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Cite This: Chem. Mater. XXXX, XXX, XXX-XXX

Computational and Experimental Investigation of the Electrochemical Stability and Li-Ion Conduction Mechanism of LiZr2(PO4)3 Yusuke Noda,*,† Koki Nakano,‡ Hayami Takeda,‡,§ Masashi Kotobuki,∥,⊥ Li Lu,∥,⊥ and Masanobu Nakayama†,‡,§,# †

Center for Materials Research by Information Integration (CMI2), Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan ‡ Frontier Research Institute for Materials Science (FRIMS), Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi 466-8555, Japan § Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, 1-30 Goryo-Ohara, Nishikyo, Kyoto 615-8245, Japan ∥ Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore ⊥ National University of Singapore Suzhou Research Institute, Dushu Lake Science and Education Innovation District, Suzhou 215123, P. R. China # Global Research Center for Environment and Energy Based on Nanomaterials Science (GREEN), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0047, Japan S Supporting Information *

ABSTRACT: Solid electrolytes possessing sufficient ionic conductivity and electrochemical stability are urgently needed for the fabrication of all-solid-state Li-ion batteries (LIBs). In this study, we focus on a solid-state oxide electrolyte LiZr2(PO4)3 (LZP), which has NASICON structure and electrochemically stable Zr4+ ions. Using density functional theory (DFT) to calculate the electrochemical window of LZP, we find that it is unstable against Li metal, in accordance with our experimental results. The Li-ion transport is investigated using first-principles molecular dynamics (FPMD) simulations. The calculated Li-ion conductivity at room temperature (5.0 × 10−6 S/cm) and the activation energy for Li-ion diffusion (0.43 eV) are in fair agreement with experimental results. The mechanism of Li-ion conduction in LZP is revealed by analyzing the Li-ion trajectories in the FPMD simulations. It is found that each Li ion migrates between 6b sites as it is pushed out or repelled by other Li ions around these 6b sites. Hence, the high Li-ion conductivity is attributed to a migration mechanism driven by Frenkel-like defect. three-dimensional diffusion channels.3−5 However, sulfides present difficulties in the fabrication of all-solid-state batteries, as they tend to react with water and generate hydrogen sulfide gas. From this point of view, it is advisable to use oxide-based solid electrolytes instead. Unfortunately, compared with sulfidebased solid electrolytes, the oxide-based ones exhibit lower Liion conductivity at room temperature (in the order of 10−3 S/ cm at the highest). Therefore, it is essential to improve their ionic conductivity. Na super ionic conductor (NASICON)-type oxide-based solid electrolytes, as well as perovskite-type and garnet-type

1. INTRODUCTION The Li-ion battery (LIB) is one of the most popular types of rechargeable batteries with high energy density, long cycle life, and good safety. LIBs have been widely used for electric vehicles, smartphones, laptops, and so on.1 At present, the prevailing electrolytes for LIBs are organic liquid solvents, such as dimethyl carbonate and ethylene carbonate. However, these electrolytes are at risk of liquid leakage, inflammation, and/or explosion caused by short circuit.2 One attractive and important solution to this problem is replacing the organic liquid electrolytes with inorganic solid electrolytes. Such solid electrolytes are indispensable for allsolid-state batteries. Sulfide-based solid electrolytes such as Li10GeP2S12 (LGPS) are well-known as good ionic conductors with high Li-ion conductivity (10−2 S/cm) because of their © XXXX American Chemical Society

