Strong Li-Content Dependence of Li Diffusivity in TiO2-B - The Journal

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Strong Li-Content Dependence of Li Diffusitivity in TiO-B Qian Zhang, and Payam Kaghazchi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06319 • Publication Date (Web): 01 Sep 2016 Downloaded from http://pubs.acs.org on September 6, 2016

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The Journal of Physical Chemistry

Strong Li-Content Dependence of Li Diffusitivity in TiO2-B Qian Zhang and Payam Kaghazchi∗ Physikalische und Theoretische Chemie, Institut f¨ ur Chemie und Biochemie, Freie Universit¨ at Berlin, Takustr. 3, 14195 Berlin, Germany E-mail: [email protected]

Abstract Lithiation process in TiO2 -B as function of Li content x is studied using density functional theory. Considering a variety of possible pathways we find that stepwise insertion of Li in TiO2 layers followed by insertion of Li in O layers is kinetically the most favorable scenario. Diffusion coefficient (D) varies only by 3 orders of magnitude with x for Li contents up to x = 0.75 (3.03×10−10 cm2 /s ≤ D ≤ 7.94×10−8 cm2 /s), but it becomes almost 6 and 26 orders of magnitude smaller for 0.75 < x ≤ 1.0 and 1.00 < x < 1.25, respectively. To make a direct comparison to experimental measurements, the maximum diffusion length was estimated for different values of Crate. It is found that for any reasonable value of C-rate between 0.1C and 10C bulk TiO2 -B can not attain capacities larger than 251 mAh g−1 . However, larger capacities up to 335 mAh g−1 can be obtained by nanosized TiO2 -B. In addition, we find that a capacity higher than 335 mAh g−1 can not be achieved. Our results suggest that the small discharge capacity of bulk TiO2 -B is due to the large increase in the energy barrier of Li diffusion for Li contents above x = 0.75.

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Introduction Titanium dioxide (TiO2 ) polymorphs have been recently received considerable attention as anode materials for lithium-ion batteries. 1–3 Bronze phase (B) has the lowest density among the TiO2 polymorphs. 4,5 As a result, more number of lithiums per formula unit can be inserted in TiO2 -B than in other TiO2 polymorphs: Li0.10 TiO2 (35 mAhg−1 ) for bulk brookite, 6 Li0.25 TiO2 (83 mAhg−1 ) for bulk rutile, 7 Li0.50 TiO2 (167 mAhg−1 ) for bulk anatase, 8 and Li0.75 TiO2 (251 mAhg−1 ) for bulk TiO2 -B. 9 Nanostructuring can further enhance the Li-insertion capacity of TiO2 -B. For example, discharge capacities of 305 mAhg−1 , 332 mAhg−1 , and 338 mAhg−1 have been achieved in small nanowires, 10 nanotubes, 11 and nanosheets, 12 respectively. Wilkening et al. 13 performed an echo nuclear magnetic resonance (NMR) study to characterize the dynamic properties of Li0.3 TiO2 -B nanowires and found that Li mobility is slow. They proposed that nanowires with shorter diffusion length can compensate the slow Li self-diffusivity so that a larger number of Li atoms per unit volume can be incorporated/removed in/from nanowires than the bulk form of TiO2 -B. Furthermore, a galvanostatic intermittent titration technique (GITT) measurement by Hoshina et al. 14 reported a significant lowering of diffusion coefficient in bulk Lix TiO2 -B above a Li content of x = 0.7. Lithiation of TiO2 -B has also been studied extensively using density functional theory (DFT). Armstrong et al. 15 have calculated voltage versus Li content from x = 0.00 to 0.75 and found a qualitative agreement with the experimental measurements. Furthermore, Van der Ven et al. 16 have carried out a couple cluster Monte Carlo simulation and extracted phase diagram and voltage curve for Lix TiO2 -B. Their voltage curve is qualitatively similar to that of Armstrong et al. 15 for x = 0.00 to 0.75. However, they found that bulk Lix TiO2 -B structures with Li contents from x = 0.75 to 1.25 are thermodynamically favorable, but voltage drops to 0.6 V at the highest Li content. These results indicate that discharge capacities higher than 251 mAhg−1 are thermodynamically possible in bulk TiO2 -B. On the other hand, Arrouvel et al. 17 have calculated different possible pathways and their energy 2


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barriers for Li transport at a low Li-content (x = 0.125) and found a low barrier of ∼0.30 eV for Li diffusion along the most favorable pathway. In the present work, we study Li diffusion in TiO2 -B and show how a Li-content dependence of lithation process controls the discharge capacity of TiO2 -B of different sizes.

