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

Cornucopia of Structures in the Pseudobinary System (SnSe)xBi2Se3: A Crystal-Chemical Copycat Frank Heinke,† Philipp Urban,† Anton Werwein,† Christina Fraunhofer,†,‡ Tobias Rosenthal,‡ Stefan Schwarzmüller,† Daniel Souchay,† Felix Fahrnbauer,† Vadim Dyadkin,§ Gerald Wagner,† and Oliver Oeckler*,† †

Faculty of Chemistry and Mineralogy, IMKM, Leipzig University, Scharnhorststraße 20, 04275 Leipzig, Germany Department of Chemistry, LMU Munich, Butenandtstraße 5-13 (D), 81377 Munich, Germany § European Synchrotron Radiation Facility, 71 avenue des Martyrs, CS 40220, 38043 Grenoble, France ‡

S Supporting Information *

ABSTRACT: Pseudobinary phases (SnSe)xBi2Se3 exhibit a very diverse structural chemistry characterized by different building blocks, all of which are cutouts of the NaCl type. For SnSe contents between x = 5 and x = 0.5, several new phases were discovered. Next to, for example, Sn4Bi2Se7 (x = 4) in the NaCl structure type and SnBi4Se7 (x = 0.5) in the layered defect GeSb2Te4 structure type, there are at least four compounds (0.8 ≤ x ≤ 3) with lillianite-like structures built up from distorted NaCltype slabs (L4,4-type Sn2.22Bi2.52Se6, L4,5-type Sn9.52Bi10.96Se26, L4,7-type Sn11.49Bi12.39Se30, and L7,7-type Sn3.6Bi3.6Se9). For two of them (L4,7 and L7,7), the cation distributions were determined by resonant X-ray scattering, which also confirmed the presence of significant amounts of cation vacancies. Thermoelectric figures of merit ZT range from 0.04 for Sn4Bi2Se7 to 0.2 for layered SnBi4Se7; this is similar to that of the related compounds SnBi2Te4 or PbBi2Te4. Compounds of the lillianite series exhibit rather low thermal conductivities (∼0.75 W/mK for maximal ZT). More than other “sulfosalts”, compounds in the pseudobinary system SnSe-Bi2Se3 adapt to changes in the cation−anion ratio by copying structure types of compounds containing lighter or heavier homologues of Sn, Bi, or Se and can incorporate significant amounts of vacancies. Thus, (SnSe)xBi2Se3 is a multipurpose model system with vast possibilities for substitutional and structural modification aiming at the optimization of thermoelectric or other properties. Seebeck coefficient, κ: thermal conductivity, T: temperature), which determines their efficiency for energy conversion. Bi2Te3, which exhibits a ZT value of up to 0.9 at about 150 °C,11 consists of distorted NaCl-type slabs interconnected via van der Waals gaps.12 Its properties can be tuned by substitution on the anion position with S or Se13,14 as well as on the cation position, e.g., with Sb.15 The introduction of additional Bi2 layers into the van der Waals gaps, similar to those in elemental Bi, as well as the alteration of the slab sizes by introducing PbTe (leading to, e.g., PbBi2Te4 or related compounds) represents other ways of influencing the thermoelectric performance.16,17 SnBi2Te4, which crystallizes in a derivative of the tetradymite (Bi2Te2S) structure type, as well as Bi2Te3 itself is also being investigated as potential topological insulators.18,19 Such properties are observed for Bi2Se3 and Sb2Te3, too.20

1. INTRODUCTION Multinary chalcogenides are an intriguing research topic due to their multifaceted structural chemistry. They exhibit structure types with various building blocks extended in one, two, or three dimensions.1 A broad range of solid solutions may lead to high-performance semiconductors.2,3 The spectrum of possible applications ranges from sulfides and selenides for solar cells to tellurium- and selenium-containing materials for thermoelectric devices.4,5 Derivatives of kesterite Cu 2 (Zn,Fe)SnS 4 or stannite Cu2FeSnS4, for example, are excellent materials for solar cells due to their favorable band gaps of 1.1−1.8 eV, which are tunable by substitution in solid solution series.6−8 On the other hand, tellurides such as Bi2Te3 or Sb2Te3 benefit from much smaller band gaps of 0.17 and 0.23 eV, respectively.9,10 Bi2Te3 is the most commonly used material for thermoelectric generators at relatively low temperatures, in addition to PbTe for application at elevated temperatures. The performance of thermoelectric devices is characterized by a dimensionless figure of merit ZT = (σS2T)/κ (σ: electrical conductivity, S: © XXXX American Chemical Society

Received: January 11, 2018

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DOI: 10.1021/acs.inorgchem.8b00105 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

contains related lillianite-like phases with different slab sizes as these phase can easily adapt to different anion−cation ratios.21 Due to the high degree of disorder on the cation sites, the cation distribution in these materials is difficult to elucidate, and various crystal structure refinements show rather large residual electron densities.30,31 Some lillianite-like compounds in related systems are promising thermoelectric materials as shown for Pb7Bi4Se13 (L4,5 type) with a ZT value of 0.8 at elevated temperatures, resulting from its very low thermal conductivity (0.3 W/mK) and large power factor σS2.43 Thus, phases derived from lillianite, in general, may be promising materials for thermoelectric applications. Therefore, we aim at the evaluation of the transport properties of ternary tin bismuth selenides and their correlation with the crystal structures and real-structure effects. Not much is known about vacancies in different structure types of tin bismuth selenides and the interplay of defects and physical properties. High resolution transmission electron microscopy (HRTEM) can image, e.g., stacking disorder but gathers only information from small parts of the sample. Single crystal X-ray diffraction patterns, on the other hand, provide information on real structure phenomena over a scale of several microns. Spatial resolution may be provided by microfocused synchrotron radiation, which is also ideal to analyze very small crystallites (down to 2 was obtained by doping with small amounts of Bi; scanning tunneling microscopy revealed cation vacancies in this.24 Multinary tin bismuth selenides, on the other hand, may consist of modified strand-like elements from SnSe and/or of distorted NaCl-type slabs,25 as shown in our recent study on Sn4.11Bi22.60Se38 (x = 0.36).26 In addition to this phase, only a few crystal structures of pseudobinary compounds (SnSe)xBi2Se3 have been reported: a cubic high-temperature (HT) phase (SnSe)4Bi2Se3 with a NaCl-type structure,27 a layered phase (SnSe)0.5Bi2Se3 derived from the tetradymite structure type,28 and two phases derived from the lillianite (Pb3Bi2S6) structure type,29 namely, (SnSe)3Bi2Se3 and (SnSe)6Bi2Se3.30,31 Further complex tin bismuth selenides with additional In or Mn have been reported.32,33 In the NaCl-type HT phase (SnSe)4Bi2Se3, Sn and Bi share the cation position with additional vacancies.27 This is comparable with the related system Ge/Sb/Te (GST materials), where quenched cubic HT phases tend to exhibit pronounced real-structure effects. Quenched (GeTe)12Sb2Te3, for example, exhibit a herringbone-like arrangement of vacancies that are partially ordered in finite layers perpendicular to all pseudocubic directions. The resulting domain structure exhibits low thermal conductivity and a high ZT value of ca. 0.6 at 300 °C compared to ca. 0.1 for the low-temperature layered phase.34 The layered compound (SnSe)0.5Bi2Se3 = SnBi4Se7 was reported to crystallize in the GeSb2Te4 structure type35 with NaCl-type-like slabs separated by van der Waals gaps.28 The cation positions were assumed to contain vacancies to match the composition while remaining in the GeSb2Te4 structure type. Isostructural phases such as PbBi2Te4 or PbBi4Te7 are known as promising thermoelectric materials with maximum ZT values of 0.5 and 0.4, respectively.36,37 However, layered phases are often characterized by stacking disorder which is easily detected by diffuse streaks in diffraction patterns.16,38,39 Such real structure effects often alter the physical properties, especially the thermal conductivity.40 The lillianite derivatives with the idealized formulas Sn3Bi2Se6 and Sn6Bi2Se9 are characterized by tilted, distorted NaCl-type slabs interconnected by trigonal-prismatically coordinated cations.30,31 The corresponding structure refinements indicate possible nonstoichiometry, which has not been investigated so far. According to Makovicky, these phases can be characterized by the maximal number of octahedra sharing edges along one direction in pairs of neighboring slabs.41 Adopting this nomenclature, the structure of lillianite Pb3Bi2S6 itself would be described as an L4,4 type. In the system Sn/Bi/ Se, only the L4,4 type of Sn3Bi2Se6 and the L7,7 type of Sn6Bi2Se9 have been reported; however, with respect to sulfosalt minerals containing other elements, more variations of the slab sizes are expected.42 There is a large phase field (“phase X”) in the pseudobinary (SnSe)x(Bi2Se3) phase diagram with x ranging from ∼0.8 to ∼3, which most likely

