Insight into the Discharge Products and Mechanism of Room

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C: Energy Conversion and Storage; Energy and Charge Transport

Insight Into the Discharge Products and Mechanism of RoomTemperature Sodium-Sulfur Batteries: A First Principles Study Ya-Tong Wang, Yu Hao, Li-Chun Xu, Zhi Yang, Mao-Yun Di, Rui-Ping Liu, and Xiu-Yan Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10858 • Publication Date (Web): 29 Jan 2019 Downloaded from http://pubs.acs.org on January 31, 2019

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The Journal of Physical Chemistry

Insight into the Discharge Products and Mechanism of Room-Temperature Sodium-Sulfur Batteries: A First Principles Study Yatong Wang,† Yu Hao,† Li-Chun Xu,∗,† Zhi Yang,† Mao-Yun Di,‡ Ruiping Liu,† and Xiuyan Li† †College of Physics and optoelectronics, Taiyuan University of technology, Taiyuan 030024, China ‡National Laboratory of Solid State Microstructures and Jiangsu Provincial Key Laboratory for Nanotechnology, Nanjing University, Nanjing 210093, China E-mail: [email protected]

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Abstract Room temperature sodium-sulfur (RT-Na/S) batteries have recently gained much attention as a low-cost candidate for application in large scale energy storage, especially in stationary energy. For performance improvement of RT-Na/S batteries, a full understanding of the actual reaction process and discharge products is in need. In this work, we discovered the most stable structure of Na2 S3 and a new phase of Na2 S2 (γNa2 S2 ) by using first-principles unbiased structure searching calculations. Analysis of the thermodynamics and electrochemical activity indicates that Na2 S3 acts as a stable product like Na2 S2 and Na2 S, but it can spontaneously disproportionate into Na2 S2 , Na2 S, and S in a RT-Na/S battery. The structure of Na2 S3 not only matches the last sloping region of the experimental discharge profile but also gives a direct explanation of the experimental Raman peaks at 476, 458 and 238 cm−1 . Our work makes a contribution to a full understanding of the mechanism for the discharge progress in RT-Na/S batteries.

Introduction Energy storage is one of the key aspects of global sustainability and societal welfare, 1 so the technology of it will be of vital importance in the near future as a result of energy demand and the gradual increase in the price of fossil fuels and their environmental impact. 2 Among the various available energy storage technologies, rechargeable lithium-ion batteries (LIBS) have attracted tremendous attention over the past two decades, 3,4 but the limited availability of lithium sources prompt the exploration and development of new battery technologies based on earth-abundant elements for large-scale applications, such as grid storage of electricity produced from renewable sources as well as for next-generation electric vehicles. In this regard, sodium-sulfur (Na-S) batteries are appealing due to the high theoretical specific energy, high energy efficiency and excellent cycle life. The materials of Na-S batteries primarily include sulfur and sodium, which are relatively non-toxic, abundant and environmentally 2


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benign. 5 The traditional high-temperature sodium-sulfur (HT-Na/S) batteries with high-capacity sulfur cathodes and high operating temperatures (300∼350 ◦ C), have been under development for over 50 years since 1960s, 6 they have a high theoretical specific energy of 760 W h kg−1 , and low rate of self-discharge so that can fulfill the requirements of power source economically, efficiently, and also in terms of reliability. 2 But the high operating temperatures and the use of β-alumina solid electrolytes have led to cost and safety problems, such as explosion, corrosion, and power consumption. To solve these issues, room-temperature sodium-sulfur (RT-Na/S) batteries have been developed since 2006, 7 and are currently attracting a lot of attention on them. 8,9 Because of the ambient temperature during operating, RT-Na/S batteries are much safer than commercial HT-Na/S batteries, and are viable for a broad range of applications, 5 Meanwhile, the ambient temperature also caused many challenges like Li-S batteries, in terms of the electrochemical utilization of the sulfur active material and capacity retention during cycling, especially, the shuttle phenomenon is even exacerbated. 7 The performance of rechargeable Na-S batteries correlates closely with both reaction pathways of the charge/discharge process and the structure, composition and physical proprieties of the discharge products. It is known that, in a typical discharge process, when sodium gives off an electron, pure sulfur (S8 ) accepts the electron and reacts to form sodium polysulfide (Na2 Sn , 1≤n≤8), the overall reaction can be described as: 2Na+nS↔Na2 Sn in both HT-Na/S and RT-Na/S batteries, 10 but the final products of discharge process and their properties are still not yet fully understood. It is well believed that in RT-Na/S battery, the overall practical discharge capacity (1050 m Ah g−1 ) of the cell is between the theoretical capacities of the discharge products Na2 S2 and Na2 S, indicating that the elemental sulfur is not completely discharged to the final states/products (S2− ), it means that the final discharge products may consist of a mixture of Na2 S2 and Na2 S. 1 While another work also proposed that the final discharge products are Na2 S3 and Na2 S2 . 9 To resolve this

