Crystal Structure and Thermoelectric Properties of the 7, 7L Lillianite

Dec 19, 2016 - Therefore, Pb6Bi2Se9 corresponds to a 7,7L member of the lillianite homologous series. Electronic transport measure- ments indicate tha...
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Crystal Structure and Thermoelectric Properties of the Homologue Pb6Bi2Se9

7,7

L Lillianite

Joseph Casamento,†,⊥ Juan S. Lopez,†,⊥ Nicholas A. Moroz,† Alan Olvera,† Honore Djieutedjeu,† Alexander Page,‡ Ctirad Uher,‡ and Pierre F. P. Poudeu*,† †

Laboratory for Emerging Energy and Electronic Materials, Department of Materials Science and Engineering, and ‡Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *

ABSTRACT: Pb6Bi2Se9, the selenium analogue of heyrovsyite, crystallizes in the orthorhombic space group Cmcm (#63) with a = 4.257(1) Å, b = 14.105(3) Å, and c = 32.412(7) Å at 300 K. Its crystal structure consists of two NaCl-type layers, A and B, with equal thickness, N1 = N2 = 7, where N is the number of edge-sharing [Pb/Bi]Se6 octahedra along the central diagonal. In the crystal structure, adjacent layers are arranged along the c-axis such that bridging bicapped trigonal prisms, PbSe8, are located on a pseudomirror plane parallel to (001). Therefore, Pb6Bi2Se9 corresponds to a 7,7L member of the lillianite homologous series. Electronic transport measurements indicate that the compound is a heavily doped narrow band gap n-type semiconductor, with electrical conductivity and thermopower values of 350 S/cm and −53 μV/K at 300 K. Interestingly, the compound exhibits a moderately low thermal conductivity, ∼1.1 W/mK, in the whole temperature range, owing to its complex crystal structure, which enables strong phonon scattering at the twin boundaries between adjacent NaCl-type layers A and B. The dimensionless figure of merit, ZT, increases with temperature to 0.25 at 673 K.

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INTRODUCTION Homologous structures have attracted considerable interest as a fertile playground for the search for promising thermoelectric materials.1−5 Their structural and compositional flexibility offers the possibility of engineering the electronic band structure as well as the phonon vibration modes of various members of the homologous series in order to achieve compounds with high thermoelectric performance, i.e., high electrical conductivity (σ) and Seebeck coefficient (S) and ultralow thermal conductivity (κ). The performance of a thermoelectric material is described by the dimensionless figure of merit, ZT = (S2σ)T/κ, where T is the temperature in Kelvin.6 It is necessary to tune the electronic and thermal properties to maximize ZT.7−11 This is a rather difficult task to achieve in a single-phase semiconductor due to the interdependence between various parameters (electrical conductivity, thermopower, and thermal conductivity) that enter in the calculation of ZT. Therefore, thermoelectric materials research over the past decade largely focused on the development of concepts and strategies, such as solid solutions, nanostructuring,12−18 and band alignments,13,18 that resulted in large enhancements of the figure of merit of simple binary compounds such as Bi2Te3, PbTe, half-Heuslers, Cu2Se, CoSb3, and SnTe.19−24 The enhancements in the figure of merit of these engineered materials arose either from a drastic reduction in the thermal conductivity due to nanostructuring with minimal disruption of the power factor (PF = S2σ) or from an enhancement of the PF © XXXX American Chemical Society

