Prediction of New Phase and Electrochemical Properties of Li2S2 for

Mar 22, 2018 - ABSTRACT: The intermediate product Li2S2 plays a pivotal role in the charge/discharge process of lithium−sulfur batteries. However, t...
0 downloads 0 Views 3MB Size
Download PDF
Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

pubs.acs.org/IC

Prediction of New Phase and Electrochemical Properties of Li2S2 for the Application of Li‑S Batteries Y. Pan*,†,‡ and W. M. Guan*,‡ †

State Key Lab of Oil and Gas Reservoir Geology and Exploitation, School of Materials Science and Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China ‡ State Key Laboratory of Advanced Technologies for Comprehensive Utilization of Platinum Metals, Kunming 650106, People’s Republic of China ABSTRACT: The intermediate product Li2S2 plays a pivotal role in the charge/discharge process of lithium−sulfur batteries. However, the structural configuration and relevant properties of Li2S2 are unclear. In this work, by using ab initio calculations, we present results of novel phases, average open circuit voltages (Vocs), and electronic properties of the stable Li2S2. Two new Li2S2 phases are predicted: orthorhombic (Cmca) and orthorhombic (Immm) structures. The calculated Vocs of hexagonal (P63/ mmc), orthorhombic (Cmca), and orthorhombic (Immm) are 3.91, 3.95, and 3.88 V, respectively. In particular, the calculated band gap of the Immm structure is about 0.225 eV, which is smaller than that of Li2S. The narrow band gap of Li2S2 derives from the electronic lump between the Li s state and S 3p state for the orthorhombic structure. Therefore, the electronic properties of Li2S2 are markedly influenced by the structural configuration.

■

INTRODUCTION The development of safe, light, high energy density, environmentally friendly, and less expensive batteries has been pursued greatly for future energy storage devices such as portable electronics, electric vehicles, etc.1−5 In comparison to Li ion batteries, Li-S compounds are promising batteries because of their high energy density, theoretical specific capacity (2600 Wh kg1−), nonpolluting nature, low cost, etc.6−10 Nevertheless, the commercial applications of Li-S batteries are plagued by the shuttle effect and volumetric expansion of discharge products, especially for the insulating nature of deposits.11,12 During the process of charge and discharge, the electrochemical reaction of Li-S batteries is described by 16Li+ + S8 + 16e− → 8Li2S. Numerous experiments show that intermediate products such as Li2S8, Li2S4, Li2S2, and Li2S can be formed.13,14 Those intermediate products play a pivotal role in the charge and discharge processes: that is to say, the theoretical specific capacity of Li-S batteries is markedly influenced by these discharge products. Furthermore, the poorer electrical conductivity of Li-S batteries is determined by discharge products such as the insulating S8 and Li2S/Li2S2. In particular, the formation of the S2 ion is mainly attributed to the formation of Li2S2.15 The structural configuration and electrical properties of Li2S have been widely studied by experiments and theoretical methods, respectively.16,17 However, the crystal structure of the intermediate product Li2S2 remains the subject of considerable controversy.18 Despite intense experimental investigations, the intermediate product Li2S2 has not been observed over the last few years.19 To reveal the intermediate product Li2S2, the © XXXX American Chemical Society

crystal structure, cycle life, and energy density of Li2S2 have been studied by Nazar et al.20 A series of stoichiometric Li2S2 reactions are predicted. Unfortunately, the structural configuration of Li2S2 is unclear.18 As a result, the structural configuration and electrochemical behavior of Li2S2 are unknown. To explore the electrochemical properties of Li-S batteries, the crystal structure, band structure, and average open circuit voltage (Voc) of Li2S2 are studied on the basis of ab initio calculations. On the basis of the Inorganic Crystal Structure Database (ISCD) and their similar structural configurations, four possible Li2S2 structures are predicted by the dynamics and thermodynamics, respectively. The phonon dispersion curves of Li2S2 are calculated in detail. We find that Li2S2 with hexagonal (P63/mmc) and orthorhombic (Cmca and Immm) structures are dynamically stable. In particular, the calculated band gap of Li2S2 with Immm structure is 0.225 eV, which is smaller than that of Li2S.

