Lithium Diffusion Pathways in β-Li2TiO3: A Theoretical Study - The

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Lithium Diffusion Pathways in β‑Li2TiO3: A Theoretical Study Mazharul M. Islam* and Thomas Bredow Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Beringstr. 4-6, D-53115 Bonn, Germany S Supporting Information *

ABSTRACT: In recent experimental studies based on NMR techniques, the ion dynamics in β-Li2TiO3 has been discussed controversially. In order to shed light on this discussion, Li ion diffusion processes in β-Li2TiO3 are investigated theoretically using periodic quantum−chemical DFT methods. It is observed that Li+ migrates along the ab plane as well as in the direction perpendicular to the LiTi2 layers with the activation energies ranging between 0.44 and 0.54 eV, suggesting a slow ion dynamics. In addition, the structural, electronic, and defect properties and the electric field gradient (EFG) parameters at Li positions of βLi2TiO3 are calculated. According to our results, β-Li2TiO3 is a wide gap insulator with an indirect band gap at Γ−C. The calculated defect formation energy values as well as the EFG parameters show that there are three different Li sites in the structure, namely, Li(1), Li(2), and Li(3), which are in well accord with the experiment. frequencies.8,15 Diffuse reflectance spectroscopic measurements11 predict that β-Li2TiO3 is a wide gap insulator with an optical band gap Eg of 3.9 eV. The investigation on point defects and nonstoichiometry of β-Li2TiO313 shows that cation vacancies predominate under standard conditions. Our study is motivated by the discussion that arose from two recent NMR measurements for Li ion dynamics by Ruprecht et al.8 and Vijayakumar et al.9 According to Ruprecht et al., Li diffusion in β-Li2TiO3 is extremely slow with activation energies ranging from 0.47 to 0.80 eV.8 This finding is consistent with the activation energies (0.6−0.9 eV) obtained with dcconductivity measurements.16 On the other hand, in a combined molecular dynamics simulation and NMR measurement study, Vijayakumar et al.9 obtained a much smaller activation energy (0.27 eV) for Li diffusion in β-Li2TiO3. This small activation energy with respect to the other studies was attributed to impurities and deviation from ideal stoichiometry.8,9 In this study, a theoretical investigation of bulk properties for β-Li2TiO3, such as lattice parameters, bond distances, and the electronic structure, is presented. The formation of Li vacancies and the EFG parameters such as EFG tensors, asymmetry parameters, and quadrupole frequency are investigated in order to identify and characterize the inequivalent Li sites observed in experimental studies. Various possible migration pathways for Li+ ion diffusion via vacacny sites are studied using firstprinciples methods and periodic supercell models. The effect of nonstoichiometry on the calculated activation energies is investigated by considering oxygen vacacncies in the diffusion mechanisms.

1. INTRODUCTION In recent years, lithium metatitanate (Li2TiO3) has attracted considerable attention due to its practical industrial applications, especially in the fields of energy production, energy conversion, and energy storage. Because of its good thermal stability and fast tritium release performance, Li2TiO3 is considered as a promising candidate for tritium breeding materials in nuclear fusion reactors.1,2 In the field of fuel cells, Li2TiO3 is used in a double-layer cathode material for molten carbonate fuel cells.3,4 In the field of rechargebale Li ion batteries, Li2TiO3 has been successfully used as a stabilizer for the high capacity cathode materials.5 At low temperature (LT), Li2TiO3 crystallizes in the Li2SnO3-type β-Li2TiO3 structure with the space group C2/c (No. 15, Z = 8).6,7 It consists of alternating LiTi2 layers and pure Li layers.7 This phase has been investigated in previous experimental studies of Li diffusion8,9 and is therefore the subject of the present study. The experimental lattice parameters of β-Li2TiO3 are a = 5.062 Å, b = 8.788 Å, c = 9.753 Å, and β = 100.212°.7 The structure,6,7 energetics,10 electronic properties,11 and defect properties12−14 of β-Li2TiO3 have been intensively invesitgated in the recent past. Both the Li and Ti cations reside in octahedral sites in β-Li2TiO3.6,7 According to the refined structure data,7 there are three crystallographically inequivalent Li positions, namely, Li(1), Li(2), and Li(3), occupying 8f, 4d, and 4e Wyckoff sites, respectively, and two inequivalent Ti positions Ti(1) and Ti(2) on 4e sites. The Ti and Li(3) cations share together the 4e position in the LiTi2 layers, and a pure Li layer is fully occupied by Li(1) and Li(2) as shown in Figure 1(a). Experimental investigations by 7Li NMR spectroscopy revealed that there are magnetically inequivalent Li sites characterized by individual (site-specific) NMR resonance © XXXX American Chemical Society

