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Article pubs.acs.org/JPCC First-Principles Study of Redox End Members in Lithium−Sulfur Batteries Haesun Park,† Hyun Seung Koh,† and Donald J. Siegel*,†,‡,§,∥ †Mechanical Engineering Department, ‡Applied Physics Program, §Michigan Energy Institute, and ∥Joint Center for Energy Storage Research, University of Michigan, Ann Arbor, Michigan 48109-2125, United States *S Supporting Information ABSTRACT: The properties of the solid-phase redox end members, α-S, β-S, Li2S, and Li2S2, are expected to strongly influence the performance of lithium−sulfur batteries. Never- theless, the fundamental thermodynamic and electronic properties of these phases remain poorly understood. From a computational standpoint, the absence of these data can be explained by the omission of long-ranged van der Waals interactions in conventional density functionals; these interactions are essential for describing the molecular-crystal nature of S-based compounds. Here we apply van der Waals augmented density functional theory (vdW-DF), quasi-particle methods (G0W0), and continuum solvation techniques to predict several structural, thermodynamic, spectroscopic, electronic, and surface characteristics of these phases. The stability of the α allotrope of sulfur at low temperatures is confirmed by calculating the sulfur phase diagram. Similarly, the stability of lithium persulfide, Li2S2, a compound whose presence may limit capacity, was assessed by comparing the energies of several hypothetical A2B2 crystal structures. In all cases Li2S2 is predicted to be unstable with respect to 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, the equilibrium crystallites are comprised entirely of stoichiometric (111) surfaces, while for α-S a complex mixture of several facets is predicted. Finally, G0W0 calculations reveal that all of α-S, β-S, Li2S, and Li2S2 are insulators with band gaps greater than 2.5 eV. ■ INTRODUCTION Batteries based on lithium-ion chemistries have dramatically altered the energy storage landscape and in so doing have enabled a variety of new technologies such as portable electric devices.1−8 Despite the higher energy density of Li-ion systems (∼350 Wh/kg1−7 theoretically and ∼120 Wh/kg9 at the system level) compared to earlier approaches based on nickel−metal- hydride or lead−acid systems, further gains in capacity are highly desirable for emerging applications such as in vehicle electrification.1−7,9 Lithium−sulfur (Li−S) batteries present a promising alternative to the Li-ion chemistry due to their high theoretical specific energy (∼2200 Wh/kg),2,7 and potential for low cost.10 Recent cell designs involving nanostructured cathodes have improved cyclability and sparked renewed interest in sulfur- based systems.10−14 Nevertheless, several performance gaps should be addressed before these systems become commercially viable, such as capacity fade15 arising from the so-called “polysulfide shuttle” effect and the presumably insulating nature of solid-state redox end members consisting of sulfur and metal sulfides.11 Understanding the properties of these compounds will foster the development of rational strategies that can overcome the aforementioned limitations. © 2015 American Chemical Society 4675 One issue of both fundamental and practical importance is the relative stability of Li−S redox end members. For example, lithium persulfide, Li2S2, has been proposed as an insoluble discharge product in Li−S batteries.20,26,27 The formation of Li2S2 would be undesirable, as it has been suggested to limit capacity.15−17 However, as Li2S2 does not appear in the Li−S phase diagram,18 its presence as a discharge phase remains a matter of debate. A recent study based on X-ray absorption near-edge spectroscopy (XANES)19 found no evidence for the presence of Li2S2 during battery operation. Likewise, Hagen et al. employed Raman spectroscopy to characterize polysulfide formation in the Li−S system but was unable to directly identify Li2S2.20 In a similar vein, the presence of higher-temperature allotropes of sulfur has been suggested to impact the longevity of Li−S batteries. Recent experiments employing encapsulated sulfur or carbon fiber−sulfur composite cathodes18,26 have observed the presence of β-sulfur, a monoclinic phase which in bulk form has been reported to be stable at temperatures above Received: December 31, 2014 Revised: February 6, 2015 Published: February 9, 2015 DOI: 10.1021/jp513023v J. Phys. Chem. C 2015, 119, 4675−4683PDF Image | First-Principles Study of Redox End Members in Lithium Sulfur
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