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Sodium Iron(II) Pyrosilicate Na2Fe2Si2O7: A Potential Cathode Material in the Na2O‑FeO-SiO2 System Abhishek Panigrahi,† Shin-ichi Nishimura,†,‡ Tatau Shimada,† Eriko Watanabe,† Wenwen Zhao,† Gosuke Oyama,† and Atsuo Yamada*,†,‡ †
Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ‡ Elements Strategy Initiative for Catalysts & Batteries (ESICB), Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8245, Japan S Supporting Information *
ABSTRACT: As lithium-ion battery technology becomes widely popular with increasing demand for efficient energy-storage devices for a wide range of applications, the scarcity of lithium resources poses a concern for increasing costs. Replacing lithium with much more abundant sodium in combination with abundant transition metals such as iron (instead of traditionally used cobalt or nickel) as the charge compensation center in the cathode materials is expected to make large-scale battery technology a reality. To activate iron as a reversible redox center, oxyanions (XO4)n− have been introduced to stabilize the structures and raise the redox potentials, and silicates (X = Si, n = 4) form the best candidate group in terms of abundance and cost. In this regard, we explored the Na2O-FeO-SiO2 pseudoternary system and identified a new phase, Na2Fe2Si2O7, with an efficient chemical composition for charge accumulation (Na/Fe = 1), providing a large one-electron theoretical capacity of 164.5 mAhg−1 as a sodium-ion battery cathode.
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INTRODUCTION Electrochemical energy storage is a key technology toward creating a sustainable society based on renewable energy sources. The present lithium-ion battery technology includes cathode materials such as layered LiCoO2, spinel-structured LiMn2O4, and olivine-structured LiFePO4. However, the rapid expansion of these cathodes to large-scale applications has created concerns about cost and scarcity of Li resources. In a typical lithium-ion battery, the cathode materials account for the majority of the cost; therefore, alternative inexpensive cathode materials are necessary to reduce the overall cost. Replacing lithium with sodium, as one of the most abundant elements in the Earth’s crust, may provide a realistic alternative for large-scale stationary applications such as smart grids, where the energy density and/or battery size/weight is not necessarily the key limiting factor. Because of the similar chemistries of sodium-ion and lithium-ion batteries, advances in lithium-ion systems are a source of inspiration for investigations of their sodium-ion counterparts.1 In particular, the layered NaxMO2 system, which is based on the same intercalation chemistry as the LixMO2 system, tends to show more stable operation and accommodate a greater variety of transition metals M than its Li counterpart because of the size difference between Na+ and Li+ (Na+ > Li+). For the Li system, M is limited to Co and Ni because of the thermodynamic stability of LiMO2. On the basis of this logic, layered cathode materials composed of Fe as the transition metal, such as O3-NaFeO22,3 and P2-Nax[Fe0.5Mn0.5]O2,4 have been reported to show reversible reactions but suffer from poor © 2017 American Chemical Society
cyclability, an initial irreversible capacity, and low operating voltages. Overcoming these difficulties requires the addition of a large proportion of rare metals, as demonstrated in the case of O3-NaFe0.5Co0.5O2, to achieve superior electrochemical performance.5,6 In these layered oxides, the initial valence state of Fe is trivalent. During charging, Fe is expected to be oxidized to a tetravalent state, which is much less stable than the trivalent state, hindering the use of the Fe4+/Fe3+ redox couple in the cathode materials. Instead, the most commonly applied strategy to date has been to use the Fe3+/Fe2+ redox couple in a polyanion framework. A stable structural framework enables the full utilization of one-electron reactions with an elevated operating voltage by the inductive effect.7 This strategy provides an impetus for a search of Fe-based polyanionic compounds for lithium battery cathodes and has led to the discovery of the commercially viable LiFePO4. Naturally, similar materials exploration led to the development of sodium-containing Fe-based cathodes such as Na2+2xFe2−x(SO4)3,8−10 Na2FePO4F,11−13 Na2FeP2O7,14,15 and Na4Fe3(PO4)2P2O7.16 The target of this study is to identify new cathode materials in the Na2O-FeO-SiO2 pseudoternary system (see Figure 1). Silicon is widely distributed in dusts and sands as various forms of silicon dioxide (silica) or silicates. Silicate minerals compose more than 60% of the Earth’s crust, making silicon the second Received: February 22, 2017 Revised: April 27, 2017 Published: April 28, 2017 4361
DOI: 10.1021/acs.chemmater.7b00764 Chem. Mater. 2017, 29, 4361−4366
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Chemistry of Materials
pattern are summarized in Figure 2(a). The fitting parameters can be found in Table 1.
