Thermoelectric Material SnPb2Bi2S6: The 4,4L Member of Lillianite

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Thermoelectric Material SnPb2Bi2S6: The 4,4L Member of Lillianite Homologous Series with Low Lattice Thermal Conductivity Jingpeng Li,†,# Yiming Zhou,‡,# Shiqiang Hao,§ Tianyan Zhang,† Chris Wolverton,§ Jing Zhao,*,† and Li-Dong Zhao*,‡ †

Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 01/01/19. For personal use only.

The Beijing Municipal Key Laboratory of New Energy Materials and Technologies, School of Materials Sciences and Engineering, University of Science and Technology Beijing, Beijing 100083, China ‡ School of Materials Science and Engineering, Beihang University, Beijing 100191, China § Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *

ABSTRACT: Although the binary sulfides Bi2S3, PbS, and SnS have attracted extensive interest as thermoelectric materials, no quaternary sulfides containing Sn/Pb/Bi/S elements have been reported. Herein, we report the synthesis of a new quaternary sulfide, SnPb2Bi2S6, which crystallizes in the orthorhombic space group Pnma with unit cell parameters of a = 20.5458(12) Å, b = 4.0925(4) Å, c = 13.3219(10) Å. SnPb2Bi2S6 has a lillianite-type crystal structure consisting of two alternately aligned NaCl-type structural motifs separated by a mirror plane of PbS7 monocapped trigonal prisms. In the lillianite homologous series, SnPb2Bi2S6 can be classified as 4,4L, where the superscripted numbers indicate the maximum numbers of edge-sharing octahedra in the two adjacent NaCl-shaped slabs along the diagonal direction. The obtained SnPb2Bi2S6 phase exhibited good thermal stability up to 1000 K and n-type degenerate semiconducting behavior, with a power factor of 3.7 μW cm−1 K−2 at 773 K. Notably, this compound exhibited a very low lattice thermal conductivity of 0.69−0.92 W m−1 K−1 at 300−1000 K. Theoretical calculations revealed that the low thermal conductivity is caused by the complex crystal structure and the related elastic properties of a low Debye temperature, low phonon velocity, and large Grüneisen parameters. A reasonable figure of merit (ZT) of ∼0.3 was obtained at 770 K.

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INTRODUCTION Thermoelectric (TE) materials enable the direct conversion of heat into electricity, and vice versa, which is especially important for waste heat collection and efficient energy utilization as nearly 60% of energy is currently lost in the form of waste heat.1−5 The conversion efficiency of TE materials depends on the magnitude of the dimensionless figure of merit ZT, which can be expressed as ZT = S2σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature in kelvin, κ is the total thermal conductivity, and S2σ is the power factor (PF). However, the interdependence of these TE parameters makes it challenging to obtain large ZT. Several methodologies have recently emerged to overcome this limitation, including band structure engineering,6,7 nanostructure adjustment,8−10 and enhanced phonon scattering,11−13 resulting in greatly improved ZT values. To date, the most widely studied TE materials include Bi2Te3-, PbTe-, and SiGe-based materials, which can be used at room temperature (RT), intermediate temperature, and high temperature, respectively. Even though Bi0.5Sb1.5Te3 is the most well-developed p-type material that can be used in refrigeration,14−16 its TE conversion efficiency is low, and its © XXXX American Chemical Society

cost is relatively high because of the incorporation of the scarce Te element. Therefore, it is necessary to identify new earthabundant and low-cost TE materials. Studies have revealed that ternary and quaternary chalcogenides containing heavy elements exhibit reduced thermal conductivity without compromising the electrical conductivity as their complex compositions can effectively scatter short-wavelength phonons.17,8 Moreover, their complex band structure enables high Seebeck coefficients to be obtained because of the large effective mass produced.18 For example, CsBi4Te6 exhibited good TE properties below RT with a maximum ZT of 0.8 at 225 K;19 NaPbmSbTem+2 exhibited the highest ZT of 1.6 at 673 K.20,21 (PbTe)0.65−x(PbSe)0.35(PbS)x(x = 0.05, 0.10) exhibited the highest ZT of 1.4 at 850 K;21 AgPbmSbTe2+m exhibited a maximum ZT of approximately 2.2 at 800 K.22 To date, several quaternary Sn−Pb−Bi−Se compounds, including Sn 2 Pb 5 Bi 4 Se 13 , 23 Sn 8.65 Pb 0.35 Bi 4 Se 15 , 23 and PbxSn6−xBi2Se9 (x = 0−4.36),24 have been shown to exhibit promising TE properties; however, no quaternary sulfur counterparts have been reported. Additionally, the binary Received: October 12, 2018