Method Most of the DFT calculations were performed using the SeqQuest code 18 with localized basis sets represented by linear combinations of contracted Gaussian functions (double-zeta plus polarization), norm-conserving pseudopotentials, and the generalized gradient approximation (GGA) exchange-correlation (XC) functional proposed by Perdew, Burke, and Ernzerhof (PBE). 19 Bulk Lix TiO2 -B structures were modelled by 1×2×2 super cells with 2×3×2 kpoint meshes. The diffusion pathways were calculated with the Nudge Elastic Band (NEB) method. To study the influence of XC functional on our results we recalculated the diffusion barriers of the most favorable pathways (determined with PBE) using PBE+U implemented in the VASP code. 20 We used an energy cutoff of 450 eV and the same unit cell size and k-point mesh as the SeqQuest calculations.

Results and Discussions There are three different types of interstitial sites for Li insertion in TiO2 -B: the so-called A1, A2, and C sites (see Fig. 1). 15–17,21 To model a low-coverage regime we consider Li0.032 TiO2 B (1 Li in a 1×2×2 unit cell, capacity of 10.72 mAhg−1 ). Our GGA-PBE calculations for Li0.032 TiO2 -B, in agreement with previous GGA-PBE calculations for x = 0.125 by Morgan et al., 21 shows the following order of binding energy for Li in TiO2 -B: C (–1.90 eV) < A1 (–1.92 eV) < A2 (–2.00 eV). The corresponding values of equilibrium voltages with respect to Li metal are 1.90 V, 1.92 V, and 2.00 V (approximated by total energy values). Gale et al. 22 have also reported that the A2 site is the most favorable site, but they found that 3



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Figure 1: Structure of TiO2 -B (1×2×2 unit cell) and possible insertion sites, namely A1, A2, C. For Li contents higher than x = 0.25, after geometry optimization Li atoms move from C sites to nearby C′ cites. Li is more stable at the C site than at the A1 site.

Afterwards, we studied Li diffusion

in Li0.032 TiO2 -B by considering the following pathways (see Fig. 2): (I) Li hopping along c (perpendicular to the channel direction), (II) Li hopping along a (perpendicular to the channel direction), (III) Li hopping along b (along the channel direction). Pathway I consists

Figure 2: Atomic structures and energy profiles for different studied Li-insertion pathways in Li0.032 TiO2 B (1 Li in a 1×2×2 unit cell corresponding to a capacity of 10.72 mAhg−1 ). The positions of Li atoms in intermediate and transition states are in purple and grey, respectively. 4


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Figure 3: Atomic structures and energy profiles for different studied Li-insertion pathways in Lix TiO2 -B with 0.25 < x ≤ 1.00 via scenario one (left panel). Positions of Li atoms in intermediate and transition states are in purple and grey, respectively. Schematic of gradual lithation of Lix TiO2 -B is also presented (right pannel). of –A1–A1–C–A1– hops with energy barriers of 0.26 eV (A1→A1), 0.23 eV (A1→C), and 0.30 eV (C→A1), which are in fair agreement with DFT-PW91 calculations by Arrouvel et al.: 17 ≈0.38 eV, ≈ 0.18 eV, ≈ 0.30 eV, respectively. Pathway II consists of –A2–A2–C– jumps with energy barriers of 0.76 eV (A2→A2) and 0.06 eV (A2→C). The DFT-PW91 calculations by Arrouvel et al. 17 have reported diffusion barriers of ≈ 1.1 eV and ≈ 0.06 eV for the first and second jumps. The reason of finding lower energy barrier in our work is related to a larger number of images (14 images) we used in our calculations compared to the Arrouvel et al. study (7 images). Pathway III consists of –C–C–C– hops with an energy barrier of 0.22 eV, which is again in agreement with the value of ≈ 0.25 eV reported by Arrouvel et al.. 17 Diffusion barriers calculated in the present work and those calculated by Arrouvel et al. 17 are also qualitatively in agreement with GGA-PBE results by Gale et. al.. 22 We reference energy profiles of pathways I–III with respect to the energy of the 5



