Unraveling the Nature of Anomalously Fast Energy Storage in T

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Unraveling the Nature of Anomalously Fast Energy Storage in T‑Nb2O5 Dongchang Chen,†,§ Jeng-Han Wang,‡ Tsung-Fu Chou,‡ Bote Zhao,†,⊥ Mostafa A. El-Sayed,§ and Meilin Liu*,† †

School of Materials Science and Engineering, Center for Innovative Fuel Cell and Battery Technologies, Georgia Institute of Technology, 771 Ferst Drive, Atlanta, Georgia 30332-0245, United States ‡ Department of Chemistry, National Taiwan Normal University, 88, Sec. 4 Ting-Zhou Road, Taipei 11677, Taiwan, R.O.C. § Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, 901 Atlantic Drive, Atlanta, Georgia 30332-0400, United States ⊥ New Energy Research Institute, School of Environment and Energy, South China University of Technology, Guangzhou 510006, China S Supporting Information *

ABSTRACT: While T-Nb2O5 has been frequently reported to display an exceptionally fast rate of Li-ion storage (similar to a capacitor), the detailed mechanism of the energy storage process is yet to be unraveled. Here we report our findings in probing the nature of the ultrafast Li-ion storage in T-Nb2O5 using both experimental and computational approaches. Experimentally, we used in operando Raman spectroscopy performed on a well-designed model cell to systematically characterize the dynamic evolution of vibrational band groups of T-Nb2O5 upon insertion and extraction of Li ions during repeated cycling. Theoretically, our model shows that Li ions are located at the loosely packed 4g atomic layers and prefer to form bridging coordination with the oxygens in the densely packed 4h atomic layers. The atomic arrangement of T-Nb2O5 determines the unique Li-ion diffusion path topologies, which allow direct Li-ion transport between bridging sites with very low steric hindrance. The proposed model was validated by computational and experimental vibrational analyses. A comprehensive comparison between T-Nb2O5 and other important intercalation-type Li-ion battery materials reveals the key structural features that lead to the exceptionally fast kinetics of TNb2O5 and the cruciality of atomic arrangements for designing a new generation of Li-ion conduction and storage materials.

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pseudocapacitance”.5,12 Therefore, T-Nb2O5 holds a great perspective on the development of thick electrodes with high volumetric energy densities without compromising power densities5 and has been utilized by various works related to device engineering.15−20 However, the fundamental structural features that lead to the faster Li-ion storage kinetics than that of classic battery materials are still unknown. Unraveling the Li-ion intercalation mechanism is a challenging task because the crystal structure of T-Nb2O5 is complex, as shown in Figure 1a. In the T-Nb2O5 crystal, Nb ions are coordinated with either six or seven oxygen ions, forming either tilted octahedral (NbO6) or tilted pentagonal bipyramids (NbO7).21,22 These NbO6 and NbO7 polyhedra share either corners or edges, constituting an orthorhombic structure (space group: Pbam, No. 55).21,22 Since the discovery of its anomalously fast energy storage behavior, various state-ofthe-art characterization techniques have been applied to

INTRODUCTION In the search for advanced energy storage and conversion materials, undoubtedly, understanding the fundamental energy storage and conversion mechanism is vital to effective utilization of materials properties1,2 and to rationally designing new materials with desired properties.3,4 This is especially true for the development of novel materials with exceptional performances. In recent decades, tremendous efforts have been devoted to the development of extraordinarily high-rate electrochemical energy storage materials,5−9 in order to develop a new generation of high-power energy storage devices. The most remarkable progress in this pursuit is the discovery of the anomalously fast energy storage behavior of TNb2O5.5,10,11 In contrast to the mainstream intercalation-type energy storage materials (e.g., LiCoO2, LiMn2O4, and LiFePO4), the rate of Li-ion intercalation into T-Nb2O5 (even for a very thick composite electrode) increased almost linearly with the scan rate,5,12−14 which is believed to be the exclusive characteristic of surface-bound capacitive reactions. This unique energy storage behavior was defined as “intercalation © 2017 American Chemical Society