A

DOI: 10.1021/acs.inorgchem.8b02899 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry compounds SnS,25,26 PbS,27−30 and Bi2S331,32 have been reported as potential TE materials. Therefore, good TE performance is expected from quaternary Sn−Pb−Bi−S compounds, which can integrate the merits of all the binary compounds mentioned above. These factors prompted us to select the heavy elements Sn, Pb, Bi, and S to synthesize quaternary chalcogenides for TE applications. In this paper, we report a new member of the lillianite structure type, SnPb2Bi2S6, which crystallizes in the Pnma space group. SnPb2Bi2S6 can be synthesized using a hightemperature solid-state reaction and exhibits good thermal stability up to 1000 K. SnPb2Bi2S6 possesses low thermal conductivities in the measured temperature range (300−1000 K) originating from its phonon structures and elastic properties. The highest ZT of ∼0.3 was obtained at 773 K. These results indicate that the SnPb2Bi2S6-based system is a promising candidate for TE applications, with improved performance expected upon optimization of the carrier density.

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The atomic positions, site occupancies, displacement parameters, and selected bond distances are tabulated in Tables S1−S3. Powder X-ray Diffraction (PXRD). The resulting sample was ground into a powder and subjected to PXRD analysis using an X’Pert PW-3040 diffractometer. The measurements were conducted using Kα rays emitted from a Ni-filtered Cu target at a voltage of 40 kV and a current of 15 mA. The simulated PXRD spectrum for comparison purposes was calculated using Mercury software using the CIF of the refined structure.36 Thermal Analysis. Approximately 50 mg of SnPb2Bi2S6 powder was placed into a fused silica tube with an inner diameter of ∼4 mm and flame-sealed under vacuum. Differential scanning calorimetry (DSC) measurements were conducted using a NETZSCH STA 449F3 thermal analyzer at a heating/cooling rate of 10 K/min with a maximum temperature of 1273 K. After the test, the sample was collected and ground into a powder and subjected to PXRD analysis again. Scanning Electron Microscopy. EDS analysis was performed using a JEOLJSM-6510A scanning electron microscope equipped with a PGT energy dispersive X-ray analyzer. The data are the average of several (∼10) independent measurements. Spark Plasma Sintering (SPS). The obtained SnPb2Bi2S6 sample was pulverized and loaded into a graphite die with a diameter of 12.7 mm. The sintering was performed using an SPS-1050 instrument from Japan Sumitomo Carboniferous Co. The sample was sintered at 823 K for 10 min under a pressure of 40 MPa. The density of the sintered sample was ∼95% of the theoretical density. Electrical Transport Properties. The obtained cylinder was cut into bars with dimensions of ∼3.0 × 3.0 × 9.0 mm3 for the sample measured perpendicular to the pressure and ∼3.0 × 3.0 × 7.0 mm3 for the sample measured parallel to the pressure. The electrical conductivity and Seebeck coefficient were measured simultaneously. The bars were spray-coated with boron nitride to reduce gas release, except in locations needed for electrical contact with thermocouples, heaters, and voltage probes. The temperature was increased from RT to 773 K using an Ulvac Riko ZEM-3 instrument in a low-pressure helium atmosphere. The errors for the experimentally measured conductivity and Seebeck coefficients were ∼5%. Thermal Transport Properties. The thermal diffusivities were measured on samples with dimensions of ∼6 × 6 × 1.5 mm3 using a Netzsch LFA457 instrument. The surfaces of the samples were coated with a layer of graphite to minimize errors caused by thermal reflection of the material. The Cowan model was used for pulse correction of the thermal diffusion data. The equation κtot= DCp d was used to calculate the total thermal conductivity of the samples, where D is the thermal diffusion coefficient; d is the actual density calculated by dividing the mass by the actual volume of the sample; and Cp is the specific heat capacity of SnPb2Bi2S6 calculated using Dulong−Petit’s law Cp = 3R/M̅ , where R is the gas constant 8.314 J mol−1 K−1 and M̅ is the average molar mass of the atoms in SnPb2Bi2S6. The uncertainty of the thermal conductivity and ZT values were approximately 8 and 20%, respectively.37 Hall Coefficient Measurements. The samples for the Hall measurements were polished into square shapes of ∼6.0 × 6.0 × 0.5 mm3 and were contacted by four copper probes using the Van der Pauw method. The Hall coefficients (RH) were measured under a magnetic field of ±1.5 T using a Hall measurement system (Lake Shore 8400 Series, Model 8404, USA) at RT. Electronic Structure Calculations. Density functional theory (DFT) was used to calculate the total energies and relaxed geometries within the generalized gradient approximation (GGA) of the Perdew−Burke−Ernzerhof exchange correlation functional using projector-augmented wave potentials.38 The spin orbit coupling effect was considered in the band structure calculations. We used periodic boundary conditions and a plane-wave basis set as implemented in the Vienna ab initio simulation (VASP) package.39 The total energies were numerically converged to approximately 3 meV/cation using a basis set energy cutoff of 500 eV and dense k-meshes corresponding to 4000 k-points per reciprocal atom in the Brillouin zone.