Figure 1. Phase relation in the Na2O-FeO-SiO2 pseudoternary system. Color map in the triangular diagram indicates expected initial charge capacity based on the Na extraction reaction with Fe3+/Fe2+ charge compensation.
most abundant element in the Earth’s crust.17 Therefore, silicon dioxide (SiO2) is quite inexpensive and is widely used commercially in the manufacture of clays, silica sand, and stone. Because various silicates can be synthesized directly from silica, silicate-based polyanion chemistry is an attractive research topic for Fe-based Li- and Na-ion batteries. Lithium iron silicate materials − Li2FeSiO4 and its derivatives − have been reported and widely studied.18−24 As a counterpart in sodium-ion batteries, Yang and co-workers have recently reported the synthesis and reversible electrochemical activity of Na2FeSiO4.25 However, the low operating voltage of approximately 1.8 V versus sodium has impeded the further development of this material. In the pursuit of a new material, we further explored the Na2O-FeO-SiO2 pseudoternary system to identify better compounds. In this system, we expect more candidates with various compositions and structures than found in the Li2O-FeO-SiO2 system because of the greater difference in ionic size between Na and Fe than between Li and Fe.
Figure 2. Observed and calculated powder X-ray diffraction patterns (a) and 57Fe Mössbauer spectra (b) of Na2Fe2Si2O7.
Table 1. Fitting Parameters of Mössbauer Spectrum for Na2Fe2Si2O7a
Fe1 Fe2 a
fraction (%)
isomer shift δIS (mm s−1)
quadrupole splitting ΔQS (mm s−1)
line width Γ (mm s−1)
46.6 52.4
1.079(5) 0.864(5)
2.454(10) 1.429(11)
0.288(15) 0.326(16)
Normalized χ2 = 1.04.
The new compound Na2Fe2Si2O7 is isostructural with Na2Mn2Si2O7 (ICSD no. 20534) with slightly different local environments of the transition-metal ions.26,27 Two distinct Fe ions in Na2Fe2Si2O7, Fe1 and Fe2, are coordinated by five and four oxygen atoms, respectively, and form distorted FeO5 bipyramids and distorted FeO4 tetrahedra, respectively. By contrast, in Na2Mn2Si2O7 both Mn ions are in a tetrahedral MnO4 environment.26,27 The differences in MOx coordination between M = Mn and Fe are due to slight differences of the relative oxygen positions. The characteristic Fe environment was further verified by 57Fe Mössbauer spectroscopy (Figure 2(b)). As summarized in Table 1, the isomer shifts δIS of the two major components, 1.079(5) mm s−1 and 0.864(5) mm s−1, are in the typical range for Fe(II) species with high-spin configurations.28 The large difference in the quadrupole splitting ΔQS reflects a substantial difference in the coordination environments around Fe1 and Fe2 (FeO5 or FeO4). According to the well-known empirical trend of quadrupole splitting versus local asymmetry, the larger ΔQS is assigned to the Fe1O5 bipyramidal site, and the smaller one is assigned to the Fe2O4 tetrahedral site.28 These two alternative Fe polyhedra form continuous one-dimensional chains running along the [001] direction, sharing apexes and edges (Figure 3). Two SiO4 tetrahedra share an apex to form a pyrosilicate Si2O7, interconnecting a chain of the Fe polyhedra to form the three-dimensional Fe2Si2O7 framework. Na+ ions occupy two
