First-principles investigations on sodium superionic conductor

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First-principles investigations on sodium superionic conductor Na11Sn2PS12 Kyungbae Oh, Donghee Chang, Inchul Park, Kyungho Yoon, and Kisuk Kang Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04965 • Publication Date (Web): 05 Aug 2019 Downloaded from pubs.acs.org on August 5, 2019

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Chemistry of Materials

First-principles investigations on sodium superionic conductor Na11Sn2PS12 Kyungbae Oh,† Donghee Chang,† Inchul Park,† Kyungho Yoon,† and Kisuk Kang*,†,‡,§ †Department

of Materials Science and Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea ‡Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul National University, 1 Gwanak-ro, Gwanakgu, Seoul 08826, Republic of Korea §Department of Materials Science and Engineering, Research Institute for Advanced Materials (RIAM), Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea ABSTRACT: Sodium superionic conductors are key components of solid-state sodium ion batteries, which are regarded as promising alternative energy storage options for large-scale application. Recently, a new crystalline sodium superionic conductor Na11Sn2PS12 was reported with a remarkably high ionic conductivity over 1 mS/cm at room temperature. Herein, we report the comprehensive first-principles investigations on this new sodium superionic conductor. Our ab initio molecular dynamics simulations confirm the intrinsically fast and isotropic diffusion of sodium ions in Na11Sn2PS12 involving all the sodium sites. From series of first-principles calculations, we propose a sodium diffusion mechanism and discuss on the effects of various defects or substitutions on the diffusion kinetics, which may aid in further development of this class of materials. Moreover, we argue that the inherent vacant sites (Wyckoff position 8b), whose presence has been claimed to be critical for the fast sodium diffusion in this material, are less likely to contribute to the sodium diffusion. Finally, the thermodynamic stability and chemical compatibility of Na11Sn2PS12 are comparatively explored. Our theoretical study provides a more comprehensive understanding of Na11Sn2PS12-type conductors as well as helpful guidance on their optimal design for application in solid-state batteries.

INTRODUCTION Sodium-ion batteries have received much attention as an alternative to lithium-ion batteries for large-scale applications, because of the global availability and low cost of sodium resources relative to those of lithium.1-3 Recently, solid-state sodium ion batteries, which use a solid electrolyte, are being considered as feasible options in terms of cost and safety,4-6 since the use of flammable organic electrolytes in conventional sodium-ion batteries is one of the concerns that may become important with respect to safety, especially for large-scale applications. While much research has been reported on lithium superionic conductors in recent years for all solid-state lithium ion batteries;7-10 the development of sodium ionic conductors has been less actively sought after. For the practical use of solid-state batteries, highly conductive solid electrolytes with ionic conductivities comparable to that of a liquid electrolyte (> 1 mS/cm at room temperature (RT)) are indispensable. Traditionally, oxides-based sodium conductors have been extensively studied including β′′-alumina and sodium (Na) superionic conductor (NASICON)-type conductors, which are reputed to exhibit ionic conductivities over 1 mS/cm at RT.11-14 Nevertheless, rigorous heat-treatment conditions for the

synthesis and the technical difficulties in controlling the grain-boundary and interfacial resistance for the oxidebased materials are challenging issues to be resolved, which have retarded their applications in solid-state batteries.11-14 Sulfide-based sodium superionic conductors have been lately highlighted with their high ionic conductivity and the mechanical properties that enable easy fabrication using simple cold pressing,15 and in part due to the success of the sulfide-based lithium superionic conductors.8-10 Na3PS4,16 Na10M2PS12 (M = Si, Ge, Sn),17, 18 and Na7P3S1119 have been reported experimentally or computationally; exhibiting promising electrochemical performances. Reported with an ionic conductivity of over 0.1 mS/cm at room temperature, Na3PS4-type conductors have been the intensively studied group, and various compositional tuning methods, such as aliovalent doping of P5+ with Si4+ 20, 21 or S2– with Cl–/I– 22, 23 and isovalent substitution of P5+ with As5+/Sb5+ 24-28 or S2– with Se2– 29-31, have been applied to achieve higher conductivity.20-32 Simultaneously, series of computational studies have been carried out to elucidate the fast sodium kinetics of Na3PS4-type conductors, with respect to the crystal symmetry and defect concentrations such as vacancy or sodium interstitialcy.33-35