Received: April 26, 2017 Revised: October 18, 2017 Published: October 18, 2017 A

DOI: 10.1021/acs.chemmater.7b01703 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials ionic conductors, are considered promising in LIBs.3−7 Since the discovery of the fast Na-ion conducting NASICON-type system of Na1+xZr2SixP3−xO12 in 1976,8,9 many kinds of Li-ion conducting NASICON-type solid electrolytes with the general formula of LiM4+2(PO4)3 have been investigated. One of the most popular among them is Li1+xAlxTi2−x(PO4)3 (LATP), which can be generated by partially substituting Ti4+ with Al3+ in LiTi2(PO4)3 (LTP).10,11 Especially, LATP with x = 0.3 exhibits enhanced bulk Li-ion conductivity in the order of 10−3 S/cm at room temperature.12,13 However, it is also well-known that LTP-based materials react with Li metal at around 2.5 V vs Li+/Li due to the Ti4+/Ti3+ redox reaction.14,15 This precludes the use of negative electrodes that react at around this potential, because they will reduce the energy density of the battery. In this respect, another NASICON-type solid electrolyte, LiZr2(PO4)3 (LZP), is attractive, since it is known to form an insulating solid electrolyte interface consisting of Li3P and Li8ZrO6 when in contact with Li metal, with no redox reaction up to 5.5 V.16 It is well-known that phase transitions of LZP between triclinic (α′) and rhombohedral (α) phases,17,18 and between monoclinic (β′) and orthorhombic (β) phases19 occur at ∼60 °C and ∼300 °C, respectively. However, the initially reported stoichiometric LZP phase shows very low ionic conductivity (in the order of 10−6−10−5 S/cm at room temperature).20 Recently, significantly enhanced Li-ion conductivity (in the order of 10−4 S/cm) has been reported by replacing of Zr in LZP by Ca or Y.21−23 These new LZP-based materials may therefore possess both high Li-ion conductivity and wide electrochemical window. The ideal LZP has the rhombohedral phase with the spacegroup symmetry R3̅(−)c (167). The Li atoms are known to be located in Wyckoff positions of splitting 36f sites around 6b sites in the crystal structure (Figure 1). Various properties of

window of LZP is evaluated by both computational and experimental techniques. The ionic conduction mechanism is also investigated using first-principles molecular dynamics (FPMD) simulations. The FPMD technique is advantageous since one does not need to assume empirical force-field parameters and migration pathways although it has rather high computational cost. The remainder of this paper is organized as follows. In Computational and Experimental Details section, we describe the first-principles methodologies: static electronic structure calculations and the FPMD simulations, and the experimental procedures to investigate the chemical stability of LZP against Li metal. In the Results and Discussions section, we discuss the results of electrochemical stability and Li-ion conductivity of pure LZP. Through first-principles simulations, we clarify factors affecting the electrochemical window and ionic conductivity in terms of the atomic configurations and electronic level structure. The electrochemical stability is estimated using density functional theory (DFT),32 taking into account both the kinetic and thermodynamic stabilities. The room-temperature Li-ion conductivity is estimated by extrapolating the diffusion coefficients calculated from FPMD simulations in accordance with the Arrhenius equation. In addition, the Li-ion conduction mechanism is discussed in detail from the results of the FPMD simulations. Finally, we conclude this paper in Conclusions section.

