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Enhanced Sodium-Ion Mobility and Electronic Transport of Hydrogen-Incorporated VO Electrode Materials 2

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Xiang-Mei Shi, Jian-Chen Li, Xing-You Lang, and Qing Jiang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00481 • Publication Date (Web): 06 Mar 2017 Downloaded from http://pubs.acs.org on March 10, 2017

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The Journal of Physical Chemistry

Enhanced Sodium-Ion Mobility and Electronic Transport of Hydrogen-Incorporated V2O5 Electrode Materials

Xiang-Mei Shi, Jian-Chen Li, Xing-You Lang, Qing Jiang* Key Laboratory of Automobile Materials (Jilin University), Ministry of Education, and School of Materials Science and Engineering, Jilin University, Changchun, 130022, China

Corresponding author *E-mail: [email protected]

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ABSTRACT Although α-V2O5 as an attractive electrode material for electrochemical energy storage devices exhibits a high theoretical capacity, its atomic structure with the confined size of channels for Na-ion transport and low electronic conductivity lead to the poor rate performance. Here we demonstrate that hydrogen incorporation in α-V2O5 is an effective way to improve the kinetics of ionic and electronic transports by

using

the

density

functional

theory.

Among

various

structures

of

hydrogen-incorporated α-V2O5, H2V2O5 presents both enlarged diffusion channels along the [010] and [001] directions where the diffusion energy barriers decrease to 0.844 eV (-34.93 %) and 1.737 eV (-41.81 %) respectively. Improved electronic conductivity is also achieved for H2V2O5 due to the insulator-metal transition attributed by the high concentration of hydrogen atoms. As H2V2O5 has smaller volume expansion occurred during the Na-intercalation process, H2V2O5 at the comparable specific capacity exhibits higher rate capability and cyclability than α-V2O5.

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1. Introduction Environmental and energy concerns arisen from the ever-growing use of vehicles promote the development in electrochemical energy storage systems as new clean energy powers.1-3 In particular, pursuing high energy and power densities simultaneously in metal-ion batteries and pseudocapacitors are long-standing issues, which store charge by the reversible redox reactions within electrodes.4-6 As the charging/discharging processes include reversible flows of electrons and ions in the electrodes, the kinetics of carrier transports is the key in improving performances of metal-ion batteries and pseudocapacitors, especially the rate capability.7-10 Accordingly, increasing the electronic conductivity and lowering the diffusion energy barrier (Ebarrier) of the ion transport are highly desirable, which can be achieved by modifying geometrical and electronic structures of electrode materials.11-15 V2O5 is a very attractive electrode material because the high oxidation state of vanadium leads to the possibility of storing more than 1 electron per formula unit. As a result, its theoretical capacity is up to 443 mAh g-1 by assuming the insertion of three monovalent ions.16-17 At room temperature, V2O5 crystallizes in α-phase, which has an orthorhombic structure (space group Pmmn) with a band gap of ~2 eV.18-19 Meanwhile, its Ebarrier values for the Na-ion diffusion are 1.131 eV and 2.986 eV along the [010] and [001] directions respectively,20 where two possible pathways are one-dimensional channels, as shown in Figure 1. Consequently, the low electronic conduction and sluggish Na-ion diffusion result in the poor rate performance of α-V2O5 as an electrode for Na-ion batteries or pseudocapacitors. To address these 3



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issues, several strategies have been proposed in experiments. For examples, carbon materials,21-22 porous metals,23 and conducting polymers24 are employed as the conductive skeletons in nanostructured electrodes to enhance the electrical conductivity of α-V2O5. However, the task to improve Na-ion and electron transports of intrinsic α-V2O5 still remains beyond the nanostructured hybrid design of electrodes. The confined diffusion channels of α-V2O5 should be enlarged to decrease the strain generated during the adsorption and diffusion of Na ions inside channels, which has a close relationship with Ebarrier.11,25-27 Hydrogen incorporation is an alternative way to modify both atomic and electronic structures of oxides through the formation of O-H bonds. A recent experimental study supported by first-principles calculations has reported that the monoclinic-rutile phase transition in VO2 is present by doping atomic hydrogen at room temperature.28 α-V2O5 has three crystallographically unequivalent O atoms denoted as Oa (singly coordinated), Ob (two-fold coordinated), and Oc (three-fold coordinated), forming different bond lengths with V atoms. Thus, incorporating hydrogen is a way to easily operate various kinds of coordination environments for Na ions in α-V2O5 and further achieve moderate sizes of diffusion channels. In addition, hydrogen is the smallest and lightest interstitial atom which requires the least space for incorporation. Thus, the theoretical specific capacity can be retained. Aiming at enlarging diffusion channels without the volume expansion, we expect that the incorporated H atoms are located inside the region R* marked in Figure 1, which is the residual space in contrast to the channels for Na-ion transport. Indeed, 4