EXPERIMENTAL SECTION

Reagents. Analytical pure tin metal, sulfur powder, bismuth metal, and lead metal were purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. All the reactants were used as obtained. Synthesis. Sn (237.4 mg, 2.00 mmol), Pb (414.4 mg, 2.00 mmol), Bi (836 mg, 4.00 mmol), and S (288.9 mg, 9.00 mmol) were weighed and loaded into a fused silica tube with an inner diameter of 12 mm. The tube was flame-sealed under a low vacuum (∼10−4 mbar) and then placed into a muffle furnace. The temperature was raised from RT to 573 K over 6 h and then held at 573 K for an additional 6 h. The temperature was then raised to 1173 K over 6 h and held at 1173 K for an additional 18 h. Next, the temperature was lowered from 1173 to 823 K over 45 h and held at 823 K for 24 h before cooling to RT in 10 h. Black blocky crystals with edges larger than 0.1 mm were obtained. To obtain pure SnPb2Bi2S6, experiments were conducted using various starting material ratios, including stoichiometric starting materials (Sn/Pb/Bi/S = 1:2:2:6) and starting materials with a 0.5 mol % excess of S or Bi or both Bi and S. The samples were heated from RT to 1173 K over 12 h and held at 1173 K for 18 h before cooling to RT in 6 h. Powder X-ray diffraction (PXRD) analysis indicated that the sample with an excess of 0.5 mol % Bi was the purest material with the highest crystallinity. Specifically, the starting materials used to obtain the pure phase were Sn (59.36 mg, 0.50 mmol), Pb (207.2 mg, 1.00 mmol), Bi (219.45 mg, 1.05 mmol), and S (96.21 mg, 3.00 mmol)). Single-Crystal X-ray Diffraction. A selected crystal with dimensions of up to ∼20 μm was subjected to X-ray diffraction analysis using a Rigaku XtaLAB PRO single crystal diffractometer with Mo Kα radiation. The XPREP software was used to determine the crystal structure using the direct method, and the SHELXTL package was used for structure refinement.33 All the cationic sites were refined with a mixture of Sn under the constraints of equal coordinates and displacement parameters, with the result that only two of the five positions (Pb/Sn4 and Pb/Sn5 sites) appeared to be mixed with Sn. It should be noted that Pb2+ and Bi3+ cannot be distinguished because they show the same diffraction contrast to X-rays. Bond valence sum (BVS) calculations were performed assuming full occupation of each site by either Bi or Pb.34 The BVS results indicated values of 2.85 for Bi1 sites, 1.88 for Pb2 sites, and 2.67 for Bi3 sites. The ratio of Pb to Bi in the formula was determined by comprehensively considering electrical neutrality and energy-dispersive X-ray spectroscopy (EDS) results. Finally, the sum formula of Sn0.9Pb2.1Bi2S6 was refined, and considering the ambiguity of the Bi and Pb ratio, we referred to this compound as SnPb2Bi2S6. The PLATON software was used to check for possible missing symmetry elements; however, no higher symmetry was detected.35 B


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Inorganic Chemistry

integer.48 Unexpectedly, SnPb2Bi2S6 was obtained, belonging to the lillianite family, which is closely related to the pavonite structure.49 The SnPb2Bi2S6 single phase was fabricated by heating a mixture of Sn/Pb/Bi/S = 0.50:1.00:1.05:6.00 at 1173 K and rapidly cooling to RT (∼150 K/h). As shown in Figure 1a, SnPb2Bi2S6 without any observable impurities was

