Transport Properties of Nanostructured Li2TiO3 Anode Material Synthesized by Hydrothermal Method

Li2TiO3 nanopowders were synthesized by hydrothermal process using anatase TiO2 and LiOH·H2O as raw materials. Li2TiO3 crystallizes in the layered monoclinic structure (space group C2/c) with average crystallite size of 34 nm. Morphology, elemental composition and local structure of products were carried out using high-resolution transmission electron microscopy, field-emission scanning electron microscopy, Raman and Fourier transform infrared spectroscopy. Transport properties investigated by d.c. (4-probe measurements) and a.c. (complex impedance spectroscopy) show the activation energy of 0.71 and 0.65 eV, respectively. The ionic transport properties of Li+ ions in nanocrystalline Li2TiO3 characterized by cyclic voltammetry and impedance spectroscopy validate the good electrochemical properties of this anode material for lithium-ion batteries.

Various synthesis methods have been reported to grow nanocrystalline Li2TiO3.Conventional solid-state synthesis reaction was used to produce Li2TiO3 with the mixture of Li2CO3 and TiO2 at 900-1100 °C for 10 h to several days [21,[24][25][26].Other preparation methods such as wet-chemical methods include sol-gel technique [27], combustion method [28,29], polymer solution synthesis [30], ball milling [31,32] and extrusion-spheronisation sintering [33] that involve at least one high temperature step (over 900 °C) to obtain a well-crystallized Li2TiO3 phase (named LTO hereafter).To the best of our knowledge, only few reports are available on hydrothermal synthesis of Li2TiO3 using microsized TiO2 powder as raw material [17].Uniform nano-Li2TiO3 powder particles were prepared via a cetyltrimethyl-ammonium bromide (CTAB)-assisted hydrothermal method [34].Unlike many synthesis methods, the hydrothermal method allows the control of shape and size of the particles by control of the rate of precipitation of the crystallized powders directly from the solution, the uniformity of nucleation, growth and aging.Expensive surfactants or template are not necessary in this method.Thus, hydrothermal synthesis is a suitable method to produce large scale crystals with high quality at a reasonable price [35].
However, β-Li2TiO3 is a wide gap semiconductor with an indirect band gap at Γ-C (Eg ≈ 3.9 eV) with low electrical conductivity of 10 −11 S cm −1 at room temperature [35][36][37] and it was considered as a material with electrochemical inactiveness similarly to the rock-salt Li2MnO3 [38].However, synthesis of nanocrystalline LTO, under the form of nanoparticles, nanorods, nanoflowers and nanofibers, provides more active surface area and shorter diffusion paths for Li + ions in the structure, which makes the material electrochemically active and improves the rate capability [39,40].Several attempts on Li2TiO3-based composites as cathode or anode materials were reported considering the merits of lithium metatitanate, namely its excellent structural stability and improved electrochemical performance for Li-ion batteries [41][42][43][44][45][46][47].The Si/LTO nanocomposite synthesized by sol-gel process as an anode material exhibited a specific capacity of 471 mAh g −1 even after 50 cycles.In this nanocomposite, the structural stability is due to Li2TiO3, which acts as excellent buffer to the Si powders and partly compensate the capacity loss [44].The composite 0.55Li2TiO3-0.45LiCrO2prepared by spray pyrolysis exhibits the highest initial discharge capacity of 203 mAh g −1 [45].Due to its three-dimensional (3D) path for Li + -ion migration and its excellent structural stability, LTO has The crystal structure of β-phase Li 2 TiO 3 was first determined by Lang [18] and subsequently refined by Kataoka et al. [19].It can be described by the chemical formula Li  2) ions [22,23].