Received: March 13, 2016

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DOI: 10.1021/acs.jpcc.6b02613 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

The PBE approach was used as implemented in the planewave program VASP.30,31 The projector-augmented wave (PAW) method was used for the core−electron representation.32,33 After preliminary convergence tests, we used a cutoff energy Ecut = 520 eV for the valence basis set. In both programs the integration in reciprocal space was performed with 4 × 4 × 4 Monkhorst−Pack grids.34 It was checked that the k-point density is sufficient for an energy convergence smaller than 1 meV. The defective structures were simulated with a series of supercells with increasing size, Li8Ti4O12, Li16Ti8O24, and Li64Ti32O96 supercells, in order to investigate the effect of long-range interactions on the calculated activation barriers. The transition-state search for the migration processes was conducted with the climbing-image nudged-elastic-band (cNEB) method35 and VASP-PBE. Vibrational analysis calculations were performed to verify the true local-minimum or saddle-point character of the optimized geometries.

3. RESULTS AND DISCUSSION 3.1. Bulk Properties of Stoichiometric β-Li2TiO3. The calculated bulk properties of stoichiometric β-Li2TiO3 such as optimized lattice parameters, bond distances, and band gap Eg are compared with the available experimental data in Table 1. Table 1. Comparison of Calculated Lattice Parameters a, b, c (Å) and β (deg), Bond Distances (Å), and Band Gap Eg (eV) with Available Experimental Data

a

Figure 1. (a) 2 × 4 × 2 supercell of β-Li2TiO3 where the blue, red, and violet spheres represent Ti, O, and Li atoms, respectively. (b) Band structure and (c) density of states of stoichiometric β-Li2TiO3, obtained with PW1PW approach. 0 eV denotes the Fermi energy level.

lattice parameters

PW1PW

PBE

exptla,b

a b c β bond distances Li(1)−O Li(2)−O Li(3)−O Ti(1)−O Ti(2)−O Eg

5.05 8.77 9.73 100.2

5.10 8.85 9.83 100.2

5.06 8.79 9.75 100.212

2.096 2.135 2.110 1.960 1.960 5.16

2.094 2.148 2.126 1.976 1.977 3.20

2.141 2.139 2.114 1.963 1.963 3.90

Structural data.7 bOptical band gap.11

As observed in previous studies, the PW1PW method reproduces the best agreement with experimental lattice parameters with a deviation of 0.02 Å for a, b, and c and 0.003° for the β. The GGA-DFT approach PBE gives slightly overestimated lattice parameters compared to experiment with a maximum deviation of +0.08 Å for the c parameter. The deviation of β from the experiment is less than 0.012°. The calculated Li−O and Ti−O bond lengths are compared to measured values (Table 1). The average measured distances for Li(1)−O, Li(2)−O, Li(3)−O, and Ti−O octahedra are 2.141, 2.139, 2.114, and 1.963 Å, respectively.7 The deviation of the calculated bond distances from the measured values is smaller than 2.2% in all cases. The band structure was calculated along the path that contains the highest number of high-symmetry points of the Brillouin zone (Z → Γ → C → Y → M → Γ→ A → L → Z → Γ).36 According to our calculation, the valence band maximum (VBM) is located at Γ, whereas the conduction band minimum (CBM) is located at C (as shown in Figure 1(b)). Therefore, βLi2TiO3 has an indirect band gap (Eg) with a Γ → C transition.

2. COMPUTATIONAL METHODS The structural, electronic, and defect properties of β-Li2TiO3 are investigated with two complementary approaches. Periodic LCAO calculations performed with the hybrid functional PW1PW17 are compared with plane-wave-based PBE calculations,18,19 in order to investigate the functional and basis set dependence of the calculated properties, in particular for the band gap. The PW1PW approach was used in connection with the CRYSTAL program.20 We have used the following basis sets for the elements: 7-11G11d (9s2p2d/3s2p2d) on Li, 86411G31d (20s12p3d/5s4p2s) on Ti, and 8-411G1d (14s6p1d/ 4s3p1d) on O, which provided accurate results for structural, electronic, and defect properties of Li2O and TiO2 containing materials.21−29 B