■

THEORETICAL METHODS

As mentioned above, Li2S2 is an intermediate phase. Although recent work has predicted a stable structure (space group: P63/mmc, No. 194),21,22 the calculated theoretical band gap of Li2S2 is 1.80 eV. Therefore, it is necessary to explore the structural configuration of Li2S2. According to the similar structural configurations and Inorganic Crystal Structure Database, we designed and examined three similar phases: a K2S2-type hexagonal structure with space group P6̅̅2m (No. 189), a K2O2-type orthorhombic structure with space group Cmca Received: March 22, 2018

A

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Optimized structural models of Li2S2: (a) hexagonal structure (P63/mmc); (b) hexagonal structure (P6̅2m); (c) orthorhombic structure (Cmca); (d) orthorhombic structure (Immm).

Table 1. Calculated Lattice Parameters (Å), Formation Enthalpy (ΔH, eV/mol), and Atomic Coordinates of Li2S2 structure

method

space group

a

c

atomic coordinates

ΔH

Na2S2-type

GGA

P63/mmc

3.908

9.336

−1.244

K2S2-type

GGA

P6̅2m

6.806

5.024

K2O2-type

GGA

Cmca

6.424

6.325

8.380

Cs2S2-type

GGA

Immm

5.151

7.042

3.902

Li(0, 0, 0) Li(0.3333, 0.6667, 0.25) S(0.3333, 0.6667, 0.6397) Li(0, 0.6453, 0) Li(0, 0.3388, 0.50) S(0, 0, 0.2095) S(0.3333, 0.6667, 02534) Li(0.25, 0.2103, 0.25) S(0, 0.0302, 0.8761) Li(0, 0.1979, 0.50) S(0.2084, 0, 0)

b

−1.206

−1.233 −1.190

Figure 2. Calculated phonon dispersion curves of Li2S2: (a) hexagonal structure (P63/mmc); (b) hexagonal structure (P6̅2m); (c) orthorhombic structure (Cmca); (d) orthorhombic structure (Immm).

(No. 64), and a Cs2S2-type orthorhombic structure with space group Immm (No. 71), respectively. Figure 1 shows the structural models of Li2S2.

To predict the new crystal structure and investigate the electrochemical properties of Li2S2, all calculations in this paper were calculated by using ab initio calculations within the CASTEP code.23 B

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 3. Calculated phonon densities of state (PhDOS) of Li2S2: (a) hexagonal structure (P63/mmc); (b) hexagonal structure (P6̅2m); (c) orthorhombic structure (Cmca); (d) orthorhombic structure (Immm). To compare the calculated results, we used the GGA within the PBE functional24 and the LDA within the CA-PZ functional25 to treat the exchange correlation function of Li2S2. The valence electronic configurations of Li and S were 1s22s1 and 3s23p4. After the convergence test, the cutoff energy of all systems was 350 eV. The k points 14 × 14 × 5, 8 × 8 × 10, 15 × 15 × 8, and 14 × 14 × 11 were selected for the hexagonal structure (P63/mmc), hexagonal structure (P6̅2m), orthorhombic structure (Cmca), and orthorhombic structure (Immm), respectively. The dynamic stability of Li2S2 mainly derives from the vibration frequency of the atoms in a system, which is measured by the phonon dispersion curves. Therefore, the phonon dispersion curves of Li2S2 were calculated by the PHONON code.26,27

dynamically unstable because of the existence of imaginary phonon frequencies. However, another hexagonal structure (P63/mmc) and our predicted orthorhombic structures (Cmca and Immm) are dynamically stable because there are no imaginary phonon frequencies. Figure 3 displays the calculated phonon density of states (PhDOS) of Li2S2 with the various structures. It is clear that negative frequencies for the hexagonal structure (P6̅2m) are observed, confirming that Li2S2 with hexagonal structure (P6̅2m) is mechanically unstable at the ground state. The calculated phonon density of states shows that the dynamic instability of this structure mainly derives from the vibration of S atoms in the low-frequency region. However, the hexagonal structure (P63/mmc) and the orthorhombic structures (Cmca and Immm) are mechanically stable because there are no negative frequencies in those structures. It is worth noting that the low-frequency region of the hexagonal structure (see Figure 3a) is due to the mixture of Li and S vibrations and the high-frequency region of this structure can be attributed to the vibration of S atoms. However, the PhDOS profiles of orthorhombic structures (see Figure 3c,d) are different from the hexagonal structure. For the orthorhombic structure (Cmca), the PhDOS profile of this structure mainly divides into three parts. The first part between 0.94 and 6.21 THz consists mainly of vibrations of S atoms. The second part from 7.02 to 13.19 THz contains a mixture of Li atoms and part of the S atoms. In contrast, the highfrequency region is due to the vibrations of S atoms. For the orthorhombic structure (Immm), the whole frequency region is due to a mixture of vibrations of Li atoms and S atoms. Thus, we can suggest that the PhDOS profiles determine the structural configuration and electronic contribution near the Fermi level (EF), which is confirmed by the electronic structure. As mentioned above, we can conclude that hexagonal (P63/ mmc) and orthorhombic (Cmca and Immm) structures are stable.

