Article pubs.acs.org/IC
Structural, Electronic, and Optical Properties of K2Sn3O7 with an Offset Hollandite Structure Rebecca D. McAuliffe,† Christopher A. Miller,† Xiao Zhang,‡ Benjamin S. Hulbert,† Ashfia Huq,¶ Clarina dela Cruz,§ André Schleife,*,∥ and Daniel P. Shoemaker*,† †
Department of Materials Science and Engineering, Frederick Seitz Materials Research Laboratory, ‡Department of Mechanical Science and Engineering, and ∥Department of Materials Science and Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ¶ Spallation Neutron Source and §High-Flux Isotope Reactor, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ABSTRACT: We present the compound K2Sn3O7, a Sn4+-containing oxide with a unique structure type among oxides. The compound is orthorhombic and reminiscent of an offset hollandite, where open channels hold a row of four K+ per channel per cell. UV−visible spectroscopy indicates a wide band gap semiconductor, which is confirmed by first-principles electronic-structure calculations of band structures, densities of states, and optical properties. The continued discovery of new structure types in ternary tin oxides should remain a priority for the identification of prospective ion conductors and transparent conducting compounds.
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INTRODUCTION Tin-containing oxides form the basis of many electronic device technologies, including the quintessential n-type transparent conducting oxides (TCOs) In2O3 and SnO2.1 SnO2 has been investigated as a TCO2 and Li-ion battery anode,3,4 along with other compounds derived from octahedral SnO6 units, including spinel-type Zn2SnO45,6 and mixed hollandites such as K2(MSn6)O16 and K2(MSn7)O16, where M = Mg, Fe, Mn, or Ga.7 Binary oxides with filled d states and wide band gaps such as SnO2 and Ga2O3 are potential candidates for p-type TCOs, but their performance is limited by low hole mobility, which resides in the O p states at the Fermi energy. The low mobility has been explained by formation of stable polarons (self-trapped holes), which would persist even in the event of doping, but this behavior is structure-dependent.8 In contrast to SnO2, oxides of Sn2+ with a 5p2 electron configuration such as SnO have Sn s and pz mixed with O porbital character near the valence band maximum, with more dispersed bands that may indicate higher mobility in the absence of unfavorable defects.9,10 Subsequent doping leading to an effective p-type TCO remains elusive but has been proposed for SnO11 and systems with additional ions, such as K2Sn2O3.12 In our quest to investigate new oxides that can host Sn in either valence state, under-studied ternary phase spaces are of interest. Detailed investigations of phase equilibria in the systems A−Sn−O, where A is an alkali, are rare. This may be because many of the precursors (alkali oxides and carbonates) © XXXX American Chemical Society
are hygroscopic. K2CO3 noticeably absorbs water when being weighed in air, as does K2O. Both are deliquescent. The products of these reactions, however, can be quite stable. In 2002, a report by Iwasaki et al. presented the new compound Na4Sn3O8 from the reaction of Na2CO3 and SnO2 at 1300 °C.13 The K−Sn−O system contains five phases with known crystal structures. There are two Sn4+ compounds K2SnO3 and K4SnO4,14,15 as well as the Sn2+ compounds K2SnO2, K2Sn2O3, and K4SnO3.16−19 Tournoux performed the only systematic phase equilibria study on this system.20 His elemental analysis of a K2SnO3 decomposition product revealed an estimated stoichiometry K2Sn3O7, but the structure was never solved. Here we present a single-step synthesis for this compound, its crystal structure, optical characterization, and first-principles electronic-structure calculations of electronic and optical properties. K2Sn3O7 has a unique structure type among oxides, reminiscent of an offset hollandite with bowtie-shaped channels, which is shared only with the recently discovered compound Cs2U3Se7.21
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EXPERIMENTAL PROCEDURE
Powdered K2CO3 (Fisher, 99%) and SnO2 (Acros 99.9%) were ground by hand in air in an agate mortar and pestle with molar ratios of 1/1 K/Sn. The carbonate was periodically checked by X-ray diffraction (XRD) for evidence of hydration or KOH formation. Each Received: December 12, 2016
A
DOI: 10.1021/acs.inorgchem.6b03007 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry mixture was pressed into 12 mm diameter pellets and fired in air, inside beds of sacrificial powder in uncovered alumina crucibles. The samples were fired at 900 °C for 9 h in air with heating and cooling rates of 10 °C/min. Powder diffraction was performed using a Bruker D8 diffractometer with Mo Kα radiation and a capillary mount, with samples mixed with SiO2 to reduce absorption. Neutron powder diffraction was performed on the POWGEN instrument at the Spallation Neutron Source, and the HB-2A instrument at the High Flux Isotope Reactor, on airexposed and argon-bottled samples, respectively. The structure was initially solved using the FOX software,22 fitting to XRD data. Rietveld refinements to X-ray and neutron data were performed using GSAS.23 Structures were plotted using VESTA.24 Scanning electron microscopy (SEM) was performed using a JEOL 6060LV with energy-dispersive X-ray spectroscopy (EDS). Optical spectroscopy was performed in diffuse reflectance geometry with a Cary 5000 UV−vis−near-IR spectrometer.
