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ACS Nano 2013, 7, 2829−2833. (26) Chen, Y.-X.; Kaghazchi, P. Metalization of Li2S particle surfaces in Li-S batteries. Nanoscale 2014, 6, 13391−13395. DOI: 10.1021/jp513023v J. Phys. Chem. C 2015, 119, 4675−4683 fundamental thermodynamic and electronic properties of these phases remain poorly understood. In the present study several computational techniquesvan der Waals augmented density functional theory (vdW-DF), quasi-particle methods (G W ), 00 and continuum solvation techniquesare employed to predict key structural, thermodynamic, spectroscopic, electronic, and surface characteristics of these phases. The stability of the α allotrope of sulfur at low temperatures was confirmed by revisiting the sulfur-phase diagram. Likewise, the stability of lithium persulfide, Li S a phase whose 22 presence during discharge is believed limit capacitywas assessed by comparing the energies of several hypothetical A2B2 crystal structures. In all cases Li2S2 was predicted to be unstable with respect to decomposition into a two-phase mixture of Li2S and α-S, suggesting that Li2S2 is a metastable phase. Regarding surface properties, the stable surfaces and equilibrium crystallite shapes of Li2S and α-S were predicted in the presence and absence of a continuum solvation field intended to mimic the effect of a dimethoxyethane (DME)- based electrolyte. In the case of Li2S, equilibrium crystallites are comprised entirely of stoichiometric (111) surfaces, while for α- S a complex mixture of several facets is predicted. Finally, G W calculations reveal that all of α-S, β-S, Li S, and 002 Li2S2 are insulators with band gaps greater than 2.5 eV. The properties revealed by this study provide a “baseline understanding” of the solid-phase redox end members in Li−S batteries. We anticipate that this data will be of value in understanding pathways associated with charge and discharge reactions in these systems and foster development of approaches that move the Li−S chemistry closer to commercial v■iability. ASSOCIATED CONTENT *S Supporting Information Calculated lattice constants of redox end members using different vdW-DF methods and their associated experimental values; total energy of the β-S unit cell as a function of cell volume using various methods; calculated X-ray diffraction patterns for Li2S and Li2S2; calculated surface energies for Li2S as a function of sulfur chemical potential, surface normal, and calculation method; relaxed structures of Li2S and sulfur surfaces. This material is available free of charge via the Internet a■t http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: djsiege@umich.edu. Tel.: +1 (734) 764-4808. Notes T■he authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported as part of the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, and Basic Energy Sciences. H.P. acknowledges support from the Kwanjeong Educational Foundation. ■ REFERENCES (1) Whittingham, M. S. Lithium Batteries and Cathode Materials. Chem. Rev. 2004, 104, 4271−4302. (2) Bruce, P. G.; Freunberger, S. A.; Hardwick, L. J.; Tarascon, J.-M. Li-O2 and Li-S batteries with high energy storage. Nat. Mater. 2012, 11, 19−29. 4682PDF Image | First-Principles Study of Redox End Members in Lithium Sulfur
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