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RESULTS AND DISCUSSION Crystal Structure. The as-synthesized powder targeted for the composition Na2Fe2Si2O7, with a primary particle size of approximately 200−500 nm (see Figure S1), exhibited a darkgray color. Powder X-ray diffraction revealed that the sample contained trace amounts of impurities such as α-Fe and carnegieite-like unknown phases; however, most of the reflections were identified as originating from a hitherto unreported phase. We attempted to solve the structure using the high-resolution X-ray diffraction (HRXRD) pattern, and the observed reflections were indexed to a monoclinic lattice with P121/n1 symmetry and with lattice constants of a = 9.07499(8) Å, b = 12.91082(12) Å, and c = 5.48835(4) Å and angles of α = 90°, β = 91.9854(5)°, and γ = 90° (see Tables S1 and S2 for details). We extracted the integrated intensities of each reflection by the Pawley method and applied the chargeflipping method to obtain an initial phase set. All of the atomic positions were readily found in the electron-density distribution map. The subsequent Rietveld refinement converged successfully to Rwp = 5.65%, Rp = 4.63%, GoF = Rwp/Re = 1.65, and RBragg = 1.94%. The final refinement results for the diffraction 4362
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where VNa is the BVS for Na, and Vf is the formal valence of the target ion. This value is well-established as an empirical indicator of the stability of the ionic positions and hence of the ion migration pathways (e.g., the global instability index (GII)).31 By simply examining the expansion of the isosurface, we can easily estimate the likely pathways, including the most stable original positions. The isosurface for Na+ in Na2Fe2Si2O7 is shown in Figure 4, with = 0.15 and 0.30, where the inner space wrapped by the smaller surface represents a set of more suitable positions for Na+. Overall, the space spreads along the [001] direction, interconnecting with each other to form a ladderlike channel, which is expected to be the major Na+ diffusion path in Na2Fe2Si2O7. For a more quantitative analysis, the Na+-vacancy migration paths and energy barriers were investigated with density functional theory (DFT) calculations along the directions expected by ΔBVS surfaces, i.e., the [001] and [110] directions. The initial geometry and total energy were calculated by setting the Na+-vacancy at either Na1, Na2, Na1′, or Na2′. Afterward, migration energy barriers between these positions were calculated by the climbing image nudged elastic band (CINEB) method.32 Here, the site notations of Na1′ and Na2′ represent the nonidentical sites distinguished from Na1 and Na2, respectively, by the hypothetical polaron introduced into Fe1* (Fe•Fe1). Figure 5(a) shows the intermediate Na+ positions optimized for each step set during the Na+-vacancy migration along the [001] direction. As shown in Figure 5(c), the calculated energy barriers for Na+-vacancy migration were 0.60, 0.17, 0.59, and 0.15 eV for the sequential hopping processes of ′ → vNa2 ′ → vNa2′ ′ → vNa1′ ′ , respectively, where the highest vNa1 ′ → vNa2 ′ does not energy value of 0.60 eV found for vNa1 significantly disturb the Na+ diffusion at room temperature. In this system, the variance of the polaron configuration did not result in a notable difference in the migration barrier (99.9%), and SiO2 (Kanto, >99.9%) were mixed in a molar ratio of 2:2:3 by planetary ball-milling at 300 rpm for 6 h followed by sintering at 1173 K. Material Characterizations. X-ray powder diffraction measurements were carried out with a two-axis powder diffractometer (BrukerAXS D8 ADVANCE) in the Bragg−Brentano geometry equipped with a CoKα radiation source (35 kV, 40 mA). Scattered X-ray was collected by a linear position sensitive detector VÅNTEC-1 with Fe foil as a Kβ filter. All the samples were sealed in a gastight sample cell under Ar atmosphere to prevent exposure of the sample to air and moisture. High-resolution X-ray diffraction (HRXRD) data was obtained by a high-resolution diffractometer installed at BL-4B2 of Photon Factory in High-Energy Accelerator Organization, Tsukuba, 4364
