Native defects in Li10GeP2S12 and their effect on lithium diffusion

Subscriber access provided by Kaohsiung Medical University

Article 10

2

12

Native defects in Li GePS and their effect on lithium diffusion Kyungbae Oh, Donghee Chang, Byungju Lee, Do-Hoon Kim, Gabin Yoon, Inchul Park, Byunghoon Kim, and Kisuk Kang Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b01163 • Publication Date (Web): 03 Jul 2018 Downloaded from http://pubs.acs.org on July 4, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials

Native defects in Li10GeP2S12 and their effect on lithium diffusion Kyungbae Oh,1 Donghee Chang,1 Byungju Lee,1 Do-Hoon Kim,1 Gabin Yoon,1 Inchul Park,1 Byunghoon Kim,1 Kisuk Kang1, 2, * 1Department

of Materials Science and Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea 2Center for Nanoparticle Research Institute for Basic Science (IBS), Seoul National University, 1 Gwanak-ro, Gwanakgu, Seoul 08826, Republic of Korea ABSTRACT: Defects in crystals alter the intrinsic nature of pristine materials including their electronic/crystalline structure and charge-transport characteristics. The ionic transport properties of solid-state ionic conductors, in particular, are profoundly affected by their defect structure. Nevertheless, a fundamental understanding of the defect structure of one of the most extensively studied lithium superionic conductors, Li10GeP2S12, remains elusive because of the complexity of the structure; the effects of defects on lithium diffusion and the potential to control defects by varying synthetic conditions also remain unknown. Herein, we report, for the first time, a comprehensive first-principles study on native defects in Li10GeP2S12 and their effect on lithium diffusion. We provide the complete defect profile of Li10GeP2S12 and identify major defects that are easily formed regardless of the chemical environment while the presence of path-blocking defects is sensitively dependent on the synthetic conditions. Moreover, using ab initio molecular dynamics simulation, it is demonstrated that the major defects in Li10GeP2S12 significantly alters the diffusion process. The defects generally facilitate lithium diffusion in Li10GeP2S12 by enhancing the charge carrier concentration and flattening the site energy landscape. This work delivers a comprehensive picture of the defect chemistry and structural insights for fast lithium diffusion of Li10GeP2S12-type conductors.

group revealed that Li9.54Si1.74P1.44S11.7Cl0.3, a Li10GeP2S12type analogue, exhibits even higher lithium ionic conductivity at room temperature.8 The authors attributed the fast lithium diffusion of Li10GeP2S12 to the one-dimensional lithium conduction pathway along the c-axis (Figure 1a).21 Kato et al. further reported that the enhanced mobility in Li9.54Si1.74P1.44S11.7Cl0.3 stems from the small amount of chlorine, which facilitates the lithium diffusion along the a- and b-directions.8 Discovery of the Li10GeP2S12-type conductors with unexpectedly high ionic conductivity has led to extensive theoretical studies aimed at elucidating the origin of this property and guiding the design of improved solid electrolytes for LIBs.22-28 Mo et al. attributed the fast ionic conduction to the facile lithium diffusion along the c-axis based on ab initio molecular dynamics (AIMD) simulations,22 and Adams et al. observed an interstitialcy-type lithium diffusion primarily within the c-channel in atomistic molecular dynamics simulations.23 Furthermore, Xu et al. reported that the correlated motion of lithium ions along the c-axis promotes the fast ionic conduction.24 However, Mo et al. later argued that the ab-plane diffusion also plays a critical role in the fast ionic conductivity and is indispensable at the macroscopic scale,22 as evidenced by the serious performance degradation of generic one-dimensional conductors caused by possible path-blocking defects.29 Adams et al. further confirmed the substantial contribution of lithium diffusion within the ab-plane in Li10GeP2S12.23 Similar results on the contribution of the ab-plane diffusion have

INTRODUCTION Lithium-ion batteries (LIBs) are some of the most widely used power sources for modern portable electronic devices due to their high energy density and reliable performance.1, 2 With increasing demands for new large-scale energy storage systems for electric vehicles, the importance of LIBs is expected to be ever growing. Nevertheless, recent incidents involving swelling/burning of current LIBs have led to safety concerns regarding their widespread use in large-scale systems. As these incidents are closely linked to the flammable organic electrolytes present in current LIBs, intensive efforts have been placed on developing non-flammable all-solid-state batteries,3 which employ an inorganic solid electrolyte, as an alternative technology.4-6 The absence of the organic electrolyte significantly enhances the safety characteristics of the batteries and, moreover, is expected to aid in further improving the energy density of systems by enabling the potential use of a lithium metal anode and high-voltage cathode as well as versatile (e.g., bipolar) stackings of the individual cells.6-9 In the journey to all-solid-state batteries, various solidstate ionic conductors have been developed such as garnets,10-13 perovskites,14-17 and argyrodites,18-20 some of which exhibit promising properties as solid electrolyte materials. In particular, Li10GeP2S12 and its derivatives, first introduced by Kamaya et al., have attracted significant interest because the room-temperature ionic conductivity of lithium is comparable to or even exceeds that of liquid electrolytes.21 Moreover, a recent study from the same