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hydrogenated V2O5,29-30 TiO231 and Li4Ti5O1232 have been reported as electrode materials for lithium-ion batteries, where a large amount of oxygen vacancies are produced instead of O-H bonds due to the high temperature (> 200 ºC) treatments in the H2 atmosphere. Although the superior rate performances are confirmed in these oxygen-deficient oxides, the case of oxides with the efficient incorporation of hydrogen atoms has not been studied. By the hydrogen spillover method, the vanadium pentoxide hydrogen bronze (HxV2O5) can be fabricated at much lower temperatures (even at room temperature), which reserves O-H groups.33-36 Therefore, to explore a novel method to elevate the rate performance of α-V2O5 for Na-ion energy storage devices, atomic structures and electronic properties of HxV2O5 merit the specific attention. Herein, we investigate the hydrogen-incorporated α-V2O5 targeted as an electrode material by density functional theory (DFT) calculations. HxV2O5 with a wide range of hydrogen concentration of x = 0 ~ 5 was calculated to consider its stability and structural characteristics. Among all configurations, H2V2O5 shows the most desirable atomic structure for the rapid Na-ion transport. Further studies on H2V2O5 show improved kinetics of Na-ion and electron transports as well as the decreased volume expansion during the Na intercalation/deintercalation relative to α-V2O5. This concept provides an effective way to increase the intrinsic rate capability of electrode materials by modifying atomic structures. 2. Calculation Methods The spin-polarized DFT calculations with Ultrasoft pseudopotentials37 as 5



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implemented in the CASTEP code38 were performed in this work. The exchange-correlation

effects

were

described

by

the

generalized

gradient

approximation (GGA) with Perdew-Burke-Ernzerhof functional (PBE).39 The minimum energies for all structures were obtained by simultaneously relaxing unit cells and the atomic positions in them until energy, maximum force, and maximum displacement have become less than 1×10-5 eV/atom, 0.03 eV/Å, and 0.001 Å, respectively. The calculations were carried out using plane-wave cutoff energy of 500 eV with Monkhorst-Pack k point separations of 0.04 Å−1 in the Brillouin zone. It has been reported that van der Waals force corrections are crucial to the DFT calculations for alkali and alkaline-earth ion insertion into α-V2O5.40 In order to include van der Waals interactions, the DFT-D method within the Tkatchenko-Scheffler (TS) scheme41 was used in all calculations for dispersion corrections. As V-based oxides involve strong electron-electron correlations, a Hubbard U value was applied to d-states of V atoms. Several different U values of 2.45, 3.1 and 4.0 eV have been used in previous studies by empirical fits.42-44 With the similar consideration, the band gap and lattice parameters of optimized α-V2O5 with different U values were tested, as shown in Figure S1. In light of the experimental results that the indirect and direct optical band gaps of α-V2O5 are about 2.1 eV and 2.34 ~ 2.4 eV respectively,18,45 the U value of 2.7 eV is finally taken in all calculations, which is located within the range of literature data.42-44 With this correction, the indirect and direct band gaps in our calculations are 2.11 eV and 2.36 eV respectively. The lattice parameters of α-V2O5 and α-NaV2O5 calculated are listed in Table 1, which also accord well with the 6