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COMPUTATIONAL APPROACH
First-principles calculations were performed using density functional theory25,26 (DFT) with the generalized-gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE) for exchange and correlation (XC).27 The cell shape and atomic positions are relaxed within DFT-PBE until all Hellmann−Feynman forces are smaller than 5 meV/Å. The electronic band structure and density of states (DOS) were computed using the hybrid XC functional by Heyd, Scuseria, and Ernzerhof (HSE06)28 and Hedin’s GW approximation.29 This yields an accurate description of single-quasiparticle effects and renders our results directly comparable to experiment. Dielectric functions are computed based on the DFT-PBE Kohn−Sham states using the longitudinal approximation30 and are compared to results from the solution of a Bethe−Salpeter equation (BSE) for the optical polarization function,31 which accounts for excitonic effects. We applied a scissor shift of Δ = 1.61 eV to both spectra so that the band gap matches with our DFT+GW result. The wave functions are expanded into plane waves up to a cutoff energy of 550 eV, and a γ-centered 6 × 2 × 2 k-point grid is used to sample the Brillouin zone for structural relaxations and electronicstructure calculations. Converged calculations of optical properties require a denser 9 × 3 × 3 k-point grid with a random shift to lift degeneracies. All calculations are done using the Vienna Ab Initio Simulation Package32,33 and the projector-augmented wave scheme.34 BSE calculations are performed using the implementation discussed in references 35 and 36.
Figure 1. Rietveld refinements to laboratory X-ray data (top) and two banks of time-of-flight neutron powder diffraction for K2Sn3O7. The large X-ray scattering factor for Sn necessitates neutron diffraction measurements to reliably refine the oxygen displacement parameters. The peak profile is shown in gray for a second phase K2CO3·1.5H2O that was not present in the XRD data.
The structure of K2Sn3O7 is shown in Figure 2, and parameters are given in Table 1. The structure forms with a
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RESULTS AND DISCUSSION K2Sn3O7 forms as a quantitative product of the decomposition of K2CO3 and SnO2. It is surprising that such a common reagent combination, in air, forms a compound that is unsolved and unique among oxides. Excess carbonate is left unreacted or vaporized, depending on the duration of the reaction. Using a K/Sn ratio less than 2/3 in the reagents leads to the presence of excess SnO2. In that case, K2Sn3O7 seems to be the only ternary product of these reactants in air. Reactions conducted below 830 °C are incompletely reacted, and the compound is stable in air up to the maximum temperature we attempted, 1000 °C. Rietveld refinements are shown in Figure 1 for XRD data and two banks of time-of-flight neutron diffraction data from POWGEN. The XRD data appear phase-pure, while a small amount (9 wt %) of K2CO3·1.5H2O is evident in the neutron diffraction data. The invisibility of the carbonate to XRD may arise from the much stronger scattering power of Sn in XRD data. For the same reason, neutron diffraction was required to refine the positions and atomic displacement parameters of the seven oxygen positions in the cell. No carbonate impurities were seen in EDS or backscattered SEM imaging of the samples used for UV−vis analysis.