2. EXPERIMENTAL SECTION 2.1. Synthesis. All samples were synthesized from stoichiometric mixtures of the elements Sn (99.999%, Koch chemicals or AlutervFKI), Bi (99.999%, Aldrich or Alfa Aesar), and Se (ChemPur, 99.999%). In typical reactions, mixtures with total weights of 250−300 mg were fused in sealed silica glass ampules (length ∼5 cm, diameter 10 mm) under dry Ar atmosphere. Some samples were annealed after previous melting at 900−950 °C. Samples for thermoelectric characterization were synthesized under the same conditions; however, mixtures with a total weight of 2−3 g were fused and annealed in flatbottom ampules in order to meet the samples sizes necessary for the B


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Inorganic Chemistry physical characterization. Detailed information on the synthesis parameters and later utilization of the samples are given in Table S1 in the Supporting Information. In addition, single crystals of (SnSe)4Bi2Se3 and (SnSe)0.5Bi2Se3 were obtained by chemical vapor transport. Typically, ca. 150 mg of fused and air-quenched material was crushed and sealed in a silica glass ampule (length ∼20 cm, diameter 15 mm) under a vacuum with ∼3 wt % iodine (Alfa Aesar, sublimed, 99.8%) as a transport agent. In a two-zone furnace, crystals of cubic (SnSe)4Bi2Se3 were grown in a temperature gradient from 640 to 585 °C in 19 h and crystals of (SnSe)0.5Bi2Se3 from 547 to 445 °C in 94 h. 2.2. X-ray Methods. Crystals were isolated under an optical microscope; those obtained by chemical vapor transport were washed with acetone in order to remove traces of the transport agent. Subsequently, they were mounted on glass fibers. Laboratory singlecrystal data were collected on an IPDS-I diffracttometer (Stoe & Cie. GmbH, Germany) equipped with an image plate detector using Ag-Kα radiation (0.56085 Å, graphite monochromator). Numerical absorption correction was performed with X-RED46 after optimizing measured crystal faces with X-SHAPE.47 Data sets at the low-energy sides of the Sn-K edge (λ = 0.4256 Å, E = 29.203 keV) and the Bi-K edge (λ = 0.13701 Å, E = 90.456 keV), as well as off-edge (λ = 0.1518 Å, E = 81.659 keV) were collected at beamline ID11 (ESRF, Grenoble) using a Huber heavy-duty diffractometer and a FReLON4K fast CCD detector (dynamical range 216).48 At the Sn−K edge, an additional measurement with detector offset ensured sufficient highresolution data. Data were indexed and integrated with CrysAlis; semiempirical absorption was carried out with CrysAlis (Bi−K edge and off-edge) or SADABS (Sn−K edge) when it was necessary to combine data with different detector settings.49 The structures were solved with direct methods; in the case of L4,4- and L7,7 type structures (Sn2.22Bi2.52Se6 and Sn3.6Bi3.6Se9), starting models from the literature were used. Structure refinements were performed with SHELX-2014 and JANA2006.50,51 For the refinements based on resonant X-ray scattering data sets, dispersion correction terms Δf ′ and Δf ″ were taken as implemented in JANA.52 Refinements with f ′ and Δf″ terms from the NIST database53 did not result in significantly different values. A recent study of Sn4.11Bi22.60Se38 showed that these values are close to experimental ones for related compounds and enable reliable structure refinement regarding the cation and vacancy distribution in complex tin bismuth selenides.26 Further details of the structure determinations are available from Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (Germany), on quoting the depository numbers (CSD) given in the corresponding tables below as well as the names of the authors and citation of the paper (email: crysdata@fiz-karlsruhe.de) A program based on the work of I. D. Brown was used for bond valence sum (BVS) calculations54 in order to compare the refined site occupancies with those derived from BVS values according to ref 55. The following BVS parameters were used: R0 = 2.7 and b = 0.35 for Bi3+ bonded to Se2− and R0 = 2.59 and b = 0.37 for Sn bonded to Se2−. R0 for the Sn−Se pair is not assigned to a specific oxidation state because the ionic radius of Sn2+ cannot be determined reliably.56 Powder X-ray diffraction (PXRD) patterns were measured on a G670 Guinier camera with an image plate detector (Huber, Germany) using Cu-Kα1 radiation (1.54051 Å, Ge(111) monochromator). Samples were crushed, dispersed in ethanol, and fixed on Mylar foil with hair-fixing spray. Rietveld refinements were performed with TOPAS.57 Reflection profiles were described using a direct convolution approach with fundamental parameters and an emission profile described with a Lorentzian function. The background of each diffraction pattern was fitted by a set of individual parameters (shifted Chebychev function). Structure models for known phases were taken from the PCD or ICSD databases as well as own single crystal structure determinations.58,59 Lattice parameters from PXRD data obtained by Rietveld refinement are given with the original standard deviations, although empirical knowledge shows that the accuracy of lattice parameters is usually limited to ca. 0.01%. 2.3. Electron Microscopy. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) were performed on a LEO 1530 Gemini (Zeiss, Germany; acceleration voltage 20 kV)

equipped with an energy-dispersive X-ray (EDX) detector (Oxford Instruments, United Kingdom). EDX spectra were evaluated with the INCA software.60 Transmission electron microscopy (TEM) of (SnSe)4Bi2Se3 was performed on a Titan 80-300 (FEI, USA) with a field emission source (300 kV acceleration voltage) and an Ultra Scan 1000 CCD detector (Gatan, USA). TEM measurements of (SnSe)0.5Bi2Se3 (GeSb2Te4 type35) and (SnSe)2Bi2Se3 (lillianite type29) were performed on a CM200 (Philips, Netherlands, LaB6 source, supertwin lens, 200 kV acceleration voltage) equipped with an R-TEM 13-5 EDX detector (EDAX). Scanning transmission electron microscopy (STEM) and EDX were evaluated with the program Genesis.61 Evaluation of selected-area electron diffraction (SAED) patterns was done using the analySIS software and the jEMS program suite.62,63 2.4. Thermoelectric Characterization. Thermal diffusivity measurements were performed under He atmosphere using a Linseis LFA1000 apparatus equipped with an InSb detector. Simultaneous heat loss and finite pulse corrections were performed using Dusza’s model.64 Values were averaged from five measurement points at each temperature. For κ calculation, the values were multiplied with the Dulong−Petit heat capacity, which is quite reliable for compounds with heavy elements at elevated temperature (where the relevant ZT values are observed), and the density as derived from the weight and the volume determined by Archimedes’ principle. All densities were higher than 98% of the X-ray densities of the matrix material. The values of each sample are given in Table S2 of the Supporting Information. S and σ were measured simultaneously under He atmosphere with a Linseis LSR-3 instrument with NiCr/Ni thermoelements (also used as contacting electrodes) and Ni electrodes and a continuous reverse of the polarity of the thermocouples (bipolar setup). The samples consisted of randomly oriented grains (according to SEM images); therefore, no effects from anisotropy are expected. The errors of S and σ are smaller than 10%; for κ, they are ca. 5%. As a result, ZT values exhibit an absolute uncertainty of ca. 20%, which is within the typical range.65