Various synthesis methods have been reported to grow nanocrystalline Li 2 TiO 3 .Conventional solid-state synthesis reaction was used to produce Li 2 TiO 3 with the mixture of Li 2 CO 3 and TiO 2 at 900-1100 • C for 10 h to several days [21,[24][25][26].Other preparation methods such as wet-chemical methods include sol-gel technique [27], combustion method [28,29], polymer solution synthesis [30], ball milling [31,32] and extrusion-spheronisation sintering [33] that involve at least one high temperature step (over 900 • C) to obtain a well-crystallized Li 2 TiO 3 phase (named LTO hereafter).To the best of our knowledge, only few reports are available on hydrothermal synthesis of Li 2 TiO 3 using microsized TiO 2 powder as raw material [17].Uniform nano-Li 2 TiO 3 powder particles were prepared via a cetyltrimethyl-ammonium bromide (CTAB)-assisted hydrothermal method [34].Unlike many synthesis methods, the hydrothermal method allows the control of shape and size of the particles by control of the rate of precipitation of the crystallized powders directly from the solution, the uniformity of nucleation, growth and aging.Expensive surfactants or template are not necessary in this method.Thus, hydrothermal synthesis is a suitable method to produce large scale crystals with high quality at a reasonable price [35].
However, β-Li 2 TiO 3 is a wide gap semiconductor with an indirect band gap at Γ-C (E g ≈ 3.9 eV) with low electrical conductivity of 10 −11 S cm −1 at room temperature [35][36][37] and it was considered as a material with electrochemical inactiveness similarly to the rock-salt Li 2 MnO 3 [38].However, synthesis of nanocrystalline LTO, under the form of nanoparticles, nanorods, nanoflowers and nanofibers, provides more active surface area and shorter diffusion paths for Li + ions in the structure, which makes the material electrochemically active and improves the rate capability [39,40].Several attempts on Li 2 TiO 3 -based composites as cathode or anode materials were reported considering the merits of lithium metatitanate, namely its excellent structural stability and improved electrochemical performance for Li-ion batteries [41][42][43][44][45][46][47].The Si/LTO nanocomposite synthesized by sol-gel process as an anode material exhibited a specific capacity of 471 mAh g −1 even after 50 cycles.In this nanocomposite, the structural stability is due to Li 2 TiO 3 , which acts as excellent buffer to the Si powders and partly compensate the capacity loss [44].The composite 0.55Li 2 TiO 3 -0.45LiCrO 2 prepared by spray pyrolysis exhibits the highest initial discharge capacity of 203 mAh g −1 [45].Due to its three-dimensional (3D) path for Li + -ion migration and its excellent structural stability, LTO has served as both a Li ion conductive layer and a protective coating layer of cathode material against the attack of HF in the electrolyte [48][49][50][51][52].
In previous works, we have investigated the electrochemical properties of pristine nano-LTO [53], and the improve performance of LTO/CNT and LTO/graphene composites [54].The effect of nanosized Li 2 TiO 3 was evidenced by the excellent cyclability and the stable specific discharge capacity of 113, 143 and 150 mAh g −1 , respectively, retained over 30 charge-discharge cycles at 1C rate.In the present study, we report additional measurements that evidence the beneficial effect of nanosized scale on the transport properties of LTO specimens prepared by hydrothermal synthesis after heat treatment at 800 • C in ambient conditions.The transport properties are investigated using d.c. and a.c.electrical conductivity, cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS).Finally, the structural stability and the cyclability of LTO nanopowders cycled in aqueous cell is discussed.

Synthesis
Nanocrystalline β-Li 2 TiO 3 was synthesized by hydrothermal reaction using 1.198 g (0.015 mol) TiO 2 powder (anatase phase, Sigma-Aldrich, USA) and 1.259 g (0.03 mol) LiOH•H 2 O (Sigma-Aldrich, USA) as raw materials.TiO 2 and LiOH•H 2 O powders (molar ratio 2:1) were added into a Teflon lined autoclave (50 mL) together with 15 mL distilled water and heated at 200 • C for 10 h.During the reaction period the autoclave was kept at the autogenous saturation vapor pressure of the solution without agitation.Then, the product was filtered, rinsed with deionized water.The as-prepared powder was dried at 50 • C in ambient conditions.The obtained powder was calcined at 800 • C for 2 h in air.