2. COMPUTATIONAL AND EXPERIMENTAL DETAILS 2.1. Electrochemical Stability. In order to clarify the electrochemical stability of pure LZP, we constructed a convex-hull of cohesive energy versus the chemical composition using the Qhull code.33 For the convex-hull construction, we extracted data of 110 crystal structures including Li, Zr, P, and/or O (without other elements) from the Materials Project database,34 and calculated their cohesive energies using first-principles methods. In this process, a Vienna ab initio simulation package (VASP)35−38 based on DFT with a projector augmented-wave (PAW) method39,40 and a plane-wave basis set was used. A generalized gradient approximation (GGA)-type exchange-correlation functional developed by Perdew, Burke, and Ernzernhof and modified for solid materials (PBEsol)41 was used. The cutoff energy for the plane-wave basis was set to 500 eV. The unit cells of all structures were optimized with k-point resolution set to 400 for high-throughput investigations (i.e., Nx, Ny, and Nz, the number of grids in kx-, ky-, and kz-directions of the reciprocal space, were set to satisfy Nx × Ny × Nz × Natom ≈ 400, where Natom is the number of atoms in each unit cell). All structures were optimized, and the cohesive energies per atom were calculated. At last, the electrochemical potential window for LZP stability was obtained as follows. The convex-hull facets (multidimensional surfaces) for the compositions of infinitesimally lithiated and delithiated LZP were determined, the energy of the corresponding convex-hull facets at the chemical composition of pure Li was extrapolated (i.e., chemical potential), and the energy differences between Li metal and the corresponding chemical potentials are the electrochemical window of the reduction and oxidation ends, respectively. In addition, we calculated the Li intercalation voltage of LZP to estimate its reactivity with Li metal. In detail, the optimal Li configuration in pure LZP (Li6Zr12P18O72) was determined by a genetic algorithm (GA) approach,42−44 because the splitting 36f sites of Li (Figure 1) are 1/6 partially occupied, making it difficult to select Li positions in DFT calculations. In this study, the structure data of pure LZP were extracted from the Inorganic Crystal Structure Database (ICSD)45 (ID: 92250, original data reported by Catti et al.18 In the GA procedure, two-point and uniform crossover, and mutation operations were used, and the number of configurations for each generation was set to 18. The electrochemically lithiated LZP (Li7Zr12P18O72) was considered without structural modification of

Figure 1. Wyckoff positions of all atoms in LZP with the rhombohedral lattice. Experimental results of fractional coordinates are shown in a note of SI Table S1.

stoichiometric rhombohedral LZP have been investigated experimentally (by 7Li and 31P nuclear magnetic resonance,24,25 X-ray diffraction (XRD),16,20,24,26−29 and neutron diffraction18,30 for crystallographic characterization; and alternating current impedance technique16,20,24−26,28,29 and direct current polarization method27 for Li-ion conductivity) and theoretically (classical molecular dynamics (MD) simulations31 for evaluating the Li-ion conductivity and activation energy). In this paper, we revisit the electrochemical stability and Liion conduction mechanism of stoichiometric rhombohedral LZP by using first-principles calculations. The electrochemical B


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Table 1. Predicted Cathodic Decomposition Reactions of LZP with Much Larger Li/LZP Molar Ratio and the Corresponding Voltagesa

a

decomposition reaction

voltage [V]

4 LiZr2(PO4)3 + 5 Li → P + 3 Li3PO4 + 4 Zr2P2O9 LiZr2(PO4)3 + 5 Li → P + 2 Li3PO4 + 2 ZrO2 5 LiZr2(PO4)3 + 28 Li → 2 ZrP2 + 11 Li3PO4 + 8 ZrO2 11 LiZr2(PO4)3 + 84 Li → 6 ZrP2 + 21 Li3PO4 + 16 Li2ZrO3 23 LiZr2(PO4)3 + 196 Li → 14 ZrP2 + 41 Li3PO4 + 16 Li6Zr2O7 4 LiZr2(PO4)3 + 56 Li → 7 Li3P + 5 Li3PO4 + 4 Li6Zr2O7 LiZr2(PO4)3 + 24 Li → 3 Li3P + 2 Li8ZrO6 7 LiZr2(PO4)3 + 197 Li → 12 Li3P + 84 Li2O + Zr14P9 7 LiZr2(PO4)3 + 200 Li → 13 Li3P + 84 Li2O + 2 Zr7P4

2.15−2.20 2.10−2.15 1.83−2.10 1.73−1.83 1.37−1.73 1.10−1.37 1.02−1.10 0.95−1.02 0.00−0.95

The unit of voltage is V vs Li+/Li.