3. RESULTS AND DISCUSSION 3.1. Cubic Phases (SnSe) x Bi 2 Se 3 (3 ≤ x ≤ 5). 3.1.1. Powder Diffractometry of Melt-Quenched Samples. The phase diagram reported by Adouby et al. (see Figure S1 in the Supporting Information)21 shows a HT phase within the compositional range (SnSe)xBi2Se3 with 2 ≤ x ≤ 4 and a maximum stability range from 575 to 732 °C for x = 4. This stability range decreases significantly with increasing Bi2Se3 content (∼650 °C to ∼710 °C for x = 3). Quenching Sn4Bi2Se7 (x = 4) to RT yields samples that crystallize in a NaCl-type structure according to PXRD patterns.27 Bi, Sn, andassuming charge neutrality14.3% vacancies are randomly distributed on the one cation site of the average structure. Mößbauer spectra confirmed Sn to be octahedrally coordinated.27 In order to ascertain the existence range of this cubic phase at the tinrich end, samples within nominal compositions corresponding to Sn3Bi2Se6 (x = 3), Sn4Bi2Se7 (x = 4) and Sn5Bi2Se8 (x = 5) were prepared by quenching melts to RT, for Sn5Bi2Se8 even to the temperature of liquid nitrogen. Whereas Sn3Bi2Se6 was obtained as a homogeneous phase, a small amount of SnSe was identified as a side phase (∼3 wt %) in Sn4Bi2Se7. For Sn5Bi2Se8, a multiphase product was obtained in all cases, a NaCl-type-like phase being the main component and a SnSe side phase (Figure S2, Tables S3 and S4; S denotes material in the Supporting Information). This shows that the existence range of the cubic phase cannot be extended to higher SnSe contents than x ≈ 4. Profile fits from the Rietveld refinements on PXRD data of the samples with x = 3 and x = 4 are depicted in Figures 1 and S3, respectively. Corresponding C


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already be formed even if they are not detectable by PXRD. This would result in an increased concentration of Bi and vacancies in the NaCl-type phase, influencing the progression of the lattice parameter with increasing temperature. 3.1.2. Single-Crystal Structure Analysis of Sn4Bi2Se7 (x = 4). Single crystals of Sn4Bi2Se7 (x = 4), i.e., Sn0.57Bi0.29Se, are accessible via the gas phase in the existence range of the cubic HT phase (585 °C). Exsolution of SnSe as observed in quenched bulk sample can be avoided, most likely due to faster cooling of the small crystals compared to ingots. For the refinement, a rock salt-type structure was assumed as derived from the powder diffraction pattern. Crystal data and details of the structure refinement are given in Table 3, and atom positions and displacement parameters are listed in Table 4. Figure 1. Rietveld refinement for a melt-quenched sample with the nominal composition Sn3Bi2Se6 (x = 3; strongest reflection truncated at 50% of the maximum intensity): data points as circles, calculated data as gray line; difference plot as black line below; reflection positions indicated by vertical lines at the bottom.

Table 3. Crystallographic Data and Structure Refinement of Sn4Bi2Se7 = Sn0.57Bi0.29Se

crystallographic data are given in Tables 1, 2, S5 and S6. The treatment of peak broadening as well as further details Table 1. Crystallographic Data and Results of the Rietveld Refinement of Quenched Sn3Bi2Se6 = Sn0.5Bi0.33Se formula

Sn0.5Bi0.33Se

formula mass crystal system space group Z cell parameter cell volume X-ray density radiation 2θ range refined parameters (thereof background) Rp/Rwp RBragg GOF

207.98 g mol−1 cubic Fm3m 4 a = 5.95007(8) Å 210.652(8) Å3 6.5578(3) g cm−3 Cu-Kα1 (λ = 1.54051 Å) 4° < 2θ < 100° 20 (12) 0.0186/0.0253 0.0181 1.159

a

atom

x

y

z

s.o.f.

Biso/Å2

Sn/Bi Se

4b 4a

1/2 0

1/2 0

1/2 0

1/2 / 1/3 1

1.62(3) 1.20(4)

Sn0.57Bi0.29Se CSD-430258 207.22 g mol−1 cubic, Fm3m a = 5.9359(12) Å 209.15(13) Å3 6.581 g cm−3 4 26.050 mm−1 345.2 Ag-Kα (0.56085 Å) 9.39° < 2θ < 48.64° numerical46,47 666 34 (all observed)/3 0.0136/0.0525 0.0332/0.0902/1.391 −2.611 e Å−3/0.847 e Å−3

w = 1/[σ2(Fo2) + (0.0609P)2] with P = [2Fc2 + Max(Fo2,0)]/3.

Table 4. Coordinates, Site Occupancies, and Equivalent Isotropic Displacement Parameters of Sn4Bi2Se7 (Ueq = 1/ 3[U11 + U22 + U33])

Table 2. Coordinates, Site Occupancies and Equivalent Isotropic Displacement Parameters of Sn3Bi2Se6 Wyckoff position

formula ICSD number formula mass crystal system, space group cell parameter cell volume X-ray density Z absorption coefficient F(000) radiation 2θ range absorption correction measured reflections independent data/parameters Rσ/Rint R1/wR2a/GOF Δρmin/Δρmax

atom

Wyckoff position

x

y

z

s.o.f.a

Ueq/Å2

Sn/Bi Se

4b 4a

1/2 0

1/2 0

1/2 0

4/7 / 2/7 1

0.0277(7) 0.0191(7)

a

concerning the corresponding Rietveld refinements are explained in the Supporting Information (footnote of Table S5). Lattice parameters of the quenched cubic phases as a function of x (Figure S4) decrease with increasing Bi2Se3 content due to the increased amount of vacancies which are incorporated in the NaCl-type structure. A high-temperature PXRD study of quenched NaCl-type Sn4Bi2Se7 showed the cubic NaCl-type phase exclusively up to 200 °C and revealed exsolution of SnSe at higher temperatures (cf. Figure S5a,c−f in the Supporting Information). This stability range is close to the one of quenched pseudocubic Ge4Sb2Te7 at 260 °C,66 indicating similar activation energies of diffusion. However, a change in the progression of the cubic lattice parameter a upon heating at 125 °C (cf. Figure S5b) suggests that at this temperature minor amounts of SnSe may

Site occupancies constrained to the composition Sn0.57Bi0.29Se.