Figure 2. A 2 × 1 × 2 view of K2Sn3O7, with the unit cell shown, as refined from neutron powder diffraction with K in purple, O in red, and Sn shown in gray octahedra. The short b axis implies that the structure forms one-dimensional channels of K+ ions into the page.
very short orthorhombic b axis of 3.12 Å, which corresponds to a single O−O distance and portends the one-dimensional, channel-type structure that is typical of hollandites, among other compounds. Tin has been shown to form substituted hollandites of the type K2−δMxSn8−xO16 (monoclinic C2/c or tetragonal I4/m), where M = Mg, Fe, Co, Mn, or Zn, or the mono- and trivalent analogues with Li and Ga, respectively.4,37,38 These compounds form a typical hollandite with channels bound by 2 × 2 edge-sharing SnO6 octahedra B
DOI: 10.1021/acs.inorgchem.6b03007 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry Table 1. K2Sn3O7 Structurea as Refined from POWGEN Neutron Diffraction Data atom
x
y
z
Uiso
Sn1 Sn2 Sn3 K1 K2 O1 O2 O3 O4 O5 O6 O7
0.0120(3) 0.2916(3) 0.3730(3) 0.3073(7) 0.4346(5) 0.0934(3) 0.1725(4) 0.1767(4) 0.2517(4) 0.4007(3) 0.4802(3) 0.5503(4)
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.1086(4) 0.7084(4) 0.1649(4) 0.447(1) 0.8967(9) 0.5737(4) 0.7584(4) 0.3008(4) 0.1144(4) 0.6318(4) 0.2463(4) 0.5530(4)
0.83(8) 0.9(1) 1.2(1) 6.3(4) 4.5(4) 1.6(1) 1.2(1) 1.8(1) 1.1(1) 1.1(1) 2.1(1) 0.7(1)
width and tens of microns in length. Electron backscatter imaging in Figure 3c does not reveal any substantially higher- or lower-Z-density regions that would indicate impurities. The band gap of K2Sn3O7 is difficult to characterize using UV−vis spectroscopy, since it is wide enough to approach the edge of the detector. However, the downturn in reflectivity of ∼3 eV is apparent, with nearly full absorption occurring at ∼4 eV in Figure 4. As a comparison, rutile-type SnO2 (cassiterite) has a known band gap of ∼3.6 eV.40
a
Space group Pnma, a = 16.8640(4) Å, b = 3.122 50(8) Å, c = 12.8523(5) Å. Uiso units are 1 × 10−2 Å2.
enclosing a single row of alkali ions. In all these compounds, the deviation from SnO2 stoichiometry is balanced by the M cation with valence below 4+. In K2Sn3O7, the channels are significantly more open, creating four rows of alkali cations with a zigzag arrangement that is apparent in the structure in Figure 2. No such substitution with M is necessary to stabilize K2Sn3O7 due to its offset hollandite structure. In this sense it also contrasts with uncommon hollandite-related compounds such as Ba6Mn24O48, which forms a composite structure with two channel sizes (hollandite 2 × 2 and rutile 1 × 1) but is nevertheless multivalent.39 It remains to be seen if K2Sn3O7 can be partially reduced to form a K2Sn8O16-type structure while ejecting excess potassium into a second phase. SEM interrogation of crushed K2Sn3O7 pellets revealed porous agglomerates visible in Figure 3, with some large agglomerates remaining such as the piece in Figure 3b. EDS analysis gave K/Sn ratios of ∼2/3, which were used with the unit cell obtained by FOX to solve for the number of Sn ions on the cell. Closer inspection of these agglomerates reveals them to consist of needle-shaped grains, which are ∼1 μm in
Figure 4. UV−vis spectroscopy of powdered K2Sn3O7 shows a large band gap, under 4 eV. Our DFT+GW results predict a direct gap of ∼3.15 eV, while that of cassiterite SnO2 is ∼3.6 eV.40
Cell shape and atomic positions were relaxed using DFTPBE, starting from the experimentally determined structure of K2Sn3O7. We varied the volume within 1.5% of the optimized volume, and the resulting energy-versus-volume curve in Figure 5a can be fit to the Murnaghan equation of state41 to obtain
Figure 5. Energy vs volume curve (per formula unit) for the relaxation of K2Sn3O7 as computed within DFT-PBE. The solid line shows the fit to the Murnaghan equation of state.