DOI: 10.1021/acs.jpcc.6b02613 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C The calculated minimum vertical transition (MVT) and minimum indirect transition (MIT) energies are compiled in Table 2. The MIT energies (5.2 eV (PW1PW) and 3.2 eV

Table 3. Calculated Defect Formation Energy (DFE, eV), Asymmetry Parameter (η), and Quadrupole Frequency (νQ, kHz) in β-Li2TiO3

Table 2. Comparison of Calculated Minimum Vertical Transition (MVT) and Minimum Indirect Transition (MIT) Energy Values ΔE (eV) for β-Li2TiO3 MVT ΔE MIT ΔE

PW1PW

PBE

C−C 5.45 Γ−C 5.16

C−C 3.44 Γ−C 3.20

DFEa

quadrupole frequency

Li types

PW1PW

PBE

PBE

exptl15

PBE

exptl15

Li(1) Li(2) Li(3)

5.73 5.83 5.53

4.88 4.94 4.72

0.21 0.30 0.69

0.13 ± 0.05 0.33 ± 0.0 0.7 ± 0.3

40 67 11

27 ± 3 59 ± 6 6±1

a

Converged DFE values with Li16Ti8O24 supercell.

ion diffusion. In general Ede(Li) is slightly larger with PW1PW compared to PBE. This is in line with the previous findings for defect formation energy in Li2O,25,26 Li2O:B2O3 mixed compounds,21−23 and TiO2.29 Irrespective to the calculated methods applied, there are three slightly different Ede(Li) values, namely, 5.73, 5.83, and 5.53 eV with PW1PW and 4.88, 4.94, and 4.72 eV with PBE for Li(1), Li(2), and Li(3), respectively. This indicates that there are three energetically distinguishable Li sites in β-Li2TiO3. 3.3. Electric Field Gradient. In order to identify magnetically inequivalent Li sites characterized by 7Li NMR spectroscopy,8,15 the EFG parameters for β-Li2TiO3 are calculated using the VASP-PBE approach. First, the tensor components V of EFG are calculated. Then the asymmetry parameters η and quadrupole frequency νQ are calculated according to the folowing equations as discussed in ref 38.

(PBE)) are slightly smaller than the MVT energy values (5.5 eV (PW1PW) and 3.4 eV (PBE)). As expected, the Eg obtained with PW1PW is larger than that with PBE, mainly due to the well-known self-interaction error of GGA methods. Experimental diffuse reflectance spectra predict an optical 11 band gap (Eopt As stated by Baerends et al.,37 g ) of 3.9 eV. GGA-DFT gives a good account of the experimental Eopt g . MIT and MVT energies obtained from hybrid DFT rather correspond to photoelectron spectroscopy and cannot be directly compared to optical transitions. This was shown by us for rutile TiO2.29 There the Eg obtained with PW1PW (3.54 eV) is within the experimental range of the fundamental band gap (3.3−4.0 eV) and larger compared to the experimental value of the optical band gap (3.0 eV). Similarly, for Li2O,26 PW1PW (Eg = 7.95 eV) gave an almost perfect account of the experimental fundamental band gap (Eg = 7.99 eV), whereas the GGA-DFT approach gave a much smaller value (Eg = 5.80 eV). The density of states (DOS) of stoichiometric β-Li2TiO3 calculated with the PW1PW method is shown in Figure 1(c). The calculated valence bandwidth is about 5.0 eV which is in well accord with the experimental range of 5.0−5.5 eV.11 Similar to TiO2,11 the valence band (VB) is mainly composed of O 2p states with some hybridization with Ti 3d orbitals. The conduction band (CB) is composed of mainly Ti 3d states with small contribution from O 2p states. The contribution of Ti 3d states is several times higher than that of O 2p states. 3.2. Li Point Defect. In order to model the experimentally observed nonstoichiometry of β-Li2TiO3, one neutral Li atom was removed from the supercells Li8Ti4O12, Li16Ti8O24, and Li64Ti32O96. In this way the defect content was varied from 1/8 to 1/64, and the distances between a vacancy and its periodic image were systematically increased. A full relaxation of all atom positions was performed taking the optimized lattice parameters from the stoichiometric bulk optimization. The optimized fractional coordinates of the nondefective supercell were taken as starting structure for the defective system. The formation energy of a Li vacancy Ede(Li) is calculated according to the following equation Ede(Li) = ESCM(V) + E(Li) − ESCM

asymmetry parameter

η = (Vyy − Vxx)/Vzz

(2)