The composition of the crystal was verified by EDX analysis. This yielded Sn30(3)Bi14.6(7)Se55(2) (atom %, averaged from 5 point analyses) and is in agreement with the nominal composition Sn4Bi2Se7 = Sn30.8Bi15.4Se53.8. A structure refinement with a constraint for charge neutrality yielded a refined composition of Sn0.41(3)Bi0.39(2)Se with extremely large uncertainties for the site occupancies; therefore, the composition was fixed at Sn0.57Bi0.29Se (= Sn4Bi2Se7) during structure refinement. Minor deviations between the lattice parameters from the Rietveld refinement on PXRD data (a = 5.95581(4) Å) and those of the single crystal data (a = 5.9359(12) Å) are most likely due to slightly different compositions not detectable by SEM-EDX measurements but may in part also be related to the D


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Inorganic Chemistry underestimation of errors on lattice parameters by the Rietveld method (cf. Section 2.2). 3.1.3. Real Structure of Sn4Bi2Se7 (x = 4). According to the phase diagram, cubic phases (SnSe) 3−4 Bi 2 Se 3 are not thermodynamically stable at RT.21 Related pseudocubic compounds in the system (GeTe)nSb2Te3 or substituted variants thereof are known for their real structure phenomena such as defect ordering in planes with limited lateral extension.66−69 Their different orientation leads to nanodomain structures in quenched samples. Structured diffuse scattering was not detected in single crystal diffraction patterns of cubic tin bismuth selenides, most likely due to its low intensity. In order to probe the real structure of Sn4Bi2Se7, a sample quenched from a melt with the nominal composition Sn4Bi2Se7 was investigated by means of TEM (Figure 2). In the SAED

Figure 3. Thermoelectric performance ZT of a sample with the nominal composition Sn4Bi2Se7, solid spheres: averaged heating curves, hollow spheres: averaged cooling curves after decomposition, solid squares: first heating step.

3.2. Lillianite-Type Structures (SnSe)∼1.7−2.0Bi2Se3. 3.2.1. Overview. As outlined in the introduction, the sizes of the distorted NaCl-type slabs are characteristic for structures derived for the lillianite structure (Pb3Bi2Se6, ref 29) and related ones. Compounds with an odd number of edge-sharing coordination octahedra in neighboring slabs crystallize in the monoclinic crystal system whereas compounds with an even number of coordination octahedra in neighboring slabs form orthorhombic structures. In the system (SnSe)x(Bi2Se3), four lillianite-like materials were found and structurally characterized in this study, two monoclinic (L4,5- and L4,7-type) and two orthorhombic ones (L4,4- and L7,7-type). Some structure types are known from minerals: lillianite (Pb3Bi2S6) for the L4,4-type, heyrovskyite (Pb6Bi2S9) for the L7,7-type, and vikingite (Pb8Ag5Bi13S30) for the L4,7-type.41 The L4,5-type is known from KSn5Bi5Se13.70 All structures turned out to contain significant amounts of vacancies distributed over the cation positions, which are in most cases mixed occupied by Sn and Bi. Vacancies tend to concentrate at octahedral sites far from the centers of the slabs; however, general trends concerning the Sn and Bi distribution in the related structures are not evident. 3.2.2. Single Crystal Structure analysis of L7,7-Sn3.6Bi3.6Se9. The initial structure model of a L7,7-type crystal in the system Sn/Bi/Se was obtained from a laboratory data set (Ag-Kα radiation) and was close to the structure proposed for Sn6 Bi2 Se 9.30 However, chemical analysis by SEM-EDX (averaged from 11 points) revealed Sn21.8(3)Bi22.2(5)Se55.9(5) (idealized as Sn3.6Bi3.6Se9) in accordance with the nominal composition Sn2Bi2Se5 of the sample. As this composition hints at cation vacancies, three synchrotron data sets were obtained at the Sn−K edge, the Bi−K edge as well as off-edge. Utilizing anomalous dispersion at the absorption edges, the cation site occupancies with Sn and Bi are accessible in an independent way and thus the amount of cation vacancies. Initial refinements in space group Cmcm revealed significant residual electron density next to cation sites that interconnect the NaCltype slabs. As this might result from assuming too high symmetry, a description as a twinned crystal in space group Cmc21 with a mirror plane perpendicular [001] (corresponding to inversion twinning) did not eliminate the residual electron densities in models with the atom on one side of the previous mirror plane (Figure S7 in the Supporting Information). The introduction of a split position removed the residual densities and yielded a model in Cmc21 (Figure S8) that can equally well

Figure 2. TEM of a crystallite from a sample with the nominal composition Sn4Bi2Se7: SAED pattern (left) of the crystal investigated by HRTEM (right); the inset shows the Fourier transform of the highlighted area (white box).

pattern, the Bragg reflections of a rock salt-type structure are interconnected by diffuse streaks along all cubic directions. That indicates a twinned structure with planar defects, which can be interpreted as stacking disorder in each domain. The HRTEM image clearly shows that finite defect planes occur in different orientations and lead to domains, which form a herringbone structure. Thus, only the average structure corresponds to a disordered NaCl type; locally the structure is layered. Similar phenomena have been observed for compounds (GeTe)nSb2Te3.34 However, only the real structure of quenched materials is accessible via TEM. At elevated temperatures, the defects are most likely not short-range ordered but randomly distributed in the sample. 3.1.4. Thermoelectric Properties of Sn4Bi2Se7 (x = 4). Due to its pronounced real structure, the thermoelectric characterization of Sn4Bi2Se7 (x = 4) is of interest. According to the HTPXRD pattern (cf. Figure S5), the initial heating step corresponds to the quenched cubic phase; ZT peaks at 0.04 at 225 °C (see Figure 3). However, due to the decomposition of the sample upon heating above 200 °C, the following cooling and heating cycles show the thermoelectric performance of a mixture of the cubic phase with lower x and SnSe. Sn4Bi2Se7 profits from its low thermal conductivity of around 0.8 W/mK compared to the phase mixture that is present after the decomposition of the cubic Sn4Bi2Se7; however, this effect is overcompensated by the very low absolute Seebeck coefficient (see Figure S6). The rather low ZT values for Sn4Bi2Se7 are in the same range as those of phases with related structures and compositions such as Ge4Sb2Te7.66 E


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phase X area in the pseudobinary phase diagram SnSe-Bi2Se3.21 In combination with an initial structure refinement using laboratory data (Ag−Kα radiation), the chemical analysis (SEM-EDX averaged from 10 points: Sn20.1(5)Bi22.8(3)Se57.1(5), calculated for the final structure model Sn11.49Bi12.39Se30 [= (SnSe)1.86Bi2Se3]: Sn20.3Bi23.0Se55.7) indicated the presence of cation vacancies as the cation−anion ratio from EDX does not match the ratio given by the multiplicities of the atom sites. For the determination of the cation occupancies, again three diffraction data sets were collected at the Sn−K and Bi−K edges as well as off the edges. The chemical composition was introduced as a constraint in the final refinement, which is justified by the chemical analysis and the phase purity of the sample with the same nominal composition and quantitative yield. A tentative less rigid constraint assuming only charge neutrality resulted in almost the same concentration of cation vacancies, but less precise agreement with the chemical composition. In contrast, refinements assuming fully occupied sites lead to sum formulas strongly deviating from the chemical analysis and from charge balance. As the vast majority of lillianite-like compounds are semiconductors with normal valent cations, which is also corroborated by our own results for the related L4,4-type structure (see below, section 3.2.6), the assumption of Sn and Bi with oxidation states deviating from II and III, respectively, does not seem reasonable. The joint refinement on three data sets revealed significant amounts of cation vacancies: 3−10% on most positions and 25% for Bi4/Sn4. Crystallographic data are listed in Table 6, and coordinates and displacement parameters are given in