ACS Paragon Plus Environment

1

Chemistry of Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

been reported by several other research groups, with Li10GeP2S12 being designated a three-dimensional conductor based on the comparably low activation barriers calculated in the ab-plane diffusion.26-28 In this series of theoretical studies, it was emphasized that the ab-plane diffusion could act as a mitigator, alleviating the detrimental effect of the potential presence of path-blocking defects.22, 23, 26-28 These claims were supported by subsequent experimental characterization, in which multi-dimensional lithium ion conduction in Li10GeP2S12 was revealed through a singlecrystal X-ray diffraction study with analysis of thermal ellipsoids,30 nuclear magnetic resonance studies,31, 32 and maximum entropy analysis of the neutron diffraction.33 In these studies, it was also proposed that the diffusion along the c-axis could be limited by the potential presence of path-blocking defects, thereby suggesting that the diffusion in the ab-plane is essential for fast lithium diffusion in the Li10GeP2S12 structure. Defects often play a crucial role in determining key properties of materials.34, 35 For example, lithium diffusion in solid-state ion conductors is significantly affected by the presence of defects with the lithium transport kinetics and mechanism varying significantly depending on the types and concentrations of defects.29, 36-38 Accordingly, the importance of defects in Li10GeP2S12 and its derivatives in blocking the diffusion path or altering the diffusion mechanism has been consistently reported in both theoretical and experimental studies. Nevertheless, it is still elusive what the native defects are, what their intrinsic concentrations are, how they are affected by chemical conditions, and how they influence on the diffusion mechanism in the Li10GeP2S12. In this study, we explore the defect chemistry of Li10GeP2S12 and investigate the effect of the presence of various defects on lithium diffusion using first-principles calculations and AIMD simulations. In particular, we identify major defects that exhibit relatively low formation energy and the effect of varying chemical conditions on their concentrations, which may aid in achieving a higher practical ionic conductivity through tuning of the synthetic conditions. Moreover, the effects of each major defect on lithium diffusion are discussed based on analysis of the lithium site occupancies and hopping rates using AIMD simulations. This study offers a comprehensive overview of the defect nature of Li10GeP2S12, which can potentially guide further optimization of this class of materials for use as fast lithium ionic solid conductors for all-solid-state batteries.

Page 2 of 12

less than 0.02 eV/Å within the spin-polarized calculation. After prescreening of the ground-state configurations using GGA functional, the final energies of pristine and defected structures were calculated again with Heyd−Scuseria−Ernzerhof (HSE)44 functional to secure the accuracy of the defect formation energy. The parameters for mixing and range-separation were set at 0.25 and 0.2, respectively (HSE06).45 Due to higher computational costs of using the hybrid functional, a kinetic energy cutoff of 340 eV and a 2×2×1 k-point grid were used for a 1×1×1 supercell structure of Li20Ge2P4S24. Phase stability of Li10GeP2S12 The energy of the structures with and without defects was determined by finding the lowest DFT energy of all the possible atomic configurations within a given supercell. The Li10GeP2S12 structure has many possible atomic configurations +because of the partial occupancy of Li and Ge/P1 sites;30 therefore, the more computationally costeffective electrostatic energy criterion46 was first used to exclude the high-energy structures, as applied in previous studies.22, 25 DFT calculations were then performed for the 1,000 lowest electrostatic energy structures to find the ground-state configuration with the lowest DFT energy. In the construction of the quaternary Li–Ge–P–S phase diagram, all known Li–Ge–P–S compounds in the inorganic crystal structure database (ICSD)47 were considered. In addition, all LixPySz compounds modeled by Holzwarth et al.48 and all possible phases obtained by anion substitution were also included to increase the reliability of the phase diagram, as suggested in previous studies22, 25 (see Supporting Information for additional computational details regarding the phase stability calculations). Nomenclature of cation sites Because of the complexity of the structure and various local environments present, the following notations of each site in the structure of Li10GeP2S12 were used. There are two symmetrically distinctive P sites and four Li sites in Li10GeP2S12. We denote P sites that share (Ge/P)S4 tetrahedra with Ge ions as P1 (4d site in Wyckoff position) and the other P sites that are solely occupied by P ions as P2 (2b site in Wyckoff position). For the Li sites, those forming one-dimensional channels along the c-axis (i.e., channel sites) are denoted as Li1 (16h site in Wyckoff position) and Li3 (8f site in Wyckoff position) sites, whereas those bridging the channels in the ab-direction (i.e., bridge sites) are denoted as Li2 (4d site in Wyckoff position) and Li4 (4c site in Wyckoff position) sites. We note that each of the four Li sites can be further subdivided due to the reduced symmetry in a specific Ge/P1 arrangement in the firstprinciples calculations. There are three potential arrangements of Ge and P in (Ge/P1)S4 tetrahedra because of its partial occupation, which can be a zig-zag arrangement of Ge and P ions in Ge/P1 sites (denoted as Z) or parallel arrangements along the ab- or c-direction (denoted as Pa and Pc, respectively), as illustrated in Figure S1.27 Accordingly, more specific notations were used for bridge sites (Li2 and Li4) by indicating the neighboring Ge/P1 sites (Figure S2). For example, Li4 sites were subdivided into Li4_Ge or Li4_P sites depending on the cation species in the edgesharing Ge/P1 sites. For channel sites (Li1 and Li3), however, the fractional coordinates of the c-axis in the unit cell were indicated after its own notation to help understand

METHODS First-principles calculations All the initial prescreening calculations were performed based on density functional theory (DFT) using the generalized gradient approximation (GGA) with the Perdew– Burke–Ernzerhof (PBE) functional.39 The interaction between ion cores and valence electrons was treated using the projector augmented wave (PAW)40, 41 method as implemented in the Vienna Ab initio Simulation Package (VASP).42 A kinetic energy cutoff of 520 eV and at least 1,000/(number of atoms in the supercell) k-point grid based on the Monkhorst–Pack scheme43 were used. A 4×4×2 k-point grid was used to calculate a 1×1×1 supercell structure of Li20Ge2P4S24, corresponding to 50 atoms. The structures were fully relaxed until the residual forces were


2

Page 3 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials that corresponds to the pristine structure. The term for the charged defects can be expressed as:49 2 "# &', 2 3 2$% where # is the lattice-dependent Madelung constant,46 $ is the macroscopic dielectric constant, % is the linear dimension of the supercell, and &' is the potential alignment term. We calculated the &' by comparing the average electrostatic potential at S core in the bulk-like region. To obtain $, the linear response method based on density functional perturbation theory50 was used. We used a denser kpoint grid in each direction (8×8×4 Monkhorst–Pack grid) for this calculation43 because the linear-response computation tends to be sensitive to k-point sampling.51 AIMD simulations We investigated the diffusion behavior of lithium ions in Li10GeP2S12 with and without defects using AIMD simulations. To mitigate artificial self-interactions between periodic images (see Figure S4 for details), 2×2×1 supercell structures were used. A kinetic energy cutoff of 258.689 eV and a (-point-only k-point grid were used. AIMD simulations were performed using non-spin-polarized calculations. Simulation temperatures between 500 K and 1300 K with an interval of 100 K were selected. Before the AIMD simulation, the pristine structure was fully relaxed until the residual forces were less than 0.02 eV/Å. For the structures with defects, only the internal atomic positions were allowed to be relaxed within the fixed lattice of the fully relaxed pristine structure. The integration of Newton’s equation was treated based on the Verlet algorithm,52 as implemented in VASP, and the time step for the simulation

the diffusion along the channel. Their corresponding local structures are depicted in Figure S3. Defect formation energy calculations Possible defects including path-blocking defects, configurational defects, and electron defects were considered (more than 35 different defect types were investigated as tabulated in Table S1). The formation energy of defect with charge state was calculated using the following equation:34, 35, 49