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Another important milestone for sulfide-based sodium superionic conductors was more recently achieved by several groups.36-40 Zhang et al.36 and Duchardt et al.,37 independently, introduced the Na11Sn2PS12 phase with the highest sodium ionic conductivity reported to date for sulfide-based materials. It was demonstrated that Na11Sn2PS12 is capable of delivering an ionic conductivity of 1.4 mS/cm with an activation energy of 0.25 eV36 or 3.7 mS/cm with an activation energy of 0.387 eV37 at room temperature. Zhang et al. proposed that the occurrence of quasi-isotropic diffusion is the origin of the fast sodium ion diffusion, which involves equi-energetic sodium sites in the structure.36 On the other hand, Duchardt et al. suggested that the structural aspect containing a relatively large vacant space (Wyckoff position 8b) that aids in the overall sodium diffusion was attributable for the high sodium ionic conductivity.37 It was claimed that the Na11Sn2PS12 structure is analogous to Na3PS4 structure containing a vacant space (8b sites), and the sodium ions could easily migrate though this vacant site.37 Thus, the presence of the vacant sites and the local hopping near the sites were regarded as the key prerequisites for the fast diffusion, referring it as vacancy-controlled Na+ superion conduction.37 However, the role of the vacant sites (8b) in the structure remains controversial and currently under debate. In a more recent report by Ramos et al., it was speculated that sodium diffusion involving those vacant sites (Wyckoff position 8b) does not govern the overall ionic conductivity.38 They claimed that, from a comparative study with Sb analogue (Na11Sn2SbS12), the major sodium diffusion did not take place through these 8b vacant sites. And, it was suggested that the 8b vacant site simply provides an accessible parking spot for the major sodium conduction pathway.38 The application of Na10.8Sn1.9PS11.8 electrolyte in the all solid-state battery was explored by Yu et al.39 While its performance was promising, it was reported that the bilayer pellet (Na3PS4–Na10.8Sn1.9PS11.8) was necessary to alleviate interfacial side reactions with Na metal electrode, indicating the potential compatibility issue between Na10.8Sn1.9PS11.8 electrolyte and the electrode. Herein, we performed extensive first-principles investigations on the Na11Sn2PS12 phase. While the previous experimental studies successfully identified the exceptionally high ionic conductivity from the material, the detailed diffusion mechanisms and their chemical/electrochemical stability or compatibility remain elusive. The potential factors affecting the diffusion, the role of the characteristic vacant sites in the diffusion, and the thermodynamic stabilities of the material itself or at the interfaces have yet to be addressed for the better understanding of this class of materials. From the ab initio molecular dynamics (AIMD) simulations, we propose sodium diffusion mechanisms based on the site occupancies and hopping rates obtained. The effects of introducing a sodium vacancy/interstitial and isovalent substitution of Sn sites by Si or Ge are also examined to offer the guidelines for the further optimizations of the material. Moreover, the electrochemical stability and interfacial compatibility with representative electrode materials are evaluated to elucidate the thermodynamic stability of the Na11Sn2PS12 phase.

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METHODS First-Principles Energy Calculations. First-principles calculations were performed using the Vienna ab initio Simulation Package (VASP)41 based on density functional theory (DFT). The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional was applied to consider the exchange-correlation energy.42 The projector augmented wave (PAW)43, 44 method was used to treat the interaction between ion cores and valence electrons. A plane-wave basis set with a kinetic energy cutoff of 340 eV and an at least 500/(number of atoms in the supercell) k-point grid based on the Monkhorst–Pack scheme45 were used for the total energy calculations. A 2×2×1 k-point grid was used to calculate a 1×1×1 supercell structure of Na88Sn16P8S96, corresponding to 208 atoms. To obtain the ground-state configuration for the Na11Sn2PS12 structure containing partially occupied sodium sites,37 the electrostatic energy criterion46 was applied, and the 100 configurations with the lowest electrostatic energies were considered, which were further calculated using firstprinciples methods. The structures were fully relaxed until the residual force was less than 0.2 eV/Å. All the total energy calculations were performed with spin-polarized. Details on AIMD Simulations. Newton’s equation was integrated using the Verlet algorithm,47 as implemented in VASP. To ensure a reasonable computational time, potentials containing a small number of electrons (see Supporting Information for details) with a cutoff energy of 258.689 eV and 𝛤-point-only k-point grid were used. The simulations were performed using step-by-step procedures with a time step of 2 fs similar to those used in previous studies.36, 48, 49 The initial velocities of the ions were designated according to the Boltzmann distribution at 100 K, and the samples were heated to elevated temperatures using velocity scaling. After an equilibrium step of longer than 10 ps, data sampling was performed until the diffusivity converged (40–100 ps) in the canonical (NVT) ensemble with a Nosé–Hoover thermostat.50, 51 The sodium ionic conductivity 𝜎 was derived from the Nernst– Einstein equation: 𝜎(𝑇) =

𝜌𝑧2𝐹2 𝑅𝑇

𝐷(𝑇)

(1)

where 𝜌, 𝑧, 𝐹, 𝑅, and 𝑇 are the molar density of sodium ions, the charge of a sodium ion, Faraday constant, gas constant, and temperature, respectively. The diffusivity, 𝐷, was calculated from a linear fitting as48, 49, 52 1