Phonon Structure Calculations. The dynamical properties of the SnPb2Bi2S6 system were calculated using the frozen-phonon method.40,41 In this method, the elements of the force-constant matrix are calculated from ab initio forces exerted on all the cell atoms when a particular cell atom is slightly displaced from its equilibrium position. The vibrational phonon modes are obtained from the diagonalization from the corresponding dynamical matrix. We used the Debye−Callaway model to quantitatively evaluate the lattice thermal conductivity to explore the origin of the low lattice thermal conductivity at the atomic level. The Grüneisen parameter characterizes the relationship between the phonon frequency and crystal volume change, allowing us to estimate the anharmonicity of the lattice and better understand the physical properties of the lattice thermal conductivity. The phonon and Grüneisen dispersion were calculated using first-principles DFT phonon calculations within the quasi-harmonic approximation. The phonon dispersion was calculated in two volumes, the equilibrium volume V0 and the isotropic compression volume of 0.98 V0. The Debye−Callaway formalism42 has been shown to produce accurate values of the lattice thermal conductivity of low-conductivity TE compounds when compared with those determined experimentally.43−47 The total lattice thermal conductivity can be written as the sum of the longitudinal κLA and two transverse κTA and κTA′ acoustic phonon branches: κLatt = κLA + κTA + κTA′. The partial conductivities κi (i corresponds to the TA, TA′, and LA modes) are given by l ÅÄÅ Θi / T τ i(x) x4e x ÑÉÑ2 | o o c o ÅÅ∫ ÑÑ o o i 4 x o o Å Ñ o i x 2 dx Ñ T Θ / o Å i τ − e ( 1) 0 τc(x) x e 1 o ÅÇ ÑÖ o N 3o κi = CiT m dx + } i 4 x x 2 o o Θ T / τ x x e ( ) o 0 o i c 3 − ( e 1) o o o ∫ i i x 2 dx o o o − τ τ e ( 1) 0 o o N U o o n ~ (1) In this formula, Θi is the longitudinal (transverse) Debye temperature, 1/τiN is the scattering rate for normal phonon processes, 1/τiR is the sum of all resistive scattering processes, 1/τic = 1/τiN + 1/τiR, x = ℏω/ kBT, and Ci = k4B/2π2ℏ3vi. Here, ℏ is the Planck constant, kB is the Boltzmann constant, ω is the phonon frequency, and vi is the longitudinal or transverse acoustic phonon velocity. In this case, the resistive scattering rate includes the scattering rates due to Umklapp phonon−phonon scattering (1/τiU) and normal phonon scattering (1/τiN). The normal phonon scattering and Umklapp phonon−phonon scattering can be expressed as

∫

1 τNLA(x)

2 kB5γLA V

=

5 M ℏ4vLA

1 τNTA/TA′(x) 1 τUi (x)

=

=

x 2T 5

2 kB5γTA/TA V ′ xT 5 4 5 M ℏ vTA/TA ′

kB2γi2 M ℏvi2 Θi

x 2T 3 e−θi /3T

Figure 1. (a) Comparison of PXRD pattern of as-synthesized SnPb2Bi2S6 with simulated pattern. (b) Thermal stability of SnPb2Bi2S6.

obtained. The EDS elemental analysis revealed a Sn/Pb/Bi/S ratio of 1.03/2.06/2.43/6, which is consistent with the crystallographic analysis results (Figure S1). It is noteworthy that an attempt to synthesize the selenium analogue SnPb2Bi2Se6 was performed using a stoichiometric starting ratio; however, the reported lillianite PbxSn6−xBi2Se9 (x = 0−4) (7,7L) was obtained.24 DSC measurements were performed to investigate the thermal stability of SnPb2Bi2S6 from RT to 1273 K (Figure 1b). In the heating curve, the maximum endothermic peak was observed at 1027 K, which is attributed to the melting of SnPb2Bi2S6. A shoulder endothermic peak appeared at approximately 1049 K due to the melting of the secondary higher level lillianite phase, similar to that observed in the pavonite homologous family.50 In the cooling curve, two major crystallization events were detected at 1023 and 1005 K, corresponding to the melting events observed upon heating at 1049 and 1027 K, respectively. Two small peaks also appeared at 1053 and 947 K, indicating that the compound decomposed into different N-members of the same homology, which tend to exhibit incremental changes in their physical properties. This finding was further confirmed by the PXRD analysis of the sample after the DSC measurement, with the results showing few changes (Figure S2). Crystal Structure. SnPb2Bi2S6 crystallized in the orthorhombic space group Pnma, and the unit cell parameters and structure refinement details are provided in Table 1. Figure 2a shows the unit cell of SnPb2Bi2S6, which only contains one type of crystallographic Wyckoff position 4c. Figure 3 shows the coordination environments of the cations; all the cations formed distorted 5−7 coordination geometries. Bi1 is linked with six S atoms to form a distorted octahedra with Bi1−S distances in the range of 2.676(9)−2.967(5) Å. The Pb2 atom

(2)

(3)

(4)

In the above expressions, γ, V, and M are the Grüneisen parameter, volume per atom, and average mass of an atom in the crystal, respectively. The Grüneisen parameter characterizing the relationship between the phonon frequency and volume change can be defined as V ∂ω γi = − ω ∂Vi .