νQ = 3e 2qzzQ /2I(2I − 1)h × Vzz

(3)

Here Vxx, Vyy, and Vzz are elements of the traceless EFG tensor V; e is the proton charge: qzz corresponds to the largest principal component of the EFG, i.e., Vzz; I = 3/2 is the spin quantum number of 7Li; h is the Planck constant; and Q = −4.01 × 10−30 m2 is the electric qaudrupole moment of 7Li.39 The calculated η and νQ show three distinct values, 0.21, 0.30, and 0.69 for η and 40, 67, and 11 kHz for νQ, respectively (see Table 3). These findings confirm three magnetically inequivalent Li sites observed by 7Li NMR spectroscopy.8,15 The calculated EFG parameters are in good agreement with the experimental range.15 3.4. Li Migration Pathways. There are two possibilities for Li+ migration in β-Li2TiO3 (see Figure 2): (i) a direct Li exchange between Li(1) and Li(2) along the crystallographic ab plane (denoted as in-plane) and (ii) Li(1)−Li(3) or Li(2)− Li(3) hopping in the direction perpendicular to the LiTi2 layers (denoted as interplane). In the following, these two migration pathways are discussed applying a Li16Ti8O24 supercell. In-Plane Li Migration. In-plane Li diffusion occurs via direct Li hopping from the Li(1)O6 octahedral site to the nearest empty Li(2)O6 octahedral site and vice versa, as shown in Figure 3. In this case Li+ migrates via a transition state structure (TS) that corresponds to a distorted LiO6 octahedron (Li−O distance: 1.65 Å × 2, 2.6 Å × 2, and 2.7 Å × 2). The average Li−O distance of the TS (2.32 Å) is larger than those of Li(1)O6 (2.10 Å) and Li(2)O6 (2.14 Å). The calculated activation energy for the Li(1) → Li(2) migration process is 0.50 eV (Table 4), whereas for the backward Li hopping process (Li(2) → Li(1)), the activation energy is slightly reduced to 0.45 eV (Table 4). This discrepancy is associated

(1)

Here ESCM(V) and ESCM denote the total energy of the supercell model with and without vacancy, respectively, and E(Li) is the total energy of bulk lithium in a body-centered cubic phase. The calculated defect formation energies are given in Table 3. With both methods, the Ede(Li) values are converged within 0.04 eV with the medium-sized supercell (Li16Ti8O24); therefore this model was employed for further studies of Li C

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Figure 2. Local structure showing various migration pathways in βLi2TiO3. The blue, red, and pink spheres represent Ti, O, and Li atoms, respectively.

Figure 4. Local structures for the interplane Li+ migration. (a) The starting structure where Li(1) passes to the nearest Li(3) vacancy position. (b) The transition state where the Li is located in a tetrahedral interstitial (marked with green line) between Li(1) and Li(3). (c) The final structure showing the vacancy at Li(1). (d) The MEP for the diffusion of Li(1) to Li(3). The blue, red, pink, and yellow spheres represent Ti, O, and Li atoms and Li vacancy, respectively.

Comparing all these three exchange processes (Li(1)↔Li(2), Li(1)↔Li(3), and Li(2)↔Li(3)), we observe that with the smallest activation energy the Li(1)↔Li(3) and Li(2)↔Li(3) migration pathways are the most preferable pathways. Therefore, the interplane diffsuion process is the most likely mechanism in β-Li2TiO3. Our calculated activation energies for all considered migration pathways are in well accord with the experimentally measured range of 0.47−0.80 eV8 and 0.6−0.9 eV.16 At the same time, our results contradict the combined molecular dynamics and NMR study by Vijayakumar et al. where a much smaller activation energy (0.27 eV) was obtained.9 The molecular dynamics simulations were performed with a classical force field.9 Since the results obtained with this kind of approach strongly depend on the empirical parameters, it is possible that the selected parameter set has led to an underestimation of the barriers. On the other hand, the lowering of the measured activation energy could be due to the presence of impurities and deviation from ideal stoichiometry in the experiments. A recent analysis shows that β-Li2TiO3 may contain traces of many impurities such as Al, Ca, Cr, Fe, K, Ni, S, Si, Na, C, etc.40 The effect of these impurities on the cation diffusion in β-Li2TiO3 may therefore require a careful investigation which is not in the scope of the present study. However, in order to estimate the effect of nonstoichiometry which can be indirectly caused by doping with heterovalent atoms, we have considered the presence of an oxygen vacancy for the above-mentioned diffusion mechanisms. As for the Li vacancy (described in a previous part), a neutral oxygen atom was removed from the supercells. Since two electrons are formally left behind by removal of O2−, two Ti atoms are redued from 4+ to 3+ similar to titania.29 We therefore assumed a triplet state for the following calculations. The

