Article pubs.acs.org/cm
Concerted Migration Mechanism in the Li Ion Dynamics of GarnetType Li7La3Zr2O12 Randy Jalem,† Yoshihiro Yamamoto,† Hiromasa Shiiba,† Masanobu Nakayama,*,†,‡ Hirokazu Munakata,§ Toshihiro Kasuga,† and Kiyoshi Kanamura§ †
Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya City, Aichi, 466-8555, Japan ‡ PRESTO Program, Japan Science and Technology Agency (JST), Japan § Department of Applied Chemistry, Tokyo Metropolitan University, 1-1 minami Oosawa, Hachioji, Tokyo 192-0397, Japan S Supporting Information *
ABSTRACT: The garnet-type Li7La3Zr2O12 (LLZO) belonging to cubic symmetry (space group Ia3d̅ ) is considered as one of the most promising solid electrolyte materials for all-solid state lithium ion batteries. In this study, the diffusion coefficient and site occupancy of Li ions within the 3D network structure of the cubic LLZO framework have been investigated using ab initio molecular dynamics calculations. The bulk conductivity at 300 K is estimated to be about 1.06 × 10−4 S cm−1 with an energy barrier of 0.331 eV, in reasonable agreement with experimental results. The complex mechanism for self-diffusion of Li ions can be viewed as a concerted migration governed by two crucial features: (i) the restriction imposed for occupied site-to-site interatomic separation, and (ii) the unstable residence of Li ion at the 24d site, which can serve as the trigger for ion mobility and reconfiguration of surrounding Li neighbors to accommodate the initiated movement. Evidence for Li ordering is also found at low temperature for the LLZO system. KEYWORDS: diffusion mechanism, garnet materials, lithium ionic conductivity, molecular dynamics, solid electrolytes
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INTRODUCTION Conventional electrolytes in Li-ion batteries based on organic solvents or polymers with a dissolved Li-salt pose serious limitations such as flammability, difficulty of miniaturization, and serious impact to the environment if poorly disposed of or recycled.1−3 As a replacement, stable inorganic solid electrolytes with high Li conductivity and suppressed electronic conductivity has become increasingly appealing, with several advantages including nontoxicity, ease of preparation, and low cost.4−6 So far, Li ion conductors with garnet-type structure are considered as promising electrolytes because of their high conductivity and excellent stability vs Li metal. One notable composition is the Li7La3Zr2O12 (LLZO) material, which has two reported polymorphs, the cubic7−10 and low-temperature tetragonal symmetry11,12 via a diffusionless transformation. The cubic-type LLZO is known to exhibit Li ionic conductivity values which can reach on the order of 1 × 10−4 S cm−1 at room temperature.7 Figure 1a presents the crystal structure of the cubic-type LLZO which belongs to the space group no. 230 (Ia3̅d). The La and Zr ions are located at Wyckoff positions of 16a and 24c sites, respectively, forming LaO8 dodecahedra and ZrO6 octahedra. Seven-ninth of the total Li ions and two-ninth vacancies are distributed at 24 tetrahedral and 48 octahedral interstitial sites corresponding to 24d and 48g/96h sites, respectively; the latter Wyckoff position © 2013 American Chemical Society
Figure 1. (a) Crystal structure of cubic-type LLZO (Ia3̅d), (b) Li environment, and (c) ground state energy vs volume plot taken from randomized Li−Li vacancy arrangement using a reduced cell with a formula Li28La12Zr8O48.
indicates split-atom 96h sites from 48g sites. As depicted in Figure 1b, 24d tetrahedra and 48g/96h octahedra are faceshared to each other and form the 3D network structure, which Received: November 2, 2012 Revised: January 9, 2013 Published: January 9, 2013 425
dx.doi.org/10.1021/cm303542x | Chem. Mater. 2013, 25, 425−430
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is thought to be responsible for the observed fast Li ion conduction in the said material. In contrast, the tetragonal-type LLZO which belongs to the space group no. 142 (I41/acd) with lattice parameter ratio c/a = ∼0.964 shows a lower conductivity value on the order of 10−6 S cm−1 at room temperature owing to the complete ordering of the Li atoms.11 The three distinct Li sites are fully occupied, characterized by tetrahedral 8a, octahedral 16f, and octahedral 32g. A closer inspection of the symmetry reveals that 8a sites comprise one-third occupation of the analogue 24d sites in cubic LLZO, whereas the remaining two-thirds are kept as vacancies, formally described as 16e in the tetragonal polymorph. Meanwhile, 16f+32g sites correspond to 48g/96h sites of cubic LLZO, differing only in terms of relative atomic displacement and distortion of the octahedra. A number of studies conducted both by X-ray and neutron diffractions were geared upon establishing the crystal structure of garnet-type oxides.8,12 However, the phase stability and the Li ion migration mechanism in these materials are still controversial up to this point. One source of the problem is the failure of existing experimental techniques to correctly determine the exact Li occupancy on the two aforementioned tetrahedral and octahedral Li sites.13−16 X-ray diffraction experiments have the dilemma of poor scattering due to Li. While neutron diffraction-based measurements are considered to have higher sensitivity, still the information that can be drawn is limited especially when determining sufficiently accurate atomic displacement parameters. As a consequence of this ambiguity for the Li ion distribution within the garnet framework, the exact mechanism for Li ionic transport and the factors controlling it remains without consensus. Ab initio-based calculation within the density functional theory (DFT) framework has been successful in computing ground state properties for a variety of battery materials with sufficient accuracy.17−21 One particular approach, the nudged elastic band (NEB) method, has been used to probe the mechanism for Li ionic transport in LLZO.22 However, only limited insights can be drawn out from this method since inherently it cannot take into account the dynamical aspect arising from the very large number of conceivable Li/Li vacancy arrangements in the LLZO framework. Hence, it is also unsuitable when aiming to completely elucidate complex migration mechanisms. In this study, for the first time, we investigated the ion dynamics and Li occupancy of LLZO using ab initio-based molecular dynamics (MD) study. The MD approach offers a means to statistically evaluate Li ion jump events and quantitatively assess the migration behavior of Li ions in a collective manner. The mechanism predicted and insights obtained in here may motivate new experiments and interpretations of Li ionic conduction processes relevant to battery applications. This work is organized as follows. First, the lattice parameter of the LLZO model is optimized by structurally relaxing primitive cells with different randomized Li/Li vacancy arrangements. Next, MD production runs using a pre-equilibrated cell is carried out at different temperatures (873 K, 1073 K, 1273 K, 1473 K, 1773 K) for trajectory sampling of the diffusing Li ions. Li ionic conductivity at 300 K and the corresponding activation energy are then estimated from the mean square displacement (MSD) and MSD-derived Arrhenius plots, respectively. Li occupancy at 24d and 48g/96h sites for the LLZO system is also investigated through Li ion distribution analysis and Li−Li radial distribution function (RDF) analysis.