Received: March 28, 2017 Published: April 26, 2017 7071

DOI: 10.1021/jacs.7b03141 J. Am. Chem. Soc. 2017, 139, 7071−7081

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Journal of the American Chemical Society

structural change in the material. Therefore, it is necessary to systematically probe the detailed structural information on the complex material using in operando Raman spectroscopy performed on a well-designed model cell under well-controlled operating conditions, together with a comprehensive theoretical analysis of the vibrational structures. In this article, we report our findings in revealing the mechanism for accommodation of Li ions in the T-Nb2O5 structure during anomalously fast energy storage. On the basis of our model of Li-ion incorporation, in operando Raman spectroscopic evolution is highly consistent with the computed distribution of Ramanactive vibrational modes and vibrational density of states (VDOS), which explains the essential factors of “intercalation pseudocapacitance” in terms of crystallographic sites, Li-ion coordination behavior, and transport paths of Li ions. The proposed mechanism not only reveals the fundamental reason for the capacitive behavior of bulk T-Nb2O5 but also provides useful information for other intercalation materials that dominate the industry of secondary Li-ion batteries.

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RESULTS AND DISCUSSIONS Model Electrode and Its Properties. Fabrication of a thin-film model electrode of a controlled geometry is the first step for a systematic mechanism study. The electrode was fabricated on the basis of a method described elsewhere with some minor modifications (Supporting Information).5,11 Scanning electron microscope (SEM) images indicate the dispersion of T-Nb2O5 is generally uniform. XRD was used to confirm the phase of the T-Nb2O5 thin-film electrode. As shown in Figure 1b, the XRD pattern of the T-Nb2O5 powder used for the thin-film electrode fabrication matches the standard diffraction pattern of T-Nb2O5 completely (Powder Diffraction File: 27-1003).11,23,42,43 The specific surface area of the T-Nb2O5 powder is 3.72 m2 g−1 (Supporting Information). Having a rather low specific surface area is beneficial to efficient spectroscopic acquisitions since the incident laser can illuminate more materials in a unit volume. Shown in Figure 1c is a typical Raman spectrum of the model electrode. Obviously, the Raman peaks have satisfactory signalto-noise ratio. However, the broad band widths and irregular band profiles suggest that the observed Raman bands are considerably overlapped, a direct indication of the structural complexity of T-Nb2O5. Since more than 50 atoms exist in the unit cell of T-Nb2O5, the number of independent vibrational modes will be more than 150.44−46 A large number of Ramanactive vibrational modes populated in a particular wavenumber range will inevitably lead to the experimental observation that the Raman spectrum cannot be well-resolved to individual peaks. In this work, such overlapped Raman signals are classified in different band groups: a high-wavenumber band group (νHi) ranging from 570 to 770 cm−1, a mid-wavenumber band group (νMid) ranging from 180 to 360 cm−1, and a lowwavenumber band group (νLo) ranging from 80 to 160 cm−1 as marked in Figure 1c. The key information on these band groups (e.g., position, profile, and relative intensity), which is the overall sum of individual Raman modes of T-Nb2O5, will be traced during in operando experiments to reveal the structural change induced by Li-ion incorporation. The nature of the Raman bands (symmetry assignments and atomistic motions) which compose the observed band groups can only be analyzed through systematic theoretical vibrational analyses. It should be noted that a large number of reported works attempted to interpret the experimentally overlapped Raman bands for a

Figure 1. (a) Sketch of the unit cell of T-Nb2O5. The locations of Nb atoms are subjected to slight uncertainties (∼0.3 Å). (b) X-ray diffraction pattern of T-Nb2O5 powder used in this study. (c) Raman spectrum of T-Nb2O5 thin film used in this study. The ranges for major band groups are defined.

probing the Li-ion storage mechanism in T-Nb2O5. Unfortunately, the understanding of the Li-ion intercalation mechanism is still at a preliminary stage because of the complexity of the structure.13,23−25 In situ X-ray diffraction (XRD) revealed that Li-ion incorporation into T-Nb2O5 forms a solid solution, resulting in lattice expansion/contraction during lithiation/ delithiation.13,23,24 In situ X-ray absorption spectroscopy (XAS) analysis confirmed the change of oxidation states of niobium ions as well as evolution of Nb−O bond lengths under cycling conditions.5,24 Very recently, ex situ NMR analyses further confirmed the ultrafast kinetics of T-Nb2O5.26 Nonetheless, the exact Li-ion intercalation mechanism that is responsible for the above-mentioned change of lattice parameters, the change of Nb oxidation states, and the ultrafast kinetics is yet to be determined. Raman spectroscopy is a powerful tool for probing chemical and structural properties of electrode materials, especially when properly combined with theoretical vibrational analyses.27−29 The use of in situ and/or in operando techniques makes it possible to directly probe the structural changes of electrode materials at different stages of electrochemical cycling under a wide range of testing conditions.30−32 These approaches have been successfully applied to the study of electrode materials with simple crystal structures, including our previous works on popular supercapacitor materials (MnO2 and NiO2Hx),33,34 classic Li-ion-based energy storage materials (LiCoO2, LiMn2O4, LiFePO4, and Li-graphite),35−41 and catalysts for chemical and energy conversion. Since the number of vibrational modes is limited for these simple crystal structures, the evolution of a Raman peak or band can be directly linked to a specific structural change, thus offering critical insights into the mechanism of charge storage in the electrode material. For a material with a complex structure such as T-Nb2O5, however, the vibrational structures are so complex that it becomes extremely difficult, if not impossible, to straightforwardly correlate a single vibrational band with a specific 7072