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experimental data.46-47 Various structures of HxV2O5 with different kinds of H arrangement at x = 0, 0.5, 1, 2, 3, 4, and 5 based on the structure of α-V2O5 were built, where H5V2O5 includes the H-saturation of all O atoms. The corresponding formation energy Ef per formula unit was calculated by: Ef = EHx V2O5 − EV2 O5 −

nx E n 2 H2

(1)

where EHx V2 O5 , EV2 O5 and EH2 are the total energies of HxV2O5, α-V2O5 and hydrogen gas respectively. n is the number of the formula unit in the calculated supercells for HxV2O5 and α-V2O5. A negative (positive) Ef indicates an exothermic (endothermic) process. The diffusion behaviors of Na in α-V2O5 and H2V2O5 are simulated by varying the Na position along the [010] and [001] directions to determine the minimum energy paths in channels I and II.48-49 The optimized configurations with the most stable Na-adsorption site are set as the initial and final states. Within the smallest period length between them, 9 images are spaced equally along the channel direction. Here, the atomic coordinate of Na along the channel direction in each image is fixed. Then the atomic coordinates of Na in the plane perpendicular to the channel direction and other atoms around Na are freely optimized. The minimum energy point in each image plane finally forms the diffusion pathway and the highest value (corresponds to a saddle point in three dimensions) determines the activation energy. Note that in order to avoid any mixing of the diffusion barrier with a charge transfer barrier, the standard GGA functional without U correction is used in the Na-diffusion 7



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calculations.50-51 According to the tests for Ebarrier values of α-V2O5 with different supercell sizes in Table S1, 1 × 2 × 2 supercell was selected as the substrate for transporting a Na atom. 3. Results and Discussion The inserted H atoms can be bonded with three kinds of O atoms in α-V2O5, as shown in Figure 2a. To determine the stable configuration of α-V2O5 with a low H doping, Ef of an adsorbed H atom calculated in the 1 × 2 × 2 supercell are -0.084, -0.100 and -0.058 eV/f.u. at Oa, Ob and Oc sites respectively. Despite the electron-withdrawing ability of Oa atoms is the strongest among them due to their highest charge of -0.32 e (-0.54 e for Ob and -0.64 e for Oc) by Mulliken population analysis, a single H atom binding with an Ob atom exhibits the most stable configuration. To unravel the origin of this contradiction, the location of O-H bonds and the electron density difference for each configuration are shown in Figure 2b. In all configurations, the H atom forms a short covalent bond d1 with one O atom and bifurcated hydrogen bonds of d2 and d3 with two other O atoms. According to the calculated bond lengths in Figure 2c, similar values for d1 were found for all adsorption sites while d2 and d3 show discrepancies between different configurations. These results indicate that the number and length of hydrogen bonds mainly determine the energetic stability of H-adsorption sites, which benefits for the spillover mechanism during the fabrication of hydrogen-incorporated oxides.52 Two comparable hydrogen bonds d2 = d3 = 2.02 Å are formed in the Ob-H configuration, exhibiting a lower structural energy than that in the Oa-H configuration [a shorter d2 8


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(1.88 Å) and a longer d3 (2.24 Å)]. Besides, the Oc-H configuration with two comparable hydrogen bonds d2 = d3 = 2.15 Å gives the poorest energetic stability. As a consequence, H atoms prefer binding to Ob atoms at the low H concentration, which locate inside the diffusion channel along the [010] direction of α-V2O5. Various configurations of HxV2O5 with a wide range of x = 0 ~ 5 are investigated to continue searching an expected structure. By the calculated Ef values of HxV2O5 shown in Figure 3a, hydrogen incorporation in α-V2O5 with all considered x values are exothermic processes, suggesting the enhanced stability of HxV2O5. Note that the unit cell of HxV2O5 here was adopted to calculate Ef in order to optimize both atomic positions and cell parameters. To confirm the validity of the unit cell, Ef values of HxV2O5 in a lager supercell (1 × 3 × 3) were calculated, which are in consistence with those in the unit cell, as shown in Figure S2. Although the calculated Ef decreases as x increases, the high concentration of hydrogen inserting in α-V2O5 leads to the loss of crystallinity. It has been reported that the crystalline structure of HxV2O5 is preserved well only when x < 3.2.35-36 Yoshikawa et al. have measured the lattice constants of crystalline HxV2O5 by X-ray diffraction and found three orthorhombic phases (α, β and γ) for different x values, which differ slightly from that in α-V2O5.36 As shown in the inset of Figure 3a, the lattice parameters for the most stable configuration of HxV2O5 at each x calculated match well with the experimental results, and the corresponding configurations are given in Figure 3b. The atomic coordinates of optimized HxV2O5 are provided in Tables S2-S6. For x = 0.5 and 1, all H atoms bond to Ob atoms, conforming to the above discussion. However, at x = 2, H atoms saturate 9



