First-Principles Investigation of the Na+ Ion Transport Property in

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First-Principles Investigation of the Na Ion Transport Property in Oxyfluorinated Titanium (IV) Phosphate NaTiPO F 3

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Randy Jalem, Ryosuke Natsume, Masanobu Nakayama, and Toshihiro Kasuga J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b12115 • Publication Date (Web): 08 Jan 2016 Downloaded from http://pubs.acs.org on January 13, 2016

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The Journal of Physical Chemistry

First-Principles Investigation of the Na+ Ion Transport Property in Oxyfluorinated Titanium (IV) Phosphate Na3Ti2P2O10F Randy Jalem,†,‡,* Ryosuke Natsume,‡ Masanobu Nakayama,†,‡,§ Toshihiro Kasuga⊥ †

Unit of Elements Strategy Initiative for Catalysts & Batteries (ESICB), Kyoto University,

Katsura, Saikyo-ku, Kyoto 615-8520，Japan ‡

Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso,

Showa, Nagoya, Aichi 466-8555, Japan §

Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho Kawaguchi, Saitama 332-

0012, Japan ⊥

Department of Frontier Materials, Nagoya Institute of Technology, Gokiso, Showa, Nagoya,

Aichi 466-8555, Japan. KEYWORDS. all-solid state sodium ion batteries, sodium-based anode materials, oxyfluorinated metal phosphates, density functional theory, molecular dynamics.

ACS Paragon Plus Environment

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ABSTRACT. Na+ ion batteries have now raised strong interest as replacements or alternatives of conventional Li+ ion batteries. In this work, we investigated by first-principles calculation the Na+ ion transport property of oxyfluorinated titanium (IV) phosphate Na3Ti2P2O10F, a recently reported candidate anode material. We have revealed in our simulation the 2-D ionic conduction in Na3Ti2P2O10F, with Na+ ions moving cooperatively through a combination of intra-ring and inter-ring jumps in the ab-plane. This type of mechanism is made energetically favorable by: i) the dynamic Na distribution in the ring paths and ii) the tendency for intra-ring Na+ ions to assume maximum separation during actual synchronous motions. By modulating the amount of Na in the rings through aliovalent doping at Ti and P sites, significant improvement in the Na diffusion may be expected.

1.

INTRODUCTION The present consensus on the availability and access of Li reserves has led to economic

uncertainties and speculations on the future use of Li+ ion batteries, particularly on their projected massive deployment in low emission plugin hybrid electric vehicles (PHEVs) and electric vehicles (EVs). This has prompted intense research efforts to develop alternatives or replacements. One example is Na+ ion batteries which can offer a potential cost advantage because of the almost inexhaustible supply of Na. Another interesting point is the similarity between Na and Li intercalation chemistry which allows for similar compounds to be used, in both battery types.1-2 Generally though, the relatively larger Na+ ion (vs. Li+ ion) is often viewed to pose a problem for ionic conduction.1-5 However, several Na-based materials have been reported already to demonstrate good or even better ionic mobility (than their Li counterpart),


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facilitated by the large enough tunnels and void spaces in a variety of structures.5-17 High-voltage novel cathodes, such as Na3V2O2x(PO4)2F3-2x and Na2Fe2(SO4)3, have been developed as well that address the issue of lower energy density in Na-based systems stemming from the higher reduction potential of Na metal (-2.7 V vs. standard hydrogen electrode or SHE for Na as compared to -3.0 V vs. SHE for Li) and the higher equivalent weight of Na (vs. Li).15-16 Recently, safety enhancement of Li/Na batteries has been pursued by substituting conventional organic-/liquid-based electrolytes with inorganic or solid-based ones. Up to date, NASICONtype (Na Super Ionic CONductor) compounds7-11 and Na beta’’-alumina12-14 are considered as among the few that show promise for solid electrolyte use. In this regard, discovery of new materials and optimization of existing compounds are still greatly needed to realize the wide- and large-scale application of next generation Na+ ion battery technology. Oxyfluorinated metal phosphates belong to a class of materials that are still relatively unexplored as battery materials. Some of the compositions in this group include Ti2(PO4)2F4•N2C2H10 (P21/c)18, Ti2(PO4)2F4•N2C3H12•H2O (C2)18, Na5M(PO4)2F2 (M: Al3+, Ga3+,