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i

RESULTS AND DISCUSSION Phase Structure and Thermal Behavior. The SnPb2Bi2S6 sample for the PXRD analysis was obtained by slowly cooling (∼7.8 K/h) a high-temperature melt (1173 K) in a vacuum-sealed fused silica tube. The initial elemental ratio of Sn/Pb/Bi/S = 1:2:4:9 was used to synthesize a new compound belonging to the pavonite homologous series, which has the general formula of MN+1Bi2QN+5 (with N = 5 here), where M is a six-coordinated metal and N is an C


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Inorganic Chemistry Table 1. Crystallographic Data and Structural Refinement Results of SnPb2Bi2S6 at RT empirical formula formula weight temperature wavelength crystal system space group unit cell dimensions volume Z density (calculated) absorption coefficient F(000) θ range for data collection index ranges reflections collected independent reflections completeness to θ = 25.00° refinement method data/restraints/ parameters goodness-of-fit final R indices [>2σ(I)] R indices [all data] largest diff. peak and hole

SnPb2Bi2S6 1152.19 293(2) K 0.71069 Å orthorhombic Pnma a = 20.5458(12) Å, b = 4.0925(4) Å, c = 13.3219 (10) Å 1120.2 Å3 4 6.832 g/cm3 65.840 mm−1 1917 3.21−25.00° −24 ≤ h ≤ 24, −4 ≤ k ≤ 4, −15 ≤ l ≤ 15 7156 1124 [Rint = 0.0331]

Figure 3. Atomic coordination environments of Bi1, Pb2, Bi3, Pb/ Sn4, and Pb/Sn5 in the SnPb2Bi2S6 structure.

99% full-matrix least-squares on F2

sharing S atoms, forming a three-dimensional SnPb2Bi2S6 structure. SnPb2Bi2S6 belongs to the lillianite mineral structure type, as shown in Figure 2b. In the lillianite homology, there is typically a triangular prism coordination layer extending infinitely along a two-dimensional plane, which can be regarded as a mirror, and NaCl-like slabs composed of slightly to moderately distorted edge-sharing octahedra are distributed over both sides.52 In the lillianite homologous series, N1,N2L is used for classification, where N1 and N2 represent the octahedra numbers along the diagonal direction of the two neighboring NaCl-type slabs (the two N numbers can be equal or different). Currently, the SnPb2Bi2S6 structure can be expressed as 4,4L, which can be classified by the general formula of (Pb/Sn)N−1Bi2SN+2 (N = 4). In SnPb2Bi2S6, the mirror plane is perpendicular to the a-axis and consists of Pb2S 7 monocapped trigonal prisms; such coordination geometry has been observed in some other lillianites.53,54 The arrows in Figure 2b show the two adjacent strip-like structures in the NaCl-type slab. Upon close inspection of the crystal structure, atomic-scale differences can be detected between the two adjacent strips. Strip 1 is generated by the inversion of the edge-shared irregular octahedra (Pb/Sn4S6) and the square pyramid (Pb/

1124/0/69 1.131 Robs = 0.0545, wRobs = 0.1334 Rall = 0.0561, wRall = 0.1358 3.897 and −2.333 e·Å−3

and neighboring seven S atoms form a monocapped trigonal prism, with the Pb−S bond lengths ranging from 2.816(3) to 3.252(4) Å. The Bi3 atom is surrounded by six S atoms, forming a distorted octahedra, and the bond lengths vary from 2.663(0) to 3.191(9) Å. The Bi/Pb−S bond distances agree well with those reported for Pb3Bi2S6.51 Pb4/Sn4 (Pb 58.8% and Sn 41.2%) form a distorted octahedra with bond lengths ranging from 2.677(4) to 3.012(7) Å. Pb5/Sn5 (Pb 51.0% and Sn 49.0%) is surrounded by five S atoms, forming a distorted square pyramid geometry, with bond lengths ranging from 2.629(5) to 2.893(0) Å. Additionally, there is a sixth distant S surrounding the central Pb5/Sn5 atom with a bond distance of ∼3.442(6) Å, which is not close enough to be considered chemical bonding. These diverse cationic coordination geometries are connected to each other by point-sharing or edge-