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most stable structure in which a A2 site is occupied. Considering this reference we still find that the lowest energy barrier for Li diffusion is 0.32 eV for pathway III. The present work and previous theoretical investigations 17,22 show that Li diffusion in Lix TiO2 -B with a low Li content is direction dependent. We are not aware of any experimental study reporting values of diffusion barrier of Li along different directions that can be compared with our theoretical diffusion barriers. Experimental values of overall diffusion barriers for TiO2 -B are 0.48 eV 13 and 0.56 eV. 23 The diffusion barriers calculated in Fig. 2 are relevant for all Li contents of x ≤ 0.25 since Li atoms can diffuse independently along pathway III (b direction) in two separate channels. However, for Li contents higher than x = 0.25 Li–Li interactions start to play role. The separation between two A2 sites at each channel is shorter (by 1.48˚ A) than the A1–A1 separation. Therefore, in a channel occupation of two A1 sites is energetically more favorable than that of two A2 sites. The calculated energy of Li0.5 TiO2 -B (capacity of 167.5 mAhg−1 ) with Li atoms at 4A1 sites is 0.22 eV (per unit cell) more favorable than with Li atoms at 4A2 sites. The more stability of occupation of 4A1 sites than that of 4A2 sites in Li0.5 TiO2 -B has been also reported by Van der Ven et al.. 16 Since diffusion barriers (i.e. diffusion coefficients) for 0.25 < x depend strongly on whether pre-inserted Li atoms are at A1 or A2 sites, we consider two scenarios to study lithiation of TiO2 -B for 0.25 < x ≤ 1.00: the Li transport occurs along pathway III but insertion of Li takes place to (1) A1 or (2) A2 sites. Before discussing these scenarios we should mention that in both cases, pre-inserted Li atoms at A1 or A2 sites push nearby Li atoms at C sites to interstitial sites between two O atoms (hereafter called C′ ). This causes that zigzag like hops between C′ and A1 or C′ and A2 sites become possible. Scenario 1 To find the minimum energy pathway for 0.25 < x ≤ 0.50 (see Fig. 3) we consider zigzag –C′ –A1–C′ – hops (pathway IV) and –C′ –A2–C′ – hops (pathway V) besides the simple –C′ –C′ –C′ – hops (pathway III). The –C′ –C′ –C′ – jumps have curved paths because of repulsion of diffusion Li with pre-inserted Li at A1 sites. Although the calculated value of

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Figure 4: Atomic structures and energy profiles for different studied Li-insertion pathways in Lix TiO2 -B with 0.25 < x ≤ 1.00 via scenario two (left panel). Positions of Li atoms in intermediate and transition states are in purple and grey, respectively. Schematic of gradual lithation of Lix TiO2 -B is also presented (right pannel). ∆Eb for the pathway III is 0.18 eV lower than that of pathway IV, the site energy is 0.25 eV less favorable in the former case. Therefore, the most favorable pathway for 0.25 < x ≤ 0.50 is pathway IV with a ∆Eb of 0.34 eV. The same pathway and diffusion barrier is also expected for the forth Li diffusing along pathway III in the other channel. After occupation of all four A1 sites, insertion of Li atoms to A2 sites starts for 0.50 < x. Besides pathway III, we consider the zigzag pathway V. Because of occupation of all A1 sites pathway IV is not possible. Due to the Li–Li repulsion between diffusing Li and pre-inserted Li at A1 sites ∆Eb values for 0.50 < x ≤ 0.75 are higher than those for 0.25 < x ≤ 0.50. The lowest value of ∆Eb in the former case is calculated to be 0.47 eV for pathway III. After occupation of one of A2 sites of each channel, besides the occupation of all A1 sites, ∆Eb for Li diffusion along the channel is significantly higher than lower Li content cases. The lowest diffusion barrier for 0.75 < x ≤ 1.00 is along the pathway V with ∆Eb = 0.83 eV. 7