, 1

where is the formation energy of defect , is the energy of the structure with defect , is the energy of the pristine Li10GeP2S12 structure, is the number of species of type added to ( 0) or removed from ( 0) the structure when the defect was created, is the corresponding chemical potential of species in the Li10GeP2S12 phase, is the valence band maximum of the pristine structure, is the Fermi energy in reference to , and is the correction term for a charged defect in a finite-size supercell.49 In the calculation of , only the internal atomic positions were allowed to be relaxed, whereas the lattice parameters were fixed as those of the pristine structure. When constructing the defectcontaining structures, redistributions of lithium ions over all the partially filled lithium sites were considered to identify the lowest energy configuration out of 1,000 configurations. Except for the case of configurational defects, the Ge/P1 arrangement was also fixed as the Z configuration

Figure 1. Crystal structure of Li10GeP2S12. (a) Overall structures including framework structure and Li sites parallel (left) and perpendicular (middle) to the c-axis. Ultrafast lithium diffusion channels along the c-axis with lithium polyhedral are illustrated on the right with notations for channel sites. Local atomic structures of (b) Li1 site, (c) Li2 site, (d) Li3 site, and (e) Li4 site.


3


was set at 2 fs. At the beginning of the simulation, the initial temperature of the samples was set at 100 K and the velocity of ions was set according to the Boltzmann distribution; then, the samples were heated to the desired temperature (500 K to 1300 K) by velocity scaling at a rate of 0.5 K/fs. At the assigned temperature, the AIMD simulation was performed until the diffusivity converged (50–200 ps) in the NVT ensemble with a Nosé–Hoover thermostat.53, 54 The site occupancy of lithium during diffusion was determined by counting the frequency of lithium occupancy at a particular site. For the hopping rate, only the number of effective hops contributing to the lithium diffusion at the particular site was counted and divided by the simulation time. The hopping rate of channel sites was not considered because the atomic vibrations in these sites are not localized to one specific site but spread over the channel24 (see Supporting Information for additional computational details regarding the AIMD simulations).

Page 4 of 12

equidistant along the c-direction, indicating the occupancy of the octahedral Li1 site as described above, while the others filled the remaining Li3 sites. These results are in good agreement with the findings of previous studies.27, 28 More detailed information about the Li10GeP2S12 structure in the ground-state configuration is provided in Table S2. Intrinsic defects in Li10GeP2S12 The calculations of the defect formation energy require information about the chemical potentials of individual elements in Li10GeP2S12. As such, the possible chemical potential range of Li, Ge, P, and S was calculated and is displayed as the gray area in the Δ. vs. Δ/ plane in Figure 2a, which was determined from the stability conditions of the Li10GeP2S12 phase (see Supporting Information for details).34, 35 All the possible phases in the quaternary phase diagram involving Li10GeP2S12 were considered, and four limiting conditions (A, B, C, and D in Figure 2a) were imposed for the stability of Li10GeP2S12 by the phase equilibria with the S, Li2S, Li2GeS3, and Li2PS3 phases, respectively. The stability condition of the Li10GeP2S12 phase allows a set of chemical potentials within the gray region in Figure 2a depending on the surrounding chemical conditions; thus, a specific set of chemical potential values practically implies the synthetic environments of Li10GeP2S12.34, 35 For example, the chemical potential set on line AB in Figure 2a represents the S-rich conditions during the synthesis of the Li10GeP2S12 phase. On the other hand, limiting condition C corresponds to a S-poor environment, where the chemical potential of S has the lowest value. Similar discussions can be applied to Ge, P, and Li, as summarized in Figure 2b for each limiting condition. Given a chemical potential set, the formation energies of various defects can be determined as a function of the Fermi energy, as shown in Figure 2c–f. Note that the defect formation energies are dependent on the Fermi energy due to the charged nature of some defects, and the Fermi level is determined at the value satisfying the charge neutrality of the system.34, 35 Figure 2c–f display the formation energies of various defects with the determined Fermi level (a vertical dotted line) for each chemical potential limit. Note that the calculated band gap is about 2.3 eV confirming the determined Fermi levels are reasonable. Although many defects may coexist in the system, five defect types exhibited notably lower formation energies than the others and were thus suspected to dominantly affect the defect properties of the system.34, 35 Accordingly, we defined these five defects (represented with solid lines in Figure 2c–f) as major defects, which include Pa (configurational defect with parallel Ge/P1 arrangement along the a- or b- direction), Pc (configurational defect with parallel Ge/P1 ar3 rangement along the c-direction), P12 (substitution of Ge4+ 7 5+ by P ), V56 (negatively charged lithium vacancy), and Li63 (additional Li+ at interstitial sites). The formation energies of the major defects were comparable with values of approximately 0.20–0.25 eV, implying their abundance in the structure. Moreover, these values did not significantly vary with the different chemical potential limits of conditions A, B, C, and D. It is worthy of noting that the formation energy of the path-blocking defects in LiFePO4 (e.g., anti-site defects) has been reported to be within the range of 0.36– 1.67 eV,55 and its presence/content is known to be sensitively affected by the synthetic conditions.29, 36, 55, 56 Thus, it is expected that these major defects would be prevalent in