without increase in the total thermal conductivity. The concept of phase homology is gaining considerable attraction as an elegant alternative way to successfully engineer both the thermal and electrical properties of various members within a given homologous series. Several naturally occurring and synthetic mixed-metal chalcogenide homologous series have been reported. These include Am[M1+lSe2+l]2m[M2l+nSe2 + 3l+n] (A = K, Rb, Cs and M = Sn, Pb); 2 5 , 2 6 [BiQX]2[AgxBi1−xQ2−2xX2x−1]N+1 (Q = S, Se; X = Cl, Br; 1/2 ≤ x ≤ 1);4,5 the pavonite, MN+1Bi2SN+5 (M = Ag/Bi or Cu/Bi; N ≥ 2);27 the lillianite, PbN−1−2xBi2+xAgxSN+2;28 PbN−1Bi2SeN+2;29 and homologous series. Among these homologous families of complex mixed-metal chalcogenides, compositions belonging to the pseudobinary PbSe−Bi2Se3 phase diagram, such as ternary compounds consisting of varying ratios of (PbSe)m(Bi2Se3)n layers,30−34 and PbN−1Bi2SeN+2,29 have been attracting considerable attention for thermoelectric application due to their moderately lower electrical resistivity compared to their sulfide analogues. For example, an in-plane electrical conductivity of ∼157 S/cm and an out-of plane value of ∼41 S/cm were reported for Pb5Bi6Se14.35 The out-of-plane electrical conductivity value is comparable to the electrical conductivity value of 57 S/cm measured for Pb7Bi4Se13, the (4,5)L member of the lillianite PbN−1Bi2SeN+2 homologous series, which was recently Received: September 1, 2016

A

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry studied as a potential thermoelectric material.29 Lillianite homologues are characterized by the thickness (N1 and N2) of the two layered NaCl-type building units parallel to (001) that alternate along the c-axis in their crystal structure. Various lillianite homologous structures are therefore denoted (N1,N2)L, where N1 and N2 are the number of edge-sharing octahedra along the central diagonal of adjacent NaCl-type layers.28,36 Examples of naturally occurring lillianite homologues are mineral sulfides such as lillianite, Pb3Bi2S6 (4,4L),37 heyrovskyite, Pb6Bi2S9 (7,7L),38 galenobismutite, PbBi2S4 (2,2L),38,39 and Cosalite Pb2Bi2S5 (2,3L).40 Some known selenide members that were chemically synthesized and structurally characterized include Pb2Bi2Se5 (3,3L N = 3),41 PbBi2Se4 (2,2L),42 and Pb3Bi4Se9 = Pb1.5Bi2Se4.5 (4,4L N = 2.5).42 Although a model structure was previously proposed for α-Pb6Bi2Se9,43 no careful crystal structure analysis has been reported to the best of our knowledge. Therefore, this work focuses on the synthesis, crystal structure determination using X-ray data on a single crystal, and the thermoelectric behavior of a polycrystalline single-phase powder of Pb6Bi2Se9, a new member of the lillianite PbN‑1Bi2SeN+2 homologous series with N1 = N2 = 7. Single-crystal X-ray structure data revealed that the compound adopts the (7,7)L lillianite homologous structure. Differential scanning calorimetry (DSC) of polycrystalline single-phase powders of Pb6Bi2Se9 indicates that the compound melts congruently and crystallizes at 990 °C. Thermal and electronic property measurements show that Pb6Bi2Se9 is a narrow band gap degenerate n-type semiconductor with low thermal conductivity (∼1.1 W/m K) and a moderate figure of merit, ZT ≈ 0.25 at 650 K.

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ground powder. DSC data were recorded on a F401 DSC apparatus (NETZSCH) using approximately 25 mg of the synthesized material and an equivalent mass of quartz as the reference. The sample and reference were simultaneously heated to 1373 K at a rate of 10 K min−1, isothermed for 2 min, and then cooled to 373 K at a rate of 10 K min−1. This process was repeated for a second cycle. The onset temperatures of the endothermic and exothermic event on the DSC curves are reported as the melting or crystallization points. Crystal Structure Determination. A single crystal of Pb6Bi2Se9 (0.01 × 0.03 × 0.08 mm) was mounted on the tip of a glass fiber using epoxy glue, and the intensity data were recorded at 300 K on a STOE IPDS-2T diffractometer using graphite-monochromated Mo Kα radiation (λ = 0.710 73 Å). The intensity data were best indexed in the orthorhombic crystal system with unit cell parameters a = 4.2567(9) Å, b = 14.105(3) Å, c = 32.412 (7) Å and four formula units per unit cell (Z = 4). The structure solution was obtained by direct methods in the space group Cmcm (#63) and refined by full-matrix least-squares techniques using the SHELTXL package.45 The asymmetric unit cell contains five crystallographically independent metal positions (Pb1 to Pb5) and five Se atom positions (Se1−Se5). The refinement of this model yielded R1 = 11% with reasonable atomic displacement parameters for all metal atoms. However, the composition of the crystal, Pb8Se9, showed an excess of two negative charges, indicating that one of the Pb positions is occupied by a Bi atom. Since Pb and Bi cannot be distinguished by X-ray, we performed bond valence sum (BVS)46 calculations assuming full occupation of each metal site by either Bi or Pb in order to determine which of the five Pb positions is occupied by a Bi atom. The results of the BVS calculations (Table 1) indicate that the Bi atom is located at Pb3 (8f)