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Figure 5: Atomic structure and energy profile for lithiation of Lix TiO2 -B with 1.00 < x < 1.25 (left panel). Positions of Li atoms in intermediate and transition states are in purple and grey, respectively. Schematic of gradual lithiation of Lix TiO2 -B is also presented (right pannel). Scenario 2 To find the minimum energy pathway for 0.25 < x ≤ 0.50 (see Fig. 4) we consider pathways III, IV, and V similar to the scenario 1. Considering site energies and diffusion barriers, the pathway V has the lowest value of ∆Eb = 0.50 eV, which is 0.16 eV higher than that of the same Li content in scenario 1. This result is because of stronger Li–Li repulsion between diffusing Li with pre-inserted Li at A2 sites compared to those at A1 sites. This is due to the fact that the A2–A2 separation is 1.48 ˚ A shorter than the A1– A1 separation (considering theoretical lattice parameters). For this reason diffusion barriers (∆Eb = 0.77 eV) are high after both A2 sites of each channel are occupied by Li atoms (0.50 < x ≤ 0.75). For 0.75 < x ≤ 1.00, diffusing Li atoms along the –C′ –C′ – pathway interact with two Li atoms at two A2 sites and one Li atom at one A1 site at each channel and therefore the value of ∆Eb = 1.03 eV is very high. However, zigzag –C′ –A1–C′ – hops have smaller repulsion with pre-inserted Li atoms and therefore the diffusion barrier along the pathway IV (∆Eb = 0.81 eV) is comparable to ∆Eb of pathway IV for 0.50 < x ≤ 0.75. A comparison between scenario 1 and 2 shows that scenario 1 is kinetically more favorable than scenario 2. Moreover, a recent experimental study shows that diffusion coefficient, which depends strongly on the activation energy, decreases above x = 0.7, 14 which again confirms scenario 1 is more probable. From thermodynamics point of view, scenario 1 is more favorable than scenario 2 for 0.25 < x ≤ 0.50 since the total energy of Lix TiO2 -B 8


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Figure 6: Maximum length of diffusion of Li in Lix TiO2 -B for x < 0.75 (capacity < 251 mAhg−1 ), 0.75 < x ≤ 1.00 (251 mAhg−1 < capacity ≤ 335 mAhg−1 ) and 1.0 < x (335 mAhg−1 < capacity) as function of C-rate. (a) with PBE functional as well as atomic coordinates and unit cells optimization, (b) with PBE functional and only atomic coordinates optimization, (c) with PBE+U functional as well as atomic coordinates and unit cells optimization. with Li atoms at 4A1 sites is more favorable than that with Li atoms at 4A2 sites. For Li contents of 0.50 < x ≤ 0.875 we have explored the following arrangement of Li insertions: 4A2+2A1, 4A1+2A2, 4A2+2C′ , and 4A1+2C′ . It was found that the first configuration is most favorable. Our calculations (using 1×2×2 unit cell) show that 4A2+2A1 is 0.20 eV more favorable than 4A2+2C′ which has been reported by Van der Ven et al. 16 (using 1×1×1 unit cell) to be the most favorable arrangement for x = 0.75. Therefore, the scenario 2 is expected to be thermodynamically more favorable than the scenario 1 for Li contents of 0.50 < x ≤ 0.875. After occupation of all A1 and A2 sites, further lithiation of Li1.00 TiO2 -B occurs via –C′ –C′ –C′ – hops (pathway III). As can be seen from Fig. 5 the calculated diffusion barrier for this case is around 2.03 eV. Therefore, further lithiation of Li1.00 TiO2 -B is kinetically very unfavorable. A previous study by Arrouvel et al. 17 shows that the most favorable Li insertion and barrier sites for Li0.125 TiO2 -B have the largest mean Li–Ti distances. We also find that average binding energies of Li in the Li0.25 TiO2 -B, Li0.50 TiO2 -B, and Li0.75 TiO2 -B structures with the longest mean Li–Ti separations are strongest. In the most favorable structure of

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Li1.00 TiO2 -B, the mean Li-Ti separation is not largest , but the mean Li–Li separation is largest. Afterwards, we estimated (1D diffusion approximation) diffusion coefficients for different Li contents using 1 ∆Eb D ≈ νl2 exp(− ). 2 kB T

(1)

Here l, ∆Eb , and T are the distance between interstitial sites, diffusion barrier of Li hopping, and temperature (T =300 K), respectively. In eq. 1, ν is the frequency of a successful jump between interstitial sites (i.e. jump frequency), which was calculated using harmonic transition state theory approximation: 3N Q

ν=

νiG

i 3N Q−1

,

(2)

νiT

i

where, νiG and νiT are all real vibrational frequencies of the ground and transition state, respectively. Calculated (maximum) values of D are 3.03×10−10 cm2 /s (∆Eb = 0.47 eV), 1.26×10−16 cm2 /s (∆Eb = 0.83 eV), and 1.15×10−36 cm2 /s (∆Eb = 2.03 eV) for Li contents of 0.50 < x ≤ 0.75, 0.75 < x ≤ 1.00, 1.00 < x < 1.25, respectively. We estimate the maximum (1D) diffusion length in Lix TiO2 -B for a given time t using

L≈

√

2Dt.

