eg = 2eSmaxTmax of 0.35 eV for thermoelectric materials.26 As shown in Figure 7, the band structure calculations performed for pristine and 6.3 at.% doped BiCuOS confirm the indirect band-gaps of the compounds with valence band maximum (VBM) on the Γ-M line and conduction band minimum (CBM) located at the Γ point of the Brillouin zone. The computed band gap of BiCuOS compound is determined to be 1.08 eV which is in very good agreement with experimental measurements, estimated between 1.07 and 1.1 eV.27,51 Replacing Bi by Pb decreases the overall ionic character of the system with the effect of reducing the band gap to 0.55 eV for the 6.3 at.% doped sample. This value is high enough in order to prevent the bipolar conduction and maintain a high Seebeck coefficient. Our calculations show that, just below the top of the valence band, several other bands are present and may contribute to the transport properties with appropriate tuning of the heavy-light valence band and the position of the Fermi level. Since the substitution of Bi by Pb decreases the number of the electrons, the Fermi level moves downward as the content of Pb increases. As shown in the Figure 7b, Pb doping increases the number of holes pockets and several band degeneracies appear around the Fermi level. In order to clarify this concept, we calculated the Fermi surface for 6.3 at.% Pb doped BiCuOS (Figure 7c). It can be viewed that the number of hole pockets is enlarged, and the increase of


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Nv implies an enhancement of the power factor. Also, similar band modifications were found in Sn-/Pb-doped BiCuOSe and Ga-doped SnTe.52–54

Fig. 7 Electronic band structure of BiCuOS (a) and Bi0.937Pb0.063CuOS (b). In Bi0.937Pb0.063CuOS, the hole pockets formed on R-A line and A-Z line are represented (c). The projected density of states (PDOS) of BiCuOS and Bi0.937Pb0.063CuOS are represented in Figure 8. From the computed density of states, it can be inferred that the top of the valence band mainly results from the hybridization between Cu 3d and S 3p orbitals while the minimum of the conduction band is dominated by Bi 6p states. Compared to BiCuOSe, the hybridization is higher between Cu 3d and Se 4p and explains the decrease of carrier mobility in the sulfur derivative. It is clear that, Pb-derived states seem to contribute substantially to the energy region near the top of the valence band (Figure 8b). The Pb contribution is dominated by the 6s components into the states close to the valence band (Figure S2). Such delocalized 6s orbitals from the lone pair electrons in Pb are considered as an important


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criteria to enhance the electronic transport as proved in the variation of the carrier concentration and mobility with Pb concentration. Similar results have been found in PbBiCuOSe doped sample.52

Fig. 8 Projected density of states of BiCuOS (a) and Bi0.937Pb0.063CuOS (b). Figure 5d illustrates the temperature dependences of the thermal conductivity in the Bi1xPbxCuOS

(0 ≤ x ≤ 0.05) series. The thermal conductivity of all the samples is close to 1.1 W

m-1 K-1 at room temperature and falls down to 0.67–0.71 W m-1 K-1 at 700 K. The intrinsically low thermal conductivity is characteristic of the BiCuOCh (Ch = S, Se, Te) family and represents the main advantage of these compounds for thermoelectric applications. This particularity originates from the structure itself which involves weak chemical bonding between the oxide and chalcogenide layers (i.e. low Young’s modulus), high anharmonic interactions of phonons (i.e. large Grüneisen parameter), a low vibration frequency provided by Cu atoms and strong phonons scattering at layers interfaces.55 Furthermore, point defects induced by copper/bismuth vacancies may play a role in the reduction of the lattice thermal conductivity. The total thermal conductivity (κ) stems from the contributions of the lattice thermal conductivity (κL) and the electronic thermal conductivity (κe) according the relation κ = κL + κe. The electrical thermal conductivity is proportional to the electrical conductivity


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according to the Wiedmann-Franz relation κe = LTσ. Here, the Lorenz number L, was estimated as function of temperature from the experimental Seebeck coefficients using single parabolic band model (L and κe are respectively displayed in Figures S3 and S4).56 The calculated Lorenz numbers for all samples are in the range of 1.45 × 10-8 W Ω K-2 and 1.55

× 10-8 W Ω K-2, which are lower than the metallic limit of 2.45 × 10-8 W Ω K-2.57

The lattice thermal conductivity curves show no obvious trend related to the lead percent doping, indicating a weak effect of the induced point defects over the phonon scattering. This can be explained by the small mass fluctuation between Pb (207.20 g mol-1) and Bi (208.98 g mol-1) and the moderate atomic size mismatch of Pb2+ (129 pm) and Bi3+ (117 pm). Due to the low carrier concentration (2.6×1019 cm-3), the electronic heat transport contribution is limited below 2.7 % of the total thermal conductivity at 700 K even for the highest lead concentration. Thus the lattice thermal conductivity is the dominant contribution to the total thermal conductivity. In order to understand the low thermal conductivity of BiCuOS, we calculated the Grüneisen parameters and phonons dispersion of BiCuOS compound. As displayed in Figure 9a, the three acoustic modes have low boundary frequency around 65 cm-1 along Γ-X (010 direction) and Γ-M (110 direction), and 50 cm-1 along Γ-Z (001 direction). It was shown that low acoustic modes frequencies are beneficial for thermoelectric materials and lead to very low thermal conductivity.58,59 All these low frequencies acoustics modes indicate small group velocities around center (Γ-X, Γ-M and Γ-Z) and low Debye temperatures (Table 2), which lead to low lattice thermal conductivities. It can be seen that the acoustic modes are soft along Γ-Z direction are suggesting weak interatomic bonding between the layers and possible strong anharmonicity. It is known that the Grüneisen parameters are useful to estimate the lattice thermal anharmonicity and to interpret the physical nature of the lattice thermal conductivity.