DOI: 10.1021/jacs.7b03141 J. Am. Chem. Soc. 2017, 139, 7071−7081

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Journal of the American Chemical Society

shown in Figure 2b and basically agrees with the CV profile of T-Nb2O5 reported previously.5,11 The electrochemical current as a function of potential indicates that the incorporation of Li+ mainly occurs in the low potential range (below 2.0 V approximately). The electrochemical response of Li-ion incorporation will serve as an important reference for further in operando Raman spectroscopic analyses as a function of cell potential. In Operando Raman Spectroscopic Evolution. Performed synchronously with CV operations, the in operando Raman spectroscopic signal acquired in consecutive electrochemical cycles is shown as a two-dimensional image (Figure 3)

complicated structure (not limited to T-Nb2O5), such as to assign the high-wavenumber bands as stretching modes.22,47,48 However, these simple approaches can provide only preliminary interpretations and are mostly based on empirical judgements. In Operando Raman Cell and Electrochemical Behavior. The reliability of in operando Raman configurations is vital to the successful application of the in operando Raman techniques. Since the incorporation of Li ions into Nb2O5 has to be performed in a Li+-based nonaqueous electrolyte with Li metal as the counter electrode, strict airtightness is required for the in operando Raman cell. In order to achieve hermetic sealing and to perform feasible Raman spectroscopic acquisitions, we constructed our in operando Raman cell based on ultra-high-vacuum CF flanges and viewports (Figure 2a). To confirm the reliability of the in operando cell, we used

Figure 2. (a) Detailed construction of the in operando Raman cell used in this study. (b) Cyclic voltammogram (CV) of the T-Nb2O5 thinfilm model electrode acquired in the in operando Raman cell.

Figure 3. In operando Raman spectroscopic evolution of a T-Nb2O5 thin-film electrode acquired in 9 cycles. The evolution is shown as a two-dimensional image, and the Raman intensity is depicted using a color bar. In each cycle, the electrochemical potential is cycled from 3.0 to 1.2 V and back to 3.0 V, while Raman acquisitions are performed simultaneously with an interval of 0.1 V. Raman spectra near each cycle number represent the higher potential states, whereas Raman spectra acquired at the lower potential states lie in the middle between each cycle number. Major Raman band groups of T-Nb2O5 and electrolyte bands are marked.

both an in operando Raman cell and a normal Swagelok cell to test the cycling performance of a LiMn2O4 electrode, which is a well-understood Li-ion battery cathode material, and found that the capacity retentions for both cells are almost identical (Supporting Information), confirming that the designed in operando cell can provide the same electrochemical environment as a normal lithium-ion battery and reliable operando Raman spectroscopic acquisitions. On this basis, cyclic voltammograms (CV) were used to change the stage of Liion incorporation of T-Nb2O5 electrochemically. The electrolyte is 1 M LiClO4 dissolved in dimethyl carbonate (DMC) and the potential range is between 3.0 to 1.2 V. The CV profile is

to examine the general band evolution and reversibility. As shown in Figure 2b, the CV scan rate was controlled to be 2.6 mV s−1 so that one Raman spectrum is acquired in a potential interval of 0.1 V. Each in operando cycle starts/ends at 3.0 V (high potential state). In Figure 3, Raman spectra near each cycle number represent higher potential states, whereas Raman spectra in between each cycle number represent lower potential states. Obviously, the Raman spectroscopic evolution is completely reversible and consistent for different cycles. During the cycling between high potential states and low potential states, the νHi band group exhibits periodic intensity increase and decrease, respectively. Also, the νMid and νLo band groups 7073