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argument, a deeper understanding of the final products properties and the charge/discharge mechanism of Na-S batteries are needed. The existence of Na2 S3 has been questioned for a long time, but it has never been isolated from a Na-S cell by experimental means even though there were a lot of work had been done. 11–13 Oei et al reexamined the sodium-sulfur diagram by the differential thermal analysis (DTA), and also discussed the existence by both XRD and DTA, the conclusion was that Na2 S3 was unstable and disproportionate at about 100 ◦ C into 1:1 eutectic Na2 S2 -Na2 S4 . 11 Janz et al explored it by Raman spectra, but they concluded that by the laser-Raman tech12 nique to detect S2− Another work gave the information 3 was not supported at the end of it.

of Na2 S3 ·NH3 , 14 and some other work assumed that the structure of it is consistent with Na2 S3 , 13,15 but it should be questioned. Inspired by these decoupling between experiment and theory, we reproduce the structure of Na2 S, α-Na2 S2 , and β-Na2 S2 , determine the structure information of them which is consistent with experiment. We also predict the structure of Na2 S3 and a new phase of Na2 S2 , namely γ-Na2 S2 , which were uncovered before. Based on the structures we predicted, we discussed the role of these polysulfides in discharge process of sodium-sulfur batteries. The work we have done enable the natural explanation of earlier experimental observations, and may promote the development of RT-Na/S batteries.

Computional methods The first principles study of solid (crystalline) Na2 Sn (n≤3) consists of two parts: the prediction of crystal structures and the density functional theory (DFT) calculation based on those structures, and there already a large number of works has been done in this way. 16–18 The structural prediction approach in our work was performed using the structure swarm global optimization algorithms through CALYPSO package, 19 and a lot of significant and meaningful works recently have done by use it, 20–23 especially in the field of lithium-ion bat-

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teries and sodium-ion batteries. 24–26 The structures were searched with simulation cell sizes of 1∼4 formula units, in each generation 60% of them with lower enthalpies are selected to produce the next generation structures by PSO, 40% of the structures in the new generation are randomly generated. For most of cases, the structure searching simulation for each calculation was stopped after generated 900∼1500 structures (about 30∼50 generations). The subsequent structure relaxation and total energy calculations were carried out with DFT method as implemented in the Vienna Abinitio Simulation Package (VASP). 27 We choose projected-augmented-wave (PAW) potentials with 3s1 3p0 and 3s2 3p4 electrons as valence for Na and S atoms respectively to describe the electron-ion interaction. The exchangecorrelation interaction functional was the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) functional, 28 and the energy cutoff for the expansion of wavefunctions into plane waves is set to 500 eV. To include vdW interaction corrections in total energies and forces acting on atoms, we adopted the semiempirical DFT-D2 approach. 29 The convergence of total energy for the self-consistent wave function a between atoms for geometrical optimization were set to 10−5 eV. The phonon dispersion curves were calculated using the DFPT method as implemented in the Phonopy code. 30 Bader’s quantum theory of atoms in molecules analysis was used for the charge-transfer calculations. 31 To compare the stability of these polysulfides, the formation energy (Ef ) of the predicted structure are calculated using the following formula:

Ef =

EN ax Sy − xµN a − yµS x+y

in which Ef and EN ax Sy denote the formation energy and the total energy of the corresponding polysulfide; µN a and µS represent the chemical potentials of sodium and sulfur in their crystalline respectively. 32 The RAMAN properties were calculated by combined a python program RAMAN-SC and VASP. The calculated XRD results and the images in this article were both obtained by software VESTA. 33