Characterization
The structure of samples was investigated by the X-ray diffraction (XRD) technique using a Siefert computerized X-ray diffractometer (model 3003-TT) equipped with a CuK α radiation (λ = 1.5406Å) source filtered by Ni film operated at a scan speed of 0.03 degree per second in the 2θ range 10 • -70 • .Raman scattering (RS) spectra were recorded at room temperature in the range of 50-1000 cm −1 with a spectral resolution of ≈1 cm −1 using a HR800UV Raman spectrometer (Jobin-Yvon, Longjumeau, France) using air-cooled frequency doubled Nd:YAG laser 532 nm with an excitation source of 50 mW.The spectral calibration was carried out using the 520 cm −1 scattering line of silicon.A 100× objective lens was used to focus the laser light on sample surface.The Fourier transform infrared (FTIR) measurements were carried out using a VERTEX 80v (Bruker, Karlsruhe, Germany) in the spectral range 100-1000 cm −1 .High resolution transmission electron microscope (HRTEM) (model FEI, TECHNAI G 2 -30 S-twin D905) was used to analyze the microstructure of the sample.The surface morphology of the sample was observed by a field emission scanning electron microscope (FESEM, SIRION 200).The composition of the sample was analyzed by energy dispersive spectroscopy with FESEM (FESEM, SIRION 200).
A.C. conductivity was performed by impedance spectroscopy using a phase sensitive multimeter (model PSM 1700, Newton, Leicester, UK) at various temperatures from 300 to 500 • C. The amplitude of the A.C. signal was 50 mV over the frequency range 1 Hz-1 MHz.The synthesized powder was pressed into 12 mm diameter pellet with the thickness of 1.25 mm and annealed at 600 • C for 2 h to enhance the packing density.The pellet was used for electrical studies.Cyclic voltammetry (CV), galvanostatic charge-discharge experiments were conducted to evaluate the specific discharge capacity of the electrode as reported elsewhere [54].A conventional three-electrode glass cell (Pt/saturated Li 2 SO 4 aqueous solution/Li 2 TiO 3 ) was used with an Ag/AgCl reference electrodes.

Elemental and Structural Studies
The elemental analysis of the as-prepared Li 2 TiO 3 powders sintered at 800 • C for 2 h carried out by energy dispersive spectroscopy (EDS) gives the composition of 74.5 and 25.5% (accuracy of ±0.5%) of titanium and oxygen, respectively (see Figure 2 in Ref. [54]).The LTO samples have a white color, which indicates a stoichiometric composition, according to Hoshino et al. [55] for products sintered in oxidizing conditions.
Figure 2b presents the XRD pattern of Li 2 TiO 3 sample recorded using the Bragg-Brentano geometry.All the X-ray diffraction lines can be readily indexed to the monoclinic β-Li 2 TiO 3 structure (JCPDS Card No. 33-0831).The XRD diagram exhibits predominant (002) reflection at 2θ = 18.48 • along with other characteristic orientations (131), ( 133), ( 043), (006), (312) and (062) corresponding to monoclinic β-Li 2 TiO 3 structure with C2/c space group (ordered phase).In the hydrothermal reaction, the Li-Ti-O framework is formed, characterized by the basic (133) lattice plane.The strong intensity of (133) diffraction peak gives evidence of the good ordering of lithium and titanium ions in the LiTi 2 slab of the monoclinic structure in which Li, Ti and O atoms are arranged in the sequence Li interslab (Li 1/3 Ti 2/3 ) slab O 2 .In this lattice, lithium ions occupy 1/3 of 4e sites, while the titanium ions occupy 2/3 other 4e sites (Wyckoff notation) [37].Note that the intensity of the (002) supercell XRD peak is enhanced by the sintering process at 800 • C for 2 h.Rietveld refinements of XRD data were performed by the FULLPROF program [56].The comparison between observed (dots) and calculated (solid line) patterns is shown in Figure 2 where β is the full width half maxima (FWHM) in radians, λ is wavelength of the X-ray, θ is corresponding Bragg angle and K is a dimensionless shape factor (K = 0.94).The estimated crystallite size is 34 ± 2 nm with a lattice strain 0.009 in the rock-salt Li 2 TiO 3 powders.