■

RESULTS AND DISCUSSION To our knowledge, the structural stability of unknown phase is estimated by the dynamics and thermodynamics, respectively. The assessment of dynamic stability is measured by the phonon frequency, where the thermodynamic stability is related to the chemical potential. Therefore, the thermodynamic stability of Li2S2 is calculated by the formation enthalpy (ΔH), which is given by ΔH = E(Li 2S2 ) − 2E(Li) − 2E(S)

(1)

where E(Li2S2), E(Li), and E(S) are the total energies of Li2S2, bulk Li, and S8 chain, respectively. To examine the structural stability, Table 1 gives the space groups, equilibrium lattice parameters, atomic positions, and ΔH values of Li2S2. It is found that the calculated ΔH values of Li2S2 with those structures are smaller than zero. Thus, it is concluded that our predicted Li2S2 is thermodynamically stable. Note that the calculated ΔH value of the P63/mmc structure is −1.244 eV/mol, which is lower than that of other structures. This is why Li2S2 with a P63/mmc structure was first predicted over the last few years. In addition to thermodynamic stability, we further investigated the dynamic stability of those predicted Li2S2 species. Figure 2 shows the calculated phonon dispersion curves of Li2S2. We find that that Li2S2 with P6̅2m structure is C

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 4. Calculated charge density contour plots of Li2S2: (a) hexagonal structure (P63/mmc) along the (110) plane; (b) hexagonal structure (P6̅2m) along the (111) plane; (c) orthorhombic structure (Cmca) along the (110) plane; (d) orthorhombic structure (Immm) along the (001) plane.

Figure 5. Band structures and partial densities of states (PDOS) of Li2S2: (a) hexagonal structure (P63/mmc); (b) hexagonal structure (P6̅2m); (c) orthorhombic structure (Cmca); (d) orthorhombic structure (Immm).

The structural stability of Li2S2 cab be further estimated by the lattice parameters and atomic positions. Hence, we studied the lattice parameters and atomic positions of Li2S2 with various structures. From Table 1, the calculated lattice parameters of P63/mmc structure are a = 3.908 Å and c = 9.336 Å, respectively. For P63/mmc structure, Li atoms occupy the Wyckoff 2a (0, 0, 0) and 2c (0.3333, 0.6667, 0.2500) sites, and the S atom is located at the 4f (0.3333, 0.6667, 0.6397) site. In particular, the alternating stacking of Li and S layers can be viewed along the c axis. As a result, the cohesive force of the layered structure depends on the Li−S bond. For the P63/mmc structure, the calculated Li−S bond length is 2.555 Å. For our predicted new phases, the calculated lattice parameters of Li2S2 with Cmca structure are a = 6.424 Å, b = 6.325 Å, and c = 8.380 Å. In this structure, Li and S occupy the Wyckoff 8e (0.250, 0.2103, 0.250) and 8f (0, 0.0302, 0.8761) sites, respectively. However, the structural configuration of the

orthorhombic structure (Cmca) is different from that of hexagonal structure (P63/mmc). As shown in Figure 1, eight Li atoms can form the derivative cubic structure. As a result, the symmetrical Li−S bonds effectively improve the structural stability of the orthorhombic structure (Cmca). The calculated Li−S bond length is 2.452 Å, which is smaller than the corresponding bond length for the hexagonal structure (P63/ mmc). Although Immm and Cmca are orthorhombic structures, the structural configuration of the former is different from that of the latter. For the Immm structure, the calculated lattice parameters are a = 5.151 Å, b = 7.042 Å, and c = 3.902 Å, respectively. For this structure, Li and S occupy the Wyckoff 4h (0, 0.1979, 0.500) and 4e (0.2084, 0, 0) sites, respectively. Importantly, the alternative stacking of Li and S layers can be formed along the b axis. D

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 6. Band structure and partial density of states (PDOS) of Li2S2: (a) hexagonal structure (P63/mmc); (b) hexagonal structure (P6̅2m); (c) orthorhombic structure (Cmca); (d) orthorhombic structure (Immm).