𝐷 = 2𝑑𝑡〈[𝛥𝒓(𝑡)]2〉

(2)

where 𝑑 is the dimension of diffusion, 𝑡 is time, and 〈[𝛥𝒓(𝑡)]2〉 is the mean square displacement of sodium ions. The probability density 𝑃, a time-averaged value of sodium ions on a three-dimensional grid, was calculated by counting the number of sodium ions at each grid point and averaging the values over the simulation time.33 To construct the structures with a sodium vacancy/interstitial, one sodium ion was removed from or added to the supercell of Na88Sn16P8S96, while the lattice parameters were fixed to those of the pristine structure to evaluate the effects independently. The lattice parameters


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Figure 1. Illustrations of (a) crystal structure of Na11Sn2PS12, (b) Sn layer (x, y, 4/8), and (c) P layer (x, y, 3/8). Iso-surface (red) of sodium probability density distribution 𝑃 = 𝑃max/1024 at 800 K of (d) Sn layer (x, y, 4/8) and (e) P layer (x, y, 3/8). S ions are placed at the vertices of each polyhedron. Note that partial occupancies of sodium sites were not illustrated for the clarity of the crystal symmetry.

were not significantly altered even when the full relaxation of the structure was carried out. Constructing Phase Diagrams. Relevant phase diagrams were constructed using all the stable phases (Table S1) in the Na–Sn–P–S–Ti chemical space of the Materials Project database.52-55 We recalculated the stable phases using the calculation conditions described in FirstPrinciples Energy Calculation. The energy correction for sulfur was applied, as adopted in the Materials Project database.33, 56 To examine the intrinsic electrochemical stability, a sodium grand potential phase diagram was constructed by opening the system to a sodium reservoir with a chemical potential of sodium,53, 57 which can be expressed as 𝜇𝑁𝑎(𝑈) = 𝜇0𝑁𝑎 ―𝑒𝑈 (3) where 𝜇𝑁𝑎 is the chemical potential of sodium, 𝜇0𝑁𝑎 is the elemental chemical potential of sodium, 𝑈 is the applied potential reference to sodium metal. The grand potential 𝛷, the characteristic thermodynamic potential in the grand canonical ensemble, can be defined as 𝛷(𝑐,𝑈) = 𝐸(𝑐) ― 𝑛𝑁𝑎(𝑐) 𝜇𝑁𝑎(𝑈) (4) where 𝐸(𝑐) is internal energy of the structure and 𝑛𝑁𝑎(𝑐) is the number of sodium atoms in the structure with composition 𝑐. Then, the reaction energies of the intrinsic 𝐸𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 electrochemical decomposition were 𝑑𝑒𝑐𝑜𝑚𝑝. (𝑈) calculated: 𝐸𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑑𝑒𝑐𝑜𝑚𝑝. (𝑈) = 𝛥𝛷(𝑐𝑆𝐸,𝑈) = ∑ 𝐸(𝑐𝑖) ―𝐸(𝑐𝑆𝐸) ―𝛥𝑛𝑁𝑎 𝜇𝑁𝑎(𝑈) (5) 𝑖

where 𝑐𝑆𝐸 is the composition of the solid electrolyte, ∑ 𝐸(𝑐𝑖) is the sum of the internal energies of the 𝑖 decomposed phases, and 𝛥𝑛𝑁𝑎 is the change in the number of sodium atoms after the reaction. To investigate the interfacial compatibility between the electrodes and electrolyte, the interfaces were regarded as pseudo-binary phase diagrams, and potential mutual decomposition reactions were examined.58, 59 The pseudo-binary phase

diagrams were extracted from the multi-dimensional phase diagrams by taking the compositions of the electrode and electrolyte to each end-point. The reaction energies of mutual decomposition at the interface 𝐸𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 𝑑𝑒𝑐𝑜𝑚𝑝. (𝑥) were determined using the following equation: 𝐸𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 𝑑𝑒𝑐𝑜𝑚𝑝. (𝑥) = ∑ 𝐸(𝑐𝑖) ― [(1 ― 𝑥)𝐸(𝑐𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒) + 𝑥𝐸(𝑐𝑆𝐸)] (6) 𝑖

where 𝑥 is the fraction of the solid electrolyte calculated from the normalized formula unit and 𝑐𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑑𝑒 is the electrode composition. We normalized the formula units of each phase as if they contained one atom per formula unit. For example, the Na11Sn2PS12 phase was regarded to have the formula unit Na11/26Sn2/26P1/26S12/26. The introduction of the normalized formula units helps to determine the relative amount of the fraction of the phases. For the estimation of the electrical and ionic transport properties of byproducts from the decomposition reaction at the interface, we applied simple rules; the phase is regarded as being electronically conductive if it possesses zero band gap and ionically insulative if a sodium ion is not included in the composition.