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Results and Discussion Structure search and configuration

Figure 1: Relative formation energy with respect to solid Na and S for various Na-S compounds calculated by GGA-PBE (red square) and PBE-D2 (blue circle) at 0 K. The β-phase of elemental Na and the β-phase of S were used. Data points located on the convex hull represent stable species against any type of decomposition. Table 1: Calculated relative formation energy (eV per atom) of the various Na-S compounds. Phase Na2 S4 Ef (PBE) -0.596 Ef (PBE-D2) -0.724

Na2 S3 -0.690 -0.833

α-Na2 S2 -0.850 -0.990

β-Na2 S2 -0.854 -0.997

γ-Na2 S2 -0.849 -0.987

Na2 S -1.097 -1.246

We performed a comprehensive global structure search calculation unbiased by any prior known structure with Na2 S3 , Na2 S2 , and Na2 S, and the crystal information of Na2 S4 was get from literature, 34 then the final stable structures were selected according to their formation energies at 0 K relative to the products of dissociation into their constituent elements. 35 In order to explore the influence of Van der Waals forces on our research system, we optimized these selected structures and then calculated the formation energy by PBE and PBE-D2. The detailed structural information is shown in Table S2, we can see that the influence of 6


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vdW interactions on lattice constants of Na-S compounds are weak, and the lattice constants calculated by PBE agree well with experimental values and another work done by Momida et al. 15 As for the formation energy shown in Table 1 and Fig 1, PBE-D2 values are closer to the experiment. In addition, the β-phase of elemental Na and the β-phase of S were used in the calculating process of Table 1 and Fig 1. To make a comprehensive comparison, we also calculated the formation energy by using α-phase S as a reference, and the results are shown in Table S1 and Fig S1 (Supplementary Information). The energy of α-S can be 0.01 eV/atom higher than β-S by PBE, and 0.007 eV/atom by PBE-D2, which means that β-S is more thermodynamically stable than α-S in our calculation. So that β-S was chosen as the reference in the fallowing calculation part. As illustrated in Figure 1 and Table 1, the relative formation energy data of Na2 S sits right on the convex hull, while α-Na2 S2 , β-Na2 S2 and the new structure γ-Na2 S2 sit nearly and above the convex hull, Na2 S3 sits higher than Na2 S2 and Na2 S, Na2 S4 sits highest both at PBE and PBE-D2 level. Indicating that Na2 S is the most stable compound at ambient pressure, which is in agreement with the Na-S phase diagram, 36 and all of these compounds are energetic stable respect to pure Na and S solid since they have negative relative formation energies. It should be noticed that the calculated relative formation energy of β-Na2 S2 is lowest in all the three phases of Na2 S2 . The relative formation energy of α-Na2 S2 is higher than β-Na2 S2 by 0.004 eV per atom by PBE and 0.007 eV by PBE-D2, and 0.005 eV by PBE and 0.01 eV by PBE-D2 for γ-Na2 S2 compared with β-Na2 S2 . While β-Na2 S2 is the stable phase only in high temperature which confirmed by experiment, 37 and the phase transition of α-Na2 S2 to β-Na2 S2 occurs at a high temperature of 170 ◦ C according to the Na-S phase diagram. 36 So we speculate that γ-Na2 S2 can also exist as stable as α-Na2 S2 and β-Na2 S2 in the discharge process. Moreover, the total energy of a structure is also indicative of an intermediate product during the Na-S battery discharge process. The estimated standard reaction free energy by PBE for Na2 S2 =Na2 S+S is +0.11 eV of α-Na2 S2 , +0.12 eV of β-Na2 S2 , and +0.10 eV