Table 1. Bond Valence Sum (BVS) Calculations for Pb6Bi2Se9 at 300 K

EXPERIMENTAL SECTION

Synthesis and Processing. A polycrystalline powder of Pb6Bi2Se9 was synthesized from a solid-state reaction of high-purity elemental powders (Pb (Alfa Aesar 99.5%), Bi (Aldrich, 99.999%), and Se (CERAC, 99.999%)) in the desired ratio. A mixture of the starting reagents was loaded into fused quartz tubes (diameter = 7 mm, length = 20 cm) under an argon atmosphere, and the tubes were flame sealed under a residual pressure of 10−3 Torr. The sealed tubes were loaded into a furnace, heated to 773 K over 12 h, and held at that temperature for 120 h to allow for complete reaction of constituent elements and to improve the crystallinity of the product. The furnace was finally cooled to room temperature over 24 h. Several needle-shaped, black, single crystals suitable for X-ray structure determination were selected from the resulting polycrystalline samples. For charge-transport measurements, approximately 6 g of high-purity polycrystalline powder of the synthesized Pb6Bi2Se9 phase was consolidated into high-density pellets. Disk-shape pellets (approximate thickness of 3 mm and diameter of 9 mm) were fabricated by pressing the powder samples at 723 K under an applied pressure of 100 MPa using a uniaxial hot press system. The relative density of the pressed pellets was above 98%. Additional details on the densification procedures are described elsewhere.14,15,44 The pellets were polished to a mirror-finish, and rectangular bar specimens used for simultaneous measurement of the electrical conductivity and thermopower at high temperatures were cut from the disk using a precision wire saw (South Bay Technology). Characterization. X-ray Diffraction (XRD). To assess phase purity of the synthesized polycrystalline powder samples of Pb6Bi2Se9, experimental X-ray diffraction patterns were compared to the theoretical pattern simulated using single-crystal structure data. XRD data of finely ground powder samples were recorded on a rotating anode powder diffractometer operating under 40 kV and 100 mA using monochromated Cu Kα radiation (λ = 1.5418 Å). Differential Scanning Calorimetry. To further confirm the phase purity of the synthesized Pb6Bi2Se9 compound and also to determine its melting temperature, DSC measurement was performed on a finely

atomic position

BVS

atom type

oxidation state

Pb1 Pb2 Bi3 Pb4 Pb5

2.25 2.14 3.01 2.30 1.90

Pb Pb Bi Pb Pb

2+ 2+ 3+ 2+ 2+

position and Pb atoms occupy the remaining metal positions (Pb1(4b), Pb2(8f), Pb4(8f), and Pb5(4c)). The final refinement of this model while including a secondary extinction correction and anisotropic displacement parameters for all atoms resulted in a final R1 ≈ 4%. The final charge-balanced composition of the crystal obtained from the refinement was (Pb2+)6(Bi3+)2(Se2−)9. A summary of crystallographic data is given in Table 2. The atomic coordinates and isotropic displacement parameters of all atoms are given in Table 3. Selected interatomic distances are gathered in Table 4. The graphical software Diamond47 was utilized to create the graphic representation of the crystal structure with ellipsoid representations (98% probability level) for all atoms. Detailed crystallographic data can be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax +49-7247-808-666; e-mail crysdata@fiz.karlsruhe.de), on quoting the depository number CSD431859. Transport Property Measurement. The Seebeck coefficient and electrical resistivity were measured simultaneously from room temperature to 673 K under a low-pressure helium atmosphere using a commercial ZEM-3 system from ULVAC-RIKO. The instrument precision on the electrical resistivity and Seebeck coefficient data is ±4%. The thermal conductivity was calculated from the thermal diffusivity data measured by the laser flash method (LINSEIS; LFA 1000) from 300 to 673 K under dynamic vacuum (∼10−3 Torr). The instrument precision on the thermal diffusivity data is ±6%. Pyroceram 9606 was measured alongside the samples as a reference. The specific heat capacity (Cp) used for thermal conductivity calculations (κ = DCpd, where d is the geometrical density of the pellet) was obtained from the laser flash data. Hall Effect B