Figure 3. Local structures for the Li+ migration along the ab plane. (a) The starting structure where Li(1) passes to the nearest Li(2) vacancy position. (b) The transition state where the Li is located in an octahedral interstitial (marked with green line) between Li(1) and Li(2). (c) The final structure showing the vacancy at Li(1). (d) The MEP for the diffusion of Li(1) to Li(2). The blue, red, pink, and yellow spheres represent Ti, O, and Li atoms and Li vacancy, respectively.

with the slight energetic difference between Li(1) and Li(2) sites. Interplane Li Migration. The interplane Li diffusion occurs via Li(1)↔Li(3) or Li(2)↔Li(3) hopping in the direction perpendicular to the LiTi2 layers (Figure 4). In this case, Li passes through a slightly distorted LiO4 tetrahedron (Li−O distance: 1.82 Å × 2 and 2.2 Å × 2). Our study shows that the calculated activation energy values for the forward Li(1)→Li(3) and Li(2)→Li(3) migration pathways range between 0.39 and 0.41 eV (Table 4), whereas the backward diffusion processes, i.e., Li(3)→Li(1) and Li(3)→Li(2), yield larger activation energy, namely, 0.53 and 0.54 eV, respectively (Table 4).

Table 4. Comparison of Calculated Activation Energy EA (eV) Values with Available Experimental Results for β-Li2TiO3 migration pathways

Li diffusion type

Calc.

Exp.

along ab plane along c direction

Li(1)→Li(2), Li(2)→Li(1) Li(1)→Li(3), Li(3)→Li(1) Li(2)→Li(3), Li(3)→Li(2)