Cr3+)

(P

)19-20,

Na5Fe(PO4)2F2

(Pbca)21,

Na3Fe2(PO4)2(OH)2F

(P42/mnm)22,

Na3M2(PO4)2F3 (M: Al3+, V3+, Cr3+, Fe3+, Ga3+) (I4/mmm)23, Na3V2P2O10F (I4/mmm)24, and Na3Ti2P2O10F (I4/mmm)25. Notably, the latter was reported to have a bulk Na+ ionic conductivity of 1.0 x 10-4 S/cm at 473 K25, comparable with the NASICON-type titanium phosphate Na1+xTi2xAlx(PO4)3

(R c)11. Even with the interestingly similar composition and conductivity, the two

materials differ in their actual arrangement of vertex-sharing polyhedral units. In Na1+xTi2xAlx(PO4)3,

the structure is formed with all oxygen atoms in the (Ti/Al)O6 octahedron vertex-

linked to PO4 tetrahedra, resulting into an uninterrupted framework. As shown in the structure


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details displayed in Figure 1 for Na3Ti2P2O10F, only four oxygen atoms (Oab, at 16n Wyckoff sites) of the TiO5F octahedron are linked to PO4 tetrahedra (in the ab-plane; Ti at 4e and P at 4d sites). The remaining axial O atom (Oc, 4e sites), which exists with a double-bond character (along the c-axis), has the shortest bond within the TiO5F octahedron. The F atom (Fc, 2a sites) is shared by two Ti atoms (also along the c-axis). This leads into a structure with F-bridged and buckled square-net sheets that have highly distorted octahedral units (from the combination of long Ti-F bond and short Ti-O bonds in the octahedron). Moreover, owing to the terminated O atom (Oc), large 2D channels are generated which make the structure also relatively open just like the NASICON framework. Na+ ions are located along tunnels in trigonal prism sites (8h) and have an occupancy of 0.75. The critical path bottleneck in the ab-plane is determined by the Na tunnel height which measures the separation between vertically-aligned PO4 units (h, Fig. 1a). In the c-direction, the path bottleneck is formed by tunnels bounded by two TiO5F and two PO4 units in alternate linkage (dashed square, Fig. 1a). Buckling of the sheets have been noted in this material and can be described as an apparent bending along a- or b-direction with respect to the TiO5F-PO4-TiO5F vertex linkage,25 as described in Fig. 1c. It has been recently demonstrated that Na3Ti2P2O10F can be used as an anode for Na ion batteries, exhibiting a reversible capacity of ~100 mAh/g.26 Understanding how the Na diffusion in Na3Ti2P2O10F is governed by its crystal structure could provide insights towards the full exploitation of the inherently large tunnels found in oxyfluorinated metal phosphates. Also, it could hopefully aid in the discovery of novel fast ionic conductors with similar structures and compositions which, at present, has not been exhaustively surveyed yet. To the best of our knowledge, no computational study has been done yet on this class of materials, unlike in NASICON-type27-29 and beta’’-alumina compounds30-34. Thus, in this


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study, we investigated atomistically for the first time the Na+ ion conduction mechanism of Na3Ti2P2O10F by first-principles density functional theory (DFT) calculation. We found out that this material is essentially a 2-D Na ion conductor characterized with intra-ring and inter-ring pathways for Na+ ion transport. Na+ ions move in intra-ring pathways and have enormously low energy diffusion barriers while bottlenecks for long range transport are mainly located along inter-ring jump pathways in the ab-planes.