Elemental and Structural Studies
The elemental analysis of the as-prepared Li2TiO3 powders sintered at 800 °C for 2 h carried out by energy dispersive spectroscopy (EDS) gives the composition of 74.5 and 25.5% (accuracy of ±0.5%) of titanium and oxygen, respectively (see Figure 2 in Ref. [54]).The LTO samples have a white color, which indicates a stoichiometric composition, according to Hoshino et al. [55] for products sintered in oxidizing conditions.
Figure 1b presents the XRD pattern of Li2TiO3 sample recorded using the Bragg-Brentano geometry.All the X-ray diffraction lines can be readily indexed to the monoclinic -Li2TiO3 structure (JCPDS Card No. 33-0831).The XRD diagram exhibits predominant (002) reflection at 2θ = 18.48° along with other characteristic orientations ( 1 31), ( 1 33), ( 043), ( 006), ( 312) and ( 062) corresponding to monoclinic -Li2TiO3 structure with C2/c space group (ordered phase).In the hydrothermal reaction, the Li-Ti-O framework is formed, characterized by the basic (133) lattice plane.The strong intensity of (133) diffraction peak gives evidence of the good ordering of lithium and titanium ions in the LiTi2 slab of the monoclinic structure in which Li, Ti and O atoms are arranged in the sequence Liinterslab(Li1/3Ti2/3)slabO2.In this lattice, lithium ions occupy 1/3 of 4e sites, while the titanium ions occupy 2/3 other 4e sites (Wyckoff notation) [37].Note that the intensity of the (002) supercell XRD peak is enhanced by the sintering process at 800 °C for 2 h.Rietveld refinements of XRD data were performed by the FULLPROF program [56].The comparison between observed (dots) and calculated (solid line) patterns is shown in Figure 1 where β is the full width half maxima (FWHM) in radians, λ is wavelength of the X-ray, θ is corresponding Bragg angle and K is a dimensionless shape factor (K = 0.94).The estimated crystallite size is 34 ± 2 nm with a lattice strain 0.009 in the rock-salt Li2TiO3 powders.The short-range structural properties of the prepared samples were further investigated by Raman and FTIR spectroscopy that are considered to be powerful for either detecting impurities or determine the local environment of oxygen atoms.In lithiated oxides, where Li ions occupy The short-range structural properties of the prepared samples were further investigated by Raman and FTIR spectroscopy that are considered to be powerful for either detecting impurities or determine the local environment of oxygen atoms.In lithiated oxides, where Li ions occupy octahedral sites, the frequency of Li-O stretching is known to be observed within the 200-400 cm −1 spectral region, while for Li tetrahedrally coordination, the frequency lies in the 400-550 cm −1 region [58].Figure 3a shows the Raman spectra in the spectral range 100-900 cm −1 of several titanate oxides, i.e., TiO 2 anatase, TiO 2 rutile, Li 4 Ti 5 O 12 spinel and β-Li 2 TiO 3 , which evidence the unicity of the monoclinic structure of Li 2 TiO 3 .Among the 15 allowed Raman active modes (7A g + 8B g ) of the C 2h 6 spectroscopic symmetry, only 11 observed Raman bands are observed, which can be attributed as followed.The high-wavenumber peaks at 575 and 668 cm −1 are assigned to the Ti-O stretching vibrations in TiO 6 octahedra; the lattice modes, i.e., A g (T) translational lattice mode, and O-Ti-O bending modes appear at ν < 320 cm −1 ; the low-frequency peak at 98 cm  [64,65].All mode frequencies match well with the relation: Considering the molecular model, the Raman spectrum of the β-Li 2 TiO 3 phase essentially displays stretching and bending of the various polyhedral units constituting the monoclinic lattice without appearance of Raman bands due to anatase TiO 2 (at 144 cm −1 ) and rutile TiO 2 (at 449/610 cm −1 ).