RESULTS AND DISCUSSION Local atomistic structure of the ground-state Li10GeP2S12 crystal The crystal structure of Li10GeP2S12 consists of chains of LiS6 octahedra (blue polyhedron in Figure 1a) linked by (Ge/P1)S4 tetrahedra (purple polyhedron) along the cdirection, which are also connected by P2S4 tetrahedra (green polyhedron) in the ab-direction within the &4" /+, space group (Figure 1a).30 The structure contains partially occupied cation sites, where four Ge/P1 sites are filled by either Ge or P ions with a ratio of 1:1 and 16 Li sites are partially occupied by 10 Li ions (or 20 Li ions are in 32 Li sites within a given unit cell). Due to the complexity of the structure and various local environments present, the structure of Li10GeP2S12 is shown with the notations of each site as suggested in the Methods section. Regarding the Li1 sites, our calculations indicated that two adjacent original (or previously proposed)21, 30 Li1 tetrahedral sites (16h site in Wyckoff position or Li1tet sites) are unphysically too close to each other; thus, the double occupancy of those sites is energetically unfavorable.23, 24 Instead, a single Li1 site with an octahedral coordination (8e site in Wyckoff position) tends to be formed, as shown in Figure 1b.23 The octahedral Li1 and Li2 sites edge-share with two (Ge/P1)S4 tetrahedra and corner-share with two P2S4 tetrahedra; however, the Li3 and Li4 sites in tetrahedral coordinates edge-share with one P2S4 tetrahedron and corner-share with two (Ge/P1)S4 tetrahedra (Figure 1b–e). To investigate the defect nature of Li10GeP2S12, the ground-state structure of the pristine material was first determined. Among the many possible atomic configurations originating from the partial occupancies in cation sites, the structure with the lowest DFT energy was identified as the ground-state structure (see Methods section for additional computational details). The most stable Li10GeP2S12 structure was observed to have the Z configuration of the Ge/P1 site arrangement. Within the unit cell of Li20Ge2P4S24, 20 Li ions are populated in 32 Li sites in a way that four Li2 sites are fully filled, four Li4 sites are partially occupied by two Li ions (i.e., Li4_Ge), and the remaining 14 Li ions are distributed over four channels with three or four Li ions per channel. In the channel with four Li ions, two Li ions were observed to occupy the interstitial sites between the two adjacent Li1tet sites, being nearly


4

Page 5 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. (a) Chemical potential map for Li10GeP2S12 phase (>?@ indicates the chemical potential of species @ referenced to the ele-

mental solid atom ?@A , i.e., >?@ ?@ ?@A ). The phases corresponding to dotted lines other than S, Li2S, Li2PS3, and Li2GeS3 are shown in Figure S5. (b) Table of chemical potentials of each element at corresponding limits. Defect formation energy profiles obtained under limiting conditions (c) A, (d) B, (e) C, and (f) D. Note that the selective range of Fermi energy (1.2–2.2 eV) is depicted for clarity, refer to Figure S6 for defect profiles in extended scales.

sponds to Li-rich conditions, the concentration of V56: was much lower and the highest defect formation energy (1.74 eV) was observed (Figure S6). Of the minor defects, the possible path-blocking defects were more carefully investigated. If multi-valent cations such as Ge4+ and P5+ occupy Li sites, they may block the diffusion of lithium ions because of their low mobility in the structure.13, 29, 36, 38 Therefore, we examined the defect formation energies of all the possible Ge and P occupations of the Li sites including channel and bridge sites (Table S1). The defects with the lowest formation energy were + 4+ Ge=3 56 (substitution of Li in Li channel site by Ge ) with a

the preparation of Li10GeP2S12, suggesting that their effects on lithium transport should be clearly scrutinized, as will be discussed in detail later. The comparable formation energies of the major defects irrespective of the chemical potential limits imply that the defect nature of Li10GeP2S12 would not be notably altered by the synthetic conditions. However, the defect formation energies of minor defects, such as V56: , were observed to be more susceptibly affected by the synthetic conditions. The lowest value of the defect formation energy for V56: (1.30 eV) was observed under limiting condition A, which corresponds to Li-poor conditions. In contrast, under limiting condition C, which corre-


5


Page 6 of 12

Figure 3. Arrhenius plots of logarithms of diffusivities as a function of temperature for Li10GeP2S12 structures (a) without defects 3 7 and with defect species (b) Pa, (c) Pc, (d) P12 , (e) V56 , and (f) Li3 6 . The total diffusivities (Dtotal) were subdivided into the ab-plane contribution (Dab) and c-directional contribution (Dc). The diffusivities at 300 K were extrapolated from the values at elevated temperatures and are displayed as closed shapes, and those obtained directly from the AIMD simulations are displayed as open shapes.

studies.22, 23, 26-28, 31-33 The intrinsically low probability of the presence of path-blocking native defects in this material is thought to have contributed to the superior lithium ionic conductivity experimentally observed for Li10GeP2S12 compared with that of other one-dimensional lithium conductors such as LiFePO4, which are susceptible to pathblocking defects; thus, careful synthetic routes are often required.29, 36, 55, 56 Lithium ionic conductivity and its mechanism in Li10GeP2S12

formation energy of 2.10, 2.99 and 2.10 eV for limiting conditions A, B and D, respectively, and Ge:56 (substitution of Li in Li channel site by Ge) with formation energies of 2.86 eV for limiting condition C, indicating that the channel sites are more vulnerable to defects than bridge sites (Figure S6). Although these defects prefer Li channel sites, thus potentially blocking lithium diffusion through the cchannel, the high values of the formation energy indicate that the presence of path-blocking defects would have a marginal effect on the diffusion properties of Li10GeP2S12, which contrasts with concerns raised in previous


6

Page 7 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Lithium ionic conductivity (B) at 300 K and activation energy (EA) of structures with and without defects. Each value was subdivided into the ab-plane contribution and c-directional contribution. Defect type

overall (averaged)

ab-plane

c-channel

B [mS/cm]

EA [eV]

B [mS/cm]

EA [eV]

B [mS/cm]