be refined in Cmcm. Therefore, because there were no unexplained reflections, the space group Cmcm with a split position was chosen for the final refinement. The chemical composition Sn3.6Bi3.6Se9 (from SEM-EDX and nominal composition) was used as a constraint. This enforces cation vacancies, which were also evident in unconstrained refinements (with large standard deviations). Refinements with fully occupied cation positions yielded significantly higher residuals and large difference electron densities. The sum formula constraint ensures charge neutrality, which is in good agreement with physical data obtained from Sn2.22Bi2.52Se6 (L4,4 type, Figure S9 in the Supporting Information) as well as the reported properties of related lillianite-like compounds.43 The joint refinement on all three data sets revealed significant amounts of vacancies on all cation positions, mostly between 3% and 10% with a maximal vacancy content of 23% on position Sn2/Bi2. Crystallographic data are listed in Table 5; coordinates and displacement parameters are given in Tables S7 and S8 in the Supporting Information. Table 5. Crystallographic Data of the Joint Refinement of Sn3.6Bi3.6Se9 Using Resonant Synchrotron Data at RTa ICSD number sum formula molar mass/g mol−1 crystal system, space group cell parameters/Åa

V/Å3 Z density/g·cm−3 parameters/constraints weighting scheme Δρmin/Δρmax in e/Å3 Bi-K edge wavelength/Å absorption coeff/ mm−1 resolution/Å θmin/θmax reflections collected independent reflections Rσ/Rint R1(obs)/wR(obs) R1(all)/wR(all) goodness of fit (all)

CSD-433581 Sn3.6Bi3.6Se9 1890.3 orthorhombic, Cmcm a = 4.2032(3) b = 13.8990(10) c = 32.056(2) 1872.7(2) 4 6.7046 67/30 w = (σ2(F) + 0.000625F2)−1 −2.27/2.12 off-edge Sn-K edge

0.13701 1.011

0.1518 1.315

0.4256 29.953

0.65 1.470/6.049 11034 1497

0.65 1.457/6.705 8996 1441

0.75 2.011/22.001 5758 997

0.0250/0.0534 0.0366/0.0576 0.0469/0.0633 1.57

0.0224/0.0488 0.0361/0.0567 0.0455/0.0615 1.57

0.0241/0.0371 0.0546/0.0700 0.0553/0.0707 2.14

Table 6. Crystallographic Data of the Joint Refinement of Sn11.49Bi12.39Se30 Using Resonant Synchrotron Data at RT ICSD number sum formula molar mass/g mol−1 crystal system, space group cell parameters/Åa

V/Å3 Z density/g·cm−3 parameters/constraints weighting scheme Δρmin/Δρmax in e/Å3 Bi-K edge wavelength/Å absorption coefficient/mm−1 resolution/Å θmin/θmax reflections collected independent reflections Rσ/Rint R1(obs)/wR(obs) R1(all)/wR(all) goodness of fit (all)

a Unit cell parameters were taken from the Rietveld refinement of PXRD data from a phase-pure sample of Sn3.6Bi3.6Se9 (Figure S10 in the Supporting Information).

A Rietveld refinement (Figure S10 in the Supporting Information) based on the final structure model indicates that the respective sample is single-phase, whichtogether with a sample weight corresponding to the initial weight of the starting mixturejustifies the sum formula constraint. 3.2.3. Single Crystal Structure Analysis of L4,7Sn11.49Bi12.39Se30. Samples with the nominal composition (SnSe)1.86Bi2Se3 = (SnSe)0.65(Bi2Se3)0.35 are single-phase according to PXRD (cf. Rietveld refinement in Figure S11 in the Supporting Information). This corresponds to the so-called

CSD-433601 Sn11.49Bi12.39Se30 6321.86 monoclinic, C2/m a = 13.8520(10) b = 4.1993(3) c = 26.698(6) β = 95.781(6)° 1545.1(2) 1 6.794 109/48 w = (σ2(F) + 0.0004F2)−1 −2.48/2.61 off-edge Sn-K edge

0.13701 1.022

0.1518 1.308

0.4256 14.499

0.60 1.500/6.554 10469 2544

0.60 1.463/7.267 11172 2678

0.75 1.770/16.482 9086 1666

0.0700/0.0542 0.0366/0.0576 0.0469/0.0633 1.57

0.0224/0.0488 0.0361/0.0567 0.0455/0.0615 1.57

0.0241/0.0371 0.0546/0.0700 0.0553/0.0707 2.14

a

Unit cell parameters were taken from the Rietveld refinement of PXRD data from a phase-pure sample of Sn11.49Bi12.39Se30 (Figure S11 in the Supporting Information). F


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reflections violating the reflection conditions h + k = 2n for a Ccentered lattices (Figure 5). The symmetry reduction to space group Pnma is driven by a partial ordering of Sn and Bi on the four cation sites that is impossible on the two sites in Cmcm. The cation position interconnecting the NaCl-type slabs is again split. Refinements assuming lower symmetry and appropriate twin laws did not resolve the disorder as indicated by residual electron densities. Site occupancies of three cation sites refined to values slightly >100% and were thus constrained to full occupancy. However, the two remaining cation sites exhibit significant amounts of cation vacancies (up to 13% on position Bi4/Sn4) in good agreement with the other lillianitelike structures investigated. Sn9.52Bi10.96Se26 also exhibits unusual structural features. The cation position directly neighboring the interconnecting one is strongly underpopulated (26% vacancies), resulting in a splitting of one Se-position in its coordination sphere (octahedron 2 in Figure 4d). This Se position is part of the bicapped trigonal prismatic coordination polyhedron around the interconnecting site, which also required a split position. Refinement with anharmonic displacements factors did not improve the refinement results despite a larger number of parameters. The uncertainties of site occupancies amount to insignificant 0.072 positive charges with respect to 26 Se atoms. 3.2.5. Comparison of the Lillianite-like Structures in the System Sn/Bi/Se. All crystal structures elucidated share some structural features which are rather special among the lillianitelike structures known so far. The interconnecting site between the NaCl-type slabs is split into two positions. The bicapped trigonal prismatic coordination sphere is rather large so that an off-center position is more suitable for the cations. However, as both off-center positions are almost equal in energy, long-range ordering is unlikely and was not observed. Therefore, the space group with higher symmetry known for isostructural minerals without split atoms remains suitable. The offset of the interconnecting atom affects the extent of the displacements of the capping Se atoms, whose displacement ellipsoids become prolate. Another unifying feature of Sn/Bi/Se lillianites is the presence of cation vacancies on most of the cation sites. With vacancy contents up to ca. 25% on some sites, the structures tolerate pronounced deviations from the idealized stoichiometry derived from site multiplicities without collapsing or decomposing. However, in all structures there are only a few sites with large vacancy contents, while others remain close to or exactly at full occupancy. Thus, it seems that lillianite-type structures can tolerate vacancies only if these are limited to few sites. 3.2.6. Determination of the Thermoelectric Performance of Sn2Bi2Se5 in the L4,4-type. A sample of ∼3 g with the nominal composition Sn2Bi2Se5 was prepared to perform physical measurements. The resulting sample exhibits the L4,4-lillianite structure known from Sn2.22Bi2.52Se6; its phase purity was confirmed by PXRD (cf. Figure S12 in the Supporting Information) on a large fragment of the specimen as well as by SEM-EDX (averaged from 12 point measurements: Sn23.4(6)Bi22.8(4)Se53.8(4), nominal: Sn22.2Bi22.2Se55.6). During physical measurements, the sample was cycled three times between RT and 400 °C. The transport properties (Figure 6 and Figure S9 in the Supporting Information) exhibit two regimes: below 250 °C, the electrical conductivity remains almost unchanged in the range of 60−75 S/cm, while the Seebeck coefficient decreases up to −110 μV/K. Its negative sign indicates n-type conducting behavior. The thermal