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Chemistry of Materials Japan.34−36 The sample powder was packed into a flat sample holder and kept in a vacuum chamber during the data collection. Structure determination and Rietveld refinement were performed by using the TOPAS-Academic ver. 5. Bond valence sum was calculated by a Python program PyAbstantia37 with softness-sensitive parameters.30 The 57Fe Mössbauer spectrum was taken in a transmission geometry with a Topologic System Inc. spectrometer with a 57Co/ Rh γ-ray source, calibrated with α-Fe as standard. MossWinn 3.0i software was used for fitting. Electrochemical Measurements. Electrochemical measurements were carried out with 2032-size coin cells made in an argon-filled glovebox. Electrodes for the electrochemical measurements contained Na2Fe2Si2O7, acetylene black (Denka Co.) as conductive additive, and polytetrafluoroethylene as binder, with a weight ratio of 80:10:10. The mixture was mixed with a mortar and a pestle, and electrodes with a diameter of 10 mm were made. The as-prepared electrodes were then pressed on to Al mesh followed by drying at 293 K for 12 h under vacuum. A commercial solution, 1 mol dm−3 NaPF6 in ethylene carbonate/dimethyl carbonate (EC/DMC) (1/1 in volume) (Kishida Chemical Co.), was used as an electrolyte with a glass fiber filter (GB100R, Toyo Roshi Kashiwa, Ltd.) as separator. Calculations. All the density functional theory/hybrid density functional calculations were performed with the Vienna Ab initio Simulation Package (Vasp) code ver. 5.4.1.38,39 The exchangecorrelation energy was calculated with a generalized gradient approximation (GGA) using the Perdew−Burke−Ernzerhof (PBE) functional.40,41 The projector-augmented-wave (PAW) method and a plane-wave basis set with a kinetic energy cutoff of 550 eV were used.42,43 The k-point sampling on (3 × 3 × 6) grid is used. To correct the self-interaction error in GGA, we applied the GGA+U approach presented by Dudarev et al.44 and the Heyd-Scuseria-Emzerhof (HSE06) hybrid functional as implemented in Vasp.45−48 The Ueff = 4.2 eV was adapted for Fe d electrons in the GGA+U calculation.49,50 The average voltages were calculated in the framework of GGA+U and HSE06. To reduce the computational cost in HSE06, we used the kinetic energy cutoff of 450 eV and k-point sampling on (2 × 2 × 4) grid. For the calculation of migration energy in Na-vacancy, the climbing image nudged elastic band (CI-NEB) method was applied.32 We used a (1 × 1 × 2) supercell with the composition of Na15Fe16Si16O56 to decouple an interaction between adjacent Navacancies. The initial pathway for the CI-NEB calculation is provided by the PathFinder method.51
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ACKNOWLEDGMENTS
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REFERENCES
This work was performed under the management of ”Elements Strategy Initiative for Catalysts and Batteries (ESICB)” supported by a program of Ministry of Education Culture, Sports, Science and Technology (MEXT), ”Elements Strategy Initiative to Form Core Research Center” (since 2012), Japan. The high-resolution powder diffraction experiment was performed under the approval of the Photon Factory Program Advisory Committee (Proposal Nos. 2013G670 and 2015G684). The crystal structure and bond valence sum map was visualised by the VESTA.52 The computation in this work has been done using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.