Therefore, the stability of the Immm structure is also determined by the layered structure. The calculated layered distance of the Immm structure is 2.627 Å. Note that the electronic properties of Li2S2 are also influenced by the structural configuration. Naturally, the structural stability of Li2S2 also relies on the bonding state and bond orientation, which are reflected by the charge density. To further understand the nature of the structural stability of Li2S2, Figure 4 shows calculated contour plots of the charge density distribution of Li2S2, in which the critical features of Li2S2 are labeled. It is obvious that the localized hybridization between Li and S will form a directional Li−S bond. This discrepancy derives from the bonding state and bond length. From Figure 4a, we can see that the formation of S−S and Li−S bonds derives from the charge overlaps of Li−S and S−S atoms. The calculated bond lengths of S−S, Li−S(1), and Li− S(2) are 2.155, 2.555, and 2.675 Å, respectively. In particular, the structural stability of the P63/mmc structure is determined by the force of the layered structures. For the hexagonal structure (P6̅2m), however, there is no charge overlap between S and S. This feature is different from the other three structures. In this structure, there are two different Li−S bonds. The calculated Li−S bond lengths are 2.541 and 2.569 Å, respectively. Therefore, the structural stability of the hexagonal structure (P6̅2m) mainly depends on the strength of the Li−S bond. It is obvious that the charge density distribution of the orthorhombic structure is different from that of the hexagonal structure. For the Cmca structure, the cohesive force of the layered structure is attributed to the localized hybridization

between Li−S and S−S atoms. Here, the obtained S−S and Li− S bond lengths are 2.111 and 2.452 Å, respectively. However, we find that there is a network bonding state in the orthorhombic structure (Immm), which is consistent with the Li−S bond and S−S bond. The calculated S−S and Li−S bond lengths are 2.147 and 2.627 Å, respectively. Importantly, the average open circuit voltage (Voc) plays a pivotal role in Li-S batteries. Therefore, the average open circuit voltage of Li2S2 is calculated by28,29 Voc =

E(Li x1S2) − E(Li x2S2 ) + (x2 − x1)E(Li) e(x2 − x1)

(2)

where E(Lix1S2), E(LixS2), and E(Li) are the total energies of Lix1S2, Lix2S2, and metallic lithium, respectively. x1 and x2 represent the number of Li atoms in the Lix1S2 and Lix2S2 systems. The calculated results show that the Vocs of hexagonal (P63/mmc), orthorhombic (Cmca), and orthorhombic (Immm) structures are 3.91, 3.95, and 3.88 V, respectively. The calculated results show that the Voc value of the orthorhombic structure (Cmca) is slightly larger than those of the other structures. To explore the electronic properties, Figures 5 and 6 show the calculated band structures and densities of state (DOS) of Li2S2 with GGA and LDA functionals. To compare the electronic properties, we studied the band gap of Li2S2 within GGA and LDA, respectively. From Figure 6, the calculated band gap of Li2S2 within GGA is larger than that of LDA because of the choice of functional. Importantly, the calculated band gap of the hexagonal structure (P63/mmc) is 1.098 eV by GGA, indicating that Li2S2 with a hexagonal structure is a E