Figure 2. (a) Unit cell of SnPb2Bi2S6. (b) Crystal structure of SnPb2Bi2S6, which belongs to the lillianite homologous series with the mirror planes shown in light blue. D


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Inorganic Chemistry Sn5S5), whereas strip 2 is composed of the inversion of two irregular octahedra (Bi1S6 and Bi3S6) with the octahedra connected by edge sharing. The difference between the two strips can be mainly attributed to the lone pair of Pb/Sn5 atoms, which leads to a severely distorted coordination geometry similar to the results observed in the andorite branch of the lillianite series.52,53 There have been many reports on the promising TE properties of compounds containing such NaCl motifs, such as CsM2Bi3Te7 (M = Pb, Sn),55 β-K2Bi8Se13,56 K2.5Bi8.5Se14,56 KSn5Bi5Se13,57 and Pb7Bi4Se13.58 The NaCl-type structural motif and the complex cationic occupancies and coordination geometries of SnPb2Bi2S6 indicate that this material is a promising TE material. Electronic Structure. Because of the high carrier concentrations of the as-synthesized SnPb2Bi2S6, the band gap could not be determined using infrared and ultraviolet− visible absorption spectroscopy, as shown in Figure S3. Firstprinciples DFT electronic structure calculations were used to verify that SnPb2Bi2S6 is a direct bandgap semiconductor with a band gap of ∼0.03 eV (Figure 4a). The densities of state

Figure 5. Photographs of (a) as-synthesized SnPb2Bi2S6 powder and (b) cylinder SnPb2Bi2S6 sample obtained after SPS. (c) Schematic illustration showing cutting directions of samples for the TE transport property measurements. (d) Photograph of typical samples used for the thermal (rectangular) and electrical (bar) transport properties measurements.

characterize the anisotropy of the transport properties caused by the sintering pressure, all the TE properties of the samples were measured in two directions, namely parallel and perpendicular to the SPS pressure direction. Figure 5c,d present a schematic illustration showing the cutting directions and a photograph of the specimens used for TE measurements, respectively. In our descriptions below, the samples measured in the two directions are denoted as parallel and perpendicular samples. As shown in Figure 6, the obtained SnPb2Bi2S6 sample was very dense, with no cracks or voids observed on the freshly fractured surface. In addition, the elemental distribution was homogeneous. The temperature dependences of the TE properties of SnPb2Bi2S6 are shown in Figure 7. As observed in Figure 7a, the electrical conductivity of SnPb2Bi2S6 decreased with increasing temperature, indicating degenerate semiconductor behavior. It is widely acknowledged that the degenerate transport feature can be well illustrated by a reduced Fermi level. Therefore, a reduced Fermi level was fitted from the Seebeck coefficient S using the follow equations: ÉÑ ÄÅ kB ÅÅÅ 2F1(η) ÑÑÑ ÑÑ Å S = ± ÅÅη − e ÅÅÇ F0(η) ÑÑÑÖ (5)

Figure 4. (a) Electronic band structures and (b) and (c) DOS of SnPb2Bi2S6.

(DOS) (Figure 4b and 4c) indicate that the valence band maximum (VBM) is mainly composed of the Sn 5s and S 3p states and that the conduction band minimum (CBM) is mainly attributed to the Bi 6p state, partly due to Sn 5p and S 3p states, indicating that the carrier concentrations for n-type SnPb2Bi2S6 can be optimized by doping on Bi. Thermoelectric Transport Properties. The obtained SnPb2Bi2S6 sample exhibited good crystallinity. An ∼10 g sample was fully ground and subjected to SPS (Figure 5a), and a cylindrical sample was obtained (Figure 5b). Because the crystal structure of SnPb2Bi2S6 is not highly symmetrical, to

Fj(η) =

∫0

∞

xj e(x − η) + 1

dx

(6)

where kB is the Boltzmann constant and Fj(η) is the Fermi integral calculated from the reduced Fermi level η = EF/kBT. The reduced Fermi level of the SnPb2Bi2S6 was calculated to be approximately 5.0, which is higher than the requirement of the strongly degenerate approximation of η > 4.0.59 The Hall effect measurement revealed a high Hall carrier concentration E