Figure 1. a) Crystal structure description of 2 x 2 x 2 Na3Ti2P2O10F (I4/mmm) showing the abplane Na tunnel bottleneck height (h) which is characterized by two aligned PO4 units and the caxis bottleneck plane (dashed square) which is bounded by two TiO5F and two PO4 units in alternate linkage. b) Coordination geometries of Na, Ti and P atoms and the bond asymmetry in the TiO5F unit due to the longer Ti-F bond than Ti-O bonds (rTi-F > rTi-O). c) Buckled square-net sheets (buckling shown by arrows) in the ab-plane formed by octahedral TiO5F units connected


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by tetrahedral PO4 units via O atoms in the ab-plane (Oab) and linked in the c-axis by bridging F atoms (Fc). Doubly-bonded O atoms (Oc) create large 2D channels for Na atoms. 2.

COMPUTATIONAL DETAILS We performed molecular dynamics (MD) simulation and Na+ ion migration calculation for

different local environments using the first-principles codes SIESTA35 and VASP36, respectively, solving self-consistently the Kohn-Sham equations within the DFT framework37. For the simulation models, a 2 x 2 x 1 supercell (144 atoms) was generated with randomly initialized Na arrangement. The cells was then equilibrated for 10 ps at target temperatures (973 K-1673 K) under NPT ensemble condition in order to allow the Na atoms to redistribute into energetically favorable sites. The temperature was controlled by a Nosé thermostat38 and the pressure by the Parrinello-Rahman method39; the Nosé and Parrinello-Rahman masses were initialized to 100 Ry/fs2. The generalized gradient approximation (GGA) in the parameterization of Perdew-Burke-Ernzernhof (PBE)40 was used to account for the exchange correlation energy. For the electron-ion interaction, norm-conserving pseudopotentials were used in their nonlocal (Kleinman-Bylander) form.41 The core radii setting for the constituent atoms are tabulated in Table S1 (see SUPPORTING INFORMATION). To keep the computational cost manageable, a minimal basis set (single-ζ)42 was used with cutoff radii of 0.02 Ry for orbital confinement; convergence criterion was set to 10-4 eV for the total energy. We would like to note here that tests for convergence and accuracy (vs. lattice constants) were initially made to determine the appropriate minimal plane wave cutoff. We found out that a cutoff of 60 Ry was sufficient for the material that we are investigating (see Figs. S1 and S2 in the SUPPORTING INFORMATION) despite it being in the lower end of the usual cutoff value range, such as in


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typical water simulations.43 Numerical integration was performed over the Brillouin zone by sampling the Γ-point. The length for MD time step was set to 1 fs. The starting cell for use in trajectory sampling at each target temperature (973-1673 K) was taken from the final cell of the 10-ps NPT MD equilibration step. Actual sampling was then made for 50 ps under NVT ensemble condition. For the comparison of lattice constants and bond parameters with experimental data, an annealing procedure (10 ps) down to room temperature (300 K) was made using the end configuration of the 1073-K NPT MD run. The last configuration in this annealing step was used as input for another 7-ps NPT MD (at 300 K), and the last 3 ps steps were used for averaging. For the local Na+ ion migration energy, the nudged elastic band (NEB) method44 was used with a quasi-Newton algorithm-based ionic relaxation45. Several configuration cells were taken from snapshots with prevalent Na-Na vacancy arrangements within 50-ps NVT-MD runs. The exchange correlation energy was described using the GGA approach in the formalism of PBE for solids46. Available standard pseudopotentials were used; the electronic configuration of the atomic species are i) Na: s1p0, ii) Ti: d3s1, iii) P: s2p3, iv) O: s2p4, and v) F: s2p5. The kinetic energy cutoff was fixed at 500 eV and only the Γ-point was sampled related to the k-point grid. The total energies were converged until < 10-4 eV. It is worth mentioning at this point that the NEB results will only be used to aid in the analysis of MD results, particularly on the local dynamics, since the actual migration mechanism could be rather complex and may not be appropriately represented alone with a single reaction coordinate.

3.