DOI: 10.1021/jacs.7b03141 J. Am. Chem. Soc. 2017, 139, 7071−7081

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Journal of the American Chemical Society

minor blue shift with the maximized shift at 1.2 V. The overall effect of the evolution of the three band groups is that the Raman spectrum of the low potential state (1.2 V) is drastically different from that of the high potential state (3.0 V). During the following anodic process, the three band groups display a reverse behavior of the cathodic process, including an intensity increase of νHi, band merging of νMid, and a red shift of νLo. Moreover, it is noted that quantitative analyses of spectral evolution could offer valuable information about changes in the intrinsic properties of materials (such as doping, defects, etc.) under various conditions, as demonstrated by others in gaining insights into the correlation between structures and electrochemical properties.32,49,50 In this study, we estimated the changes in fraction of lithiation of electrode materials from their spectral evolution, which is determined solely by the degree of Li-ion incorporation. The calculated fraction of Li occupation is listed in Figure 4 for each Raman spectrum. Additionally, for the Raman bands of the electrolyte (DMC and LiClO4), the band properties (position, width, intensity, and profile) remain totally static during the entire process, indicating that the electrochemical operation has no influence on electrolyte properties at all. Quantification of Band Groups. The exact values of vibrational properties as a function of electrochemical operation can be considered as a quantitative indication of structural evolution induced by incorporation of Li ions. To perform accurate correlations with electrochemical properties, we performed systematic band fittings to quantitatively describe the band group evolution. The intensity decrease of the νHi band group is quantified by calculating the integrated intensity ratio of the νHi band group and the νMid band group. The splitting of the νMid band group is depicted by values of band fitting results. To ensure consistency of this analysis, the same fitting parameters were used regardless of the profile of νMid (merged or split, Figure S4). Combining all the quantifications mentioned above, Figure 5 shows the positions of νMid doublets

show obvious reversible evolutions as well, as the intensity distribution of the two band groups greatly changes periodically in each cycle. This reversible evolution of the Raman band groups of T-Nb2O5 is undoubtedly a convincing indication of the reversible structural evolution induced by Li-ion intercalation/deintercalation. On the basis of such reversibility, Raman spectra at each potential can be analyzed individually to further investigate the vibrational features at different stages of Li-ion storage. To evaluate the details of Raman evolution, Raman spectra at each individual potential interval in different cycles are summed, generating the spectroscopic evolution shown in Figure 4. During the cathodic process (potential sweep from

Figure 4. In operando Raman spectroscopic evolution of a T-Nb2O5 thin-film electrode as its potential was varied from 3 V to 1.2 V and to 3 V (vs Li+/Li). The dashed lines are used to show the evolution of major band groups and electrolyte bands (dimethyl carbonate and LiClO4). The potential of each spectrum is indicated by the color bar, which is divided into 36 grids. Each grid represents a potential interval of 0.1 V, and the fraction of lithiation corresonding to the potential interval is also shown next to the color bar.

3.0 V to 1.2 V), the evolution of each band group can be summarized as follows. First, the νHi band group basically remains static during the potential sweep from approximately 3.0 V to 2.0 V, which is consistent with the fact that the CV current in this potential range is not significant (Figure 2b). As the potential continues to approach 1.2 V, the relative intensity of the νHi band group greatly decreases and eventually almost disappears. Second, similar to the νHi band group, the νMid band group presents no obvious evolution during the potential sweep from 3.0 V to 2.0 V. Afterward, the νMid band group presents significant splitting gradually (marked with dashed lines). The maximized splitting for the νMid band group is observed at approximately 1.2 V. Third, for the νLo band group, after being static from 3.0 V to 2.0 V, the position of νLo experiences a

Figure 5. Quantitative correlation between key features of in operando Raman spectra and stored charge density. (a, b) Positions of νMid‑2 and νMid‑1 doublet as a function of cell potential. (c) Intensity ratio of νHi and νMid as a function of cell potential. (d) Electrochemical charge storage density of T-Nb2O5 thin-film electrode as a function of cell potential, respectively. 7074