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Figure 2: The optimized geometric structure of (a) γ-Na2 S2 and (b) Na2 S3 . In each structure, the black lines depict the unit cell, and the blue and yellow balls represent the Na and S atoms, respectively. of γ-Na2 S2 , and +0.22, +0.25, +0.21 eV by PBE-D2 respectively, means that all the three phases Na2 S2 are thermodynamic stable which consistent with experimental results. For Na2 S3 , we can also deduce that Na2 S3 is thermodynamic stable to decompose into Na2 S2 and Na2 S by estimate the standard reaction free energy in two reactions: Na2 S3 =Na2 S2 +S and Na2 S3 =Na2 S+2S, and the results are +0.04 eV and +0.15 eV by PBE, +0.19 eV and +0.43 eV by PBE-D2 respectively. However, there is another possibility that Na2 S3 can decompose into Na2 S2 and Na2 S4 , and the standard reaction free energy was estimated to be -0.09 eV by PBE and -0.02 eV by PBE-D2, which mean that Na2 S3 can disproportionate spontaneously to Na2 S2 and Na2 S4 . But considering that these values are very small and both Na2 S3 and Na2 S2 are insoluble, we may infer that this transition will be very slow, and Na2 S3 can be stable as an intermediate product. All the results above may explain why it has remained challenging to be characterized experimentally and consistent with other works. 11,18 With only the input of chemical compositions in our CALYPSO structure searching calculations, the experimental Na2 S (Fm¯3m, Z=4), α-Na2 S2 (P¯62m, Z=3), and β-Na2 S2 (P63 /mmc, Z=2) 36 are successfully reproduced. Moreover, the relaxed lattice constant of

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them are in good agreement with the experimental value, 36,38 give a strong support to the validity of our pseudopotentials adopted. For Na2 S, the relaxed lattice constant is calculated to be 6.53 Å, which is consistent with the experimental value of 6.54 Å. 36 For α-Na2 S2 and β-Na2 S2 , the relaxed lattice constants were shown in Table S2. All of these validating our structure searching methodology in application to the Na-S system. Considering that the results of lattice constants obtained by PBE are closer to the experimental values than by PBE-D2, our subsequent discussion on lattice constants are all about the results of PBE. The new phase γ-Na2 S2 we predicted has an orthorhombic structure (space group Pmmn, two formula units per cell, see Fig 2a). The Na atoms in γ-Na2 S2 occupy an equivalent position 8g (0.000, 0.500, 0.437), and 8g (0.500, 0.300, 0.249) for S atoms. Each Na atom connect to six S atoms to form irregular pentahedrons in two different shapes, in one of it, four of the six sulfur atoms form two S-S bonds, and the bond length is 2.15 Å, the distance between the other two S atoms is larger (3.22 Å). While in the other type, there is only one S-S bond. Besides, the pentahedrons formed by Na and S atoms in γ-Na2 S2 are similar to that in α-Na2 S2 (see Fig S2a), further investigation shows that the structure of γ-Na2 S2 is near to α-Na2 S2 (three formula units per cell), the difference in bond length and angel between them are insignificant. It is also worth noting that all the S atoms in Na2 S2 exist in quasi-molecular S2 forms with an intramolecular S-S bond length of 2.14 Å, 2.17 Å, and 2.15 Å (for α-Na2 S2 , β-Na2 S2 , γ-Na2 S2 respectively), and the S-S bond length for all the three phases Na2 S2 are longer than that in gas-phase S2 (1.89 Å). 39 These enlarged intramolecular bonds can be interpreted as the S2 molecules in Na2 S2 are negatively charged (Table S3), the transferred charges from Na to S2 occupy the antibonding π ∗ orbitals of S2 to lengthen the intramolecular bond length. 35 Our predicted Na2 S3 compound adopts a monoclinic structure (space group C2/c, four formula units per cell; see Fig 2b), which is different from previous woks of Na2 S3 ·NH3 (space group C2/m). The structure we predicted contains two inequivalent S’s occupying 8f (0.507, 0.357, 0.385) and 4e (0.000, 0.435, 0.750) positions, and one equivalent position 8f (0.727,

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0.085, 0.109) for Na. Each Na atom is connected to seven S atoms, wherein three of them 2− are forming S2− 3 anions. It can be seen that all S atoms exist in S3 anions, and the S-S bong

length in it is 2.11 Å, smaller than that in all the three phases of Na2 S2 , and the angel of S-S-S is 108.39◦ . Compared with the structure of Na2 S3 ·NH3 , 13 both bond length and angel are different. It is interesting to find that all the S2− 3 ions are neatly aligned in two opposite directions in an alternating manner (Fig 2b).