Article
COMPUTATIONAL DETAILS
All computations are carried out within the Vienna Ab Initio Simulation Package (VASP)23,24 with the cell size for the molecular dynamics (MD) simulation represented by the formula Li56La24Zr16O96. Before the actual MD run, the lattice constant in the cubic configuration of LLZO is determined from spin-polarized full structural optimization (T = 0 K) of primitive lattices (Li28La12Zr8O48) with a 2 × 2 × 2 k-point mesh and randomly initialized Li/vacancy arrangements. Two factors are tunable for the structural input in present NVT-FPMD computations that could significantly affect postMD observables; (1) the enormous permutations of Li/Li vacancy arrangement, which thus lead to (2) variation in cubic lattice parameter. However, the first factor can be solved by equilibration process prior to the actual MD run since Li ions are allowed to migrate and redistribute unto energetically favorable sites in the garnet structure. With this, we then decided to use an intrinsically unbiased approach (random sampling). Six different randomizations are made and the lattice constant of the cell and fractional coordinates of composed ions are fully relaxed with conjugate gradient (CG) algorithm. The kinetic energy cutoff is set to 500 eV and the exchange correlation energy was described using the parametrization of PerdewBurke-Ernzernhof for solids (PBEsol)25,26 within the standard generalized gradient approximation (GGA) approach with Projector Augmented Wave (PAW) potentials.27−29 For the MD run, the energy cutoff is reduced to 380 eV. To keep the computational cost manageable, a 1 × 1 × 1 k-point grid is employed. An equilibriation step is first carried out in the canonical ensemble (constant N, V, T) using a Nosé thermostat30 at a constant temperature of 1273 K for 5 ps; the cell volume is kept constant. This strategy promotes sufficient sampling of the phase space and allows atoms to reside onto energetically favorable sites (see also Figure S1 in the Supporting Information). The time step is fixed at 1 fs and MD runs are carried out at 873, 1073, 1273, 1473, and 1773 K for 30 ps. The observed energy fluctuation falls below 35 meV/atom and no bond breaking for La−O and Zr−O at all temperatures is observed. Time average mean square displacements (MSD)19 of the different atoms are generated using the atomic configuration information from every finite MD time step. The diffusion coefficient (D) of Li is estimated based on the slope of the diffusive regime in the MSD plot. Activation energy for Li ion migration according to Nernst−Einstein equation and Li ionic conductivity extrapolated down to 300 K are determined from the log D − 1/T Arrhenius plot.31 For the annealing step, the ionic configuration at 1273 K (after a 35 ps run) is used as input; the temperature is linearly decreased down to 300 K within a 5 ps period and then followed by another 5 ps MD run at the new temperature for final equilibration.
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RESULTS AND DISCUSSION Figure 1a shows the basic unit cell of cubic LLZO depicting partial occupancies at 24d and 96h sites.8 From the reduced form of this cell, lattice constant optimization with randomization of Li and Li vacancy arrangement (see Figure 1b) is made and the results are shown in Figure 1c. It can be deduced here that ground-state energy is directly proportional to cell volume and by extension to lattice parameter a, the lowest energy having the smallest calculated lattice parameter a = 12.9185 Å. The experimentally reported value is 12.9682 Å7 and with this comparison, the difference between computational and experimental results only falls within 1.0%. Besides, the difference among 6 computational results is less than 1.0% in lattice parameter and 10 meV/atom in energy, which is small enough to have any significant impact either during MD simulation or to the energy barrier over the course of Li ion migration. We also checked the volume difference of the optimized post-MD end structures at several temperatures in reference to the pre-MD lowest energy configuration (c.f. Figure S1 in the Supporting Information) and found out a very 426
dx.doi.org/10.1021/cm303542x | Chem. Mater. 2013, 25, 425−430
Chemistry of Materials
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calculated diffusion, with the use of Nernst−Einstein equation, extrapolates to a Li ionic conductivity value of 1.06 × 10−4 S cm−1 at 300 K, which again agrees well with experimental bulk conductivity. These simulation results apply only to bulk systems and do not address the issue of grain boundary diffusivity. To investigate the ion dynamics in more details, we examined the time-resolved Li trajectory profile taken at a sampled interval between 20 and 25 ps at 1273 K (Figure 4a). From a
small variance of