(1) Kubota, K.; Komaba, S. Review−Practical Issues and Future Perspective for Na-Ion Batteries. J. Electrochem. Soc. 2015, 162, A2538−A2550. (2) Takeda, Y.; Nakahara, K.; Nishijima, M.; Imanishi, N.; Yamamoto, O.; Takano, M.; Kanno, R. Sodium deintercalation from sodium iron oxide. Mater. Res. Bull. 1994, 29, 659−666. (3) Yabuuchi, N.; Yoshida, H.; Komaba, S. Crystal Structures and Electrode Performance of Alpha-NaFeO2 for Rechargeable Sodium Batteries. Electrochemistry 2012, 80, 716−719. (4) Yabuuchi, N.; Kajiyama, M.; Iwatate, J.; Nishikawa, H.; Hitomi, S.; Okuyama, R.; Usui, R.; Yamada, Y.; Komaba, S. P2-type Nax[Fe1/2Mn1/2]O2 made from earth-abundant elements for rechargeable Na-batteries. Nat. Mater. 2012, 11, 512−517. (5) Yoshida, H.; Yabuuchi, N.; Komaba, S. NaFe0.5Co0.5O2 as high energy and power positive electrode for Na-ion batteries. Electrochem. Commun. 2013, 34, 60−63. (6) Kubota, K.; Asari, T.; Yoshida, H.; Yaabuuchi, N.; Shiiba, H.; Nakayama, M.; Komaba, S. Understanding the Structural Evolution and Redox Mechanism of a NaFeO2-NaCoO2 Solid Solution for Sodium-Ion Batteries. Adv. Funct. Mater. 2016, 26, 6047−6059. (7) Padhi, A. K.; Nanjundaswamy, K. S.; Masquelier, C.; Goodenough, J. B. Mapping of Transition Metal Redox Energies in Phosphates with NASICON Structure by Lithium Intercalation. J. Electrochem. Soc. 1997, 144, 2581−2586. (8) Barpanda, P.; Oyama, G.; Nishimura, S.; Chung, S.-C.; Yamada, A. A 3.8-V earth-abundant sodium battery electrode. Nat. Commun. 2014, 5, 4358. (9) Oyama, G.; Nishimura, S.; Suzuki, Y.; Okubo, M.; Yamada, A. Off-Stoichiometry in Alluaudite-Type Sodium Iron Sulfate Na2.2xFe2−x(SO4)3 as an Advanced Sodium Battery Cathode Material. ChemElectroChem 2015, 2, 1019−1023. (10) Wei, S.; Mortemard de Boisse, B.; Oyama, G.; Nishimura, S.; Yamada, A. Synthesis and Electrochemistry of Na2.5(Fe1−yMny)1.75(SO4)3 Solid Solutions for Na-Ion Batteries. ChemElectroChem 2016, 3, 209−213. (11) Ellis, B. L.; Makahnouk, W. R. M.; Makimura, Y.; Toghill, K.; Nazar, L. F. A multifunctional 3.5 V iron-based phosphate cathode for rechargeable batteries. Nat. Mater. 2007, 6, 749−753. (12) Kawabe, Y.; Yabuuchi, N.; Kajiyama, M.; Fukuhara, N.; Inamasu, T.; Okuyama, R.; Nakai, I.; Komaba, S. Synthesis and electrode performance of carbon coated Na2FePO4F for rechargeable Na batteries. Electrochem. Commun. 2011, 13, 1225−1228. (13) Kawabe, Y.; Yabuuchi, N.; Kajiyama, M.; Fukuhara, N.; Inamasu, T.; Okuyama, R.; Nakai, I.; Komaba, S. A Comparison of Crystal Structures and Electrode Performance between Na2FePO4F and Na2Fe0.5Mn0.5PO4F Synthesized by Solid-State Method for Rechargeable Na-Ion Batteries. Electrochemistry 2012, 80, 80−84. (14) Barpanda, P.; Tian, Y.; Nishimura, S.; Chung, S.-C.; Yamada, Y.; Okubo, M.; Zhou, H.; Yamada, A. Sodium iron pyrophosphate: A novel 3.0 V iron-based cathode for sodium-ion batteries. Electrochem. Commun. 2012, 24, 116−119.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b00764. Scanning electron micrograph of Na2Fe2Si2O7, crystallographic information on Na2Fe2Si2O7, and structure models used for density functional calculations (PDF) Crystallographic information file of Na2Fe2Si2O7 (CIF)