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 2. Selected Crystallographic Data for Pb6Bi2Se9 at 300 K orthorhombic, Cmcm (#63) 2371.74 8.10

cryst syst, space group fw (g/mol) calc. density (g/cm3) lattice parameters (Å) a b c V (Å3); Z radiation (Å) μ (cm−1) 2θ range index range

bond type

Table 3. Wyckoff Positions (W.P.), Atomic Coordinates, and Equivalent Isotropic Thermal Displacement Parameters (Ueq/10−4 × Å2) for All Atoms in the Asymmetric Unit of Pb6Bi2Se9 at 300 K W.P.

x

y

z

Ueqa

Pb1 Pb2 Bi3 Pb4 Pb5 Se6 Se7 Se8 Se9 Se10

4b 8f 8f 8f 4c 8f 8f 4c 8f 8f

0 1/2 1/2 0 0 1/2 0 0 1/2 1/2

0.5 0.2703(2) 0.4552(2) 0.6787(2) 0.4149(2) 0.3626(2) 0.5873(2) 0.7743(3) 0.1752(2) 0.5439(2)

0.5 0.5582(4) 0.3815(3) 0.3262(4) 1/4 + wb 0.4725(2) 0.4148(2) 1/4 0.6454(2) 0.3040(2)

242(4) 286(4) 232(4) 275(4) 421(5) 191(6) 169(6) 260(6) 268(7) 228(7)

bond type

distance [Å]

Pb1Se6, 6 Pb1Se7, 7iii

3.014(2) 3.023(3)

Pb2Se6iv, v Pb2Se7ii, iii Pb2Se6 Pb2Se9

3.005(2) 3.054(2) 3.066(3) 3.130(4)

Pb4Se8 Pb4Se10, 10i Pb4Se9ii, iii Pb4Se7

2.815(3) 2.942(2) 3.102(2) 3.148(3)

Bi3Se10 Bi3Se9iv, v Bi3Se7, 7vi Bi3Se6

2.807(3) 2.945(2) 3.028(2) 3.224(3)

Pb5Se8viii, ix Pb5Se10, 10i Pb5Se9iv Pb5Se10vii, x Pb5----Se9

2.918(4) 3.191(4) 3.415(7) 3.425(4) 3.828(7)

a Operators for generating equivalent atoms: (i) − 1+x, y, z; (ii) 1−x, 1−y, 1−z; (iii) −x, 1−y, 1−z; (iv) 1/2−x, 1/2−y, 1−z; (v) 3/2−x, 1/ 2−y, 1−z; (vi) 1+x, y, z; (vii) x, y, 1/2−z; (viii) − 1/2+x, −1/2+y, z; (ix) 1/2+x, −1/2+y, z; (x) −1+x, y, 1/2−z; (xi) 1/2+x, 1/2+y, z; (xii) 1/2+x, 1/2+y, 1/2−z; (xiii) −1/2+x, 1/2+y, z; (xiv) −1/2+x, 1/2+y, 1/2−z; (xv) −x, 1−y, − 1/2+z; (xvi) 1/2−x, 1/2−y, 1/2+z; (xvii) 1+x, y, 1/2−z.