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

(3) Pan, Y. Role of S-S interlayer spacing on the hydrogen storage mechanism of MoS2. Int. J. Hydrogen Energy 2018, 43, 3087−3091. (4) Arunkumar, P.; Jeong, W. J.; Won, S.; Im, W. B. Improved electrochemical reversibility of over-lithiated layered Li2RuO3 cathodes: Understanding aliovalent Co3p substitution with excess lithium. J. Power Sources 2016, 324, 428−438. (5) Pan, Y.; Guan, W. Prediction of new stable structure, promising electronic and thermodynamic properties of MoS3: Ab initio calculations. J. Power Sources 2016, 325, 246−251. (6) Bailey, T. S.; Zakharov, L. N.; Pluth, M. D. Understanding Hydrogen Sulfide Storage: Probing Conditions for Sulfide Release from Hydrodisulfides. J. Am. Chem. Soc. 2014, 136, 10573−10576. (7) Chen, J. J.; Yuan, R. M.; Feng, J. M.; Zhang, Q.; Huang, J. X.; Fu, G.; Zheng, M. S.; Ren, B.; Dong, Q. F. Conductive Lewis Base Matrix to Recover the Missing Link of Li2S8 during the Sulfur Redox Cycle in Li-S Battery. Chem. Mater. 2015, 27, 2048−2055. (8) Gerber, L. C. H.; Frischmann, P. D.; Fan, F. Y.; Doris, S. E.; Qu, X.; Scheuermann, A. M.; Persson, K.; Chiang, Y. M.; Helms, B. A. Three-Dimensional Growth of Li2S in Lithium-Sulfur Batteries Promoted by a Redox Mediator. Nano Lett. 2016, 16, 549−554. (9) Wang, C.; Wang, X.; Yang, Y.; Kushima, A.; Chen, J.; Huang, Y.; Li, J. Slurryless Li2S/Reduced Graphene Oxide Cathode Paper for High-Performance Lithium Sulfur Battery. Nano Lett. 2015, 15, 1796− 1802. (10) Pan, Y.; Guan, W.; Mao, P. Insulator-to-metal transition of lithium-sulfur battery. RSC Adv. 2017, 7, 44326−44332. (11) Meng, X.; Comstock, D. J.; Fister, T. T.; Elam, J. W. VaporPhase Atomic-Controllable Growth of Amorphous Li2S for HighPerformance Lithium-Sulfur Batteries. ACS Nano 2014, 8, 10963− 10972. (12) Liu, J.; Nara, H.; Yokoshima, T.; Momma, T.; Osaka, T. Li2S cathode modified with polyvinylpyrrolidone and mechanical milling with carbon. J. Power Sources 2015, 273, 1136−1141. (13) Kamphaus, E. P.; Balbuena, P. B. Long-Chain Polysulfide Retention at the Cathode of Li-S Batteries. J. Phys. Chem. C 2016, 120, 4296−4305. (14) Ai, G.; Dai, Y.; Dai, Y.; Mao, W.; Zhao, H.; Fu, Y.; Song, X.; En, Y.; Battaglia, V. S.; Srinivasan, V.; Liu, G. Biomimetic Ant-Nest Electrode Structures for High Sulfur Ratio Lithium-Sulfur Batteries. Nano Lett. 2016, 16, 5356−5372. (15) Wujcik, K. H.; Wang, D. R.; Raghunathan, A.; Drake, M.; Pascal, T. A.; Prendergast, D.; Balsara, N. P. Lithium Polysulfide Radical Anions in Ether-Based Solvents. J. Phys. Chem. C 2016, 120, 18403− 18410. (16) Li, N.; Wang, Y.; Tang, D.; Zhou, H. Integrating a Photocatalyst into a Hybrid Lithium-Sulfur Battery for Direct Storage of Solar Energy. Angew. Chem., Int. Ed. 2015, 54, 9271−9274. (17) Mccloskey, B. D. Attainable Gravimetric and Volumetric Energy Density of Li-S and Li Ion Battery Cells with Solid SeparatorProtected Li Metal Anodes. J. Phys. Chem. Lett. 2015, 6, 4581−4588. (18) Feng, Z.; Kim, C.; Vijh, A.; Armand, M.; Bevan, K. H.; Zaghib, K. Unravelling the role of Li2S2 in lithiumesulfur batteries: A first principles study of its energetic and electronic properties. J. Power Sources 2014, 272, 518−521. (19) Nelson, J.; Misra, S.; Yang, Y.; Jackson, A.; Liu, Y.; Wang, H.; Dai, H.; Andrews, J. C.; Cui, Y.; Toney, M. F. In operando X-ray diffraction and transmission X-ray microscopy of lithium sulfur batteries. J. Am. Chem. Soc. 2012, 134, 6337−6343. (20) Pang, Q.; Nazar, L. F. Long-Life and High-Areal-Capacity Li-S Batteries Enabled by a Light-Weight Polar Host with Intrinsic Polysulfide Adsorption. ACS Nano 2016, 10, 4111−4118. (21) Zhou, G.; Pei, S.; Li, L.; Wang, D. W.; Wang, S.; Huang, K.; Yin, L. C.; Li, F.; Cheng, H. M. A Graphene Pure-Sulfur Sandwich Structure for Ultrafast, Long-Life Lithium-Sulfur Batteries. Adv. Mater. 2014, 26, 625−631. (22) Yang, G.; Shi, S.; Yang, J.; Ma, Y. Insight into the role of Li2S2 in Li-S batteries: a first principles study. J. Mater. Chem. A 2015, 3, 8865−8869.