EA [eV]

w/o

34

0.19±0.011

9

0.22±0.014

105

0.16±0.015

Pa

70

0.16±0.013

14

0.20±0.011

230

0.13±0.015

Pc

87

0.15±0.005

20

0.20±0.012

310

0.12±0.011

75

0.16±0.014

13

0.21±0.008

270

0.13±0.023

22

0.20±0.010

6

0.24±0.014

72

0.17±0.019

47

0.18±0.017

10

0.22±0.021

167

0.15±0.018

PGe

VLi

Li i

AIMD simulations of the Li10GeP2S12 structures with and without major defects were performed to elucidate the effect of significant concentrations of these defects on lithium diffusion even though they were not expected to directly block the channel. The lithium diffusivities of Li10GeP2S12 for each case were probed as a function of temperature in the AIMD simulations, and the results are presented in Figure 3. The lithium ionic conductivity at 300 K and the activation energy were obtained from these data and are tabulated in Table 1. The diffusivity at 300 K was determined by extrapolation of the diffusivity values measured at high temperatures based on the Arrhenius behavior. The ionic conductivity of lithium in the pristine Li10GeP2S12 was approximately 34 mS/cm with an activation energy of 0.19 eV, and the conductivity along the cdirection was approximately ten times higher than that along the a- or b-direction. This anisotropic nature of diffusion is consistent with previous reports.22, 32 However, it should be noted that our calculation overestimated the diffusion in Li10GeP2S12 compared with the experimentally measured values, 12 mS/cm with an activation energy of 0.25 eV.21 The discrepancy can be understood by nature of experimental samples such as the presence of grain boundaries as demonstrated by Kamaya et al., which is not feasible to be considered in our computational methodology.21, 57 As observed in Table 1, the overall lithium ionic conductivity was distinguishably affected by the introduction of defect species. The lithium conductivities at 300 K (and those at 500 K in Table S3) increased with the presence of major defects except for the structure with V567 . This finding is rather unexpected and demonstrates the positive effect of the presence of the major defects in Li10GeP2S12 unlike their presence in other crystalline ionic conductors, which are vulnerable to defects.13, 29, 36, 38 Moreover, the configurational defects such as Pa and Pc were observed to have a more pronounced effect on the lithium conductivity than the other defects. In addition, these defects had a more remarkable effect on the c-directional conduction with the conductivity more than doubling, implying that the slight disorder in P and Ge in the structure facilitates the lithium mobility in the channel. However, the effect of defects such as V567 and Li36 was not as significant, suggesting that the concentration of the charge carriers is less important in this type of material, whereas excess lithium content in Li10GeP2S12 is slightly beneficial to the conductivity. A discussion of the origin of the unexpected enhancement of the

conductivity will be provided later for each major defect type. To understand the lithium diffusion at the atomistic scale, we further analyzed the site occupancies and hopping rates at each Li site in Li10GeP2S12. Probing these properties offers a dynamic picture of how the local environment alteration by a certain defect statistically affected the lithium mobility at specific sites.58 As a reference, the site occupancy and hopping rate are plotted for Li channel and bridge sites in pristine Li10GeP2S12 at different temperatures in Figure 4a and 4c and Figure 4e, respectively. In general, the occupancies of different Li sites gradually converge to an average value as the temperature increases (Figure 4a and 4c), indicating that the entropy term in the site energy becomes dominant at high temperature. The presumably inactive sites such as the Li2_Ge, Li2_P, and Li4_Ge sites begin to participate in the diffusion (Figure 4e) at higher temperatures, which is consistent with previous experimental findings on the predominant threedimensional diffusion behaviors at elevated temperature.58, 59 In Figure 4a, the occupancy of the Li3_c0/4 sites in the lithium channel appears to be significantly lower than that of the other sites. It is attributed to the stronger repulsive forces of corner-sharing PS4 tetrahedra than GeS4 in the distinct Z configuration (Figure S3). The site occupancy of Li4_P in the bridge sites in Figure 4c is also notably lower than the others, which is also due to the strong repulsive forces of corner-sharing PS4 tetrahedra, as shown in Figure S2. In contrast, the remarkably high hopping rate of lithium ions in the bridge Li4_P sites in Figure 4e indicates that they are the major contributors to the ab-plane diffusion, which is in good agreement with previous studies.26-28, 30, 32, 59 Because the Li4_P sites have the lowest site occupancy among the bridge sites, the readily formed vacancy in the bridge sites can aid in facilitating the ab-plane diffusion. Effects of native defects on lithium diffusion Table 1 shows that the configurational defects such as Pa and Pc predominantly affected the lithium conductivity of Li10GeP2S12. The lithium ionic conductivity at 300 K more than doubled with the presence of both types of defects, particularly enhancing the c-directional (i.e., channel) mobility. Configurational defects, which are formed by distinct Ge/P1 arrangement that is different from the ground-state ones, alter the site energy landscape for lithium conduction. Figure 4b shows that the occupancy at the channel sites was thus significantly affected by these configura-


7


Page 8 of 12

Figure 4. Site occupancy of (a) channel sites and (c) bridge sites and (e) hopping rate in the bridge sites of pristine Li10GeP2S12 structure as a function of temperature. Site occupancy of (b) channel sites and (d) bridge sites and (f) hopping rate in the bridge sites for structures with various defect types at 500 K in reference to the pristine structure. In the analysis, the results at 500 K were selected as a representative case to describe the diffusion behaviors. The data for the pristine structure are depicted in gray on the left side of each graph for comparison. Results at other temperatures for the structure with defects are provided in Figure S7–S9.

tional defects. The site occupancy of Li3_c0/4 sites, which was very low in the pristine material, increased markedly, whereas that of Li3_c2/4 sites decreased, making the site

occupancy of these initially lowest and highest occupied Li sites identical. This change stems from the two Li3 sites in the Pa and Pc configuration becoming symmetrically indis-