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all Oa atoms rather than form any Ob-H bond. In H2V2O5, each H atom is involved in an Oa-H covalent bond (1.01 Å) as well as a relatively strong hydrogen bond (1.72 Å) with another neighboring Oa atom in the region R*, which brings out the contraction of R* and satisfies the scenario that incorporated atoms should better not share the space for Na-ion transport. As x increases, Ob-H and Oc-H bonds are also formed in addition to the H-saturation of all Oa atoms, but the space for diffusion channels in HxV2O5 are more or less interfered by H atoms. Therefore, referring to the structural preference of the fast Na-ion transport in the hydrogen-incorporated α-V2O5, H2V2O5 shows the most favorable configuration for the need of the fast Na-ion transport. As the Ef values of HxV2O5 at x = 3 ~ 5 are all lower than that of H2V2O5 in the unit cell, the energetic stability of H2V2O5 with different gradients of H concentration in a 1 × 1 × 3 supercell is further identified. In Figure 4a, the first configuration has the highest total energy, where one of O-V-O layers along the (001) plane contains the majority of H atoms and corresponds to H5V2O5 while other two layers are HV2O5 and V2O5 respectively. The calculated energy of the second configuration is lower, which consists of two H3V2O5 layers and a V2O5 layer. The homogeneous distribution of H atoms in the third configuration shows the lowest energy, inferring the possibility of the fabrication of a homogeneous crystalline H2V2O5 at the fixed x value of 2. Furthermore, an ab initio molecular dynamics (AIMD) simulation was performed for H2V2O5 in NPT ensemble with 3 ps at 300 K. According to the evolution of the total energy for H2V2O5 in Figure 4b and the snapshot at the end of 3 ps in Figure 4c, all atoms in H2V2O5 undergoes only minor movement without any geometric 10


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reconstruction, confirming the thermodynamic stability of H2V2O5 at room temperature. Then, we investigate the structural environments around two diffusion channels I and II along the [010] and [001] directions respectively in H2V2O5 in details. In Figure 5a, Oa atoms forms two ionic bonds with V atoms (2.04 and 2.06 Å) along the [001] direction, which results in the shrinkage of the lattice parameter c shown in Table 1. On the other hand, V-Oc bonds along the [100] direction are elongated to 2.17 Å in H2V2O5 and thus the lattice parameter a increases significantly. The lengths of other bonds and b value remain nearly constant. In Figure 5b, the values of O-O distance d24, d57 and d68 around the diffusion channels in H2V2O5 are all larger than those in α-V2O5 except for d13. Based on the effective radii of Na (0.99 Å for four-fold coordination) and O (1.36 Å for three-fold coordination) ions,53 the optimum distance between two O atoms at the opposite edge of the cross-section of channels is approximately 4.70 Å for a passable Na ion without in-plane strain.54 As this value exceeds all those in our calculations for α-V2O5 and H2V2O5, the compressive strain should be present in all channels during the Na-ion diffusion. Hence, path II of H2V2O5 is more favorable for the rapid Na-ion diffusion than that of α-V2O5 due to the elongated d57 and d68 which drop the compressive strain. Moreover, path I of H2V2O5 is also expected to be better than that in α-V2O5 because of the significant increase of d24 from 3.36 Å in α-V2O5 to 4.11 Å in H2V2O5 which is the smallest value in α-V2O5, although the largest value of d24 = 4.38 Å in α-V2O5 decreases to 4.05 Å in H2V2O5. Furthermore, a simple method is introduced to 11



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compare the ability of the Na-ion transport in channels with different sizes and shapes. Including the general consideration of different interactions between Na ions and neighboring atoms, areas SI and SII of the smallest cross-sections in both diffusion channels marked as blue regions in Figure 1 and Figure 5a were calculated. In Figure 5c, both SI and SII in H2V2O5 are larger than those in α-V2O5, which demonstrates the faster Na-ion transports along both paths of H2V2O5. To confirm the above discussion, we calculated Ebarrier to investigate the Na-ion diffusion behaviors in α-V2O5 and H2V2O5. The Na-ion diffusion pathway can be characterized as a series of Na-ion jumps along the potential energy surfaces, which consist of minimum energy points in each cross-section plane along the diffusion direction. The corresponding Ebarrier is calculated as the energy difference between the highest and the lowest energy points along each pathway, figuring the difficulty of success in the energy jump.55-56 In Figure 6a, the diffusion trajectories for a Na ion along path I and II in a unit cell H2V2O5 keep nearly linear and locate in the center of channels, which are similar with those in α-V2O5. The energy profiles along two paths for the Na ion in H2V2O5 and α-V2O5 are shown in Figure 6b. In our calculations, Ebarrier along path I and II for α-V2O5 are 1.297 and 2.985 eV respectively, while the values are decreased to 0.844 eV (-34.93 %) and 1.737 eV (-41.81 %) for H2V2O5, illustrating the improved Na mobility in H2V2O5. As expected, the calculated Ebarrier values are identical to the opposite tendency of SI (H2V2O5) > SI (α-V2O5) > SII (H2V2O5) > SII (α-V2O5), confirming the inversely proportional relationship between the cross-section area of diffusion channels and Ebarrier. We also estimate the diffusion 12