the Zr12P18O72 framework. Candidates for the lithiated LZP structures were determined using a bond-valence force-field (BVFF) approach.46−49 First, the entire potential distribution in the lattice is determined by BVFF, and local minimum potential sites are extracted as candidate sites of intercalation. In this method, Morse-type interactions are used for Li−O, Zr−O, and P−O combinations,50 and Coulomb repulsive interactions are considered for other combinations. The determined candidates of the lithiated LZP structures are optimized by the same DFT-based procedure described above. Here, the Li intercalation voltage ΔE is expressed as follows:51

energies and lattice constants are shown in Supporting Information, SI, Table S1). This agrees with the experimental finding that the monoclinic phase is formed in the lower temperature region.17 Since there are no stable compounds between monoclinic and rhombohedral LZP, the monoclinic LZP is discarded hereinafter for the calculation. The calculated electrochemical potential window of rhombohedral LZP is between 2.20 and 4.14 V vs Li+/Li, which is slightly shifted down in comparison with those predicted from DFT calculations performed by Richards et al.53 for other NASICON-type materials [ ∼ 2.7−4.7 V for LTP and ∼2.9− 4.5 V for LiGe2(PO4)3 (LGP)]. Predicted cathodic (Li addition) and anodic (Li removal) decomposition reactions of LZP are as follows:

ΔE = {G[Li 7Zr12P18O72 ] − (G[Li6Zr12P18O72 ] + G[Li])}/F where G[Li6Zr12P18O72], G[Li7Zr12P18O72], and G[Li] indicate, respectively, the ground-state total energy of pure LZP, lithiated LZP, and Li metal; and F is the Faraday constant. 2.2. Experimental Reaction with Li Metal. NASICON-type LZP with rhombohedral symmetry is prepared by conventional solid state reaction according to literature.17 Reagents of Li2CO3 (Kojundo Chemical Laboratory Co., Ltd.), ZrO2 (Mitsuwa Chemicals Co., Ltd.), and NH4H2PO4 (Wako Pure Chemical Industries, Ltd.) were used as starting materials. Stoichiometric amounts of the starting reagents were mixed in an agate mortar with ethanol. The mixture was heated at 1200 °C for 20 h, after preliminary heating at 500 °C and 800 °C for low-temperature decomposition reactions (forming CO2, NH3, and H2O). The obtained powder samples were pelletized under uniaxial pressing at 110 MPa, and sintered at 1200 °C for 18 h in air. Its crystal structure was identified by powder XRD. The chemical stability of NASICON-type LZP against Li metal was investigated inside an Arfilled glovebox, by reacting sample pellets with molten lithium (at ∼300 °C) for 30 min in a Zr crucible. 2.3. Li-Ion Conductivity. We performed DFT-based FPMD simulations using VASP in order to estimate the Li-ion conductivity of pure LZP. In this case, a large supercell of the LZP (Li16Zr32P48O192) was considered. The cutoff energy was reduced to 350 eV and a 1 × 1 × 1 k-point grid (only Γ point) was employed to reduce the computational cost, whereas the other calculation conditions were the same as those used for the convex-hull construction. The time step was set to 1 fs, and our FPMD simulations were carried out in the NVT canonical ensemble using a Nosé thermostat52 at 873−1773 K for 50 ps. From our FPMD simulations, the mean square displacements (MSD) of all elements were calculated, and then the Li-ion conductivity at room temperature (298 K) and activation energy for Li-ion diffusion were determined from the Arrhenius plot of diffusion coefficients.

4LiZr2(PO4 )3 + 5Li → 4Zr2P2O9 + 3Li3PO4 + P ( 4.14 V vs Li+/Li)

Decomposition voltages are determined by total energy difference between reactants and products. For example, the voltage of the cathodic decomposition reaction described above Vd is expressed as follows: Vd = {4G[LiZr2(PO4 )3 ] + 5G[Li] − (4G[Zr2P2O9] + 3G[Li3PO4 ] + G[P])}/F

where G[X] indicates the ground-state total energy of the material X. However, our results do not correspond to the recent study by Li et al.,16 which reports high electrochemical stability of LZP up to 5.5 V vs Li+/Li. One of conceivable reasons is the slow kinetics of the decomposition reaction. Thus, we investigated other cathodic decomposition reaction routes, by searching for facets at various Li/LZP molar ratios in the convex-hull. The predicted cathodic decomposition reactions of LZP and the corresponding voltages are listed in Table 1. For example, at high Li concentrations, the following reaction spontaneously occurs at 0.95 V vs Li+/Li, 7LiZr2(PO4 )3 + 200Li → 13Li3P + 84Li 2O + 2Zr7P4