RESULTS AND DISCUSSION Crystal Structure and Sodium Diffusion Path. Figure 1a schematically illustrates the crystal structure of Na11Sn2PS12 within a tetragonal space group I41/acd:2 (no. 142, Z = 8).36, 37, 39 The framework structure is constructed with isolated SnS4 and PS4 polyhedra. All the cation sites are arranged to form a three-dimensional grid with a distance of approximately 3.41 Å. The cation sublattice can be interpreted as an alternative layer-by-layer structure along the c-axis, consisting of Sn layers (including SnS4, Figure 1b) and P layers (including PS4, Figure 1c). The Sn layers contain Sn (Wyckoff position 16e), Na3 (Wyckoff position 16d), Na4 (Wyckoff position 16c), and Na5 (Wyckoff position 16e) sites, while the P layers include P (Wyckoff position 8a), Na1 (Wyckoff position 16f), and Na2 (Wyckoff position 32g) sites. It should be noted that



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Figure 2. Na diffusion behaviors of pristine Na11Sn2PS12. (a) Arrhenius plots for Na11Sn2PS12. The results at 300 K were extrapolated. (b) Occupancies and (c) hopping rates of Na and the vacant sites.

there are apparent vacant sites (Wyckoff position 8b) in the P layers, indicated by white spheres, which were reported to be important hopping sites for sodium diffusion by Duchardt et al.37 All the sodium sites are octahedrally coordinated by sulfur ions, and each NaS6 octahedron is connected through face-sharing, while the vacant sites are coordinated by eight sulfur ions forming a cubic-like structure (Figure S1a). Note that the excessive number of sodium sites (96 sites) compared with the available sodium ions (88 ions) causes the partial occupation of the sodium sites, indicating the presence of vacancies in sodium sites even in the pristine composition. In order to understand the diffusion paths of sodium ions in the Na11Sn2PS12 structure, the probability density of sodium ions was visualized in Figure 1d–e and S2 as obtained from the AIMD simulation at 800 K. The red colored channels in the figure represent the iso-surface of the sodium ions at probability 𝑃 = 𝑃max/1024, where 𝑃max is the maximum value among all considered grids. The well-connected iso-surface including all the sodium sites indicates that the sodium diffusion path involves all the sodium sites, which agrees to the previous report of Zhang et al.36 On the other hand, it was found that the vacant sites (8b) in the P layers (Figure 1e and S2) were rarely visited by the sodium ions, implying the instability of sodium ions in those sites. In order to confirm this result, we intentionally inserted a sodium ion in the 8b site in the calculations, however, the sodium ion spontaneously migrated out of the site. Despite the presence of the apparent vacant space, this instability can be simply understood based on the ionic-radius ratio rule, which relates the stable range in the radius ratio of cation to anion for specific coordination numbers.60, 61 Considering the ionic radius of S2– (1.84 Å)62 ions, the 8b vacant site which is the interstitial site for eight S2– ions (i.e., the cubiclike coordination) requires the occupancy of cation whose ionic radius is over 1.35 Å. In this respect, it is speculated that the vacant site is too large for sodium ions (1.02 Å)62 to stably reside within the site (Figure S1). Indeed, all the sodium ions are octahedrally coordinated by S2– ions in the Na11Sn2PS12 structure, which satisfies the ionic-radius ratio rule. To further support our hypothesis, we attempted to verify the potential occupation of the vacant site by other alkali ions with larger radii such as K+ (1.51 Å), Rb+ (1.61 Å) and Cs+ (1.74 Å),62 which satisfy the ionic-radius ratio

rule for cubic-like coordination with S2–. It was revealed that the vacant sites could be stably occupied by these ions even after the full relaxations unlike the case of sodium ions that migrated away from the sites. It should be noted that although analyzing the probability density of Na ions provides an intuitive picture of the diffusion path, this analysis is not sufficient to obtain quantitative understandings of the diffusion path. In particular, the low value of the probability density does not necessarily indicate the inactiveness of the sites because intermediate sites for ion migration are less frequently occupied but actively participate in the diffusion. Therefore, in the following section, we provide more detailed interpretations of the diffusion behaviors in Na11Sn2PS12 by analyzing the actual occupancies and rates of sodium ion hopping at each site. Diffusion Mechanism in Na11Sn2PS12. The ionic conductivity of sodium in Na11Sn2PS12 at 300 K was estimated from a series of AIMD simulations. In Figure 2a, the diffusivities at elevated temperatures (every 100 K from 700 K to 1300 K) are displayed as a function of temperature based on Arrhenius behavior with the extrapolated value at 300 K. Considering the tetragonal symmetry of Na11Sn2PS12, each directional component along a, b- or c-direction in the overall diffusivities could be separately examined. And, the corresponding ionic conductivities at 300 K and activation energies are summarized in Table 1. It was found that both the overall and directional ionic conductivities were approximately 2.4 mS/cm at 300 K with an activation energy of 0.248 eV, demonstrating the fast and isotropic sodium diffusion in Na11Sn2PS12, in a good agreement with the previous study.36 To investigate the sodium diffusion mechanism in detail, the site occupancies and hopping rates obtained from the AIMD results were carefully analyzed for all the available sodium sites. The site occupancy is a measure of the probability that sodium ion occupies the specific sites, thus, can be rationally converted to the site energy.18, 63 In Figure 2b, the site occupancies by sodium are plotted as a function of temperature. As expected from the probability density analysis in Figure 1d–e and S2, all the five sodium sites (Na1 to Na5) were observed to be primarily occupied with the occupancy ratio of higher than 70% for all the simulated temperatures. Slightly lower value of occupation