8

Page 9 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Chemistry of Materials 3 on ab-plane diffusion is less dramatic than the effect of P12 that along the c-direction (Table 1). The Li4_Ge site exhibited reduced occupancy and enhanced hopping rates for both regions compared with those of the pristine structure. The more frequent hopping through Li4_Ge sites triggered 3 by the introduction of the P12 defect is suspected to have contributed to the enhancement of the lithium conductivity in the ab-plane. As previously observed in Table 1, the effect of V567 and 3 Li6 , which can be grouped together as Li Frenkel defects, is not comparatively significant to the overall lithium ion conductivity. Li Frenkel defects are primarily formed by the insertion of additional lithium to or the removal of lithium from the pristine structure and are thus expected to alter the concentration of the charge carrier in the lithium conductor. According to the Nernst–Einstein equation (B EF " G " H/IJ ; E: molar density of lithium ions, F : charge of lithium ions (+1), G: Faraday constant, I: gas constant), the lithium ionic conductivity is proportional to the lithium ion concentration. However, the change in the ion concentration from the Li Frenkel defects here is only approximately 1% (there are 80 Li ions in the 2×2×1 supercell of Li10GeP2S12); thus, a negligible effect from the change in the charge carrier concentration was expected. Nevertheless, it is noteworthy that the ionic conductivity increases by approximately 40% with the introduction of Li36 and decreases by approximately 40% with the introduction of V567 (Table 1). The origin of this phenomenon is not yet clear; however, we speculate that the introduction of the Li Frenkel defects may alter the diffusivity (H) by affecting the cooperative characteristic of lithium diffusion in Li10GeP2S12, where lithium–lithium interactions are of critical importance in facilitating the lithium motion in the channel.23, 24 This phenomenon requires further investigation in a future study.

tinguishable in contrast to the case in the ground-state Z configuration (Figure S3) and ensures that all the Li sites in the channel are energetically similar to each other, as most notably observed for Pc in Figure 4b (indicated by the red circle). These unique changes in Li site energies result in the flattened energy landscape in channel sites with comparable site energies for each Li site, which gives rise to more facile lithium diffusion in the c-direction. Unlike the channel sites, the local environments of each bridge site are similar in all the Ge/P1 configurations (Figure S2); thus, the site occupancies of the Li2 and Li4 sites are relatively less affected by the local Ge/P1 arrangements, as shown in Figure 4d. Nevertheless, the lithium diffusion in the ab-plane is enhanced by the presence of configurational defects (Table 1). Interestingly, the abplane conductivity increases more than 50% with the presence of configurational defect Pa; however, the hopping rates of the bridge sites do not change significantly. This result most likely stems from the particular redistribution of Li4_P sites in the Pa configuration, which are the most active hopping centers for ab-diffusion (Figure 4f), helping to form a lithium percolating layer through the abplane, as illustrated in Figure S10. Notably, in the Pc configurational defect, the Li2_Ge and Li4_Ge sites, which were inactive in the pristine configurations, exhibit significant hopping rates, implying their participation in the diffusion process (Figure 4f). Analysis of the probability density distribution of lithium ions revealed that the highly repulsive PS4 columns are formed in the Pc configuration (Figure S11), which is believed to push the lithium ions in neighboring channel sites, activating hopping through Li2_Ge and Li4_Ge sites. The greater enhancement of lithium conductivity in Pc configurational defects than in Pa configurational defects, as observed in Table 1, is attributed to these additional contributions from Li4_Ge and Li2_Ge sites in the lithium ion transport. 3 The P12 point defect is expected to affect the energy landscape of Li sites locally unlike the configurational de3 fects. In this respect, the influence of the P12 defect was 3 individually examined for the local region near P12 (denot3 3 C ed as (P12 )), and the rest (denoted as (P12 ) ) as described in Figure S12. Figure 4b shows that the overall site occu3 pancy in the channel sites slightly decreases near the P12 3 defect (i.e., (P12 )), which we observed to arise from the increased repulsion force stemming from the presence of 3 P12 . In particular, the site occupancy of the Li3_c2/4 site 3 that corner-shares with the P12 -containing tetrahedron was observed to be most significantly reduced. Notably, despite the overall reduction in the occupancy due to the repulsion, the destabilization of the Li3_c2/4 site in the 3 (P12 ) region promotes the flattening of the energy landscape along the channel sites. The comparable Li site ener3 gies in the channels near a P12 defect, similar to the case of configurational defects, are suspected to have contributed to enhancing the lithium ionic conductivity along the cdirection. Regarding the lithium diffusion in the ab-plane, Figure 4d shows that the site occupancy of the bridge sites 3 decreases in the (P12 ) region, especially for Li4 sites, followed by higher hopping rates due to the increased vacancy occupation of Li4 sites, as observed in Figure 4f. In con3 C trast, the opposite behaviors were observed in the (P12 ) region. These two opposing phenomena may cancel out the overall effect on the lithium mobility in the ab-plane; thus,

CONCLUSION The nature of native defects in Li10GeP2S12 were investigated using first-principles calculations. The five major defects were identified as Pa and Pc (configurational de3 fects); P12 (substitutional defect); and V567 and Li36 (Li Frenkel defects) regardless of the surrounding chemical environment. The low formation energies of the major defects (less than 0.25 eV) suggest that they would be prevalent in the preparation of Li10GeP2S12. Most of the path-blocking defects were observed to be minor with relatively high formation energy, implying that they would not significantly affect the properties of Li10GeP2S12 and would thus aid in achieving a high theoretical lithium conductivity in practice. Based on the AIMD simulations, the effects of major defects on the lithium ionic conductivity were scrutinized, with the unexpected finding that the major defects promoted lithium transport in Li10GeP2S12. Detailed analysis of the site energy and hopping rate suggested that the major defects tend to offer a more flattened site energy landscape along the c-channel and the readily formed vacancy in bridge sites, leading to enhanced lithium conductivity. This comprehensive study on the defect nature of Li10GeP2S12 broadens our understanding on Li10GeP2S12 and its derivatives and informs the practical criteria to be considered for fast lithium diffusion for high-performance solid electrolytes.