R1 = ∑∥Fo| − |Fc∥/∑|Fo|. bwR2 = [∑w(Fo2 − Fc2)2/∑w(Fo2)2]1/2.

atom

distance [Å]

i, ii, iii

4.257(2) 14.105(3) 32.412(7) 1946.04(7); 4 λ(Mo Kα) = 0.710 73 865 6° ≤ 2θ ≤ 54° −5 ≤ h ≤ 5 −18 ≤ k ≤ 18 −39 ≤ l ≤ 39 0.05−0.17 +2.44 to −2.86 0.041 0.092 1.210

transmission factors diff elec density (e Å−3) R1 (Fo > 4σ(Fo))a wR2 (all)b GOF a

Table 4. Selected Interatomic Distances (Å) in Pb6Bi2Se9 at 300 Ka

octahedral metal positions with various degrees of distortion (Figure 2). For example, the Pb(1) site located at the center of the layer displays a Jahn−Teller48 distorted octahedral geometry [4+2] with four short equatorial Pb−Se bonds at 3.014(2) Å and two slightly elongated axial Pb−Se bonds at 3.023(3) Å. The metal sites Pb(2), Bi(3), and Pb(4), which are located closer to the layer borders, show more distorted octahedral coordination. For example, the octahedral coordination around Pb(2) has a [2+2+1+1] geometry with Pb−Se bond distances ranging from 3.005(2) to 3.130(4) Å (Table 4). A [1+2+2+1] distorted octahedral geometry with a Bi−Se bond length ranging from 2.807(3) to 3.224(3) Å and Pb−Se bonds ranging from 2.815(3) to 3.148(3) Å was found around Bi(3) and Pb(4) sites (Figure 2). This elongated Bi−Se bond (3.224(3) Å) observed is probably a result of the stereoactivity of the Bi lone pair electrons.26,49 The octahedrally coordinated metal atoms Pb(1), Pb(2), Bi(3), and Pb(4) share edges to form a slab with orientation parallel to the (110) plane cut from the NaCl structure (NaCl110). In the three-dimensional crystal structure of Pb6Bi2Se9, equivalent atomic planes in adjacent NaCl-type layers A and B are stitched together along the c-axis by the Pb(5) atom, which is offset (z = 1/4 + w) from the pseudomirror symmetry parallel to the ab plane. Attempts to refine the structure-constraining Pb(5) atom at the ideal 4c site resulted in a very poor agreement factor with the atomic displacement parameter about 10 times that of other Pb atoms. The current model, which assumes a slight off-centering, w = 0.007(2), gives a better description of the diffraction data, although the atomic displacement parameter of Pb(5) is still about twice that other Pb atoms. This departure from the perfect mmm point group anticipated for orthorhombic lillianite (N1 = N2, space group Cmcm, #63), where an equivalent metal position is located on the mirror plane,28,36 results in a severe distortion of the bicapped trigonal prismatic coordination (CN = 8) around Pb(5) atoms from the typical [2+2+2+2] geometry to a [2+2+1+2] geometry. The second capping Se atom lies at 3.828(7) Å (Table 4), which is too far to be considered as bonding. This coordination geometry of Pb(5) atoms is reminiscent of the monocapped trigonal prismatic

a

Ueq is defined as one-third of the trace of the orthogonalized Uij tensor. bw = 0.007(2). data were measured in the temperature range from 300 to 775 K under a magnetic field of 1 T using a large Oxford air-borne superconducting magnet cryostat that accommodates a small tubular oven and a Hall insert. The instrument uncertainty in Hall coefficient data is ±5%. Accurate information on the temperature dependence of the carrier concentration and the mobility of the charge carriers in Pb6Bi2Se9 was extracted using electrical conductivity and Hall coefficient data.

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RESULTS AND DISCUSSION Crystal Structure. Pb6Bi2Se9 crystallizes in the orthorhombic space group Cmcm (#63) with unit cell parameters a = 4.2567(9) Å, b = 14.105(3) Å, c = 32.412(7) Å, Z = 4 at 300 K and adopts the heyrovskyite (Pb6Bi2S9) structure type.38 Figure 1 shows a representation of the crystal structure of Pb6Bi2Se9 projected along the a-axis. The structure can be divided into two layers, A and B, with equal thickness, N1 = N2 = 7, where N is the number of octahedrally coordinated metal positions running across the central diagonal of an individual layer, parallel to the ab plane, and therefore can be classified as the (7,7) L member of the PbN−1Bi2SeN+2 family of the lillianite homologous series. Within each layer, Pb and Bi atoms occupy C

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Crystal structure of Pb6Bi2Se9 projected along the a-axis highlighting the layered NaCl-type building units A and B of equal thickness (N1 = N2 = 7) alternating along the c-axis.