(3)

Calculated values of L as function of C-rate (hC rate means that a discharge current will discharge the battery in 1/h hour) for different Li contents is illustrated in Fig. 6. We find three orders of magnitude difference in the calculated L for Lithiation of x ≤ 0.75 and 0.75 < x ≤ 1.00. The calculated value of D for 1.00 < x < 1.25 is 20 orders of 10


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magnitude smaller than that for 0.75 < x ≤ 1.00. In the following, we compare our results to experimental findings. The measured discharge curves by Bruce et al et al. 10 for TiO2 -B nanowires of 20-40 nm diameter using a C-rate of 0.2C shows a maximum capacity of 305 mAhg−1 (x = 0.91). Figure 6 indicates that with this C-rate a maximum size of L ∼10 nm can attain a Li capacity higher than 251 mAhg−1 (x = 0.75). With this C-rate only Li contents smaller than x = 0.75 can be achieved for L=1 µm (bulk-like). Figure 6 also shows that with 0.1C ≤ C-rate ≤ 10C, which are typically used to test rate capability of Li-ion battery electrodes, only nanometer-size TiO2 -B can reach capacities higher than 251 mAh g−1 . This is because of shorter diffusion length in nanostructures. Moreover, we find that formation of Lix TiO2 -B with Li contents of 1.00 < x < 1.25 is kinetically impossible for any reasonable values of C-rates. Therefore, the low capacity of bulk TiO2 -B is due to kinetics limitation, which is in line with experimental proposals. 8,14,15,23,24 The values reported in Fig. 6(a) are for structures with fully optimized atomic coordinates and unit cells. To investigate the influence of unit cell optimization on our results we have recalculated diffusion barriers of the most favorable pathways in Fig. 6(a) by performing only atomic coordinate optimization. Table 1 shows the comparison between energy barriers of the rate limiting steps. We find that without unit cell optimization the barriers are higher in Lix TiO2 with 0.5 < x ≤ 0.75 and 0.75 < x ≤ 1.00. The reason is that the lattice vectors a and c, which are perpendicular to the direction of Li diffusion, are shorter in these lithiated structures than in pristine TiO2 -B (see Tab. 1). However, in Lix TiO2 with 1.00 < x ≤ 1.25 calculated diffusion barrier without cell optimization is the same as that with cell optimization. This is because although the length of vector c is shorter in this structure, vector a is longer in comparison to that in pristine TiO2 . We have also recalculated Fig. 6(a) for Lix TiO2 without cell optimization (see Fig. 6(b)). It is found that the values of L become larger at most by a factor of 6, if unit cell opimization is not carried out. To study the influence of choosing exchange-correlation functional on our results we have recalculated Fig. 6(a) using GGA+U with U=4.2 eV according to the previous study by

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Table 1: Diffusion barriers of the rate limiting steps of Li diffusion in Lix TiO2 for different concentrations of Li (x) calculated using atomic coordinates and unit cells optimization with PBE (∆Eb ) and PBE+U (∆Eb′ ) as well as using only atomic coordinates optimization with PBE (∆Eb′′ ). Changes (in percentage) in the lattice parameters (∆a and ∆b) of TiO2 induced by Li insertion (with PBE) are also listed. concentration ∆Eb ∆Eb′ ∆Eb′′ ∆a ∆c

0.5 < x ≤ 0.75 0.47 0.66 0.35 –2.80 –2.25

0.75 < x ≤ 1.00 0.83 1.04 0.78 –0.72 –1.73

1.00 < x ≤ 1.25 2.00 2.28 2.00 0.58 –1.77

Morgan et al.. 21 We find that the barriers are 0.19–0.28 eV higher with GGA+U than those calculated with PBE (see Tab. 1). This result is in line with previous study by Moradabadi et al. 25 showing higher diffusion barriers for Li diffusion in LiCoO2 with PBE+U compared to PBE, which is due to the accompanied polaron (created by donated electron from Li to nearby Ti cations) hopping with Li diffusion. Because of the larger diffusion barriers, we find that maximum lengths of diffusion of Li become shorter with PBE+U (see Fig. 6 (c)) compared to those with PBE (see Fig. 6 (a)). Since PBE diffusion barriers are mainly due to the ionic diffusion and since these barriers are larger than polaron hopping barriers, the PBE results are in better agreement with experimental findings.