9


Page 10 of 12

Wakihara, M., High ionic conductivity in lithium lanthanum titanate. Solid State Commun. 1993, 86, 689-693. (15) Kawai, H.; Kuwano, J., Lithium Ion Conductivity of A-Site Deficient Perovskite Solid Solution La0. 67− x Li3x TiO3. J. Electrochem. Soc. 1994, 141, L78-L79. (16) Zhao, Y.; Daemen, L. L., Superionic conductivity in lithium-rich anti-perovskites. J. Am. Chem. Soc. 2012, 134, 15042-15047. (17) Deng, Z.; Radhakrishnan, B.; Ong, S. P., Rational Composition Optimization of the Lithium-Rich Li3OCl1–x Br x Anti-Perovskite Superionic Conductors. Chem. Mater. 2015, 27, 3749-3755. (18) Deiseroth, H. J.; Kong, S. T.; Eckert, H.; Vannahme, J.; Reiner, C.; Zaiß, T.; Schlosser, M., Li6PS5X: A Class of Crystalline Li-Rich Solids With an Unusually High Li+ Mobility. Angew. Chem. Int. Ed. 2008, 47, 755-758. (19) Chen, H. M.; Maohua, C.; Adams, S., Stability and ionic mobility in argyrodite-related lithium-ion solid electrolytes. Phys. Chem. Chem. Phys. 2015, 17, 16494-16506. (20) Wang, Z.; Shao, G., Theoretical design of solid electrolytes with superb ionic conductivity: alloying effect on Li+ transportation in cubic Li 6 PA 5 X chalcogenides. J. Mater. Chem. A 2017, 5, 2184621857. (21) Kamaya, N.; Homma, K.; Yamakawa, Y.; Hirayama, M.; Kanno, R.; Yonemura, M.; Kamiyama, T.; Kato, Y.; Hama, S.; Kawamoto, K., A lithium superionic conductor. Nat. Mater. 2011, 10, 682-686. (22) Mo, Y.; Ong, S. P.; Ceder, G., First principles study of the Li10GeP2S12 lithium super ionic conductor material. Chem. Mater. 2011, 24, 15-17. (23) Adams, S.; Rao, R. P., Structural requirements for fast lithium ion migration in Li 10 GeP 2 S 12. J. Mater. Chem. 2012, 22, 7687-7691. (24) Xu, M.; Ding, J.; Ma, E., One-dimensional stringlike cooperative migration of lithium ions in an ultrafast ionic conductor. Appl. Phys. Lett. 2012, 101, 031901. (25) Ong, S. P.; Mo, Y.; Richards, W. D.; Miara, L.; Lee, H. S.; Ceder, G., Phase stability, electrochemical stability and ionic conductivity of the Li 10±1 MP 2 X 12 (M= Ge, Si, Sn, Al or P, and X= O, S or Se) family of superionic conductors. Energy Environ. Sci. 2013, 6, 148-156. (26) Hu, C.; Wang, Z.; Sun, Z.; Ouyang, C., Insights into structural stability and Li superionic conductivity of Li 10 GeP 2 S 12 from firstprinciples calculations. Chem. Phys. Lett. 2014, 591, 16-20. (27) Du, F.; Ren, X.; Yang, J.; Liu, J.; Zhang, W., Structures, thermodynamics, and Li+ mobility of Li10GeP2S12: a first-principles analysis. J. Phys. Chem. C 2014, 118, 10590-10595. (28) Bhandari, A.; Bhattacharya, J., Origin of Fast Ion Conduction in Li10GeP2S12, a Superionic Conductor. J. Phys. Chem. C 2016, 120, 29002-29010. (29) Malik, R.; Burch, D.; Bazant, M.; Ceder, G., Particle size dependence of the ionic diffusivity. Nano Lett. 2010, 10, 4123-4127. (30) Kuhn, A.; Köhler, J.; Lotsch, B. V., Single-crystal X-ray structure analysis of the superionic conductor Li 10 GeP 2 S 12. Phys. Chem. Chem. Phys. 2013, 15, 11620-11622. (31) Kuhn, A.; Duppel, V.; Lotsch, B. V., Tetragonal Li 10 GeP 2 S 12 and Li 7 GePS 8–exploring the Li ion dynamics in LGPS Li electrolytes. Energy Environ. Sci. 2013, 6, 3548-3552. (32) Liang, X.; Wang, L.; Jiang, Y.; Wang, J.; Luo, H.; Liu, C.; Feng, J., InChannel and In-Plane Li Ion Diffusions in the Superionic Conductor Li10GeP2S12 Probed by Solid-State NMR. Chem. Mater. 2015, 27, 5503-5510. (33) Weber, D. A.; Senyshyn, A.; Weldert, K. S.; Wenzel, S.; Zhang, W.; Kaiser, R.; Berendts, S.; Janek, J. r.; Zeier, W. G., Structural insights and 3D diffusion pathways within the lithium superionic conductor Li10GeP2S12. Chem. Mater. 2016, 28, 5905-5915. (34) Van de Walle, C. G.; Neugebauer, J., First-principles calculations for defects and impurities: Applications to III-nitrides. J. Appl. Phys. 2004, 95, 3851-3879. (35) Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G., First-principles calculations for point defects in solids. Rev. Mod. Phys. 2014, 86, 253-305. (36) Islam, M. S.; Driscoll, D. J.; Fisher, C. A.; Slater, P. R., Atomic-scale investigation of defects, dopants, and lithium transport in the LiFePO4 olivine-type battery material. Chem. Mater. 2005, 17, 5085-5092. (37) Kim, J.; Lee, B.; Kim, H.; Kim, H.; Kang, K., Redesign of Li2MP2O7 (M= Fe or Mn) by Tuning the Li Diffusion in Rechargeable Battery Electrodes. Chem. Mater. 2016, 28, 6894-6899. (38) Delmas, C.; Peres, J.; Rougier, A.; Demourgues, A.; Weill, F.; Chadwick, A.; Broussely, M.; Perton, F.; Biensan, P.; Willmann, P., On the behavior of the LixNiO2 system: an electrochemical and structural

ASSOCIATED CONTENT Supporting Information. Computational details, list of considered defects, Defect formation energy profiles in extended scale, descriptions for local structures, occupancies and hopping rates for higher temperatures This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

Author Contributions K.O. conducted calculations. D.C. developed codes for analyzing site occupancy and hopping rates. K.K. supervised the overall research. All authors discussed the results and gave the approval to final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported by project code (IBS-R006-A2), and the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2015-C3-054). This work was also supported by the Korea Research Fellowship Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT under KRF Grant no. 2016H1D3A1908716.