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Inorganic Chemistry

with increasing temperature and was almost eliminated at high temperatures. The Seebeck coefficients of SnPb2Bi2S6, as given in Figure 7b, remained negative at 300−773 K, indicating electrondominated transport behavior. The linear temperature dependence of the Seebeck coefficient is in line with the degenerate semiconductor behavior indicated by the electrical conductivity results. The negligible anisotropy of the Seebeck coefficient is consistent with the well-accepted perspective in the TE community.60 The Seebeck coefficient of the SnPb2Bi2S6 sample was −55 μV K−1 at RT and decreased to −146 μV K−1 at 773 K for the parallel sample. Figure 7c shows the temperature dependence of the power factor of SnPb2Bi2S6. The power factor of the parallel sample was higher than that of the perpendicular one, especially at high temperatures. The maximum power factor of 3.7 μW cm−1 K−2 (773 K) was achieved for the parallel sample, with a maximum power factor of 3.3 μW cm−1 K−2 obtained for the perpendicular sample. These power factors are comparable to those reported for undoped AgBi3S546 and Pb7Bi4Se13. To investigate the effects of the complex crystal structure on the thermal transport properties, the electronic thermal conductivity was excluded from the total thermal conductivity (Figure 7d) to determine the lattice thermal conductivity. The electronic thermal conductivity was calculated using the Wiedemann−Franz law κele= LσT. Under the assumptions of the single parabolic band model and the acoustic-phonon dominant scattering mechanism, the Lorenz number L (Figure S4) was determined using the reduced Fermi level obtained above:30

Figure 6. Microstructure of fractured surface and elemental distributions for SnPb2Bi2S6.

of 2.71 × 1020 cm−3 at RT, yielding a DOS effective mass m* of 1.1me. nH =

16π ijj 2m*kBT yzz jj zz 3 jk h2 z{

3/2

F02(η) F −1/2(η)

ik y L = jjjj B zzzz ke {

(7)

where h is the Planck constant. According to the formula σ = neμ, the carrier mobilities in the parallel and perpendicular directions at RT are 6.40 and 6.70 cm2 V−1 s−1, respectively. Because of this high carrier concentration, the electrical conductivity of SnPb2Bi2S6 reached 302 S cm−1 in the perpendicular sample and 277 S cm−1 in the parallel sample at RT. The anisotropy of the electrical conductivities decreased

ÅÄ ÑÉ2 | o o 3F2(η) ÅÅÅ 2F1(η) ÑÑÑ o o Å ÑÑ o − m } Å o o Å Ñ o o Å Ñ η η F ( ) F ( ) o o Å Ñ 0 0 Ç Ö n ~

2l o

(8)

where kB is the Boltzmann constant and Fj(η) is the Fermi integral calculated from the reduced Fermi level, η = EF/kBT. The resultant lattice thermal conductivities, the differences between the total thermal conductivities and electronic thermal conductivities, are presented in Figure 7e. The total and lattice thermal conductivities of SnPb2Bi2S6 decreased monotonously

Figure 7. Temperature dependences of TE transport properties of SnPb2Bi2S6 along the directions parallel and perpendicular to the SPS pressure direction: (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor, (d) total thermal conductivity, (e) lattice thermal conductivity, and (f) figure of merit (ZT). F


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Inorganic Chemistry

Figure 8. (a) Calculated phonon dispersion of SnPb2Bi2S6. The red, green, and blue lines denote the TA, TA′, and LA acoustic modes, respectively. (b) DOS, (c) Grüneisen parameters, and (d) lattice thermal conductivity of SnPb2Bi2S6.

of the calculated lattice thermal conductivity in the three crystallographic directions based on a simple orthorhombic Brillouin zone. The averaged values are shown in Figure 8d, which are at the same level as the experimental results. The low lattice thermal conductivity is related to the very low phonon velocities, which are close to the averaged values of 1540, 1655, and 2535 m/s for the TA, TA′, and LA modes (Figure 8a). The phonon DOS indicates that the acoustic phonon transport in SnPb2Bi2S6 is based primarily on the local vibration of the heavier Pb and Bi atoms, with a minimal contribution from S (Figure 8b). The averaged Grüneisen parameters (Figure 8c) were relatively large, with values of 2.62, 2.46, and 3.08 for the TA, TA′ and LA modes, respectively. Generally, the calculated lattice thermal conductivities of SnPb2Bi2S6 were very low because the complex atomic structure leads to a low Debye temperature, slow phonon velocities, and large Grüneisen parameters.66−69 These features are reasonable and have been observed in other materials such as CdAg 2 Bi 6 Se 11 , 70 CdPb2Bi4S9,70 Cs6Cd2Bi8Te17,47 and Rb2ZnBi2Se5,47 where strong anisotropic lattices and corresponding low Debye temperatures and large Grüneisen parameters induce very low lattice thermal conductivities.