DOI: 10.1021/jacs.7b03141 J. Am. Chem. Soc. 2017, 139, 7071−7081

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Journal of the American Chemical Society (νMid‑2 and νMid‑1) and intensity ratio between νHi and νMid as well as the stored charge density (integrated from Figure 2b) as a function of electrochemical potential. The evolution of these band properties is in good agreement quantitatively with stored charge density. To be specific, in the potential range where charge storage/release is not significant, the νMid band group remains merged and the νHi band group is of considerably high intensities. As charge is stored/released, positions of νMid‑1 and νMid‑2 separate/merge and I(νHi)/I(νMid) decreases/increases accordingly. The lithiation fraction of T-Nb2O5 (as listed in Figure 4) was quantitatively estimated from the I(νHi)/I(νMid) ratio (Figure 5c), as described in the Supporting Information. Model of Li-Ion Storage and Transport: The Atomic Arrangement of T-Nb2O5. Undoubtedly, the Raman spectroscopic evolution as a function of electrochemical potential mentioned above is a direct consequence of the consecutive structural change of T-Nb2O5 at different stages of Li-ion incorporation. However, such structural changes responsible for fast Li-ion storage cannot be feasibly interpreted from vibrational evolution since the nature of the experimental Raman band groups is unknown. To reveal the structural information conveyed by spectroscopic evolution, a hypothetical model of Li-incorporated T-Nb2O5 is needed to calculate the vibrational structure and the effect of Li incorporation on the vibrational structure, in order to correlate with experimental Raman spectroscopic evolution. The first step to understanding the mechanism of Li-ion storage and transport in T-Nb2O5 is to systematically analyze its unique structural features, especially the atomic arrangement, which determines the locations for Li-ion incorporation and the pathways for Li-ion diffusion. Although the structure of TNb2O5 is very complicated, the general atomic arrangement is rather simple; it consists of two sets of alternating atomic layers (Figure 6a). First, the oxygen ions are not closely packed:

(Figure 6b). Accordingly, the loosely packed 4g layer is likely to provide spacious accommodation for Li ions, which will be quantified computationally in detail. Model of Li-Ion Storage and Transport: The Local Bonding Structure of Li Ions. The Li-ion incorporation mechanism was investigated in terms of both general crystallographic sites and local bonding structures (i.e., the atomic coordination of Li ions). The technical details of the computational investigation are described in the Supporting Information. Shown in Figure 7a is the structure of a lithiated

Figure 7. (a) Structure of lithiated T-Nb2O5 after geometry optimization. The eight incorporated Li ions in one unit cell are labeled, and the 4g layer where Li ions are located is highlighted. (b) Local bonding structure of an incorporated Li ion and its neighboring atomic coordination. The bridging coordination between the Li ion and the O4h is highlighted with blue dashed lines. (c) Local bonding structure viewed from the c-axis. The Li bridged between O4h is marked with a dashed circle. (d) Distribution of charge difference of neighboring Nb and O due to Li-ion coordination. (e). Comparison of Li-ion adsorption energies when a Li ion is bridged or not bridged between O4h. The viewing direction is along the c-axis, and the upward vector is [100].

Figure 6. (a) Structure of the unlithiated model T-Nb2O5 with highlighted 4h layers (i.e., the densely packed atomic layer, color: pink) and a highlighted 4g layer (i.e., the loosely packed atomic layer, color: light blue). (b) Atomic arrangements of the 4h layer and the 4g layer when viewed from the c-axis.

∼40% of oxygen ions are located at the 4g Wyckoff positions of the space group Pbam (atomic coordinates: x, y, 0) and form a rather loosely packed 4g layer; the other ∼60% of oxygen ions are located at the 4h Wyckoff positions of the space group Pbam (atomic coordinates: x, y, 1/2) and form a denser 4h layer. Second, given such an uneven oxygen packing pattern, interestingly, all Nb cations are located within the denser 4h layer. Therefore, the 4h layers become the primary Nb−O bonding layers (Figure 6b) and the atomic density of the 4h layer is approximately 2.6 times higher than that of the 4g layer

T-Nb2O5 with minimal energy after structural optimization through computation. In terms of crystallographic sites, all Li ions are located at the 4g layer (highlighted in Figure 7a). The reason for the Li-ion preference for the 4g layer is obvious: the low atomic density of the 4g layer can offer the least steric effect and minimal repulsion from positively charged Nb atoms on the densely packed 4h layer. After understanding in which crystallographic plane the Li ions are stored, it is more crucial to unravel the exact locations of the incorporated Li ions within the layer. Interestingly, we 7075

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Journal of the American Chemical Society Table 1. Adsorption Energies of Li Ions Labeled in Figure 7a label number adsorption energy (eV)