The FTIR spectrum of Li 2 TiO 3 is shown in Figure 3b.It displays only 9 infrared bands instead of 18 expected by the group factor analysis.The two broad peaks at 510 and 619 cm octahedral sites, the frequency of Li-O stretching is known to be observed within the 200-400 cm −1 spectral region, while for Li tetrahedrally coordination, the frequency lies in the 400-550 cm −1 region [58].Figure 3a shows the Raman spectra in the spectral range 100-900 cm −1 of several titanate oxides, i.e., TiO2 anatase, TiO2 rutile, Li4Ti5O12 spinel and -Li2TiO3, which evidence the unicity of the monoclinic structure of Li2TiO3.Among the 15 allowed Raman active modes (7Ag + 8Bg) of the C2h 6 spectroscopic symmetry, only 11 observed Raman bands are observed, which can be attributed as followed.The high-wavenumber peaks at 575 and 668 cm −1 are assigned to the Ti-O stretching vibrations in TiO6 octahedra; the lattice modes, i.e., Ag(T) translational lattice mode, and O-Ti-O bending modes appear at  < 320 cm −1 ; the low-frequency peak at 98 cm  2. Note that similar situation has been shown in the Raman spectrum of monoclinic Li2MnO3 [64,65].All mode frequencies match well with the relation: Considering the molecular model, the Raman spectrum of the -Li2TiO3 phase essentially displays stretching and bending of the various polyhedral units constituting the monoclinic lattice without appearance of Raman bands due to anatase TiO2 (at 144 cm −1 ) and rutile TiO2 (at 449/610 cm −1 ).
The FTIR spectrum of Li2TiO3 is shown in Figure 3b.It displays only 9 infrared bands instead of 18 expected by the group factor analysis.The two broad peaks at 510 and 619 cm

Surface Morphology
The surface morphology and microstructural features of hydrothermal synthesized Li 2 TiO 3 material calcined at 800 • C for 2 h are observed by field emission scanning electron microscopy (FESEM) and high-resolution transmission electron microscope (HRTEM) in Figures 4 and 4b, respectively.FESEM image of Li 2 TiO 3 shown in Figure 4a reveals that the sample consists of homogeneously distributed spherical-like shaped grains with an average particle size of 150 nm without any obvious aggregations.Figure 4b-d

Surface Morphology
The surface morphology and microstructural features of hydrothermal synthesized Li2TiO3 material calcined at 800 °C for 2 h are observed by field emission scanning electron microscopy (FESEM) and high-resolution transmission electron microscope (HRTEM) in Figures 4 and 4b, respectively.FESEM image of Li2TiO3 shown in Figure 4a reveals that the sample consists of homogeneously distributed spherical-like shaped grains with an average particle size of 150 nm without any obvious aggregations.Figures 4b-d show the HRTEM image, selected area diffraction pattern (SAED) and lattice fringes images of Li2TiO3, respectively.The corresponding selected-area electron diffraction (SAED) pattern of the microstructure (Figure 4c) shows that the nanoparticles are well crystallized.The d-spacing values obtained from SAED patterns are indexed to the respective planes of (002), (131), ( 133) and (312) that agree well with XRD patterns of the monoclinic structure of Li2TiO3. Figure 2d

Electrical Transport
Conductivity measurements were carried out using both d.c. and a.c.techniques to analyze the electrical transport of electrons and ions in the LTO lattice.Impedance spectroscopy is an efficient tool to study a.c.conductivity of materials, when using a large frequency domain, this technique provides analysis of intragrain, intergrain and relaxation process in material (Figure 5a-e).Figure 5a,b show the Nyquist plots (Z (ω)-Z"(ω) plane) of nanocrystalline Li 2 TiO 3 in a wide frequency range (1 Hz-1 MHz) over the temperature range 320-500 • C. The bulk resistance (R b ) of the LTO sample is determined from the intercept of each semicircle with the real axis.It is observed that both the intercept with the Z axis and the maximum of Z" shift as temperature increases.At low temperatures (T < 400 • C), the Li 2 TiO 3 pellet exhibits a high resistance that is mainly due to the bulk property of the sample.At higher temperature, all the Nyquist plots consist of a slightly depressed semicircle in the high-frequency region followed by another depressed semicircle at low frequencies (<1000 Hz).The depressed semicircle, which meets real axis at high frequencies is the response of the bulk resistance (R b ) of the material, i.e., small deviation from a Debye-type relaxation process, while the depressed semicircle originated in the low frequency region is