3. RESULTS AND DISCUSSION 3.1. Electrochemical Stability. Considering the cohesive energy values of all 110 structures extracted from the Materials Project database, we found that monoclinic LZP is one of the vertices of the convex-hull, while rhombohedral LZP which is derived from the present DFT calculation and GA approach mentioned below is slightly unstable (comparison of cohesive

in which the decomposition products Li3P, Li2O, and Zr7P4 are stable in contact with Li metal. Thus, these products prevent further decomposition reaction between Li metal and LZP. At moderate Li concentration, the following reaction occurs at 1.83 V vs Li+/Li, 11LiZr2(PO4 )3 + 84Li → 6ZrP2 + 21Li3PO4 + 16Li 2ZrO3 C


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Figure 2. Crystal structures of rhombohedral LZP (a) without and (b) with candidate positions of the inserted Li atom (orange-colored small balls).

Figure 3. (a) Crystal structure of the most stable lithiated rhombohedral LZP. (b) Local structure of the 6b site with two Li atoms (orange-colored large balls).

located at the 36f site near different 6b sites as shown in Figure 2a. Thus, each space around the 6b site tends to be occupied by a single Li atom. The calculated density of states (DOS) indicates large band gap, >4 eV, so that the compound is an electronic insulator (SI Figure S1). Next, arrangement of intercalated Li ions into stoichiometric LZP is considered. Figure 2b shows the candidate intercalation sites (18e or 36f sites) of the Li ions that correspond to local potential minima according to BVFF calculation. We consider 48 candidate positions for Li insertion in stoichiometric LZP. All lithiated LZP (Li7Zr12P18O72) structures were optimized, and we confirmed that the inserted Li ions are relaxed to the 36f sites even in case Li ions positioned at the 18e sites. In addition, their total energies were evaluated by DFT calculations. The energetically most stable structure is shown in Figure 3a. Two of the seven Li atoms in the lithiated LZP are located in the space around the same 6b site, as shown in Figure 3b. Figure 4 displays the histogram for calculated Li intercalation voltages into the 48 candidate sites. All calculated intercalation voltages are less than 0.5 V, and much lower than those driven by convex-hull calculations. Nevertheless, LZP is likely to be reactive with Li metal even for the Li intercalation scenario, since the reaction voltage of the most stable lithiated LZP is positive according to the present DFT calculations (from our convex-hull analysis, it is found that the most stable lithiated

where the decomposition voltage of Li2ZrO3 is relatively small (0.31 V vs Li+/Li) among the product materials (SI Table S2). Yet in the paper of Li et al.,16 the experimental XRD results indicate the decomposition reaction of LZP to Li3P and Li8ZrO6 as follows: LiZr2(PO4 )3 + 24Li → 3Li3P + 2Li8ZrO6

In the convex-hull analysis, Li8ZrO6 is not stable against Li metal, however the decomposition voltage of 0.04 V vs Li+/Li is very small (SI Table S2). Therefore, the formation of Li8ZrO6 and Li3P prevents further decomposition reaction at the interface of Li|LZP, where the local Li concentration is fairly high. The predicted decomposition reactions derived from the convex-hull calculations indicate that rhombohedral LZP is thermodynamically reactive with Li metal. In other respects, kinetic limitation is also conceivable, since the reaction listed in Table 1 requires the migration of existing atoms. However, the Li intercalation reaction into the LZP host lattice is also plausible in the presence of Li metal.54 Since the LZP host lattice can maintain its structural skeleton during Li intercalation, this reaction may be kinetically feasible even at room temperature. Therefore, we also investigated the electrochemical stability of the LZP by considering the Li intercalation voltage. From the result of GA, each Li atom is D


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Figure 4. Calculated Li intercalation voltage for pure LZP.