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Thus, we calculated the Grüneisen parameters (γ) of the acoustic modes in function of the Brillouin zone (Figure 9b), and found a high value γ ~ 8 along Γ-Z direction. This indicates a very strong anharmonicity between the layer. Similar results have been found in BiCuOSe.60

Fig. 9 (a) Phonon dispersion of BiCuOS compound. The black, red and blue lines highlight transverse (TA/TA’) and longitudinal (LA) acoustic modes, respectively. The green lines highlight the optical modes. (b) Acoustic phonon dispersion of transverse (TA/TA’) and longitudinal (LA) modes (straight lines), associated Grüneisen parameters (dots) in function of Brillouin zone of BiCuOS compound.

Using the phonon dispersion, we can calculate the longitudinal (LA) and transverse (TA/TA’) velocities (the slope of the acoustic phonon dispersion around the Γ point) and their Debye temperature (FG ) calculated using Debye model given by : FG = H I/K L6N O P

QD R

where H are the sound velocity associated to the longitudinal and transverse modes, and V is ACS Paragon Plus Environment

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the average volume per atom. The averages longitudinal (LA) and transverse (TA/TA’) velocities, Debye temperature and Grüneisen parameter (γ) of each acoustic dispersion are presented in Table 2. The calculated Grüneisen parameters are in very good agreement with previous reported values in the literature,61,62 and close to those average Grüneisen parameters of SnSe.58 It is noteworthy that recently, Vaqueiro et al. found that, the low frequencies phonon modes and large Grüneisen parameters have largest contribution from the Cu atoms.55 On the basis of the Debye-Callaway model,63 we calculated the lattice thermal conductivity (Figure 5d). The calculated values of 1.1–0.65 W m-1 K-1 in the temperature range of 300– 700 K are in very good agreement with the experimental values, ranging between 1.1 and 0.7 W m-1 K-1. Table 2 Average transverse (TA/TA’) and longitudinal (LA) Grüneisen parameters (γ), Debye temperatures (θ) and phonon velocities of BiCuOS (ν).

BiCuOS

γTA

γTA’

γLA

θTA (K)

θTA’ (K)

θLA (K)

3.627

3.1674

4.2

95

95

206

νTA (m/s) 1534

νTA’ (m/s) 1534

νLA (m/s) 3490

Finally, we computed the theoretical minimum thermal conductivity κmin using the shortest scattering distance within the model proposed by Cahill et al.64 and obtained a value of ∼0.23 W m-1 K-1. For all samples, the κL values remain significantly higher than the κmin value, indicating that further reduction may be possible, and might for example be achieved by enhancing structural disordering. The combination of electrical and thermal transport properties allows to estimate the figure of merit (ZT) as a function of temperature in the Bi1-xPbxCuOS series (Figure 5e). The pristine sample exhibits a value close to 0.04 at 700 K, which is lower than the 0.07 (at 650 K)


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recently reported by Zhu et al.25 However, the higher carrier concentration (4.0 × 1018 cm-3) found in their samples indicates a higher concentration of cationic vacancies with nonintentional p-type doping. With the rising of the Pb fraction, the charge carriers concentration gradually increases and a maximum ZT of 0.2 at 700 K is obtained for x = 0.05. To our knowledge, only few thermoelectric oxysulfides were reported with rather low ZT values. For instance, Bi4O4S3 and LaPbBiS3O reach respectively 0.03 and 0.0023 at 300 K,65,66 whereas LaOBiS2 peaks around 0.07 at 743 K.67 The ZT value reported for Bi0.95Pb0.05CuOS in the present study is significantly higher and thereby, becomes the best ever achieved for an oxysulfide compound. Conclusion The thermoelectric properties of the Bi1-xPbxCuOS series (0 ≤ x ≤ 0.05) have been studied both experimentally and theoretically. The Pb for Bi substitution increases the charge carriers concentration and enables to increase substantially the electrical conductivity while moderately decreasing the Seebeck coefficient. This leads to a maximum power factor for x = 0.05 sample. The intrinsically low thermal conductivity provided by weak interatomic bonding between the layers and possible strong anharmonicity, is imperceptibly increased by the cationic substitution. Finally, the combination of low thermal conductivity with a power factor of 0.2 mW m-1 K-2 at 700 K increased the figure of merit ZT up to 0.2 in 5at.% Pbdoped BiCuOS sample. This value is 5 times higher with respect to BiCuOS. To the best of our knowledge, it is considered as the best ever reported value among the family of oxysulfides. Despite the obtained low ZT value, the approaches developed to optimize the electrical and thermal properties of BiCuOS appears as an interesting playground, which can be extended to other oxychalcogenides and materials in the future.


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Table of Content Thermoelectric properties in the Bi1-xPbxCuOS series have been studied both experimentally and theoretically. A record ZT of 0.2 is obtained in the family of oxysulfides.


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Electronic Band Structure Engineering and Enhanced Thermoelectric

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