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AUTHOR INFORMATION
Corresponding Author
*Phone: +81 (0)3 5841 7295. E-mail:
[email protected]. ORCID
Shin-ichi Nishimura: 0000-0001-7464-8692 Atsuo Yamada: 0000-0002-7880-5701 Author Contributions
A.P. and S.N. contributed equally to this work. Notes
The authors declare no competing financial interest. 4365
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Chemistry of Materials (15) Honma, T.; Togashi, T.; Ito, N.; Komatsu, T. Fabrication of Na2FeP2O7 glass-ceramics for sodium ion battery. J. Ceram. Soc. Jpn. 2012, 120, 344−346. (16) Kim, H.; Park, I.; Seo, D.-H.; Lee, S.; Kim, S.-W.; Kwon, W. J.; Park, Y.-U.; Kim, C. S.; Jeon, S.; Kang, K. New Iron-Based MixedPolyanion Cathodes for Lithium and Sodium Rechargeable Batteries: Combined First Principles Calculations and Experimental Study. J. Am. Chem. Soc. 2012, 134, 10369−10372. (17) Rudnick, R.; Gao, S. In Treatise on Geochemistry (Second Edition), Second ed. ed.; Holland, H. D., Turekian, K. K., Eds.; Elsevier: Oxford, 2014; pp 1−51. (18) Nytén, A.; Abouimrane, A.; Armand, M.; Gustafsson, T.; Thomas, J. O. Electrochemical performance of Li2FeSiO4 as a new Libattery cathode material. Electrochem. Commun. 2005, 7, 156−160. (19) Nytén, A.; Kamali, S.; Häggström, L.; Gustafsson, T.; Thomas, J. O. The lithium extraction/insertion mechanism in Li2FeSiO4. J. Mater. Chem. 2006, 16, 2266−2272. (20) Nishimura, S.; Hayase, S.; Kanno, R.; Yashima, M.; Nakayama, N.; Yamada, A. Structure of Li2FeSiO4. J. Am. Chem. Soc. 2008, 130, 13212−13213. (21) Sirisopanaporn, C.; Masquelier, C.; Bruce, P. G.; Armstrong, A. R.; Dominko, R. Dependence of Li2FeSiO4 Electrochemistry on Structure. J. Am. Chem. Soc. 2011, 133, 1263−1265. (22) Sirisopanaporn, C.; Boulineau, A.; Hanzel, D.; Dominko, R.; Budic, B.; Armstrong, A. R.; Bruce, P. G.; Masquelier, C. Crystal Structure of a New Polymorph of Li2FeSiO4. Inorg. Chem. 2010, 49, 7446−7451. (23) Dominko, R.; Bele, M.; Kokalj, A.; Gaberscek, M.; Jamnik, J. Li2MnSiO4 as a potential Li-battery cathode material. J. Power Sources 2007, 174, 457−461. (24) Dominko, R.; Bele, M.; Gaberscek, M.; Meden, A.; Remskar, M.; Jamnik, J. Structure and electrochemical performance of Li2MnSiO4 and Li2FeSiO4 as potential Li-battery cathode materials. Electrochem. Commun. 2006, 8, 217−222. (25) Li, S.; Guo, J.; Ye, Z.; Zhao, X.; Wu, S.; Mi, J.-X.; Wang, C.-Z.; Gong, Z.; McDonald, M. J.; Zhu, Z.; Ho, K.-M.; Yang, Y. Zero-Strain Na2FeSiO4 as Novel Cathode Material for Sodium-Ion Batteries. ACS Appl. Mater. Interfaces 2016, 8, 17233−17238. (26) Otroshchenko, L.; Simonov, V.; Belov, N. Refinement of Crystal Structure of Two Mn-silicates Na2Mn2Si2O7 and Na5(Mn,Na)3MnSi6O18. Dokl. Akad. Nauk SSSR 1982, 265, 76−79. (27) Astakhova, L. P.; Pobedimskaya, E. A.; Simonov, V. I. The Crystal Structure of a Synthetic Silicate Na2Mn2Si2O7. Dokl. Akad. Nauk SSSR 1967, 173, 1401−1403. (28) Menil, F. Systematic trends of the 57 Fe Mössbauer isomer shifts in (FeOn) and (FeFn) polyhedra. Evidence of a new correlation between the isomer shift and the inductive effect of the competing bond T-X (57Fe) (where X is O or F and T any element with a formal positive charge). J. Phys. Chem. Solids 1985, 46, 