LZP (Li7Zr12P18O72) is unstable with the decomposition energy being 18 meV per atom). 3.2. Experimental Reactivity with Li Metal. Photographs of LZP samples before and after reaction with molten lithium at ∼300 °C are displayed in Figure 5. The color of the pellet Figure 6. Simulated XRD profiles of (a) NASICON-type LZP,18 (b) Li3P based on the reported crystal structures,55 and reported XRD patterns for (c) Li8ZrO656 and (d) Li2ZrO3.57 Experimental XRD patterns for synthesized LZP (e) before and (f) after the reaction with molten Li are also shown.

Figure 5. Photographs of LZP pellet before and after reaction with molten lithium metal at ∼300 °C for 30 min. Part (a) displays whitecolored surface of the pellet. Parts (b) and (c) display the surface of the pellet and its crushed powder, respectively, indicating that the reaction proceeds into the bulk of the pellet as well as the surface.

surface and bulk changed from white (Figure 5a) to gray (Figure 5b,c), indicating the reduction of sample by Li metal. In Figure 6, the XRD patterns of the prepared LZP sample indicate the formation of a single phase, namely rhombohedral NASICON-type LZP (ICSD 92250).18 After reaction with molten lithium, the NASICON-type phase disappeared. The XRD patterns reveal a mixture consisting of Li3P (ICSD 26880),55 Li8ZrO6 (Joint Committee for Powder Diffraction Standards (JCPDS) 26−0867),56 Li2ZrO3 (ICSD 94896),57 and the other unidentified phases by comparison with reported XRD patterns. These results show good accordance with the reaction scenario listed in Table 1 obtained by the present DFT calculations, as well as a recent report16 that suggested a small amount of NASICON-type LZP at the interface of Li|LZP decomposed at ambient temperature to Li3P and Li8ZrO6. The experimental finding here, that LZP reacts with Li metal at elevated temperatures, validates our computational results. However, further experimental studies are needed to clarify the reactivity of LZP with Li at room temperature. 3.3. Li-Ion Conductivity and Conduction Mechanism. The large supercell with a triclinic structure including 16 LZP units (i.e., Li16Zr32P48O192) was prepared in order to evaluate Li-ion conductivity in our FPMD simulations (Figure 7). The lattice constants of the supercell of the rhombohedral-phase LZP are a = 12.69 Å, b = 18.02 Å, c = 17.87 Å, α = 90.00°, β = 90.00°, and γ = 90.65°. The lattice vectors asc, bsc, and csc in the

Figure 7. Crystal structure of the LZP supercell with triclinic lattice.

supercell correspond to linear combinations of lattice vectors ap, bp, and cp in a primitive cell with a rhombohedral structure: (ascbsccsc) = (a pbpc p)Msc

where the supercell matrix Msc is expressed as follows: ⎛− 1 − 2 0 ⎞ ⎜ ⎟ Msc = ⎜−1 0 2 ⎟ ⎝− 1 2 0 ⎠

Initially, all of the Li atoms were located in 6b sites for the FPMD simulations. Figure 8 shows the MSD plots at 1173 K. E


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in Table 2, despite the fact that FPMD simulations are carried out at much higher temperatures. Alternatively, the extrapolated Li-ion conductivity estimated by the Nernst−Einstein relationship58 at room temperature (5.0 × 10−6 S/cm) is lower than the experimental results. Experimentally measured Li-ion conductivities of stoichiometric LZP are relatively scattered as shown in Table 2, because the Li-ion conductivity is largely improved by a small number of defects, such as interstitial Li ions and/or Li vacancies. In order to clarify the migration behavior of Li, the Li-ion population density at around 50 ps after equilibration is displayed in Figure 10. The three-dimensional pathway is

Figure 8. MSD plots of Li, Zr, P, and O trajectories in LZP at 1173 K. Plots for Zr, P, and O are magnified by a factor of 200, in order to illustrate their behaviors.