RESULTS AND DISCUSSION


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3.1. Structural parameters, thermal expansion and atomic motion. To evaluate the accuracy of the simulations in this work, a comparison was made between MD- and XRDderived lattice constant values25-26. For the simulation values, averaging was done using the last 3-ps steps of a 7-ps 300-K NPT MD run of an equilibrated cell (from the 10-ps NPT-MD run at 1073 K). The error difference only falls within ~2 %, with the simulation slightly overestimated (~2%) and underestimated (~1 %) in the a- and b-directions (shorter axes) and in the c-direction, respectively, vs. experimental data; c/a (calc.) = 1.60 vs. c/a (expt.) = 1.66. In order to verify if the c/a difference is significant enough to cause a large difference in the MD observables, we simulated a model cell with c/a = 1.66 by slightly decreasing together the shorter lattice constants a and b (which were slightly overestimated to within ~2 %). Results for the MSD plots (see Fig. S1 in SUPPORTING INFORMATION) have revealed that the model with c/a = 1.66 is almost the same with the present model with c/a = 1.60. We, thus, then considered the level of discrepancy for c/a as small enough, not to cause any severe deviations regarding the outcome of the analysis on Na+ ion transport mechanism and other properties. Table 1 shows the comparison of the predicted lattice constants and cation-anion distances with experimental results. Table 1. Comparison of predicted lattice constants and cation-anion distances (from 300-K NPT MD run) with experimental data. Parameter

Calculation / Å

Experiment / Å

Ratio

a

6.5363

6.420725

1.02

6.417626

1.02

10.676225

0.99

10.663626

0.99

2.51825

0.97

c

Na-O*

10.5713

2.446


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Na-F

Ti-Oc

Ti-Oab

Ti-F

P-O

2.549

1.681

1.963

2.047

1.614

2.51426

0.97

2.52625

1.01

2.50526

1.02

1.61125

1.04

1.69926

0.99

2.05625

0.96

2.01126

0.98

2.14325

0.96

2.11126

0.97

1.55225

1.04

1.53226

1.05

*Averaged from four Na(8h)-O(16n) and two Na(8h)-O(4e) bonds.

Figure 2. Mean square displacement (MSD) plots of constituent atoms taken from 1073-K NVT MD run. The motion of constituent atoms were analyzed based on their mean square displacements (MSDs), as displayed in Figure 2 for the 1073-K NVT MD sampling. Visibly, except for Na which gradually diffuses according to the increasing MSD over time, the rest of the atoms only


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experience thermal vibrations about their crystallographic sites (flat MSD trends); this is true for all the investigated temperatures (973-1673 K). These suggest that the structure framework has been well-preserved and is stable during high-temperature MD runs. It is evident at this point that Na+ ion acts as the main charge carrier. However, the accumulated NVT MD trajectory (~50 ps) was apparently not long enough to readily obtain the diffusion coefficient from the slope of the MSD regime with linear dependence, one case is the saturation-like curve for the Na MSD plot (see Fig. 2b). In order to reveal the actual local dynamics which constitute to this MSD behavior, we checked the configuration snapshots over a given MD sampling time interval. We also additionally evaluated the local migration energies for different Na arrangements between two adjacent rings by NEB approach in order to determine the likely rate-controlling local Na ion hopping process(es). Results will be discussed in the later section. 3.2. Overall Na ion transport and conductivity. To qualitatively analyze the trajectory of Na+ ions, we extracted their mobile-ion density from the NVT MD sampling data, a typical result is shown in Fig. 3 (at 1673 K). A characteristic feature here is the trajectory cloud forming rings, resulting from Na+ ions jumping from one 8h site to the next (solid circles) and eventually constituting an intra-ring type of motion. The initial occupancy in the rings prior to the MD run were set close to the experimental data (i.e., 3 Na+ ions per ring): 25% with 4 Na+ ions, 50% with 3 Na+ ions, and 25% with 2 Na+ ions. With this and with the chosen plane cutoff (60 Ry), a stable energy and temperature profiles were obtained in our MD runs (see Fig. S2 in SUPPORTING INFORMATION). The ring centers coincide with axes passing through Oc, Ti and Fc atoms. A similar concerted excitation was also reported for the candidate solid electrolyte Li3N (P6/mmm) in which 6 Li+ ions tend to rotate around a common N3- ion.47 Connecting density clouds between rings are also observed (J1, J2, J3, J4), allowing inter-ring motion and