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rate v for Na diffusion along each path at room temperature by v = L/t, where L is the diffusion distance of a Na ion and t is the characteristic time given by t = L2/D.57-58 The diffusion constant D is calculated by the Arrhenius equation of D = D0exp(−Ebarrier/RT), where D0 is the pre-exponential constant, R denotes the ideal gas constant, and T is the room temperature (298.15 K). The calculated Ebarrier, L, and v/v0 (v0 is the diffusion rate for path I of α-V2O5) for each pathway are listed in Table 2. In view of our calculations, the Na diffusion along path I of H2V2O5 is about 4.42 × 107 times faster than that along path I of α-V2O5 at room temperature. Moreover, although path II of H2V2O5 still exhibits the lower diffusion rate than path I of α-V2O5, a significant improvement is achieved relative to path II of α-V2O5 (about 1.36 × 1021 times faster). Hence, there is remarkably enhanced Na-ion diffusion behavior of H2V2O5 comparing with that of α-V2O5. The electronic conductivity of electrode materials is also pivotal to the rapid and effective electrochemical responses.59-60 Like most oxides, the intrinsic conductivity of α-V2O5 is poor due to the considerable band gap in Figure 7a. During the metal-cation intercalation in α-V2O5, such as Li+, Na+, and Ag+, electrons are transported by the polaron hopping mechanism.61-62 That is, metal dopants bring defect states into the band gap17,40 where the excess electrons accompanied by the slight lattice distortion are mainly localized around V atoms. Similarly, for HxV2O5 at x = 0.00 ~ 0.27 and x = 0.5, it has been theoretically and experimentally reported that the semiconducting properties are preserved and the dependence of the electrical conductivity on x is the competition between the increase in the carrier density and the 13



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depression of the carrier mobility due to bipolarons.61,63 However, H2V2O5 in our work shows the half-metallic characteristic where plenty of spin-up electron states are widely distributed across the Fermi level, as shown in Figure 7b. Besides, H and O atoms in H2V2O5 give a common peaks near -7.2 eV in the valence band, implying the stable formation of O-H bonds. Owing to the high concentration of H atoms, the excess electrons around V and O atoms are more delocalized and the continuous distribution of density of states (DOS) around the Fermi level intensively benefits for the electronic conductivity. Regarding the Na intercalation process, the DOS for NayV2O5 and NayH2V2O5 were also determined at y = 0.5 and 1. In Figures 7c and 7d, both Na0.5H2V2O5 and NaH2V2O5 have high and delocalized electron states in a wide energy range across the Fermi level, thereby maintaining the half-metallic or metallic behavior. In contrast, Na0.5V2O5 is still a semiconductor with a decreased band gap about 0.9 eV while NaV2O5 only furnishes several defect states dispersed around the Fermi level. Thus, H2V2O5 provides higher electronic conductivity than α-V2O5 throughout the reversible reactions in electrodes and facilitates the progressive rate performance for Na-ion batteries and pseudocapacitors. The stabilities of H and Na atoms in NaH2V2O5 are discussed by the local density of states (LDOS) in Figure 8. The hybridized peaks of Oa and H atoms lift down to -7.7 eV for spin-up states and -7.5 eV for spin-down states, denoting the improved stability of O-H bonds after the Na intercalation. In the higher energy range from -5.8 eV to -2.4 eV, the Na atom has several DOS peaks overlapped with those of Oa and Ob atoms, which are derived from Na-O bonds. Once the electrochemical 14