Tables S9 and S10 in the Supporting Information. Despite the constraint applied, the sum formula exhibits 0.24 positive charges with respect to 30 Se atoms; this corresponds to one standard deviation of the refined site occupancies. The structure is comparable to the one of Sn3.6Bi3.6Se9, including the split position between the NaCl-type slabs. In this case, the split atoms are not symmetry-related, and there is no twin element that might generate them. 3.2.4. Single Crystal Structure Analysis of L4,4Sn2.22Bi2.52Se6 and L4,5-Sn9.52Bi10.96Se26. Single crystals of the L4,4- and L4,5-types were found in inhomogeneous samples and investigated using laboratory data with Ag-Kα radiation. The chemical compositions of the crystals investigated were determined by EDX spectroscopy. A composition of Sn20.6(10)Bi23.5(5)Se55.9(8) (averaged from nine point measurements) was determined for L4,4-Sn 2.22 Bi 2.52 Se 6 (= Sn20.7Bi23.5Se55.9). EDX analysis (eight point measurements) of L4,5-Sn9.52Bi10.96Se26 (= Sn20.5Bi23.6Se55.9) yielded a composition of Sn21.7(4)Bi25.4(4)Se52.9(6). As in the lillianite-like structures discussed above, the cation-to-anion ratio from EDX does not match the ratio derived from the site multiplicities, again indicating cation vacancies. In analogy to the previously described refinements, a charge-balanced sum formula on the basis of the chemical analysis was used as a constraint. As no resonant data were available, a charge neutrality constraint alone resulted in unreasonable compositions with almost no Sn content. Crystallographic data of both compounds are given in Table 7; atomic coordinates, displacements parameters, and site occupancies are listed in Tables S11−S14 in the Supporting Information. The lillianite-like structure of L4,4-Sn2.22Bi2.52Se6 is remarkable as it crystallizes in the space group Pnma in contrast to other L4,4 structures that crystallize in Cmcm. There are many Table 7. Crystallographic Data of Sn2.22Bi2.52Se6 and Sn9.52Bi10.96Se26 at RT sum formula

Sn2.22Bi2.52Se6

ICSD number molar mass/g mol−1 crystal system, space group cell parameters/Å

CSD-433801 1264.11 orthorhombic, Pnma a = 21.186(4) b = 4.1958(8) c = 13.834(3)

V/Å3 Z density/g·cm−3 parameters/restraints weighting scheme (P = (FO2 + 2Fc2)/3) extinction coefficient wavelength/Å absorption coefficient/mm−1 resolution/Å θmin/θmax reflections collected independent reflections Rσ/Rint R1(obs)/wR(obs) R1(all)/wR(all) goodness of fit Δρmin/Δρmax in e/Å3

1229.8(4) 4 6.828 86/4 w = 1/[(σ2(Fo2) + (0.0400P)2] 0.00158(11) Ag-Kα (0.56087) 31.426 0.75 4.547/21.956 12263 1714 0.0405/0.0687 0.0347/0.0698 0.0794/0.0816 0.879 −1.653/1.762

Sn9.52Bi10.96Se26 CSD-433764 5473.92 monoclinic, C2/m a = 13.847(3) b = 4.1961(8) c = 23.309(5) β = 98.78(3)° 1338.5(5) 1 6.791 102/4 w = 1/[(σ2(Fo2) + (0.0623P)2]

31.315 0.70 4.497/23.612 8391 2259 0.0448/0.0665 0.0415/0.1005 0.0586/0.1086 1.006 −2.402/2.681 G


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Inorganic Chemistry

Figure 4. Projections of lillianite type structures (Tables 5−7) in the compositional range (SnSe)∼1.7−2.0(Bi2Se3): (a) along the [100] direction, (b− d) along the [010] direction; unit cells are outlined; according to conventional nomenclature41 together with typical compositions; representative strands of edge-sharing cation coordination polyhedra are depicted.

Figure 6. Dimensionless figure of merit ZT of a sample with the nominal composition Sn2Bi2Se5 with the L4,4-lillianite type as the predominant phase (solid symbols for averaged heating cycles, empty ones for cooling cycles). Figure 5. Reconstructed 1kS layer (with respect to the standard setting of Pnma, cf. Table 7) from a crystal of L4,4-Sn2.22Bi2.52Se6.

3.3. Layered Structures of SnBi4Se7 (x = 0.5) and Related Phases. 3.3.1. X-ray Powder Diffraction and HRTEM of Annealed SnBi4Se7. In the powder pattern of an annealed sample (∼7 days, 620 °C) with the nominal composition (SnSe)0.5Bi2Se3 = SnBi4Se7, the 21R-GeSb2Te4 structure type72 was found in accordance with the literature (for details cf. single-crystal data in section 3.3.2).21 However, slight misfits in the Rietveld refinement indicated the presence of a second phase. TEM investigations indicated Bi2Se3 as a side phase; taking this into account improved the Rietveld refinement. In addition, HRTEM confirmed the presence of endotaxially intergrown layers of Bi2Se3 (Figure 7). The exsolution of Bi2Se3 results in an increased SnSe content of the 21R-GeSb2Te4-type phase that explains the slightly larger lattice parameters (a = 4.1821(2) Å, c = 39.178(4) Å) in comparison to the single crystal data. The profile fit of the Rietveld refinement is shown in Figure S14 and corresponding crystallographic data are given

conductivity, on the other hand, decreases to 0.75 W/mK, which is remarkably low. In contrast, the electrical and thermal conductivities increase significantly above 250 °C, while the absolute Seebeck coefficient decreases. The pronounced change at ca. 250 °C may indicate an alteration of the structure or the composition, for example, due to exsolution processes or an order−disorder transition as observed for Pb 5Sb4 S11.71 Subsequent SEM and TEM studies on the sample revealed a decomposition of the sample into a Sn-enriched phase with L4,4-type structure (space group Pnma) and small amounts of a Bi-enriched unknown phase (see Figure S13 and Table S15 in the Supporting Information). The phase stability was not further investigated due to the poor thermoelectric properties. H


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Inorganic Chemistry

Table 8. Crystallographic Data and Structure Refinement of SnBi4Se7 = Sn0.571Bi2.286Se4 formula ICSD number formula mass crystal system, space group cell parameters cell volume X-ray density Z absorption coefficient F(000) radiation 2θ range absorption correction measured reflections independent data/parameters extinction coefficient Rσ/Rint R1/wR2 [I > 2σ(I)] R1/wR2a/GOF (all data) Δρmin/Δρmax

Figure 7. HRTEM image (point resolution 0.23 nm) of an annealed sample (∼7 days, 620 °C) with the nominal composition SnBi4Se7: two slab sizes are visible: the averaged slab size of ∼13.0 Å corresponding to that in the 21R-GeSb2Te4 type) and the averaged slab size of 8.8 Å corresponding to Bi2Se3 (15R stacking); a larger section of the image was used in order to average the thicknesses.