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thus, long range ion transport in the ab-plane. On the other hand, no inter-ring jumps were seen along the c-axis over the course of the MD run (for 50 ps), implying a large diffusion barrier in this direction as noted by the severely restricting narrow path bottleneck in Fig. 1a (dashed outline). Thus, Na3Ti2P2O10F can be classified as a 2D Na ion conductor; other materials with the same dimensionality for diffusion include Na beta’’-alumina12-14 and layered-type cathode materials48-50.

Figure 3. a) Trajectory clouds (yellow) showing the 3D probability of presence of Na+ ions forming the actual ring paths (eg., circles) and showing inter-ring jumps (J1, J2, J3, J4) in the abplane (from NVT-MD simulation at 1673 K), and b) side view (c-axis in vertical direction) of the trajectory exposing the Na+ ion density cross sections and the in-plane inter-ring jumps (eg., J1 and J3). The isosurface level (yellow) is set to 1 x10-6 a.u. The color scale (blue: 0, green: 0.5, and red: 1) is based on minimum and maximum saturation level of 1 x 10-6 and 2 x 10-4 a.u., respectively.


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In order to explain the Na MSD behavior in Fig. 2b and to quantitatively evaluate the ion transport in the conduction planes in Fig. 3, single-atom root MSD plots of Na+ ions were monitored together with their MD step configuration snapshots. Fig. 4a shows the initial (yellow) and 20-ps (orange) positions of Na+ ions from a portion of a 1673-K NVT-MD run as viewed on the ab-plane. In ring 1, a cooperative intra-ring motion (counter-clockwise rotation) is noted for Na1, Na17, and Na23, with their root MSD changing concurrently between 3-4 Å (Fig. 4b); a return to a root MSD value near zero for t > 0 means the Na+ ion has returned to its original position inside the ring. Meanwhile, in rings 2 and 3, successive inter-ring jumps are observed for Na7 and Na10, respectively (Fig. 4c); Na7 appears to initialize the jump starting from ring 2 (t ≈ 7 ps) into ring 4 (√MSD ≈ 6 Å). In order to reduce the Coulombic interaction within ring 4 (now with 4 Na+ ions), Na10 is forced to jump into ring 3 (t ≈ 13 ps). In ring 2, the motion proceeded with Na7, Na3 and Na12 rotating clockwise (t < 5ps) prior Na7’s inter-ring jump into ring 4 (t ≈ 7 ps). The remaining Na+ ions in ring 2 (Na3 and Na12) rotated again but in the counter-clockwise direction, with the final position of Na12 close to its initial point and Na3 almost opposite to Na12. Collectively, it is apparent that inter-ring jumps are facilitated to a large extent by the frustration in the local Na occupancy of the ring paths, i.e., the driving force being the dynamical redistribution of Na+ ions from a high Na occupancy ring into a low Na occupancy ring. Therefore, controlling the Na content by aliovalent doping at Ti (eg., by Al3+ or V5+) and P (eg., by Si4+ or S6+) sites could be the key towards optimizing the Na diffusion of Na3Ti2P2O10F. In addition, other factors such as controlling the lattice spacing and modulation of the energy landscape by modifying the Coulombic repulsion between Na+ ion and the framework are also good strategies for its Na diffusion enhancement. Also, it now becomes apparent that the shape of the Na MSD plot in Fig. 2b is indicative of the caging regime. This is mainly characterized by


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the intra-ring, rotation-type of motion for the Na+ ions (Fig. 4);

in Fig. 2b is ~2.8 Å

which is close to the 8h-8h intra-ring Na interdistance.