Figure 3: Phonon dispersion curve and partial phonon density of states (Ph DOS) for (a) γ-Na2 S2 and (b) Na2 S3 .

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Dynamic and mechanical stability It is necessary to evaluate the dynamic stability to judge whether a crystal structure can exist, the dynamic stability of the crystal structure refers to the ability of the crystal structure to maintain its original crystal structure under lattice vibrations (including zero-point vibrational energy due to quantum effects at 0 K conditions). To investigate the dynamic stability of these polysulfides, we computed the phonon dispersion curves and partial phonon density of states (Ph DOS) using the density-functional perturbation theory (DFPT) method. 40 For Na2 S, α-Na2 S2 and β-Na2 S2 , shown in Fig S3, it has been known that they are thermodynamically stable at ambient conditions, therefore it is expected to be dynamically stable at zero temperature throughout the whole Brillouin zone. While for the other two structures we predicted, shown in Fig 3, there also exist no imaginary phonon frequencies, it means that whether stable or metastable, they are dynamically stable at least. For the new phase γ-Na2 S2 we predicted (Fig 3a), it is obviously that the motion of the S ions dominates mainly the vibrational states in the high and low frequency regimes, while the Na cations contribute to the middle frequency regimes, which is similar to the vibrational character of Li2 S2 . 35 It should be noticed that the motion of the vibrational modes of the Na cations can be divided into two types, one is in relatively high frequency regimes (the red line in Fig 3a), and the other is lower (the blue line in Fig 3a). We consider it is mainly related to the position difference of four Na atoms in the single cell, in terms of their positions locate in two layers, that result in the difference between their vibration modes, and similar phenomenon also exists in the other two well-known disulfide Na2 S2 . For the highest vibrational frequency (i.e. ∼453.7 cm−1 ) (13.6 THz), the strong and sharp peak of the S partial phonon density of the states appeared to be due to the S-S stretching mode, a signature of the S-S bond indicating its existence, which is stoichiometrically analogous to 41 S2− From the picture of phonon dispersion curve and partial 2 like ions in the crystal lattice.

phonon density of states in Fig S3, it can be seen the value of S-S bond vibrational frequency in β-Na2 S2 is 12.8 THz (i.e. ∼427.0 cm−1 ) and α-Na2 S2 are 13.5 THz (i.e. ∼450.3 cm−1 ) 11



and 14.0 THz (i.e. ∼467.0 cm−1 ). It is interesting to find that the value upon in all of the three disulfide Na2 S2 are very close and also near to the experimental Raman spectra data −1 that were measured and ascribed to S2− for β-Na2 S2 ) and by 2 ions by Oei et al (451.4 cm

EI et al (449.0 cm−1 for β-Na2 S2 , 458.0 cm−1 for α-Na2 S2 ). For the trisulfide Na2 S3 (Fig 3b), it can be seen that the domination of the motion of the Na cations are similar as γ-Na2 S2 , but the situation of sulfur ions is different. There exist two sharp peaks in the high region of the S partial phonon density of states and one peak in the middle region. The higher two vibrational frequency (i.e. ∼433.6 cm−1 ) (13.0 THz) and (i.e. ∼427.0 cm−1 ) (12.8 THz) appeared due to the S-S stretching mode of the two S-S bonds in S2− 3 ions like the highest vibrational frequency in γ-Na2 S2 , the sharp peak in the middle region (i.e. ∼236.8 cm−1 ) (7.1 THz) can be assign to the S-S-S stretching mode, and also can be seen as a signature of the S-S-S bond which indicating its existence. The reason for this phenomenon is that all S atoms constitute S-S-S bonds in Na2 S3 , the vibration modes and corresponding frequencies of the two S atoms on the side and the one in the middle are different. By comparing with the experimental values of Raman spectra by Janz (476.0 cm−1 for υa (S-S), 458.0 cm−1 for υs (S-S), and 238.0 cm−1 for δ(S-S-S) stretching modes), we find that the results we calculated are consistent with the experimental values, and also confirms the structure of Na2 S3 we predicted. Besides the dynamic stability, the mechanical stability is also indispensable. The mechanical stability criteria are different of different crystal systems, all the calculated elastic constants, the formulas of elastic moduli and mechanical stability criteria for the considered crystal systems are shown in Table S4. It is clear that all the structure we predicted are mechanical stable.