763−789. (29) Brown, I. D.; Altermatt, D. Bond-valence parameters obtained from a systematic analysis of the Inorganic Crystal Structure Database. Acta Crystallogr., Sect. B: Struct. Sci. 1985, 41, 244−247. (30) Adams, S. Relationship between bond valence and bond softness of alkali halides and chalcogenides. Acta Crystallogr., Sect. B: Struct. Sci. 2001, 57, 278−287. (31) Salinas-Sanchez, A.; Garcia-Muñoz, J.; Rodriguez-Carvajal, J.; Saez-Puche, R.; Martinez, J. Structural characterization of R2BaCuO5 (R = Y, Lu, Yb, Tm, Er, Ho, Dy, Gd, Eu and Sm) oxides by X-ray and neutron diffraction. J. Solid State Chem. 1992, 100, 201−211. (32) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113, 9901−9904. (33) Chevrier, V. L.; Ong, S. P.; Armiento, R.; Chan, M. K. Y.; Ceder, G. Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 075122. (34) Toraya, H.; Hibino, H.; Ohsumi, K. A New Powder Diffractometer for Synchrotron Radiation with a Multiple-Detector System. J. Synchrotron Radiat. 1996, 3, 75−83.
(35) Ida, T. Connection of segmented intensity data measured with a multiple-detector system for powder diffractometry. J. Appl. Crystallogr. 2005, 38, 795−803. (36) Toraya, H.; Huang, T. C.; Wu, Y. Intensity enhancement in asymmetric diffraction with parallel-beam synchrotron radiation. J. Appl. Crystallogr. 1993, 26, 774−777. (37) Nishimura, S. unpublished. (38) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (39) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15−50. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (41) Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78, 1396−1396. (42) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (43) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (44) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA.U study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 1505−1509. (45) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 2003, 118, 8207− 8215. (46) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum:“Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys.118, 8207 (2003)]. J. Chem. Phys. 2006, 124, 219906. (47) Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.; Á ngyán, J. G. Erratum: “Screened hybrid density functionals applied to solids” [J. Chem. Phys. 124, 154709 (2006)]. J. Chem. Phys. 2006, 125, 249901. (48) Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.; Á ngyán, J. G. Screened hybrid density functionals applied to solids. J. Chem. Phys. 2006, 124, 154709. (49) Zhou, F.; Cococcioni, M.; Marianetti, C. A.; Morgan, D.; Ceder, G. First-principles prediction of redox potentials in transition-metal compounds with LDA + U. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 235121. (50) Wang, L.; Maxisch, T.; Ceder, G. Oxidation energies of transition metal oxides within the GGAl+U framework. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 195107. (51) Rong, Z.; Kitchaev, D.; Canepa, P.; Huang, W.; Ceder, G. An efficient algorithm for finding the minimum energy path for cation migration in ionic materials. J. Chem. Phys. 2016, 145, 074112. (52) Momma, K.; Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272−1276.
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