Figure 2. Coordination polyhedral of Se atoms around various metal atoms in the crystal structure of Pb6Bi2Se9 showing various degrees of distortion.

coordination (CN = 7) generally observed in lillianite structures with different thicknesses of layers A and B (N1 ≠ N2; space group C2/m (#12)).36,50 Therefore, the true symmetry of the Pb6Bi2Se9 crystal structure is at the border between orthorhombic and monoclinic symmetry. The complexity of the crystal structure of Pb6Bi2Se9, which features pseudomirror symmetry and atomic-scale lattice incoherency between adjacent NaCl-type layers, is expected to decrease the thermal conductivity of the material by softening phonon modes. Synthesis and Characterization. In order to probe the electronic and thermal properties, polycrystalline powders of Pb6Bi2Se9 were synthesized through solid-state reaction of the elements (lead, bismuth, and selenium) at 500 °C for five days. Figure 3a shows the X-ray diffraction pattern of the polycrystalline reaction product and the theoretical pattern calculated using single-crystal structure data. The good matching of peak positions between both experimental and theoretical patterns suggests successful synthesis of the Pb6Bi2Se9 phase. However, the mismatch in some peak intensities suggests poor crystallinity or local lattice strain of the as-synthesized material. The single-phase nature of the synthesized Pb6Bi2Se9 polycrystalline powders was confirmed by DSC. As can be observed from Figure 3b, the as-synthesized material melts congruently at 990 °C and recrystallizes at 990

Figure 3. (a) X-ray powder diffraction pattern of the synthesized polycrystalline powder of Pb6Bi2Se9 compared with the theoretical pattern calculated using single-crystal structure data. (b) Differential scanning calorimetry curves of the synthesized Pb6Bi2Se9 powder showing congruent melting and recrystallization at 990 °C upon heating and cooling.

°C upon cooling the melt to room temperature. The reproducibility of the DSC signals in the second heating and cooling cycle suggests an excellent thermal stability of the synthesized materials. The observed melting temperature of Pb6Bi2Se9 is significantly larger than the ∼560 °C melting point observed for Pb7Bi4Se13,50 which represents the (4,5)L member of the PbN−1Bi2SeN+2 homologous series. From a chemical composition viewpoint, the molecular formula of Pb6Bi2Se9 can be written as 6(PbSe)·(Bi2Se3), which denotes an atomic-scale integration of two interesting thermoelectric materials. Therefore, the large difference in the melting temperature of Pb6Bi2Se9 and Pb7Bi4Se13, phases can be attributed to the large PbSe/Bi2Se3 ratio of 6:1 in Pb6Bi2Se9 compared to 7:2 in Pb7Bi4Se13. D

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 4. Temperature dependence of the electronic transport in a hot press pellet of the synthesized Pb6Bi2Se9 showing n-type semiconducting behavior. (a) Seebeck coefficient; (b) electrical conductivity; (c) carrier concentration; (d) carrier mobility.