Raman properties and XRD patterns Inspired by the results of dynamic calculation, we calculated Raman spectra based on phonon vibrational modes in the Brillouin zone, and it is known that Raman and IR spectra were 12


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related to the symmetry of the structures. The primitive unit cell of γ-Na2 S2 has two formula units and 4 atoms each formula, a factor group analysis (Table S8) predicts there are 12 Raman-active fundamentals out of the 24 possible modes, i.e. ΓRaman = 4Ag + B1g + 3B2g + 4B3g , 11 infrared-active modes (4B1u +4B2u +3B3u ), and one silent mode (Au ). It is interesting to find that compared with α-Na2 S2 and β-Na2 S2 , there also exist a high frequency Raman vibration at 433.8 cm−1 , we may conclude that it corresponds to the S-S stretching vibration in S2− 2 ions. For Na2 S3 , the primitive unit cell of it contains ten atoms, so there are 27 optical phonon modes at the zone center. Group analysis (Table S6) showed that there are 15 Ramanactive modes (15Ag ) and 15 infrared-active modes (15Au ), no silent modes. 42 Of particular interest is the existence of the two high frequency Raman Ag vibration at 431.1 cm−1 and 428.9 cm−1 , and a middle frequency Raman Ag vibration at 245.5 cm−1 , which correlate nicely with experimental Raman peaks at 476.0 cm−1 , 458.0 cm−1 , and 238.0 cm−1 . The two high-frequency modes correspond to the S-S stretching vibration in S2− 3 intramolecular, near the S-S stretching vibration in β-Na2 S2 (Table S7). But the middle-frequency mode is not seen in Na2 S2 and Na2 S, prove that it is corresponding to the stretching vibration mode of whole S2− 3 anion. It should be noted that almost all vibration modes have Raman activity or Infrared activity, which makes it difficulty to distinguish them or find vibrational assignments by experimental means, and also consistent with the experimental conclusion. 12 The results partly explained why it is not supported to detect S2− 3 by Raman technique. To make a full understand of Raman properties, we also calculated the Raman spectra of Na2 S4 (shown in Table S5). As the existence of S-S-S-S bond in Na2 S4 , we infer that there may exist three S-S stretching vibrations, two stretching vibrations of S-S-S anion and one of S-S-S-S anion. The results of calculated Raman spectra based on phonon vibrational modes of Na2 S4 primitive unit cell are well consistence with our inference. Besides Raman properties, the XRD patterns of these Na polysulfides were also calculated and shown in Fig S6. It can be seen that the calculated XRD patterns of Na2 S4 , β-Na2 S2 and

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Na2 S are similar to the results done by Mali et al, 18 but as for Na2 S3 , a lot of differences can be found. The XRD patterns of Na2 S4 in that work were a mixture of Na2 S4 and β-Na2 S2 , but in our work, it was totally new and belong to a new predicted structure of Na2 S3 which can be tested in future experiment.

Electronic properties In view of the bonding features in the proposed structures, we then analyze the electronic localization function (ELF) maps to better understand the bonding nature. ELF is the most straightforward method to judge the chemical bonding pattern, as it can map the likelihood of finding an electron between neighborhood atoms. 27 In general, ELF values above 0.5 between the nearest atoms indicate a covalent bonding pattern, whereas ELF values below 0.5 correspond to a ionic or metallic bond. The ELF maps of γ-Na2 S2 and Na2 S3 are as shown in Fig 4, and of the others are in Fig S3. It is clear that there is almost no electron localization between S atoms and Na atoms for all the polysulfides, indicating an ionic and metallic bonding character, 43 which is further supported by the results of Bader charge calculation (Table S3). Compared with the single S atoms in 2D ELF plot of Na2 S (see Fig S4), we find that the electron localization level between all the nearest two S atoms are pretty high (∼0.76), showing a covalent bonding pattern in the quasi-molecular S2 pairs in all the three phases of disulfide Na2 S2 . Around each S atoms in S2 pairs, there are two localized charges with the largest ELF values, indicating the lone electron pairs. The situation of Na2 S3 is different from Na2 S2 and Na2 S, the electron localization level between the nearest two S atoms in quasi-molecular S3 are pretty high (∼0.80), indicating a strong covalent bonding pattern, but there is almost no electron localization between the two S atoms at edge position. Look at the results of Bader charge calculation of Na2 S3 (Table S3), the charge of the middle S atom is significantly less than that of the two edge S atoms. It can be concluded that quasi-molecular S3 is formed by the covalent bonding of the two adjacent S atoms in it. 14