optimized volume, total energy, and bulk modulus of the material. The resulting parameters agree with experiment within 2%: V = 709.7 Å3, a = 17.16 Å, b = 3.200 Å, and c = 12.92 Å. The bulk modulus of the material from our simulation is B0 = 77.3 GPa. DFT-PBE predicts a band gap of 1.54 eV for K2Sn3O7, which is approximately half the experimental value. This under-
Figure 3. Scanning electron micrographs in secondary electron imaging (a−c) reveal a mixture of fine and agglomerated powder comprised of micron-scale fused rods. Backscattered electron imaging (d) of the area in (c) indicates that the nonrod-shaped particles on the agglomerate surface are the same composition. C
DOI: 10.1021/acs.inorgchem.6b03007 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry estimation is typical for DFT-PBE due to the neglect of quasiparticle effects. To correct this problem, we adopted the GW approximation for the electronic self-energy to compute quasiparticle energies (Figure 6) using a single step of
Figure 7. Imaginary part of the dielectric function of K2Sn3O7 parallel to the three crystalline axes. The average of these is shown in the bottom right panel. Solid and dashed lines are the DFT and BSE results, respectively. Differences between the panes indicate significant anisotropy, while differences between the DFT and BSE results reveal strong excitonic effects. A scissor shift is included in these calculations.
Figure 6. Electronic band structure and DOS calculated from GGA +GW. The DOS shows a large, flat collection of bands at the Fermi energy, primarily of O p character.
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perturbation theory on top of the DFT-PBE electronic structure. This approach requires inclusion of a large number of empty states to converge the description of screening of the electron−electron interaction. Here we included between 52 and 276 empty states. Linear extrapolation of this trend to infinitely many bands yields a band gap of 3.15 eV, which agrees roughly with our UV−vis spectrum in Figure 4. For comparison we calculated the band gap using the HSE06 hybrid XC functional, which also predicts a band gap of 3.15 eV. The results obtained from the different methods are summarized in Table 2.
CONCLUSIONS We have solved the structure of K2Sn3O7 from powder diffraction and refined its structure to X-ray and neutron scattering data. This material is isostructural with only one compound, Cs2U3Se7, and is the first oxide with this structure type. It forms in air from common reagents, and has onedimensional channels that are reminiscent of a hollandite structure that has been partially opened. Optically, it is a widebandgap semiconductor with a direct gap and O p character at the Fermi level. The anisotropy of the crystal structure is evident in the complex frequency-dependent dielectric function, which also exhibits large excitonic effects. The mobility of K+ ions, their propensity to undergo cation exchange, and the redox behavior of K2Sn3O7 remain to be investigated.
Table 2. Band Gap from DFT-PBE, HSE06, and GW Calculations
a
method
PBE
GW
HSE
expta
band gap (eV)
1.54
3.15
3.15
∼3−4
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The experimental band gap is also listed for comparison.
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. (A.S.) *E-mail:
[email protected]. (D.P.S.)
Finally, the complex optical response of K2Sn3O7 was calculated both at the DFT-PBE level and including excitonic effects by solving the BSE for the optical polarization function. From the differences between the results for the imaginary part of the dielectric functions, shown in Figure 7, the strong influence of excitonic effects can be seen. Excitonic states near the onset clearly determine the optical absorption behavior of the material. Peaks at higher photon energies are also strongly affected by the electron−hole interaction, as can be seen from a large red-shift of their energy positions. Excitonic effects in this material are so large due to the weak electronic dielectric screening of the electron−hole interaction. This can be seen from the static electronic dielectric constant that we compute to be ε∞ = 4.01 as well as the large band gap. In addition, our results in Figure 7 show that light polarization parallel to the different directions of the crystal axes leads to a marked anisotropy, which is not surprising given the tunneled nature of the K2Sn3O7 structure. The optical absorption is particularly strong between 3 and 6 eV for light polarized parallel to the b axis. This should lead to a birefringence behavior of the material.
ORCID
André Schleife: 0000-0003-0496-8214 Daniel P. Shoemaker: 0000-0003-3650-7551 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Illinois Department of Materials Science and Engineering for financial support. Characterization was performed at the Frederick Seitz Materials Research Laboratory at the Univ. of Illinois. Neutron diffraction was performed at the Spallation Neutron Source and the High Flux Isotope Reactor, Department of Energy, Office of Science User Facilities operated by the Oak Ridge National Laboratory. Computational work was supported by the National Science Foundation under Grant No. DMR-1555153. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Award Nos. OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the Univ. of Illinois at Urbana− D
DOI: 10.1021/acs.inorgchem.6b03007 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry
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Champaign and its National Center for Supercomputing Applications.
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DOI: 10.1021/acs.inorgchem.6b03007 Inorg. Chem. XXXX, XXX, XXX−XXX