Figure 4. Intra-ring and inter-ring motion of Na+ ions in the ab-plane as viewed within a 20-ps NVT MD run at 1673 K: a) initial (yellow spheres) and 20-ps (orange spheres) local Na configuration, b) single-atom root MSD plots for the intra-ring motion of three Na+ ions (Na1, Na17, and Na23) in ring 1, c) single-atom root MSD plots for the inter-ring motion of two Na+


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ions (Na7 and Na10), and d) single-atom root MSD plots for the intra-ring motion of two Na+ ions in ring 2. As previously mentioned, the fast ionic conduction in Na3Ti2P2O10F can be explained by the combination of intra-ring and inter-ring correlated motions. To further elucidate this mechanism, we checked the van Hove space-time correlation function51 for distinct Na pairs, the equation is given by:

(1)

where N is the number of Na+ ions, δ[·] is the three-dimensional Dirac delta function while

are displacements of Na j and i, respectively, at time t. The evolution of the

and

for

Na3Ti2P2O10F is shown in Fig. 5a. The relevant interatomic distances (taken from experimental data26-27), for use as reference in the analysis of the

profile, are displayed in Fig. 5b. At

early stages of the MD run, such as at t = 0.1 ps (white circles),

closely resembles the

more commonly known radial distribution function g(r) plot, with the first peak assigned as the nearest intersite distance between intra-ring Na 8h sites, ~3.2 Å (2.9 Å in the idealized case shown in Fig. 5b). Occupancy for Na pairs at a distance below r = 2.25 Å are forbidden, leading to g(r) = 0. As time progresses, sites occupied by one Na+ ion (i) are being vacated and then occupied by another Na+ ion (j). The frequency of this replacement event and those of intermediate scenarios (i.e., j is still at a distance r from the site vacated by i) lead to the shape evolution away from the typical g(r) plot. Specifically, the probability build-up over time near r


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= 0 now represents the collaborative motion for Na+ ions owing to the rise of replacement events. On the other hand, the temporal decrease of the first peak can be assigned as a signature for Na+ ions rearranging locally at the given characteristic distance (i.e., at the abscissa of the peak location, ~3.2 Å). Beyond the first peak (r > 4.5 Å), no significant contribution is observed for intermediate range ordering, indicating that the local ion dynamics is the predominant process that drives the ion transport.52

Figure 5. a) Space-time van Hove correlation function for distinct Na+ ion pair i and j (

)

with sampling taken from 1673-K NVT MD run. b) Relevant interatomic distances (Na in yellow, F in teal) in the ab conduction plane taken from XRD-derived crystal structure information.25 3.3. Local Na+ ion migration analysis. Based from the collected NVT MD sampling trajectory, 18% of the rings have 4 Na+ ions, 63% have 3 Na+ ions, and 19% have 2 Na+ ions (calculated based from the counted number of Na+ ions in each ring path; radial cutoff is 3.0 Å while


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distance between ring centers in the ab plane is ~3.2 Å). This occupancy breakdown harmonizes well with the upper limit for Na occupancy per ring (4 Na), beyond which the Na-Na distance will become unphysically short. Using this information, we performed several NEB calculations to get the migration energy (Ea) values corresponding to different local Na configurations formed between two adjacent rings, as shown in Fig. 6. For the ab-plane motion, the arrangements that were evaluated are pattern 1: 4-Na ring to 3-Na ring, pattern 2: 4-Na ring to 2-Na ring, pattern 3: 3-Na ring to 2-Na ring, pattern 4: 3-Na ring to 1-Na ring, and pattern 5: 2-Na ring to 2-Na ring, respectively (Fig. 6a-6e); ring center inter-distance is ~6.4 Å. Along the c-axis, we picked an arrangement which is 4-Na ring to 1-Na ring (Fig. 5f); ring-to-ring distance is ~5.4 Å. The results are tabulated in Table 2. The trend points to a strong dependence between the number of Na+ ions residing between two rings and the local inter-ring Ea (as qualitatively implied in Fig. 4). The smaller is the number of Na+ ions in the final ring than in the initial ring, the smaller Ea becomes. In the ab-plane, the highest Ea was calculated for pattern 1 (0.88 eV in the forward direction, 4-Na ring to 3-Na ring) while the lowest is for pattern 4 (0.30 eV in the forward direction, 3-Na ring to 1-Na ring). In the backward direction, Ea also becomes smaller if the number of Na+ ions in the final ring is smaller than the initial ring. By summing up the weightage contribution for all the conceivable unique combination of initial-final ring occupancies that satisfy the Na count pairing of 3 and 3±1, the average Ea was estimated to be 0.49 eV which is consistent with experiment (Ea,expt = 0.48 eV25). However, this calculated value serves only as an indicator and does not account for the Boltzmann factor associated to experimental Ea. The difference between Ea,forward (0.30 eV) and Ea,backward (0.17 eV) for patterns 4 and 5, respectively, can be ascribed to the position of the final ring Na before actual Na jump (eg. see Na2 during the backward jump of Na1 in Fig. 7b). In the former, the final ring Na is