REFERENCES (1) Goodenough, J. B.; Kim, Y., Challenges for rechargeable Li batteries. Chem. Mater. 2009, 22, 587-603. (2) Tarascon, J.-M., Key challenges in future Li-battery research. Phil. Trans. R. Soc. A 2010, 368, 3227-3241. (3) Xu, K., Nonaqueous liquid electrolytes for lithium-based rechargeable batteries. Chem. Rev. 2004, 104, 4303-4418. (4) Quartarone, E.; Mustarelli, P., Electrolytes for solid-state lithium rechargeable batteries: recent advances and perspectives. Chem. Soc. Rev. 2011, 40, 2525-2540. (5) Manthiram, A.; Yu, X.; Wang, S., Lithium battery chemistries enabled by solid-state electrolytes. Nat. Rev. Mater. 2017, 2, 16103. (6) Li, J.; Ma, C.; Chi, M.; Liang, C.; Dudney, N. J., Solid Electrolyte: the Key for High-Voltage Lithium Batteries. Adv. Energy Mater. 2015, 5, 1401408. (7) Yada, C.; Ohmori, A.; Ide, K.; Yamasaki, H.; Kato, T.; Saito, T.; Sagane, F.; Iriyama, Y., Dielectric Modification of 5V-Class Cathodes for HighVoltage All-Solid-State Lithium Batteries. Adv. Energy Mater. 2014, 4, 1301416. (8) Kato, Y.; Hori, S.; Saito, T.; Suzuki, K.; Hirayama, M.; Mitsui, A.; Yonemura, M.; Iba, H.; Kanno, R., High-power all-solid-state batteries using sulfide superionic conductors. Nat. Energy 2016, 1, 16030. (9) Tian, Y.; Shi, T.; Richards, W. D.; Li, J.; Kim, J. C.; Bo, S.-H.; Ceder, G., Compatibility issues between electrodes and electrolytes in solid-state batteries. Energy Environ. Sci. 2017, 10, 1150-1166. (10) Murugan, R.; Thangadurai, V.; Weppner, W., Fast lithium ion conduction in garnet-type Li7La3Zr2O12. Angew. Chem. Int. Ed. 2007, 46, 7778-7781. (11) Geiger, C. A.; Alekseev, E.; Lazic, B.; Fisch, M.; Armbruster, T.; Langner, R.; Fechtelkord, M.; Kim, N.; Pettke, T.; Weppner, W., Crystal chemistry and stability of “Li7La3Zr2O12” garnet: a fast lithium-ion conductor. Inorg. Chem. 2010, 50, 1089-1097. (12) Thangadurai, V.; Narayanan, S.; Pinzaru, D., Garnet-type solidstate fast Li ion conductors for Li batteries: critical review. Chem. Soc. Rev. 2014, 43, 4714-4727. (13) Shin, D. O.; Oh, K.; Kim, K. M.; Park, K.-Y.; Lee, B.; Lee, Y.-G.; Kang, K., Synergistic multi-doping effects on the Li7La3Zr2O12 solid electrolyte for fast lithium ion conduction. Sci. Rep. 2015, 5, 18053. (14) Inaguma, Y.; Liquan, C.; Itoh, M.; Nakamura, T.; Uchida, T.; Ikuta, H.;


10

Page 11 of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


overview. J. Power Sources 1997, 68, 120-125. (39) Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (40) Blöchl, P. E., Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953-17979. (41) Kresse, G.; Joubert, D., From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758-1775. (42) Kresse, G.; Furthmüller, J., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169-11186. (43) Monkhorst, H. J.; Pack, J. D., Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188-5192. (44) Heyd, J.; Scuseria, G. E.; Ernzerhof, M., Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 2003, 118, 8207-8215. (45) Krukau, A. V.; Vydrov, O. A.; Izmaylov, A. F.; Scuseria, G. E., Influence of the exchange screening parameter on the performance of screened hybrid functionals. J. Chem. Phys. 2006, 125, 224106. (46) Ewald, P. P., Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 1921, 369, 253-287. (47) Bergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I. D., The inorganic crystal structure data base. J. Chem. Inf. Comput. Sci. 1983, 23, 66-69. (48) Holzwarth, N. A. W.; Lepley, N. D.; Du, Y. A., Computer modeling of lithium phosphate and thiophosphate electrolyte materials. J. Power Sources 2011, 196, 6870-6876. (49) Lany, S.; Zunger, A., Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs. Phys. Rev. B 2008, 78, 235104. (50) Gonze, X.; Lee, C., Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B 1997, 55, 1035510368. (51) Yim, K.; Yong, Y.; Lee, J.; Lee, K.; Nahm, H.-H.; Yoo, J.; Lee, C.; Hwang, C. S.; Han, S., Novel high-κ dielectrics for next-generation electronic devices screened by automated ab initio calculations. NPG Asia Mater. 2015, 7, e190. (52) Verlet, L., Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 1967, 159, 98-103. (53) Nosé, S., A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511-519. (54) Hoover, W. G., Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 1985, 31, 1695-1697. (55) Hoang, K.; Johannes, M., Tailoring native defects in LiFePO4: insights from first-principles calculations. Chem. Mater. 2011, 23, 3003-3013. (56) Park, K.-Y.; Park, I.; Kim, H.; Lim, H.-D.; Hong, J.; Kim, J.; Kang, K., Anti-site reordering in LiFePO4: defect annihilation on charge carrier injection. Chem. Mater. 2014, 26, 5345-5351. (57) Chu, I.-H.; Nguyen, H.; Hy, S.; Lin, Y.-C.; Wang, Z.; Xu, Z.; Deng, Z.; Meng, Y. S.; Ong, S. P., Insights into the performance limits of the Li7P3S11 superionic conductor: a combined first-principles and experimental study. ACS Appl. Mater. Interfaces 2016, 8, 7843-7853. (58) Richards, W. D.; Tsujimura, T.; Miara, L. J.; Wang, Y.; Kim, J. C.; Ong, S. P.; Uechi, I.; Suzuki, N.; Ceder, G., Design and synthesis of the superionic conductor Na10SnP2S12. Nat. Commun. 2016, 7, 11009. (59) Kwon, O.; Hirayama, M.; Suzuki, K.; Kato, Y.; Saito, T.; Yonemura, M.; Kamiyama, T.; Kanno, R., Synthesis, structure, and conduction mechanism of the lithium superionic conductor Li 10+ δ Ge 1+ δ P 2− δ S 12. J. Mater. Chem. A 2015, 3, 438-446.


11



Page 12 of 12

12

Native defects in Li10GeP2S12 and their effect on lithium diffusion

Recommend Documents