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reaction starts with extracting electrons from NaH2V2O5, Na cations should be separated prior to H cations due to the higher energy of bonding peaks located in the valence band. Additionally, the volume expansion of electrode materials during the electrochemical processes generates strain and results in the polarization of performance during charge and discharge, which has a vital influence on the cyclic performance of reversible electrodes.26,64-65 According to the calculated lattice parameters in Table 1, the volume of NaV2O5 is expanded 7.26 % from α-V2O5 while NaH2V2O5 exhibits a decreased volume expansion 4.63 % from H2V2O5. Interestingly, the volume of H2V2O5 is even 0.37 % lower than that of α-V2O5, which suggests that only the space for Na adsorption and diffusion is enlarged, which is accompanied by the decrease of region R* in H2V2O5. As discussed above, H2V2O5 shows better rate capability and cyclability than α-V2O5 at the comparable specific capacity. Although the Ebarrier value of H2V2O5 itself is not low enough for competing as a high-rate electrode material, the substantial improvements in both ionic and electronic conductivity versus α-V2O5 do a big favor in overcoming its main drawbacks as electrodes. More efforts are still needed to further lower the Ebarrier for practical applications. We expect that the hydrogen incorporation in other oxides can also achieve the same progress and broaden the range of potential electrode materials for batteries and pseudocapacitors. 4. Conclusions In summary, we investigated a series of hydrogen-incorporated α-V2O5 and identified the performances of H2V2O5 as an electrode material based on the DFT 15



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calculations. Within a wide range of x in HxV2O5 (x = 0.5 ~ 5), all transformation processes from α-V2O5 are exothermic where H2V2O5 exhibits the most favorable atomic structure for the Na-ion transport where no space in both diffusion channels I and II is possessed by the incorporated H atoms. In addition, H2V2O5 provides enlarged channels versus α-V2O5 with decreased Ebarrier values of 0.844 eV along path I and 1.737 eV along path II in H2V2O5 while those in α-V2O5 are 1.297 eV and 2.985 eV respectively. Ebarrier values coincide with the opposite tendency of SI (H2V2O5) > SI (α-V2O5) > SII (H2V2O5) > SII (α-V2O5). The half-metallic or metallic characteristics of the original and Na-intercalated H2V2O5 also realize the improved electronic conductivity throughout the charge/discharge processes with smaller volume expansion (4.63 %) than NaV2O5 (7.26 %). Overall, the enhanced ionic and electronic transports in H2V2O5 promote its potential as electrode materials for Na-ion batteries or pseudocapacitors with high rate and cyclability performance.

Supporting Information Tests for the U value (Figure S1); Effects of the supercell size on Ebarrier (Table S1) and Ef values (Figure S2); Atomic fractional coordinates of optimized structures (Tables S2-S10).

Acknowledgement We wish to thank the National Natural Science Foundation of China (No. 51631004, 51422103) and the computing resources of the High Performance Computing Centers 16


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of Jilin University and Jinan, China. The authors declare no competing financial interest.

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Table 1 Calculated lattice parameters and volumes of unit cells for α-V2O5, H2V2O5, NaV2O5 and NaH2V2O5.

α-V2O5 H2V2O5 NaV2O5 NaH2V2O5

a (Å) 11.56 12.20 11.26 11.79

b (Å) 3.57 3.67 3.65 3.85

Volume (Å3) 182.00 181.33 195.22 189.73

c (Å) 4.41 4.05 4.75 4.18

Table 2. The values of Ebarrier, L and v/v0 for path I and II of α-V2O5 and H2V2O5 H2V2O5

α-V2O5 Ebarrier (eV) L (Å) v/v0

Path I 1.297 3.57 1

Path II 2.985 4.41 2.36 × 10-29

Path I 0.844 3.67 4.42 × 107

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Path II 1.737 4.05 3.22 × 10-8


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Figure 1. Crystal structure of α-V2O5. The blue regions SI and SII are the cross-section areas of channels along the [010] and [001] directions, respectively.

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Figure 2. (a) Unit cell of α-V2O5 with three kinds of O atoms denoted as Oa, Ob and Oc. (b) Electron density differences with respect to the sum of atomic densities for the configurations of Oa-H, Ob-H and Oc-H adsorption sites. (c) Bond lengths between the adsorbed H atom and neighboring O atoms. d1, d2 and d3 are arranged as the increasing values of the length in each configuration which are marked in (b).