Sn0.571Bi2.286Se4 CSD-430257 2584.05 g mol−1 trigonal, R3m a = 4.1724(6) Å c = 38.861(8) Å 585.9(2) Å3 7.324 g cm−3 3 38.906 mm−1 1062.88 Ag-Kα (0.56085 Å) 8.94° < 2θ < 47.18° numerical46,47 2170 275 [258 with I > 2σ(I)]/17 0.0030(3) 0.0209/0.0417 0.0214/0.0588 0.0234/0.0600/1.153 −1.153 e Å−3/1.913 e Å−3

a w = 1/[σ2Fo2 + (0.0407P)2 + 0.5219P] with P = [Fc2 + Max(Fo2,0)]/ 3.

to the tetradymite structure type, all of which are comparable to the one discussed here and differ only concerning the slab thickness, exhibit fully occupied atom sites and no antisite defects.74−76 The 21R stacking sequence, however, is possible here because there are cation vacancies. Such nonstoichiometry phenomena that lead to unexpected structure types have also been observed for the related compound Ge4‑xSb2‑yTe7 (x, y ≈ 0.1) which crystallizes in the Ge3Sb2Te6 structure type.77 In contrast to the model proposed in ref 28, our refinement yielded a small tin concentration and no significant amount of vacancies on the cation site 6d neighboring the van der Waals gaps. This might result from slightly different synthesis conditions such as annealing at lower temperatures. Cation vacancies next to van der Waals gaps would result in electrostatically unsaturated Se atoms and are thus unfavorable. 3.3.3. Thermoelectric Properties. On the Bi2Se3-rich side of the pseudobinary phase diagram, a Seebeck coefficient of 25.34 μVK−1 at RT has been reported for SnBi 4Se7.78 For thermoelectric characterization (cf. Figure S16), a sample with the nominal composition SnBi4Se7 was quenched at air. The large mass (3 g compared to 0.25 g) and thus slower cooling afforded a single-phase sample (according to PXRD, cf. Figure S15 and Tables S18 and S19 in the Supporting Information) without side phases such as Bi2Se3 that were found in the water-quenched samples. According to the literature, the temperature dependency of the electrical conductivity indicates metallic behavior above RT.79 This was confirmed as the electrical conductivity decreases up to 400 °C (from ∼800 S/cm to ∼550 S/cm). However, above 400 °C, it increases again. The rather similar curve of the negative Seebeck coefficient indicates an n-type conductor with a minimum at ca. −100 μV/K at 400 °C. The electrical conductivity of the sample investigated is higher by more than 2 orders of magnitude compared to 5 S/cm in the literature.78 This value exceeds that of Bi2Se3 and is close to the ones of germanium antimony tellurides as well as substituted

in Tables S16 and S17 (in the Supporting Information, with additional remarks on composition, treatment of peak broadening, preferred orientation, and displacement parameters). 3.3.2. Single-Crystal Structure Analysis of SnBi4Se7. Crystals of the ternary phase were grown via chemical vapor transport. The initial structure refinement was based on the 21R-type model proposed in ref 28. All cation positions were assumed to be mixed occupied by Sn and Bi which were constrained to identical atomic coordinates and displacement parameters when sharing one site. The sum formula was constrained to SnBi4Se7 = Sn0.571Bi2.286Se4 which is in accordance with the literature28 and EDX measurements. The latter yield Sn8.9(4)Bi32.6(3)Se58.4(4) (averaged from 10 point measurements on the crystal investigated), well matching Sn8.3Bi33.3Se58 as calculated for Sn0.571Bi2.286Se4. The refinement revealed a high vacancy concentration on the position in the center of the slab, whereas the occupancy of the cation position (with Bi and Sn) neighboring the van der Waals gap refined to 1 within 2−3 standard deviations and was therefore set to 1 in the final refinement. Crystallographic data are given in Tables 8 and 9. The structure is shown in Figure 8 next to Sn4.11Bi22.60Se38, which represents another SnSe-poor tin bismuth selenide.26 Both compounds share distorted NaCltype like slabs. However, in Sn0.571Bi2.286Se4 these are separated by van der Waals gaps, whereas in Sn4.11Bi22.60Se38 additional building units interconnect the slabs. Moreover, all cation positions in Sn4.11Bi22.60Se38 are not fully occupied, while in Sn0.571Bi2.286Se4 the vacancies are limited to the cation position in the center of the slab. The 21R stacking sequence is very unusual for the stoichiometric formula “SnBi4Se7”. A structure type with a 12P stacking sequenceas known from, e.g., GeBi4Te7 would be expected.73 Notably, most layered structures related I


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Table 9. Coordinates, Site Occupancies, Equivalent Isotropic and Anisotropic Displacement Parameters of Sn0.571Bi2.286Se4a

a

atom

Wyckoff position

x

y

z

s.o.f.

Ueq/Å2

U11 = U22

U33

Se1 Se2 Sn3 Bi3 Sn4 Bi4

6d 6d 12d

1/3 1/3 1/3

2/3 2/3 2/3

0.53237(3) 0.37762(3) 2/3

0.0183(3) 0.0176(3) 0.0218(3)

0.0178(3) 0.0175(3) 0.0219(4)

0.0193(5) 0.0177(5) 0.0217(5)

0.0089(2) 0.0087(2) 0.0109(2)

6d

1/3

2/3

0.23840(2)

1 1 0.405(5) 0.452(5) 0.083(3) 0.917(2)

0.0210(2)

0.0196(2)

0.0236(3)

0.00982(11)

U12

Ueq = 1/3[U33 + 4/3(U11 + U22 − U12)]; U23 = U13 = 0.

Figure 8. (a) Projection of the structure of Sn4.11Bi22.60Se38 along [010]: it consists of step-like sections of the rocksalt type and ribbonlike building blocks and (b) the structure of Sn0.571Bi2.286Se4 along [100] with the typical distorted NaCl-type slabs separated by van der Waals gaps; in addition, the cation distribution of Sn0.571Bi2.286Se4 is illustrated by the s.o.f.’s revealing the presence of vacancies only at the cation position in the center of the slabs.

variants thereof.34,80,81 The bandgap was calculated using the Goldsmid−Sharp relationship,82 Eg = 2eSmaxTmax, where Smax is the maximal absolute Seebeck coefficient and Tmax the corresponding temperature. It yielded a narrow bandgap of 0.13 eV which is similar to those of well-established thermoelectric materials such as Bi2Te3 (0.17 eV) and Sb2Te3 (0.23 eV).9,10 The bandgap derived from an Arrhenius plot of the electrical conductivity in the temperature interval of intrinsic semiconduction (425−500 °C or ∼1.3−1.45 1000/ K, thus rather imprecise due to few data points) is 0.07(1) eV. The small bandgap agrees well with the high electrical conductivity. However, due to the small Seebeck coefficient and an almost constant yet rather high thermal conductivity up to 400 °C (∼1.9 Wm/K), the maximum ZT value is limited to 0.2 at 400 °C (Figure S16) which is in the range of other GeSb2Te4-type structures at this temperature.81 3.3.4. Phase Separation in SnBi4Se7. SEM employing backscattered electron images and EDX analysis revealed regions of different contrasts and compositions (Figure S16 and Table S20 in the Supporting Information) in samples heated up to 500 °C). The two major phases show compositions close to the initial one of SnBi4Se7. The minority phase, on the other hand, exhibits a higher Sn content. Crystallites of each main phase were identified by means of TEM (Figure S17 and Table S21 in the Supporting Information). Synchrotron data revealed that the structure of the slightly Sn-richer crystals is comparable to the one of the single crystal discussed in Section 3.3.2. Crystallographic data,

Figure 9. Thermoelectric data (top to bottom: Seebeck coefficient, electrical conductivity, thermal conductivity and figure of merit ZT) of SnBi4Se7 = Sn0.571Bi2.286Se4 (solid circles = averaged heating cycles, empty circles = averaged cooling cycles, the difference is within the error of the measurements).