with increasing temperature, which is attributed to Umklapp phonon scattering. Generally, complex crystal structures with large unit cells and heavy atoms can exhibit low thermal conductivity. For SnPb2Bi2S6, the lattice thermal conductivity was 0.90 W m−1 K−1 at RT and 0.69 W m−1 K−1 at 773 K for the perpendicular sample, with slightly higher values obtained for the parallel sample. As shown in Figure 7e, the thermal conductivity of SnPb2Bi2S6 is lower than that of its “binary components”, such as PbS,30 SnS,61 and Bi2S3.62 The lattice thermal conductivity of SnPb2Bi2S6 is at the same level with that of other lillianites. For example, Pb7Bi4Se13(5,4L) exhibits a lattice thermal conductivity of 0.33 W m−1 K−1 at 300 K, and Pb6Bi2Se9(7,7L) exhibits a lattice thermal conductivity of ∼1.1 W m−1 K−1 over the entire temperature range.63 In fact, SnPb2Bi2S6 can be regarded as a structure in which a Pb atom in the ternary chalcogenide Pb3Bi2S6 is replaced by a Sn atom, and Pb3Bi2S6 was reported to exhibit a lattice thermal conductivity of 0.52 W m−1 K−1 at 770 K.64 This low lattice thermal conductivity is attributed to the large unit cell of 44 atoms in SnPb2Bi2S6, which can lead to a small and folded back Brillouin zone and hence a low phonon group velocity.65 The anisotropy of the thermal conductivity was almost unaffected by temperature changes. Benefiting from the low thermal conductivity and relatively high carrier concentration, the maximum ZT of 0.3 was achieved in the parallel sample at 773 K (Figure 7f). Origins of Low Thermal Conductivity. To investigate the origins of the low thermal conductivity in SnPb2Bi2S6, DFT quasi-harmonic phonon calculations were performed to obtain all the inputs for the Debye−Callaway model. As observed in Figure 8d, the DFT-calculated lattice thermal conductivities of SnPb2Bi2S6 in the a and c directions were extremely low, ∼0.1 W m−1 K−1 at 300 K. The shorter b (4.09 Å) than a (20.55 Å) and c (13.32 Å) resulted in a larger Debye temperature and hence a higher lattice thermal conductivity of 2.4 W m−1 K−1 at 300 K. To compare the experimental polycrystalline observations shown in Figure 7, we considered the average

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CONCLUSION A new quaternary sulfosalt, SnPb2Bi2S6, was synthesized and crystallized in the orthorhombic system with Pnma space group. In the SnPb2Bi2S6 structure, mirror planes extend perpendicular to the a-axis and consist of Pb2S7 monocapped trigonal prisms with NaCl-type slabs distributed on both sides. The SnPb2Bi2S6 structure can be classified into the lillianite homologous series and is denoted as 4,4L. SnPb2Bi2S6 exhibited an outstanding low thermal conductivity of 0.69−0.92 W m−1 K−1 at 300−773 K with the highest ZT of 0.3 at 773 K. The low lattice thermal conductivity was shown to originate from the low Debye temperature, slow phonon velocities, and large Grüneisen parameters. The new phase reported here can serve as a template for further investigations of systems based on the G


Article

Inorganic Chemistry

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numerous lillianite-type structures. Our results indicate that SnPb2Bi2S6 is a promising TE candidate, with improved performance expected upon optimization of the carrier density.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02899. X-ray crystallographic data of SnPb2Bi2S6 in CIF format; atomic coordinates, displacement parameters, anisotropic displacement parameters, and bond distances of SnPb2Bi2S6; EDS spectrum of SnPb2Bi2S6; PXRD pattern of DSC product; infrared and ultraviolet−visible spectra; electronic thermal conductivities and Lorenz number derived from fitting the respective Seebeck values (PDF) Accession Codes

CCDC 1865371 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (J.Z.). *E-mail: [email protected] (L.-D.Z.). ORCID

Jingpeng Li: 0000-0002-6506-7682 Chris Wolverton: 0000-0003-2248-474X Jing Zhao: 0000-0002-8000-5973 Li-Dong Zhao: 0000-0003-1247-4345 Author Contributions #

J.L. and Y.Z. contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by Beijing Natural Science Foundation (2182080) and the National Natural Science Foundation of China (51702329 and 51632005). This work was also supported by the Fundamental Research Funds for the Central Universities 06500085 and 06103182. S.H. and C.W. (DFT calculations) acknowledge support from the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award Number DE-SC0014520.

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Thermoelectric Material SnPb2Bi2S6: The 4,4L Member of Lillianite

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