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Table 1. Na ionic conductivities at 300 K and activation energies for Na diffusion of Na11Sn2PS12.

for the Na2 and Na3 sites than others is due to the stronger repulsive force by P5+ ions than by Sn4+ ions, since those sites are placed at the first-neighboring grid points of PS4 (Figure 1). These relatively low occupations of Na2 and Na3 sites were consistently observed in the previous studies as well.36, 38, 39 For the 8b vacant sites, we obtained significantly low value of site occupancy by the sodium. In particular, the occupation of the vacant sites was almost zero at 700 K and 800 K, even though these temperatures are much higher than the practical operating temperature of batteries. Moreover, our further DFT energy calculations with a sodium ion in the 8b vacant site resulted in the unstable state with more than 1 eV higher than the state without the 8b site occupation. It should be noted that occupation of 8b site by sodium ions was not energetically stable, so we forced to fix the single sodium ion to remain placed in 8b site to estimate the instability, or the sodium ion is move out to near sodium sites such as Na2 or Na3. What is more, even if we initially put one sodium ion in the 8b site with fully occupied sodium around all six facesharing sodium sites of the 8b cubic, the sodium ion moves out of the 8b sites by pushing one of the sodium ions in the face-sharing octahedron during the relaxation. Nevertheless, it is noteworthy that the results on the occupancy of the 8b vacant site are different from previous works,38-40 where the site occupancies of 8b sites were found to be about 10–20% from single crystal X-ray diffraction data. It is uncertain at this moment what caused the apparent difference between the previous experimental works and our results here. Given the unequivocal picture from both AIMD simulations and the first-principles energy calculations along with the additional confirmation simulations (Figure S3), the ground-state structure of Na11Sn2PS12 would not contain significant sodium occupation at 8b sites at room temperature. We suspect that the probed occupation of the vacant site by experiments could originate from potential metastable states of the material such as off-stoichiometry, locally formed unstable sodium arrangement, local mismatch of lattices or native defects, which can cumulatively stabilize the 8b sites and were not considered in our crystal model (Please see the further discussion in Supplementary Information, Figure S4-S6). Indeed, the instability of 8b occupation by sodium ions, which was higher than1 eV in our ground-sate structure model, was reduced to 0.5 eV from our rough calculations assuming various metastable states. However, the detailed study on these possible scenarios is beyond the scope of this study and should be investigated further in the future. In conjunction with the analysis of site occupancies, the hopping rates at each crystallographic site can serve as an important measure in understanding the diffusion

mechanism. We counted the number of sodium-ion hoppings occurring at the center of each site for the entire simulation times and normalized it by the time scale of one second. The results are plotted as a function of temperature in Figure 2c. The hopping rates of all the sodium sites are comparable, implying that they contribute almost equally to the diffusion. These results are consistent with the 23Na MAS NMR (magic angle spinning nuclear magnetic resonance) spectrum presented by Duchardt et al.;37 they observed no spinning sidebands, which indicates no immobile sodium ions in the structure. The hopping rates increase with temperature because of the higher thermal vibration rates at higher temperatures, however, no noticeable difference was found among different sodium sites. In contrast, we did not observe any visible ionic hopping through the center of 8b vacant site below 800 K, and high thermal energies (> 900 K) were required to activate the hopping. With further confirmation of the results at 700 K (Figure S3), we think that 8b vacant site is unlikely to participate in the overall sodium diffusion process in this structure at room temperature. The observed inactiveness of 8b sites is not consistent with the previous claim by Duchardt et al.37 We further attempted to estimate the stability of the 8b site by performing the activation barrier calculations for Na ion migration by nudged elastic band (NEB) method (Figure S7). While this NEB calculations provide the kinetic information regarding the Na ion migrations, it can also offer the information about the metastability of the intermediate sites within the path. Figure S7a illustrates the most representative migration path for sodium ions near 8b sites with the calculated activation barriers. Not passing through the 8b sites, the migration barrier for the sodium ion is as low as ~0.2 eV, indicating a fast diffusion kinetics. However, as we intentionally move sodium ions along the path systematically closer to 8b sites, we could observe that the activation barrier significantly increases from ~0.6 eV (Figure S7b: slightly passing through the edge of the 8b site) to ~1.2 eV (Figure S7c: passing through the center of the 8b site). Substantially high activation barriers along the 8b sites (Figure S7b-c) compared with those between adjacent sodium sites (Figure S7a) indicate the kinetic inactiveness of the 8b sites for sodium diffusion as presented in Figure 2c. Even though relatively small activation energy via the surroundings (Figure S7b, ~0.6 eV) than that through the center (Figure S7c, ~1.2 eV) suggests a potential possibility of the 8b sites for the diffusion via passing through the surroundings, we observed nearly negligible contribution for both of mechanisms in AIMD simulations at 700 K, which was due to the comparatively much lower activation barrier for the original path in Figure S7a. Only twice migrations of Figure S7b and zero migration of Figure S7c were observed, while 589 times of hoppings such as Figure S7a occurred in 80 ps of simulation time at 700 K. It is believed that the facile sodium diffusion in Na11Sn2PS12 is mainly attributable to the well-spread and partially-occupied sodium sites forming three-dimensional diffusion paths with similar site energies and hopping rates. The isotropic diffusion channels throughout the material would benefit the practical diffusivity of this material, which would be less