The MSD profile of Li ions shows linear increase with the MD step (time) and reaches >200 Å2 at ∼50 ps, indicating that Li ions hop among these sites and diffuse over the lattice. However, MSD profiles of the other ions remained constant ( rcut) ⎩0

the Li diffusion coefficients displays linear dependence for the entire temperature region. The activation energy for Li-ion conduction (0.43 eV) is close to the experimental results listed

In the equations, ri,j(t) = |rj(t) − ri(0)| is the distance between the position of the j-th Li atom at t (rj(t)) and the

Table 2. Li-Ion Conductivity (σLi) and Activation Energy (Eact) of Rhombohedral LZP σLi [S/cm]

study experimental (ref 16) experimental (ref 24) experimental (ref 26) experimental (ref 28) experimental (ref 29) theoretical (ref 31) theoretical (this paper)

2 2.9 2.8 8 1.58 2 5.0

× × × × × × ×

−4

10 (bulk, 298 K) 10−4 (total, 603 K) 10−4−1.2 × 10−3 (total, 573 K) 10−5 (total, 327 K) 10−4 (bulk, 298 K) 10−3−4 × 10−3 (bulk, 600−940 K) 10−6 (bulk, 298 K) F

Eact [eV] 0.28 (total) 0.44 0.73−0.85 NA 0.39 0.39 0.43 DOI: 10.1021/acs.chemmater.7b01703 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials initial position of the i-th Li atom as the vicinity of the i-th 6b site (ri(0)). rcut indicates the cutoff radius from the 6b sites as the center of spheres (SI Figure S2). We set rcut to be 3.17 Å, which is equal to half of the distance between nearest-neighbor 6b sites in this study. Si,j(t) remains a positive real number less than unity. It increases as the j-th Li ion approaches the center of the sphere (the i-th 6b site), whereas the value becomes zero when the Li atom is outside the sphere. Therefore, the SDF is useful for investigating the number of Li ions situated in the specific sphere. Figure 11 shows the SDF plots of Li ions

Figure 12. Details of Li-ion conduction mechanism. (a) Different SDF plots for Li-ion trajectories. The red and orange dash lines indicate the average SDF (about 0.6 and 0.4) when one and two Li ions occupying the same 6b site, respectively. Parts (b) and (c) show the schematic image of Li-ion behaviors with one and two occupied Li ions, respectively. Part (d) describes the mechanism of Li ions diffusing in LZP.

two Li ions can be situated in the same sphere: neither is located at the exact center of the sphere (6b sites), but both at the periphery because the SDF values are less than unity. Since the SDF values for double Li occupation in the sphere (orange dashed lines) are smaller than those for single Li occupation (red dashed lines), the Li ions are located further away from the 6b center site in the former case (Figure 12b,c) in order to reduce the Coulombic repulsion between two Li ions. Meanwhile, in Figure 12a an SDF plot can appear and disappear (e.g., the black line between 29.5 and 32.6 ps), indicating that a Li ion diffuses by being repelled from another Li ion occupying the 6b site. On the basis of all these discussions, we can understand that Li ions are likely to migrate between 6b sites by a mechanism of pushing-out and repulsion, as shown schematically in Figure 12d.