1

2

3

4

5

6

7

8

−3.45

−3.25

−3.53

−3.50

−3.45

−3.23

−3.47

−3.46

found all Li ions occupy the sites in between alternating oxygens in the 4h layers (i.e., O4h, Figure 7a and Figure S6), forming linear O4h−Li−O4h coordination. We name these sites “bridging sites” since the linear O4h−Li−O4h coordination is analogous to a linear bridge. The calculated adsorption energies for each incorporated Li ion (labeled in Figure 7a) range from −3.23 to −3.53 eV (Table 1), indicating that the Li ions located at the bridging sites are highly stable. In order to better illustrate this coordination, Figure 7b and c show the typical local bonding structure for a Li ion. The bridging coordination between two O4h (marked with blue dashed lines in Figure 7b) stabilizes the incorporated Li ion. Therefore, the bridging sites between O4h are the most favorable locations for intercalated Li ions. When viewed from the c-axis, the bridged Li ion appears to be stacked under O4h (Figure 7c and Figure S6). The charge difference image of nearby Nb and O clearly exhibits the reduction of Nb and oxidation of Li as the bridging coordination is formed (Figure 7d). To further evaluate the locational selectivity of Li ions, we also calculated adsorption energies of a specific Li ion placed at various locations (Figure 7e). The adsorption energy of the Li ion located at a nonbridging site is higher than that at bridging sites (Figure 7e), which further proves the bridging sites between O4h are the most energetically favorable locations for Li ions. Model of Li-Ion Storage and Transport: Li-Ion Diffusion Path Topologies. The migration of a Li ion from one bridging site to another is the elementary step of Liion transport in T-Nb2O5. Since the structure of T-Nb2O5 is highly complicated, elementary Li-ion migration paths can be categorized into two simple path topologies in terms of the neighboring Nb−O bonding structures (Figure 8a). If the bridged O4h are edge-shared or corner-shared by neighboring NbOx (x = 6 or 7), the diffusion path topology is categorized as path A or path B, respectively. The nonbridging sites within the 4g layer correspond to the transition states of diffusion paths. After careful analyses of the diffusion path topologies, we have identified a few evident merits responsible for fast Li-ion transport. First, both transport topologies can offer direct migration for Li ions between bridging sites, without requiring Li ions to pass through a specially cramped space. Second, the void size for the Li-ion transport path is approximately 4 Å (i.e., the planar distance of 4h layers, Figure 8a), providing a spacious volume for Li-ion flow. Third, both path A and path B have no significant steric hindrance or repulsion from Nb or O atoms (Figure 8a), which results in little obstruction for Li-ion flow. Because of these unique features, T-Nb2O5 is different from other classical intercalation-type battery materials, which is elaborated in later discussions. After the diffusion path topologies and their key merits are identified, we further evaluate the kinetics of Li-ion diffusion computationally. Each incorporated Li ion can migrate to four neighboring bridging sites. To better illustrate these processes, Figure 8b and c show a local bonding motif for a particular Li ion (no. 7 labeled in Figure 7a). The Li ion can migrate from its original location to four neighboring sites (site no. 1 to no. 4, marked by black dashed lines, Figure 8b), via either path A or path B. Our computational results show that the migration

Figure 8. (a) Two Li-ion transport path topologies (path A and path B) for Li-ion migration from one bridge site to another. The bridging coordination between Li ions and O4h is marked with blue dashed lines, and the bridged O4h are marked with black dashed circles for clarity. (b and c) Schematic showing each Li ion can migrate to four neighboring bridging sites. The diffusion path topology for each migration path is labeled (path A or path B). (d) Energy profiles of Liion migration for path A (to site 1) and path B (to site 3). The Li-ion locations corresponding to transition states are shown.

barriers are 0.33 eV (to site 1, via path A), 0.39 eV (to site 2, via path A), 0.25 eV (to site 3, via path B), and 0.27 eV (to site 4, via path B). Figure 8d shows the energy profiles of Li-ion migration for path A (0.33 eV, to site 1) and path B (0.25 eV, to site 3). The calculated energy barrier is generally comparable to that of state-of-the-art solid-state Li-ion conductors,51,52 because of the merits of T-Nb2O5 diffusion path topologies as mentioned previously. In addition, the combination of diffusion path topologies throughout the entire structure of T-Nb2O5 essentially represents the overall Li-ion diffusion network. Since both path A and path B are within the 4g layer, the sum of these paths forms a quasi-2D network for Li-ion transport (Figure S7). Since the differences in adsorption energies of Li ions at different bridging sites are fairly small (