dependent on the orientations of each powder/grain in the

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On the other hand, Figure 3b illustrates that the substitution of the Sn site with Si or Ge severely impedes

Figure 3. Factors affecting Na diffusion in Na11Sn2PS12-type conductors. Arrhenius plots for structures with (a) Na vacancy/interstitial (𝛿 = 0.125), (b) Sn-site substitution with Si or Ge, and (c) various lattice constants. The results of the pristine structure are indicated by red circles. (d) Na ionic conductivities at 300 K and the logarithms of their relative ratios in reference to the pristine structure as a function of lattice constant. The ionic conductivities of Na11Si2PS12 and Na11Ge2PS12 are also depicted by red dots.

pelletized powder or poly-crystalline solid-electrolyte. Factors Affecting Sodium Diffusion Kinetics in Na11Sn2PS12-Type Conductors. To comprehend the factors affecting the sodium ionic conductivity of Na11Sn2PS12-type conductors, further simulations were performed for structures with variations in the sodium ion concentrations or the substitution of Sn sites. Figure 3a–b comparatively display the changes in the diffusivities in the Arrhenius plots as a result of the additional sodium ion vacancy/interstitial and the substitution of Sn sites by Si or Ge, respectively, which are also summarized in Table 2. Interestingly, it was found that the effect of additional vacancy or sodium interstitial in the structure is negligible on the sodium diffusion in Na11Sn2PS12-type conductors; the estimated ionic conductivities and activation energies were almost unchanged from those of the pristine structure. It is contrast to previous reports on Na3PS4-type conductors demonstrating that the ionic conductivities were drastically increased by introducing a small amount of sodium vacancy/interstitial.33, 34 We suspect that this distinct behavior of Na11Sn2PS12 originates from the presence of inherent sodium disorder along with the partial occupancy in the crystal structure. Unlike the crystal structure of Na3PS4-type conductors, Na11Sn2PS12 contains large amounts of partially occupied sodium sites and thus does not require the formation of extra sodium vacancy/interstitial to exert superionic conducting properties.

the sodium diffusion. The sodium ionic conductivity decreased by approximately one-fourth (0.6 mS/cm) and one-eighth (0.3 mS/cm) for the Ge and Si analogues, respectively. In order to elucidate this behavior, we first examined the structural alternation caused by the substitutions as tabulated in Table 3. It reveals that the substitutions of Sn sites with Ge or Si accompany noticeable reductions in the crystal volumes from 5192 to 5028 and 4962 Å3, respectively. The reduction of the crystal volume is primarily attributed to the reduced volume for MS4 polyhedron (M = Sn (7.32 Å3), Ge (5.96 Å3), Si (5.21 Å3)),64 however, it also leads to the substantial reduction in the sodium channel volume from 5039 to 4896 and 4843 Å3, respectively. It implies that the reduction in the ionic conductivity with the substitutions of Si and Ge is likely due to the shrinkage of the ionic channel for diffusion. Additionally, we attempted to verify the chemical effect of the substitution excluding the size effect by carrying out identical AIMD simulations for the substituted structures but within the fixed lattice Table 2. Na ionic conductivities at 300 K and activation energies for Na diffusion of structures with various compositions.


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Table 3. Structural parameters of Na11M2PS12 (M = Si, Ge, Sn).

aObtained b(Na

from radial distribution function of AIMD data (Figure S9).

channel volume) = (unit cell volume) – 16×(MS4 volume) – 8×(PS4 volume).