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Figure 4: Calculated electron localization function (ELF) with isosurface of 0.6 and twodimensional ELF on the (100) plane of (a) γ-Na2 S2 and (b) Na2 S3 , respectively.

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Electronic conductivity and chemical activity of the discharge products also have great effect on the performance of Na-S batteries. To provide insights into the electronic properties of these sodium-sulfur compounds, we have calculated the electronic band structure and the corresponding projected density of states (PDOS) shown in Fig 5 and Fig S5. The S atoms are predicted to exist in the form of S2− 2 ions in the three phases of disulfide, so we may consequently expect that the sulfur p− electrons to play a key role in their electronic structure near the Fermi level, 44 and it has confirmed by the results of PDOS (see Fig 5a), the electronic density of states around the Fermi level is almost entirely derived from the p-orbitals of S atoms. The nonconductive nature of both Na2 S and Na2 S2 is well known, while the specific calculated energy bandgap between the valence band maximum (VBM) and conduction band minimum (CBM) are about 0.81 eV for α-Na2 S2 , 1.23 eV for β-Na2 S2 , and 0.96 eV for γ-Na2 S2 , much smaller than 2.42 eV for Na2 S. It is also can be clearly seen that all the phases of Na2 S2 are indirect bandgap semi-conductor which cannot transport free electrons, but electron polarons (p− ) and hole polarons (p+ ) can appear in solid Na2 S2 45 due to the unique molecular orbital structure of the S2− A similar phenomenon also 2 anion.

happens in the S atoms in S2− 3 ions, analysis of the PDOS (Fig 5b) suggests that the states around the Fermi level also arise mainly from the p-orbitals of the S atoms, and the energy gap of Na2 S3 is 1.09 eV, near to that of Na2 S2 , means that Na2 S3 is also semi-conductor. According to the difference of bandgap between Na2 S3 , Na2 S2 and Na2 S, we can conclude that the available intrinsic charge carriers of Na2 S3 and Na2 S2 are more than that of Na2 S. It is known that electronic conductivity is closely related to the effective mass, and the light effective mass always means large mobility. Comparing the calculated electron effective mass of Na2 S3 (0.12 m0 ), α-Na2 S2 (0.18 m0 ), β-Na2 S2 (0.33 m0 ), γ-Na2 S2 (0.29 m0 ), and Na2 S (0.17 m0 ), we infer that all the Na-S compounds we calculated have the same order electron mobility. From all the results above, Na2 S3 and Na2 S2 are more electrochemically active than Na2 S.

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Figure 5: Calculated electronic band structure (left panel) and projected density of states (PDOS) (right panel) for (a) γ-Na2 S2 and (b) Na2 S3 . The dashed line indicates the Fermi energy.