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located next to the vacant site to be jumped into by the mobile Na, site separation is close to the 8h-8h distance (i.e., 2.9 Å in Fig. 5b). In the latter, it (again, see Fig. 7b) is positioned farther away, across the ring diameter (i.e., 4.1 Å in Fig. 5b).

Figure 6. Various local environments evaluated for local inter-ring jumps based on the number of intra-ring Na atoms. In the ab-plane: a) 4-Na ring to 3-Na ring, b) 4-Na ring to 2-Na ring, c) 3-Na ring to 2-Na ring, d) 3-Na ring to 1-Na ring, and e) 2-Na ring to 2-Na ring; along the c-axis: f) 4Na ring to 1-Na ring. Although only single jump events were evaluated, Table 2 validates the critical role of dynamic Na distribution for controlling the inter-ring Ea and the local diffusion process. As highlighted in Fig. 4, cooperative-type motions such as cluster rotation of Na+ ions basically predominate the conduction plane, mainly governed by the large reduction of electrostatic forces, in contrast with the case of single-ion displacement.53 Fig. 7 shows the NEB trajectory for pattern 5 (2-Na ring to 2-Na ring) and the corresponding displacement of surrounding Na+ ions. Accordingly, when a Na+ ion (Na1) moves in the ab-plane (the flat white surface in Fig. 7a-7c) and approaches the


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saddle point of the inter-ring jump (dashed out-line in Fig. 7c, about 3.2 Å from either ring centers), other Na+ ions in the final ring (Na3 and Na4) becomes repelled (straight arrows in blue). This ease in repulsion is presumably indicative that the rings are composed of energetically equivalent sites and that cooperative motion is the more preferred local process. The actual migration path becomes curved as Na1 tends to pivot around the nearest bridging Fion (F1) from the initial jump site and into the center of the transition plane (see Fig. 7b and 7c); we found no other intermediate pathways for inter-ring jumps. The other Na+ ion (Na2) in the initial ring does not move with moving Na1 but a Na+ ion from another ring (Na5) moves towards the direction of the Na1 initial site (straight blue arrow), a sign of local charge redistribution. The tendency for Na+ ions to reduce their interaction can be confirmed if during synchronous motions, maximum separation is maintained during the MD production runs. Typical Na-Na interdistance plots within selected rings are shown in Fig. 7d (the plots are related to rings 1 and 2 of Fig. 4a). In ring 1, the three Na+ ions (Na1, Na17, and Na23) are separated from each other by ~3.4 Å at all times, forming a triangle while moving around the ring path. In ring 2, the three Na+ ions (Na3, Na7, and Na12) behaved similarly as in ring-1 Na+ ions up until 6 - 7 ps, then one of the ions (Na7) jumped into the next ring (ring 4 in Fig. 4a) which caused the interdistance to increase and fluctuate with respect to the remaining Na+ ions (Na3 and Na12) in ring 2. At the same time, the remaining Na+ ions in ring 2 (again, Na3 and Na12) maintained their maximum separation with each other. Therefore, we have proven convincingly that the tendency for intra-ring Na+ ions to assume maximum separation during synchronous-type motions and the local frustration of occupancy in Na rings are what primarily drive the whole Na+ ion transport in Na3Ti2P2O10F. Aside from Li3N48, concerted movement of charge carriers were also determined for garnet-type cubic Li7La3Zr2O1254 and Li5La3Ta2O1255-56, tetragonal