J


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would be necessary to match the high ZT values of the binary compounds of >2 for SnSe and of >0.6 for Bi2Se3.22,88 Summing up, the unusual flexibility of crystal structures in the system (SnSe)xBi2Se3 arises from the very pronounced tendency to preserve the octahedral coordination of the cations to the largest extent possible. Under this condition, the structures intrinsically incorporate features known for their potentially favorable influence on thermoelectric properties, such as vacancies, mixed occupied atom sites, or complex crystal structures, resulting in a great potential as a model system to further understand the interplay of real structure effects and thermoelectric performance. It is also remarkable that the system contains only abundant elements.

atom positions, and displacement parameters are listed in Tables S22−S25. The Se atoms at the van der Waals gaps required the use of anharmonic displacement parameters representing the average structure of an irregularly undulated Se layer. The slightly Sn-depleted crystal, on the other hand, shows a complex diffraction pattern that may be related to that of BiSe (P3m1, a = 4.18 Å, c = 22.8 Å)83 or other bismuth selenides.84

4. CONCLUSION The in-depth structural investigation of the plethora of ternary compounds in the pseudobinary system SnSe-Bi2Se3, complemented by physical property measurements leads to a deeper understanding of these main-group chalcogenides. The system adopts several structures known for heavier or lighter homologues. This copycat-like behavior arises from the ability to compensate changes in the cation−anion ratio in different ways. For compounds with a high SnSe content, i.e., cubic defect-NaCl-type phases with x > 3 (Section 3.1), Sn is formally replaced by Bi and vacancies (2 Sn2+ → Bi3+ + □), which are randomly distributed on the cation position. SnSe in itself exhibits a long-range distortion of the NaCl type (GeS structure type) that is impossible with vacancies and atoms that prefer different local environments. With increasing vacancy concentration, the NaCl type becomes unstable, probably as it cannot tolerate a larger amount of incomplete coordination spheres. Then, lillianite-type phases (3 > x > 0.8) with a nonoctahedrally coordinated cation position are formed. This compensates the fewer number of cations (Section 3.2), although vacancies are still common as evinced by resonant X-ray diffraction studies for L7,7-Sn3.6Bi3.6Se9 and L4,7-Sn11.49Bi12.39Se30. A further increase of the Bi2Se3 content (x ≤ 0.5) leads to layered phases, e.g., Sn0.571Bi2.286Se4 with van der Waals gaps separating NaCl-type like slabs as well as cation vacancies within the slabs. In another structural variation, Sn4.11Bi22.60Se38,26 stepped distorted NaCl-type slabs are interconnected by ribbon-like elements (cutouts from the SnSe structure). This structure contains multiple nonoctahedrally coordinated cation positions and vacancies on all cation sites. Thus, an increasing number of many vacancies leads to the formation of van der Waals gaps or increased coordination numbers for an increasing number of atoms. Table S26 in the Supporting Information provides an overview of the structure reported; with additional normalization in the form (SnSe)x(Bi2Se3) illustrating the compositions moving from the SnSe-rich to the Bi2Se3-rich side of the pseudobinary phase diagram. In addition to crystal-chemical insights, transport measurements indicate potential ways of enhancing the thermoelectric performance by substitution. For Sn0.57Bi0.29Se, substitution with Li in terms of filling cation vacancies might be a task worth striving for in order to avoid the decomposition upon heating. This would be in analogy to the introduction of Li in germanium antimony tellurides, which lead to extended stability ranges of cubic phases.85 The lillianite-like phases in the so-called “phase X” region21 (0.8 < x < 3, Figure S1) are closely related so that slight changes in the composition and temperature regime might generate additional potentially metastable phases with unusual combinations of slabs sizes. On the basis of exactly determined existence ranges as a function of temperature and composition, a targeted decomposition into additional phases may be a promising pathway toward nanoscale heterostructures that have shown to drastically alter the thermoelectric performance,86,87 which

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00105. Redrawn phase diagram of (SnSe)x(Bi2Se3); information on the synthesis of the samples; densities of thermoelectrically characterized samples; Rietveld refinement of a sample with the nominal composition (SnSe)xBi2Se3 (x = 4, x = 5) with corresponding refinement data and coordinates; figure of the progression of the lattice parameters of (SnSe)xBi2Se3 (x = 3−5); high temperature PXRD of Sn4Bi2Se7 with progression of the lattice parameter upon heating an selected diffraction pattern as well as the thermoelectric data of the sample; difference Fourier maps of the interconnecting site in Sn3.6Bi3.6Se9; Rietveld refinement of Sn2Bi2Se5 (L4,4-type) with corresponding atom positions; displacement parameters and site occupancies for Sn3.6Bi3.6Se9; thermoelectric data of Sn2Bi2Se5 (L4,4-type); Rietveld refinement of a sample with the nominal composition (SnSe)1.86Bi2Se3 with the corresponding atom positions; occupancies and displacement parameters; atom positions, site occupancies and displacement parameters for Sn 2.22 Bi 2.52 Se 6 and Sn9.52Bi10.96Se26; Rietveld refinement of an annealed sample with the nominal composition Sn2Bi2Se5 as well as a backscattered electron image (SEM-BSE image) thereof and with EDX analysis of the contained phases; Rietveld refinement of a sample with the nominal composition (SnSe)0.5Bi2Se3 with corresponding refinement data, atom positions and occupancies; Rietveld refinement of the ∼3 g sample with the composition (SnSe)0.5Bi2Se3 and corresponding refinement data; atom positions and occupancies; SEM-BSE image of a thermally treated sample with the nominal composition (SnSe)0.5Bi2Se3 and with EDX analysis of the contained phases; TEM images of two microcrystal; refinement data of Sn0.85Bi2.15Se4 with corresponding atom position, site occupancies, and displacement parameters (PDF) Accession Codes

CCDC 1815181 (for Sn0.57Bi0.29Se) and 1815188−1815192 (for Sn 0.571 Bi 2.286 Se 4 , Sn 3.6 Bi 3.6 Se 9 , Sn 11.49 Bi 12.39 Se 30 , Sn9.52Bi10.96Se26 and Sn2.22Bi2.52Se6, respectively) contain 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]. uk, or by contacting The Cambridge Crystallographic Data K


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (+49) 341 97- 36251. Fax: +49 (0) 341 97-36299. ORCID

Oliver Oeckler: 0000-0003-0149-7066 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This investigation was funded by the Deutsche Forschungsgemeinschaft (Grant OE530/3-1) and the Studienstiftung des deutschen Volkes (fellowship for Stefan Schwarzmüller). We thank the ESRF for granting beamtime (experiment CH-4318) as well as Dr. Jonathan Wright, Peter Schultz, and Markus Nentwig for help with the synchrotron measurements.

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REFERENCES

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