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Discharge/charge mechanism In the charge and discharge process, sulfur volumetric expansion/shrinkage plays a key role in determining the rate capability of the battery. In Li-S batteries, the volume change of sulfur upon lithiation/delithiation is generally ∼80%. While the volume change in the Na-S batteries (especially in RT-Na/S batteries) is expected to be more prominent due to the larger ionic size of Na+ relative to Li+ . The density of Na2 S is 1.86 g·cm−3 , of the different phases of Na2 S2 are near to 2.02 g·cm−3 , of Na2 S3 is 2.13 g·cm−3 , and the value of elemental sulfur is 1.96 g·cm−3 . A simple calculation from them suggests that the volume expansion of the sulfur cathode will be ∼36% when the discharge process proceeding to Na2 S3 , and then it will be more serious. When it comes to Na2 S2 , the volumetric expansion will be ∼67%, and reach ∼157% upon a full discharge to Na2 S. Given that Na2 S2 corresponds to a depth of discharge (DOD) of ∼50% , Na2 S3 to ∼33.3%, and Na2 S to ∼100%, we can see that these volumetric expansion rates are roughly proportional to the DOD. 5,9 The dramatic volume change of the electrode can deteriorate the mechanical integrity of sulfur active materials and result in a capacity fade. The discharge voltage of sodium sulfides can be obtained by calculating the difference in Gibbs free energy: ∆G(E; V ; S) ≡ ∆E + P ∆V + T ∆S. At ambient conditions, the effects of P ∆V are much less than ∆E + T ∆S. 46,47 Thus, ∆E + T ∆S makes the major contribution to the Gibbs free energy, so we approximately consider ∆G ≈ ∆E. 35,44 Based on the electrochemical reaction Na2 S2 +2Na+ +2e− →2Na2 S, 1 and the specific discharge voltage is given by V=[E(Na2 S2 )+E(Nametal )-E(Na2 S)]/e, the calculated theoretical discharge voltage is found to be 1.59 V for both α-Na2 S2 and γ-Na2 S2 , and 1.58 V for β-Na2 S2 at PBE level, which are in good agreement with the second sloping region in the range of 1.65∼1.20 V of the discharge profile in RT-Na/S batteries. 5,9 While the values calculated by PBE-D2 are 1.76 and 1.74 V respectively, which are little higher than experimental values. The results above demonstrate that γ-Na2 S2 may also exist in this process. In addition, we also calculate the theoretical discharge voltage of Na2 S3 based on the two possible electrochemical 18


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reactions: 2Na2 S3 +2Na+ +2e− →3Na2 S2 and Na2 S3 +4Na+ +4e− →3Na2 S. For the former reaction, the calculated theoretical discharge voltage is nearly 1.66 V for all three kinds of Na2 S2 by PBE, and 1.77 V by PBE-D2. For the latter one, it is 1.60 V and 1.76 V by PBE and PBE-D2 respectively, also coincide with the second sloping region, we therefore infer that these two reactions may also occur in this discharge process which is proposed by the first time. Take into account the solid state and the nonconductive nature of Na2 S3 , Na2 S2 and Na2 S, this discharge process is kinetically slow and likely suffers from high polarization. 1 The solid state discharge products can leads to increased resistance at the positive electrode and prohibits any further discharge reaction. Therefore, most reports fail to achieve the theoretical gravimetric capacity of the sulfur electrode (1672 m Ah g−1 ), based on full reduction to Na2 S. 5 And it also explained why there is an argument of the discharge products of RT-Na/S batteries.

Conclusions Using unbiased structure searching techniques and density functional total energy calculations, we find the unknown structure of Na2 S3 , and another new stable phase of Na2 S2 (γ-Na2 S2 ). Analysis of the thermodynamics and electrochemical activity indicating that even though Na2 S3 is a stable species, but it can disproportionate spontaneously in a RTNa/S battery. Furthermore, we also reproduce the structure of Na2 S, α-Na2 S2 , and β-Na2 S2 , determined the structure information of them which is consistent with experiment. At the end of it, we also discuss the role of them in discharge/charge process of sodium-sulfur batteries. The electrochemical activity of Na2 S3 is near to that of Na2 S2 but higher than that of Na2 S, whereas the volumetric expansion is the reverse. The unresolved experimental observations of Raman peaks at 476, 458 and 238 cm−1 of Na2 S3 were fundamentally understood. Our work could help further understanding of the discharge processes of sulfur electrode of rechargeable Na-S battery, and promote the development of it.

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Supporting Information Available Deatils of structural information, bader charge analysis, phonon dispersion curve and Ph DOS, calculated elastic constants, calculated Raman activities, ELF maps, calculated electronic band structure and PDOS, calculated X-ray powder diffraction patterns.

Acknowledgement This work was supported by the National Natural Science Foundation of China (Nos. 11604235, U1510132), Natural Science Foundation of Shanxi (2016021030), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2016140), and Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi. The authors acknowledge the support from the Scientific Cloud Computing Center of Taiyuan University of Technology.

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338x190mm (96 x 96 DPI)


Insight into the Discharge Products and Mechanism of Room

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