0.45, 0.50 0.41, 0.53 0.39, 0.54

0.47−0.80,8 0.6−0.9,16 0.279

D

DOI: 10.1021/acs.jpcc.6b02613 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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(5) Zhang, L.; Wang, X.; Noguchi, H.; Yoshio, M.; Takada, K.; Sasaki, T. Electrochemical and ex situ XRD investigations on (1− x)LiNiO2.xLi2TiO3 (0.05 ≤ x ≤ 0.5. Electrochim. Acta 2004, 49, 3305−3311. (6) Dorrian, J.; Newnham, R. Refinement of the structure of Li2TiO3. Mater. Res. Bull. 1969, 4, 179−183. (7) Kataoka, K.; Takahashi, Y.; Kijima, N.; Nagai, H.; Akimoto, J.; Idemoto, Y.; Ohshima, K. Crystal growth and structure refinement of monoclinic Li2TiO3. Mater. Res. Bull. 2009, 44, 168−172. (8) Ruprecht, B.; Wilkening, M.; Uecker, R.; Heitjans, P. Extremely slow Li ion dynamics in monoclinic Li2TiO3-probing macroscopic jump diffusion via 7Li NMR stimulated echoes. Phys. Chem. Chem. Phys. 2012, 14, 11974−11980. (9) Vijayakumar, M.; Kerisit, S.; Yang, Z.; Graff, G. L.; Liu, J.; Sears, J. A.; Burton, S. D.; Rosso, K. M.; Hu, J. Combined 6,7Li NMR and Molecular Dynamics Study of Li Diffusion in Li2TiO3. J. Phys. Chem. C 2009, 113, 20108−20116. (10) Kleykamp, H. Enthalpy, heat capacity and enthalpy of transformation of Li2TiO3. J. Nucl. Mater. 2001, 295, 244−248. (11) Hosogi, Y.; Kato, H.; Kudo, A. Visible light response of AgLi1/3M2/3O2 (M = Ti and Sn) synthesized from layered Li2MO3 using molten AgNO3. J. Mater. Chem. 2008, 18, 647−653. (12) Murphy, S. T. Tritium Solubility in Li2TiO3 from FirstPrinciples Simulations. J. Phys. Chem. C 2014, 118, 29525−29532. (13) Murphy, S. T.; Hine, N. D. M. Point Defects and Nonstoichiometry in Li2TiO3. Chem. Mater. 2014, 26, 1629−1638. (14) Murphy, S. T.; Hine, N. D. M. Anisotropic charge screening and supercell size convergence of defect formation energies. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 094111. (15) Baklanova, Y. V.; Arapova, I. Y.; Shein, I. R.; Maksimova, L. G.; Mikhalev, K. N.; Denisova, T. A. Charge distribution and mobility of lithium ions in Li2TiO3 from 6,7Li NMR data. J. Struct. Chem. 2013, 54, 111−118. (16) Fehr, T.; Schmidbauer, E. Electrical conductivity of Li2TiO3 ceramics. Solid State Ionics 2007, 178, 35−41. (17) Bredow, T.; Gerson, A. R. Effect of exchange and correlation on bulk properties of MgO, NiO, and CoO. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 61, 5194−5201. (18) Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (19) Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple [Erratum Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78, 1396−1396. (20) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunell, M.; Causá, M.; Noël, Y. CRYSTAL14 User’s Manual; University of Torino: Torino. (21) Islam, M. M.; Bredow, T.; Heitjans, P. Formation and Mobility of Li Point Defects in LiBO2: A First-Principles Investigation. J. Phys. Chem. C 2011, 115, 12343−12349. (22) Islam, M. M.; Bredow, T.; Heitjans, P. The ionic conductivity in lithium-boron oxide materials and its relation to structural, electronic and defect properties: insights from theory. J. Phys.: Condens. Matter 2012, 24, 203201. (23) Islam, M. M.; Bredow, T.; Indris, S.; Heitjans, P. Enhanced Conductivity at the Interface of Li2O:B2O3 Nanocomposites: Atomistic Models. Phys. Rev. Lett. 2007, 99, 145502. (24) Maslyuk, V. V.; Islam, M. M.; Bredow, T. Electronic properties of compounds of the Li2O-B2O3 system. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 125101. (25) Islam, M. M.; Bredow, T. Density Functional Theory Study for the Stability and Ionic Conductivity of Li2O Surfaces. J. Phys. Chem. C 2009, 113, 672−676. (26) Islam, M. M.; Bredow, T.; Minot, C. Theoretical Analysis of Structural, Energetic, Electronic, and Defect Properties of Li2O. J. Phys. Chem. B 2006, 110, 9413−9420. (27) Islam, M. M.; Bredow, T. Rutile Band-Gap States Induced by Doping with Manganese in Various Oxidation States. J. Phys. Chem. C 2015, 119, 5534−5541.

calculated activation energy for the forward duiffusion between Li(1) and Li(2) decreases from 0.50 to 0.34 eV due to the presence of an oxygen vacancy in the structure. Similarly, the activation energies for the Li(3)→Li(2) diffusion process have reduced from 0.54 to 0.37 eV. A detailed investigation on the effect of impurities and nonstoichiometry on Li diffusion in βLi2TiO3 is underway.

4. CONCLUSIONS We have investigated the structure, electronic properties, defect properties, EFG parameters, possible migration pathways, and activation barriers in β-Li2TiO3 using first-principles density functional theory (DFT) methods and periodic supercell models. According to our calculated DFE and EFG parameters, we conclude that there are three energetically as well as magnetically inequivalent Li sites in β-Li2TiO3. Our investigation shows that there are two likely migration pathways for Li diffusion in β-Li2TiO3. These are direct Li(1)− Li(2) exchange along the crystallographic ab plane and interplane Li hopping between Li(1) and Li(3) or Li(2) and Li(3). Our calculated activation energies for these migration pathways range between 0.40 and 0.54 eV, which are in well accord with the experimental values of Ruprecht et al. An oxygen vacancy, which might be present due to impurities in real samples, reduces the activation energy significantly by 0.16−0.17 eV.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b02613. Local structures showing the images of Li(1)→Li(3) migration pathway in Figure S1 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49-(0)228732254. Fax: +49-(0)228-739064. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M. M. I. is grateful to Deutschen Forschungsgemeinschaft (DFG) for the postdoctorate funding within DFG-Forschergruppe 1277 molife Mobilität von Li-Ionen in Festkörpern.

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REFERENCES

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DOI: 10.1021/acs.jpcc.6b02613 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.6b02613 J. Phys. Chem. C XXXX, XXX, XXX−XXX