Figure 11. SDF plots for Li-ion trajectories in the FPMD simulation at 1173 K. Black arrows: the example of the sixth Li ion (dark-orange line) moving through the 6b(6) (sixth 6b site) → 6b(13) → 6b(3) → 6b(11) → 6b(3) → 6b(11) → 6b(3) sites.

diffusing in LZP, with each Li ion represented by a specific color line. In each panel, the Li ions repeatedly appear and disappear, indicating that they jump between any 6b sites and its periphery. Therefore, the SDF analysis indicates Frenkel-like defect formation described by Kröger−Vink notation below: 2Li ×Li = V′Li + {Li ×Li Li•i }

4. CONCLUSIONS The electrochemical stability and Li-ion conductivity of NASICON-type LZP solid electrolyte are investigated by DFT calculations. For the former, we probe the reactivity of LZP with Li metal through convex-hull creation and GA technique. From the analysis of the convex polytope in five dimensions (four elements and energy), we reveal that LZP is thermodynamically stable because it is one of the vertices of our convex-hull. The result predicted the electrochemical window of LZP to be 2.20−4.14 V vs Li metal. Indeed, our experiment shows LZP reacts with molten Li, verifying our computational results. The estimated Li intercalation voltage of LZP is positive, therefore the Li intercalation mechanism is also plausible. Since the intercalation reaction may occur even at room temperature, we conclude that LZP is unstable against Li metal. Thus, further modification of LZP, such as controlling its composition, is required to suppress the reaction with Li metal. The Li-ion conductivity at room temperature and diffusion activation energy were estimated using DFT-based FPMD calculations. The results indicate moderate Li-ion conductivity and activation energy of LZP, which are also in fair agreement with experimental results from earlier studies.16 The Li-ion trace in our FPMD simulations reveals the three-dimensional conduction pathway of Li ions between 6b sites. Furthermore, the SDF calculation allows a more detailed analysis of the Li-

where {Li×Li Li•i } represents the associated defect that Li ions occupied at the same cavity (36f sites in Figure 1) of the NASICON framework (it is found that the formation energy of the Frenkel-like defect in pure LZP is 0.13 eV from our DFT calculations and GA approach). We analyzed the behaviors of all Li ions in LZP at three different temperatures (873, 1173, and 1473 K) using the SDFs (SI Figures S3−S5). It is found that the exact centers of spheres (6b sites) are not occupied for certain periods, since the SDF values are less than unity. Thus, our results confirmed that Li ions are positioned at the periphery of 6b sites (i.e., 36f sites), as reported previously.18 Certain sites are not occupied by Li ions for various periods (e.g., between 19.6 and 24.2 ps at the third 6b site, and between 6.7 and 11.7 ps at the 13th 6b site in Figure 11). A closer inspection of the SDFs reveals that a certain SDF plot often appears when that of another Li ion disappears (e.g., darkorange and yellow SDF plots at 11.5 ps at the sixth 6b site, respectively). It indicates that a Li ion diffuses by pushing out another Li ion occupying the 6b site. Similar Li-ion conduction mechanisms in oxide-based solid electrolytes have been reported by some research groups in their FPMD and nudged elastic band simulations.58,59 Next, we focus on the 15th 6b site. In Figure 12a, one or two coexisting SDF lines are indicated by red and orange dashed lines, with the averaged values of about 0.6 and 0.4, respectively. According to the present SDF analysis, G


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ion conduction mechanism in LZP. Li ions migrate while pushing out or being repelled by other Li ions around 6b sites, and it is remarkable that two and more Li ions could exist simultaneously around the same 6b site. For the first time, the present paper clarified the electrochemical window and ionic conduction mechanism for LZP at the atomic level. These results would benefit the design of LZPrelated compounds.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.7b01703. Detailed results of first-principles calculations for rhombohedral and monoclinic LZP; decomposition voltage of predicted product materials by convex-hull analysis; partial density of states for rhombohedral LZP; and detailed results of SDFs estimated from FPMD simulations at 873, 1173, and 1473 K (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yusuke Noda: 0000-0003-0401-6731 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the “Materials research by Information Integration” Initiative (MI2I) project of the Support Program for Starting Up Innovation Hub from Japan Science and Technology Agency (JST) and by the “Elements Strategy Initiative to Form Core Research Center” of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan (Since 2012). We also thank the Information Technology Center of Nagoya University for providing computing resources (CX400). Figures of crystal structures are drawn with Visualization for Electronical and Structural Analysis (VESTA).60

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