semiconductor material. The calculated DOS profile further shows that the valence band near EF derives from the contribution of the S 3p state. However, the conduction band near EF is contributed by the Li s state and S 3p state, respectively. In particular, the Li s state is far away from the S p state. As a result, those states can result in no charge interaction between the conduction band and the valence band near EF. This is why Li2S2 with a hexagonal structure (P63/mmc) is a semiconductor. Although the calculated band gap of the Cmca structure is 1.568 eV by GGA, the calculated band gap of the Immm structure is 0.225 eV by GGA. It is obvious that the band gap of the Immm structure is smaller than that of the P63/mmc structure. According to the ab initio calculations, we observe that the S 3p state of the orthorhombic structure is across the Fermi level, indicating that this structure can improve the electronic lump between the conduction band and the valence band. In particular, the layered structure is beneficial for improving the charge interaction between Li and S. Thus, we suggest that the electronic properties of Li2S2 are markedly influenced by the structural configuration.

■

CONCLUSION In conclusion, we have studied the crystal structure, thermodynamic stability, phonon dispersion, band structure, and average open circuit voltage of four possible Li2S2 species. Those structures are thermodynamically stable because the calculated ΔH value of our predicted Li2S2 is smaller than zero. In particular, we first predict that Cmca and Immm structures are dynamically stable. The calculated band gaps of P63/mmc, Cmca, and Immm structures are 1.098, 1.568, and 0.225 eV, respectively. The calculated average open circuit voltages of P63/mmc, Cmca, and Immm structures are 3.91, 3.95, and 3.88 V, respectively. The calculated band gap of Li2S2 with an orthorhombic (Immm) structure is smaller than that of Li2S. The narrow band gap is attributed to the electronic lump between the Li s state and S 3p state for the orthorhombic structure.

■

AUTHOR INFORMATION

Corresponding Authors

*Y.P.: e-mail, [email protected]; tel, +86-028-83037437. *W.M.G.: e-mail, [email protected]. ORCID

Y. Pan: 0000-0001-8463-8156 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the State Key Laboratory of Advanced Technology for Comprehensive Utilization of Platinum Metals (Grant No. SKL-SPM-201816). We acknowledge discussions with Lady Yun Zheng.

■

REFERENCES

(1) Lee, D. J.; Yu, S. H.; Lee, H. S.; Jin, A.; Lee, J.; Lee, J. E.; Sung, Y. E.; Hyeon, T. Facile synthesis of metal hydroxide nanoplates and their application as lithium-ion battery anodes. J. Mater. Chem. A 2017, 5, 8744−8751. (2) Zu, C.; Manthiram, A. Stabilized Lithium-Metal Surface in a Polysulfide-Rich Environment of Lithium−Sulfur Batteries. J. Phys. Chem. Lett. 2014, 5, 2522−2527. F

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (23) Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys.: Condens. Matter 2002, 14, 2717−2744. (24) Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (25) Ceperley, D. M.; Alder, B. J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45, 566−569. (26) Shang, S.; Wang, Y.; Guan, P.; Wang, W. Y.; Fang, H.; Anderson, T.; Liu, Z. K. Insight into structural, elastic, phonon, and thermodynamic properties of a-sulfur and energy related sulfides: a comprehensive first-principles study. J. Mater. Chem. A 2015, 3, 8002− 8014. (27) Li, Z.; Tan, S.; Grayeli, E. B.; Kodama, T.; Asheghi, M.; Delgado, G.; Panzer, M.; Porovsky, A.; Wack, D.; Goodson, K. E. Phonon Dominated Heat Conduction Normal to Mo/Si Multilayers with Period below 10 nm. Nano Lett. 2012, 12, 3121−3126. (28) Jiang, H. R.; Zhao, T. S.; Liu, M.; Wu, M. C.; Yan, X. H. Twodimensional SiS as a potential anode material for lithium-based batteries: A first-principles study. J. Power Sources 2016, 331, 391−399. (29) Xu, Q.; Ban, C.; Dillon, A. C.; Wei, S. H.; Zhao, Y. FirstPrinciples Study of Lithium Borocarbide as a Cathode Material for Rechargeable Li ion Batte. J. Phys. Chem. Lett. 2011, 2, 1129−1132.

G

DOI: 10.1021/acs.inorgchem.8b00747 Inorg. Chem. XXXX, XXX, XXX−XXX