parameters of the pristine structure (Figure S8). The Snsite substitutions within the fixed cell did not result in the reduction of the sodium diffusivity but rather slightly increased the diffusivity, implying that the retarded sodium diffusion does not originate from any chemical influence of the substitutes. In order to further confirm the effect of reduced lattices on sodium diffusion behaviors, we systematically examined the influence of the lattice size on sodium diffusion within the Na11Sn2PS12 structure at extended scales (Figure 3c–d). The lattice constants (a, b, and c) were isotropically scaled from –4% to +4% based on those of the pristine Na11Sn2PS12 structure. Figure 3c represents the temperature-dependent diffusivities for the four representative cases (–4, –2, 0, +2 and +4%). Additionally, in Figure 3d, the obtained ionic conductivities at 300 K are plotted with respect to the changes in the lattice size. It is clearly demonstrated that the ionic conductivities systematically increase with increasing size of the lattice, which agrees to the findings above. When plotted together with the results of Si and Ge substitutions with the corresponding lattice sizes and the conductivities, they lie in the general trend following the simple correlation between the conductivity and the size. From these results, we can conclude that the retarded sodium diffusion in the case of the Si and Ge substitution was mainly due to the reduction of the lattices. Nevertheless, it was observed that much less reduction in the ionic conductivity is caused by the shrinkage of the lattice from a certain point from 2% to 4% size reduction. From a close inspection of the sodium diffusion in this case, we found that sodium ionic hopping through the 8b vacant site becomes active when the major sodium channels are narrowed to this level as illustrated in Figure S10. The additional diffusion path offered by the 8b vacant site can mitigate the effect of the shrinkage in the major sodium ion channel, thus slightly aiding in the overall diffusion, playing a role of buffer region. This type of buffering effect might be beneficial for maintaining its superior transport properties even under extreme local compressive stresses.65 Phase Stability, Electrochemical Stability and Interfacial Compatibility. For the practical use of Na11Sn2PS12 as a solid electrolyte, other important prerequisites include phase stability, electrochemical stability and interfacial compatibility with electrode materials. To understand the general stability of the Na11Sn2PS12 phase, the quaternary Na–Sn–P–S phase diagram was examined considering all the known stable phases in the given chemical space. Our calculation

revealed that Na11Sn2PS12 is thermodynamically stable at 0 K against the potential decomposition reaction of Na11Sn2PS12  Na4SnS4 + Na3PS4 with a positive reaction energy of approximately 3 meV/atom. In addition, we evaluated the phase stability of Na11M2PS12 (M = Si, Ge) against the decomposition reaction of Na11M2PS12  Na4MS4 + Na3PS4. Calculated values of both decomposition reactions were 6 meV/atom. The positive reaction energies indicate the new substituted phases are likely to be stable against the decomposition reactions. Even though the estimated stabilities are within the calculation error range due to the small energy difference, the configurational entropy from intrinsic sodium disordering in Na11Sn2PS12 guarantees the stability at elevated temperatures.39 Moreover, it should be noted that most solid electrolyte materials are prone to decompose into other phases at 0 K but are stabilized at high temperature with the help of configurational or vibrational entropy.57, 58 The predicted decomposition reaction is consistent with that previously reported by Yu et al.39 The stability of Na11Sn2PS12 was further examined upon the applied voltage. In Figure 4a, the decomposition reaction energies of Na11Sn2PS12 are plotted as a function of voltage vs. Na/Na+ as obtained from the sodium grand potential phase diagram in the quaternary Na–Sn–P–S chemical space. It is observed that the Na11Sn2PS12 phase is stable within the range of 1.16– 1.92 V, however, electrochemically decomposes when the voltage is applied outside this window both for the reductive and oxidative environment. Given with the sodium grand potential phase diagram, which describes the system open to a sodium reservoir, the reductive reaction involves the formation of sodium binary phases such as Na15Sn4, Na3P, and Na2S below 0.10 V, while the oxidative decomposition produces SnS2, P2S7, and S above 3.40 V. The narrow electrochemical window of Na11Sn2PS12 implies that an appropriate selection of electrode materials is required for practical use of Na11Sn2PS12.66 As an elemental step for selecting suitable electrode materials, we investigated the thermodynamic compatibility of the interfaces between Na11Sn2PS12 and two representative electrode materials, Na metal for the anode (0 V vs. Na/Na+) and TiS2 for the cathode (~1.7 V vs. Na/Na+). It is important to note that the decomposition reactions at the interfaces can occur in various ratios of Na11Sn2PS12 to electrode materials because of the complicated nature of interfaces. Therefore, the decomposition reactions with various ratios should be considered to probe the interfacial compatibility. In Figure 4c, the reaction energy of mutual decomposition at the



interfaces is plotted as a function of the fraction of

species

Page 8 of 12 at

the

interface

between

Na

metal

and

Figure 4. (a) Reaction energy of intrinsic electrochemical decomposition (𝐸𝑖𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑑𝑒𝑐𝑜𝑚𝑝. ) and (b) amount of Na uptake in the decomposition reaction as a function of voltage. The decomposed phases for the selected area are displayed. See Table S2 for the decomposed phases for other voltage ranges. (c) Mutual decomposition reaction energy (𝐸𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒 𝑑𝑒𝑐𝑜𝑚𝑝. ) between Na11Sn2PS12 and two representative electrode materials (anode: Na, cathode: TiS2) as a function of the fraction of Na11Sn2PS12. (d) Fraction of electronically conductive or ionically insulative phases of the products of the mutual decomposition reaction. It was simply assumed that the phase is electronically conductive if it possesses zero band gap and ionically insulative if a sodium ion is not included in the composition. Detailed information about the predicted decomposed phases in (d) is summarized in Table S3.