Charge-Transport Properties. To probe the thermoelectric behavior of the synthesized materials, electrical conductivity, thermopower, and thermal conductivity data were collected in the temperature range from 300 to 675 K using a hot pressed pellet of the synthesized material. The sample shows negative values of the thermopower in the whole measured temperature range, indicating that electrons are the majority charge carriers in Pb6Bi2Se9 (n-type semiconductor) (Figure 4a). This is consistent with the negative thermopower observed for Pb7Bi4Se13.50 At 300 K, the thermopower of Pb6Bi2Se9 is −53 μV K−1 and increases in magnitude with rising temperature to a value of −193 μV K−1 at 673 K (Figure 4a). These values are significantly lower than the thermopower of −160 and −243 μV K−1 measured for Pb7Bi4Se13 at 300 and 600 K, respectively. The nearly linear temperature dependence of the thermopower suggests that Pb6Bi2Se9 is a degenerate ntype semiconductor, where extrinsic carriers dominate electronic transport in the temperature range studied. Within the temperature range from 300 to 650 K, the carrier concentration is nearly constant (Figure 4c). At 300 K, the carrier concentration is 67 × 1019 cm−3 and slightly increases to 72 × 1019 cm−3 at 650 K. The observed nearly temperature independent carrier concentration indicates that this temperature range is below the threshold for thermal excitation of carriers from valence band into higher energy states. This trend is consistent with the temperature dependence of the thermopower measurements (Figure 4a), which follow a linear trend across the temperature range of 300−650 K. Above 650 K, the carrier concentration drastically increases in an exponential fashion. At 673 K, the carrier concentration is 80 × 1019 cm−3 and increases to 152 × 1019cm−3 at 775 K (Figure 4c). This large increase is likely the result of thermal excitation of intrinsic carriers across the band gap. The fitting of the carrier concentration data above 650 K using the Arrhenius equation n ≈ exp(−Eg/2kT) resulted in a band gap Eg = 0.58 eV (inset of Figure 4c), confirming that Pb6Bi2Se9 is a narrow band gap semiconductor.

The electrical conductivity of Pb6Bi2Se9 is 350 S/cm at 300 K and gradually decreases with increasing temperature, reaching a value of 100 S/cm at 675 K (Figure 4b). The observed rapid decay of the electrical conductivity with rising temperature suggests strong acoustic phonon scattering of charge carriers.51 Figure 4d shows the temperature dependence of the carrier mobility. The carrier mobility (μ = σ/ne) was extracted using the carrier density and electrical conductivity data. At 293 K, the carrier mobility is 3.3 cm2 V−1 s−1 and decreases monotonically with increasing temperature to 0.25 cm2 V−1 s−1. This is consistent with the increase in phonon−electron scattering with increasing temperature. The temperature dependence of the carrier mobility (Figure 4d) follows the power law T−1.66, which suggests acoustic phonon interactions as the dominant carriers scattering mechanism in this compound. Impurity-carrier scattering is considered to be negligible compared to phonon-carrier scattering in this temperature regime. The drop in the electrical conductivity can also be attributed to carrier scattering at the incoherent interfaces between the NaCl-type layers and local strain from distorted bond lengths. This metallic-like behavior of the electrical conductivity indicates that Pb6Bi2Se9 is a heavily doped n-type degenerate semiconductor. Figure 5a shows the temperature dependence of the thermal conductivity of Pb6Bi2Se9. At 300 K the total thermal conductivity of Pb6Bi2Se9 is 1.12 W/m K and remains relatively constant upon increasing the temperature to 673 K. The lattice contribution to the total thermal conductivity was estimated by subtracting the electronic contribution (κel) calculated using the Wiedemann−Franz law, κel = LσT, where L is the Lorenz number. A good approximation of the Lorenz number was calculated from the experimental thermopower using the equation L = 1.5 + exp[−|S|/116] proposed for a single parabolic band model and acoustic phonon scattering assumption.52 As shown in Figure 5a, the lattice contribution to the thermal conductivity (κph) ranged from 0.89 W/mK at 300 K to 0.96 W/mK at 673 K, whereas the electronic E

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

density of A/B interfaces, which implies a longer phonon mean free path in Pb6Bi2Se9. Figure 5b shows the temperature dependence of the figure of merit, ZT, of Pb6Bi2Se9. At 300 K, the ZT value is 0.03 and rapidly increases with temperature to a maximum of 0.25 at 650 K. The observed sharp increase in the ZT values with temperature results from the strong temperature dependence of thermopower. Given the large lattice thermal conductivity of Pb6Bi2Se9 at high temperature, we anticipate further improvements in the ZT values of Pb6Bi2Se9 through additional reduction of the thermal conductivity by applying the concepts of solid solution alloying and nanostructuring.