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Figure 3. (a) The formation energy Ef per formula unit (f.u.) as a function of x in HxV2O5. Several Ef values were calculated for different configurations at each x and dark triangles indicate the lowest energies among them. The inset provides lattice parameters of HxV2O5 from experimental results36 and our calculations. (b) The most stable configuration of HxV2O5 at each x.

24


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Figure 4. (a) The calculated total energies of H2V2O5 in three different configurations. (b) The total energy profile calculated by the AIMD simulation and the dashed line indicates the average value. (c) The snapshot at the end of 3 ps.

25



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Figure 5. (a) Projected views of H2V2O5 along the [010] and [001] directions. The blue regions are the smallest cross-section areas for diffusion channels and O atoms around them are labeled as 1 ~ 8. (b) The values of dij (i, j = 1 ~ 8) for α-V2O5 and H2V2O5 where dij is the distance between two O atoms labeled as i and j. (c) Areas SI and SII for α-V2O5 and H2V2O5.

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Figure 6. (a) Na-ion diffusion pathways I along the [010] and II along the [001] directions of H2V2O5. (b) The corresponding energy profiles along paths I and II of α-V2O5 and H2V2O5.

27



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Figure 7. Total and local density of states for (a) α-V2O5, (b) H2V2O5, (c) Na0.5V2O5, Na0.5H2V2O5, and (d) NaV2O5, NaH2V2O5. The positive values represent spin-up states and the negative values are spin-down states. The Fermi levels indicated by dashed lines are set at 0 eV.

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Figure 8. Local density of states for NaH2V2O5. The Fermi levels indicated by dashed lines are set at 0 eV.

29



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TOC Graphic

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Figure 1. Crystal structure of α-V2O5. The blue regions SI and SII are the cross-section areas of channels along the [010] and [001] directions, respectively. 29x10mm (300 x 300 DPI)



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Figure 2. (a) Unit cell of α-V2O5 with three kinds of O atoms denoted as Oa, Ob and Oc. (b) Electron density differences with respect to the sum of atomic densities for the configurations of Oa-H, Ob-H and Oc-H adsorption sites. (c) Bond lengths between the adsorbed H atom and neighboring O atoms. d1, d2 and d3 are arranged as the increasing values of the length in each configuration which are marked in (b). 58x42mm (300 x 300 DPI)


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Figure 3. (a) The formation energy Ef per formula unit (f.u.) as a function of x in HxV2O5. Several Ef values were calculated for different configurations at each x and dark triangles indicate the lowest energies among them. The inset provides lattice parameters of HxV2O5 from experimental results36 and our calculations. (b) The most stable configuration of HxV2O5 at each x. 86x91mm (300 x 300 DPI)



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Figure 4. (a) The calculated total energies of H2V2O5 in three different configurations. (b) The free energy profile calculated by the AIMD simulation and the dashed line indicates the average value. (c) The snapshot at the end of 3 ps. 82x82mm (300 x 300 DPI)


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Figure 5. (a) Projected views of H2V2O5 along the [010] and [001] directions. The blue regions are the smallest cross-section areas for diffusion channels and O atoms around them are labeled as 1 ~ 8. (b) The values of dij (i, j = 1 ~ 8) for α-V2O5 and H2V2O5 where dij is the distance between two O atoms labeled as i and j. (c) Areas SI and SII for α-V2O5 and H2V2O5. 83x49mm (300 x 300 DPI)



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Figure 6. (a) Na-ion diffusion pathways I along the [010] and II along the [001] directions of H2V2O5. (b) The corresponding energy profiles along paths I and II of α-V2O5 and H2V2O5. 77x43mm (300 x 300 DPI)


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Figure 7. Total and local density of states for (a) α-V2O5, (b) H2V2O5, (c) Na0.5V2O5, Na0.5H2V2O5, and (d) NaV2O5, NaH2V2O5. The positive values represent spin-up states and the negative values are spin-down states. The Fermi levels indicated by dashed lines are set at 0 eV. 108x83mm (300 x 300 DPI)



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Figure 8. Local density of states for NaH2V2O5. The Fermi levels indicated by dashed lines are set at 0 eV. 96x112mm (300 x 300 DPI)


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Enhanced Sodium-Ion Mobility and Electronic ... - ACS Publications

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