Na11Sn2PS12. Our calculation predicts the potential occurrence of decomposition reactions at both interfaces. However, the relatively small interfacial reaction energy between TiS2 and Na11Sn2PS12 (blue line) suggests that the interfacial reaction might be kinetically inhibited by the sluggish nature of the solid-state reactions.58, 59 The relatively good compatibility can be rationalized by the fact that the redox potential of the TiS2 cathode is within the stable electrochemical window of Na11Sn2PS12. In contrast, at the interface with Na metal, Na11Sn2PS12 is expected to spontaneously degrade with a substantial reaction energy of –0.38 eV/atom. The decomposition reaction yielded various phases at the interface between Na and Na11Sn2PS12. Considering that the electronically insulative and ionically conductive phases are believed to build desirable interfaces by passivating the interface from the decomposition,22, 66-68 we estimated the fractions of byproducts of electronically conductive and ionically insulative phases produced to examine the stability of the interface. In Figure 4d, the fractions of electronically conductive and ionically insulative phases produced from the decomposition reactions are displayed as a function of the fraction of Na11Sn2PS12. Electronically conductive Na– Sn alloys such as Na15Sn4 and Na9Sn4 were observed to be formed at the interface; these alloys are detrimental to the interface stability because they hinder surface passivation. Moreover, Sn4P3 and P, which are expected to exhibit low sodium ionic conductivity, would block the ionic paths and increase the resistivity. These results are consistent with the X-ray photoelectron spectroscopy (XPS) results performed by Yu et al., who observed Na2S and reduced Sn

Na11Sn2PS12.39 For comparison, we examined Na3PS4 using the same approach, as shown in Figure S11. The interface between Na metal and Na3PS4 is more likely to be passivated from the decomposition reaction because of the major decomposition phases with electronically insulative nature without a Sn source in the electrolyte material. However, it should be noted that some decomposed phases with a small band gap could potentially possess nonnegligible electronic conductivity. For example, the interface between Na3PS4 and Na metal is observed to be continuously degraded because Na3P is produced at the interface;68 this phase has a small band gap of 0.405 eV54 and 0.76 eV22 from the calculations based on PBE and hybrid functionals, respectively. We believe that this could be a potential reason why the previous successful experimental reports employed not only Na3PS4 as a buffer layer but also Na–Sn alloy as an anode material, which could avoid substantial side reactions at the interface.39

CONCLUSION Comprehensive investigations on the recently discovered Na11Sn2PS12 superionic conductor were performed using first-principles calculations. Our AIMD simulations indicate that the sodium diffusion in Na11Sn2PS12 is nearly isotropic with a high ionic conductivity of 2.4 mS/cm at 300 K. Analyses of the site occupancies and hopping rates demonstrated that all the sodium sites actively participate in the diffusion with well-distributed sodium vacancies. In contrast, the vacant sites (8b sites) that were argued to be important for the fast sodium conduction were shown to


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be inactive in the diffusion without the occupation of sodium in the site. In addition, it was demonstrated that the effect of the incorporation of additional sodium vacancy/interstitial was negligible on the ionic conductivity; in contrast, the isovalent substitution of Sn by Si or Ge severely retarded the sodium diffusion. It primarily stems from the reduced lattices, suggesting that improvement of the ionic conductivity could be achieved in expanded lattices. From thermodynamic calculations using phase diagrams, the Na11Sn2PS12 phase was estimated to be stable even at 0 K, unlike other sulfide-based electrolyte materials. A narrow electrochemical window of 1.16–1.92 V was determined using a Na grand potential phase diagram, indicating that careful selection of electrode materials is required with consideration of the decomposition reactions at the interfaces. The presence of Sn in Na11Sn2PS12 was revealed to produce electronically conductive phases at the interface with Na metal, leading to progressive deterioration of the interface. We believe that our comprehensive first-principles investigations provide a fundamental understanding of this new class of solid electrolytes as well as potential strategies for the further development of high-performance solid-state sodium electrolytes.

ASSOCIATED CONTENT Supporting Information Potential sets, radial distribution function, Iso-surface of Naion probability density, Analyzed results of phase diagrams for Na3PS4

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Present Addresses †If an author’s address is different than the one given in the affiliation line, this information may be included here.

Author Contributions K.O. conducted calculations. D.C. developed codes for analyzing site occupancy and hopping rates. K.K. supervised the overall research.

ACKNOWLEDGMENT This research was supported by Creative Materials Discovery Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2017M3D1A1039553). This work was also supported by project code (IBS-R006-A2).

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First-principles investigations on sodium superionic conductor

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