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CONCLUSION In summary, the crystal structure of Pb6Bi2Se9, the (7,7L) member of the lillianite homologous series PbN−1Bi2SeN+2 (N = 7), was elucidated using single-crystal X-ray diffraction data, and its thermoelectric behavior was investigated using hot pressed pellets of polycrystalline powders synthesized via solidstate reaction of the elements. It was found that the assynthesized material is a heavily doped n-type semiconductor with a moderate electrical conductivity (110 S cm−1) and a large thermopower value (−200 μV/K) at 673 K. However, the compound exhibits a slightly large thermal conductivity (1.12 W/m K) at high temperature, which results in a marginal ZT value of 0.25 at 650 K. The large thermal conductivity of Pb6Bi2Se9 when compared to the Pb7Bi4Se13 (N1 = 5, N2 = 4)50 homologue is attributed to the combination of a higher degree of coherency between the layers (A and B) and the lower linear density of A/B interfaces (along the c-axis), which results in weaker phonon scattering in Pb6Bi2Se9 compared to Pb7Bi4Se13. However, the large lattice contribution to the total thermal conductivity of Pb6Bi2Se9 suggests that significant reduction in the total thermal conductivity can be achieved through nanostructuring and/or solid-solution alloys. This should result in further improvement of the thermoelectric figure of merit of Pb6Bi2Se9.

Figure 5. Temperature dependence of the (a) thermal conductivity and (b) figure of merit, ZT, of a Pb6Bi2Se9 hot press pellet.

contribution to the thermal conductivity (κel) decreases from 0.24 W/m K at 300 K to 0.16 W/m K at 673 K. This indicates that the lattice contribution dominates thermal transport in Pb6Bi2Se9. Therefore, the total thermal conductivity in Pb6Bi2Se9 could be significantly reduced through nanostructuring and/or solid solution alloying, which should improve the thermoelectric performance. The observed total thermal conductivity of Pb6Bi2Se9 (1.12 W/m K at 300 K) is approximately 4 times the thermal conductivity of Pb7Bi4Se13.50 This large difference in the total thermal conductivity of Pb6Bi2Se9 and Pb7Bi4Se13 can be partly attributed to the difference in their electrical conductivity. However, since the lattice thermal conductivity dominates thermal transport in both compounds, we believe that the large difference in the total thermal conductivity mainly originates from the difference in the atomic structure. While the structure of both compounds contains two alternating NaCl-type layers (A and B), the thickness of the layers and their relative orientation in the crystal structure are sharply different. In the structure of Pb7Bi4Se13, the NaCl-type layers (A and B) are of different thicknesses (N1 = 5, N2 = 4) and are weakly stitched together by isolated chains of face-sharing monocapped trigonal prism around Pb atoms. The difference in the thickness of adjacent layers A and B results in a severe misalignment of atomic lattice planes at their interfaces, which significantly reduces the propagation of thermal phonons along the c-axis. However, the NaCl-type layers A and B in the structure of Pb6Bi2Se9 are of equal size (N1 = N2 = 7) and are thicker than the layers found in the structure of Pb7Bi4Se13 (N1 = 5, N2 = 4).50 This results in a more symmetrical arrangement of layers A and B with a pseudomirror plane at their interfaces. In addition, the linear density (along the c-axis) of interfaces (A/ B) between adjacent layers is significantly lower in Pb6Bi2Se9 compared to Pb7Bi4Se13 given the thicker A and B layers. Therefore, a weaker phonon scattering in Pb6Bi2Se9 compared to Pb7Bi4Se13 can be anticipated due to the combination of a higher degree of coherency between the layers and lower linear

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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.6b02118. Crystallographic information file for the structure refinement of Pb6Bi2Se9 (CIF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail (P. F. P. Poudeu): [email protected]. ORCID

Pierre F. P. Poudeu: 0000-0002-2422-9550 Author Contributions ⊥

J. Casamento and J. Lopez contributed to this work equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Science Foundation under awards nos. DMR-1237550 and DMR-1561008. C.U. and P.F.P.P. gratefully acknowledge financial support for electrical conductivity, Hall Effect, and thermopower measureF

DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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ments from the Department of Energy, Office of Basic Energy Sciences, under Award No. DE-SC-0008574.

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DOI: 10.1021/acs.inorgchem.6b02118 Inorg. Chem. XXXX, XXX, XXX−XXX