18

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Li10GeP2S1257, Na beta’’-alumina14, and tavorite-type LiMgSO4F58. On the other hand, c-axis diffusion is again determined to be highly unfavorable (see Fig. 3b) even with a large difference on occupancy between initial (four Na+ ions) and final (one Na+ ion) rings (Ea,forward = 2.47 eV in Table 2). The unlikely crossover along this direction, again, can be readily explained by the smaller bottleneck size along the c-axis (see Fig. 1a), as opposed to the ab-plane bottleneck which is bounded by six polyhedral units (see Fig. 7c).

Figure 7. a-c) Local Na+ ion migration in the ab-plane from an initial ring with 2 Na+ ions (Na1 and Na2) into an adjacent ring with also 2 Na+ ions (Na3 and Na4) (see pattern 5 in Table 2). As the mobile Na+ ion (Na1) pivots around the nearest bridging F- ion (F1) (curved arrow in blue), Na3 and Na4 are being repelled away while a neighboring Na+ ion in the other neighboring ring


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(Na5) moves towards the direction of the vacated Na1 initial site (straight arrows in blue). d) NaNa interdistance plots in rings 1 and 2 of Figure 4a showing the tendency for Na+ ions to keep maximum separation during synchronous motions. Table 2. Na ion migration energy for different local ring environments.

4.

Description

Ea,forward (eV)

Ea,backward (eV)

4-Na ring to 3-Na ring (ab-plane)

0.88

0.80


0.76

1.07


0.50

0.46


0.30

0.64


0.61

0.17

4-Na ring to 2-Na ring (c-plane)

2.47

3.02

CONCLUSIONS

The Na+ ion transport in oxyfluorinated titanium (IV) phosphate Na3Ti2P2O10F was successfully investigated by first-principles-based DFT calculation. The material is determined to be a 2-D ionic conductor characterized with a cooperative-type of conduction mechanism in the ab-plane. The overall ion migration proceeds as a combination of intra-ring and inter-ring Na+ ion jumps that is mainly driven by dynamic Na distribution and the tendency for maximum separation for intra-ring Na+ ions in the local environment. The distribution of local migration energies predicted by NEB method for prevalent Na ring arrangements (0.49 eV on the average) is in remarkable agreement with experimental data (0.48 eV25). Aliovalent doping at Ti and P sites can potentially improve the Na diffusion property in this material. ASSOCIATED CONTENT


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Supporting Information. Figure 1, Figure S2, Table S1. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author *E-mail: [email protected], TEL: +81-29-860-4953, FAX: +81-29-860-4981 Notes The authors declare no competing financial interest. Present Address * National Institute for Materials Science (NIMS), Global Research Center for Environment and Energy based on Nanomaterials Science (GREEN), Namiki 1-1, Tsukuba, Ibaraki, Japan, 3050044. ACKNOWLEDGMENT R. J. was grateful for the financial support from Nagoya Kogyokai Scholarship, Nagoya Institute of Technology. The present work was partially supported by JST, PRESTO-program and MEXT program “Elements Strategy Initiative to Form Core Research Center” (Since 2012), MEXT; Ministry of Education Culture, Sports, Science and Technology, Japan. Crystal structures were drawn with the VESTA software.59 REFERENCES (1) Palomares, V.; Serras, P.; Villaluenga, I.; Hueso, K. B.; Carretero-González, J.; Rojo, T. Na-Ion Batteries, Recent Advances and Present Challenges to Become Low Cost Energy Storage Systems. Energy Environ. Sci. 2012, 5, 5884-5901.


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