Conclusions In this work, we have calculated diffusion pathways, energy barriers, and diffusion coefficients for Li insertion in Lix TiO2 -B (0.00 < x < 1.25). For low Li contents of x ≤ 0.032 where Li–Li interaction is negligible, diffusion pathways along b and c are both possible. However, for larger Li contents only lithiation along b is favorable. Diffusion barriers (∆Eb ) were calculated to be between 0.31 and 0.47 eV for Li contents up to x = 0.75, but they become almost two times larger for 0.75 ≤ x ≤ 1.00. For high Li contents of 1.00 < x the calculated value of ∆Eb is 2.03 eV. By evaluating diffusion coefficients for different Li contents and

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thereby estimating maximum diffusion length as function of C-rate we find that Li capacity of Lix TiO2 -B is size-dependent. Our calculations, in agreement with experimental measurements, show that the maximum capacity that can be achieved for micometer-sized TiO2 -B (bulk form) is less than 251 mAh g−1 . This result is due to the large repulsion between preinserted Li atoms in O layers with diffusing Li atoms along the channel for Li contents above x =0.75. Therefore, the origin of low Li capacity of bulk TiO2 -B is kinetics limitation. The results of this work show that Li-content dependence of Li diffusion in electrode materials can strongly control Li capacity of Li-ion batteries. Acknowledgments Q. Z. and P.K. gratefully acknowledge supports from the ”China Scholarship Council” and ”Bundesministerium f¨ ur Bildung und Forschung” (BMBF). The authors also acknowledge the North-German Supercomputing Alliance (HLRN) and Zentraleinrichtung f¨ ur Datenverarbeitung (ZEDAT) at the Freie Universit¨at Berlin for providing HPC resources.

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14. Hoshina, K.; Harada, Y.; Inagaki, H.; Takami, N. Characterization of Lithium Storage in TiO2 (B) by 6 Li-NMR and X-Ray Diffraction Analysis. J. Electrochem. Soc. 2014, 161, A348-A354. 15. Armstrong, A. R.; Arrouvel, C.; Gentili, V.; Parker, S. C.; Islam, M. S.; Bruce, P. G. Lithium Coordination Sites in Lix TiO2 (B): A Structural and Computational Study. Chem. Mater. 2010, 22, 6426-6432. 16. Dalton, A. S.; Belak, A. A.; Van der Ven, A. Thermodynamics of Lithium in TiO2 (B) from First Principles. Chem. Mater. 2012, 24, 1568-1574. 17. Arrouvel, C.; Parker, S. C.; Islam, M. S. Lithium Insertion and Transport in the TiO2 -B Anode Material: A Computational Study. Chem. Mater. 2009, 21, 4778-4783. 18. http://dft.sandia.gov/Quest/ (accessed Jan 01, 2016). 19. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. 20. Kresse, G.; Furthm¨ uller, J. Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169-11186. 21. Morgan, B. J.; Madden, P. A. Lithium Intercalation into TiO2 (B): A Comparison of LDA, GGA, and GGA+U Density Functional Calculations. Phys. Rev. B 2012, 86, 035147(1)-035147(13). 22. Panduwinata, D.; Gale, J. D. A First Principles Investigation of Lithium Intercalation in TiO2 -B. J. Mater. Chem. 2009, 19, 3931-3940. 23. Lyness, C.; Armstrong, A. R.; Bruce, P. G. Li Diffusion Properties of Mixed Conducting TiO2 -B Nanowires. Phys, Rev. B 2009, 80, 064302(1)-064302(8).

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24. Zhang, Z.-H.; Zhou, Z.-F.; Nie, S.; Wang, H.-H.; Peng, H.-R.; Li, G.-C.; Chen, K.Z. Flower-Like Hydrogenated TiO2 (B) Nanostructures as Anode Materials for HighPerformance Lithium Ion Batteries. J. Power Sources 2014, 267, 388-393. 25. Moradabadi, A.; Kaghazchi, P. Mechanism of Li Intercalation/Deintercalation into/from the Surface of LiCoO2 . Phys. Chem. Chem. Phys. 2015, 17, 22917-22922.

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Table of Contents: Lithiation of TiO2 -B is studied using DFT calculations. It is found that energy barrier of Li diffusion increases with Li concentration. For this reason, Li capacity is lower for larger sizes of TiO2 -B.

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227x104mm (54 x 54 DPI)


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Strong Li-Content Dependence of Li Diffusivity in TiO2-B - The Journal

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