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The Journal of Physical Chemistry C Article Figure 4. Density of states for (a) Li2S and Li2S2 and (b) α- and β-sulfur calculated using vdW-DF, HSE06, and vdW-DF+G0W0. Surface Energy. Figure S3 (Supporting Information) shows the GGA free energies of 31 Li2S surfaces as a function of sulfur chemical potential. The surfaces were selected from the low-index (100), (110), and (111) cleavage planes and take several different terminations into account. (Relaxed config- urations of all Li2S surfaces considered are shown in Figure S4 (Supporting Information).) We adopt a naming convention wherein surfaces are identified using their respective Miller indices followed by “Li”, “S”, or “stoichi”. These identify the stoichiometry of the slab as being either lithium-rich, sulfur- rich, or stoichiometric, respectively. As previously described, the upper “S-rich” limit of the sulfur chemical potential defined as zero for conveniencecorresponds to the chemical potential of elemental sulfur. Comparison calculations similar to those in Figure S3 (Supporting Information) were also performed using the optB88-based vdW-DF functional and by combining the GGA with solvation effects. Figure 5 summarizes these results across all three calculation methodsGGA (Figure 5a), vdW- DF (Figure 5b), and GGA with solvation (Figure 5c)by plotting the lowest-energy terminations for each of the three Figure 5. Free energies of Li2S surfaces as a function of sulfur chemical potential and calculation method. (a) GGA, (b) vdW-DF, and (c) GGA + solvation. Vertical lines represent sulfur-poor and -rich limits to the S chemical potential. The three lowest-energy surfaces are plotted for each of the three surface normals considered: 100, 110, and 111. 4680 DOI: 10.1021/jp513023v J. Phys. Chem. C 2015, 119, 4675−4683 Table 3. Calculated and Experimental Band Gap of α-, β- Sulfur, Li2S, and Li2S2a band gap method type α-sulfur β-sulfur Li2S Li2S2 vdW-DF 2.20 2.34 HSE06 3.01 3.20 vdW-DF+G0W0 - 3.76 GGA+G0W0 - - Exp. 2.79,60 2.6158 - 3.46 1.07 4.34 1.98 5.10 2.58 5.11 2.70 - - aThe reported experimental band gaps were measured at near-ambient temperatures, while the calculations are performed at 0 K. Extrapolating the experimental data to zero K yields gaps in the range from 2.9 to 3.3 eV. when using the HSE06 hybrid functional and is largest for the vdW-DF + G0W0, 5.10 eV. These gaps indicate that Li2S is an electronic insulator, a fact which could limit battery perform- ance if charge transport through Li S is needed during charge or discharge. 2 To the best of our knowledge, an experimental 11 value for the Li2S band gap has not been reported.PDF Image | First-Principles Study of Redox End Members in Lithium Sulfur
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