due to grain boundary (R gb ) effect.The high-and low-frequency complex impedance plots for all temperatures can be modeled using a parallel combination of resistance and constant phase element (CPE) equivalent circuit describing the bulk resistance and grain boundary components in Li 2 TiO 3 sample.The bulk electrical conductivity (σ) was calculated using the formula: where R b is the bulk resistance, l is the thickness of the sample and S is the active area of the sample.The real Z (ω) and imaginary Z"(ω) part of the Li 2 TiO 3 sample impedance are presented for all temperatures in Figure 5c,d, respectively.The plots of Figure 5c show a decrease of Z (ω) vs. frequency, so that σ(ω) increases with frequency (see Figure 5e).At low frequency, σ increases importantly with temperature.At high frequencies, however, Z (ω) becomes almost temperature independent so that the Z (ω) curves at different temperatures merge approximately in a single curve.This is due to the release of space charges caused by reduction in barrier properties of the material [38].This unique curve at high frequency shows a dip, which is associated to charge carrier hopping in the material.In another hand, Z" = Im(Z(ω)) reaches a maximum, which shifts towards higher frequency with temperature.This is attributed to the active conduction through the grain boundaries of the sample.The magnitude of Z"(ω) decreases with increasing temperature indicating a decrease of the resistivity of the material.The peak broadening observed with increasing temperature is attributed to a temperature dependent relaxation process in the material.The asymmetric broadening of the peaks indicates the spread of relaxation time in the sample.Our data match well with the results reported in the literature [37,38,68].The ac response obeys the power law [69]: where σ 0 is the d.c.conductivity (at ω = 0), A is a thermally activated quantity and n the fractional constant that is 0.5 < n < 0.8 for an ionic conductor [70,71].The frequency exponent n (Equation ( 4)) can be analyzed by a mechanism based on charge carrier hopping between defect sites proposed by Elliott [72]: where T is the absolute temperature, k B the Boltzmann constant and W m the maximum barrier height (energy of the transport charge).Using Equation (4), from the slope of curves in Figure 5d, one can derive at the highest frequency with n ≈ 0.72 and the value of W m is 0.63 eV at room temperature.
where 0 is the pre-exponential factor, T the absolute temperature, kB the Boltzmann constant and Eac the activation energy of the conductivity.The fit of the curves T vs. 1/T in Figure 6a-b provides an activation energy Ea = 0.71 eV for and 0.65 eV for ac measured at 50 kHz.These values match well with the value 0.77 eV found for nanoparticles [37], against 0.88 eV [38] or even 0.95 eV for the bulk material [37].Thus, Ea appears to be dependent on the crystallite size.This is corroborated by the fact that the value Ea = 0.71 eV obtained in the present work (34 nm crystallite size) is slightly smaller than that for crystallites of 88 nm reported by Dash et al. [38].Therefore, nanosized particle favors the electronic transport and thus the ionic transport since both are correlated to maintain the electrical charge neutrality inside the material.Figure 6a,b display the Arrhenius plots of σ ac and σ dc , respectively.The solid lines are the fit of the temperature dependence of conductivity thermally activated according the Arrhenius-type behavior: where σ 0 is the pre-exponential factor, T the absolute temperature, k B the Boltzmann constant and E ac the activation energy of the conductivity.The fit of the curves σT vs. 1/T in Figure 6a,b provides an activation energy E a = 0.71 eV for σ dc and 0.65 eV for σ ac measured at 50 kHz.These values match well with the value 0.77 eV found for nanoparticles [37], against 0.88 eV [38] or even 0.95 eV for the bulk material [37].Thus, E a appears to be dependent on the crystallite size.This is corroborated by the fact that the value E a = 0.71 eV obtained in the present work (34 nm crystallite size) is slightly smaller than that for crystallites of 88 nm reported by Dash et al. [38].Therefore, nanosized particle favors the electronic transport and thus the ionic transport since both are correlated to maintain the electrical charge neutrality inside the material.As shown in Figure 5c, Z″ = Im(Z() exhibits a peak at the particular frequency, i.e., the relaxation frequency, which corresponds to a single relaxation time that fulfils the relation 2fmm = 1, where fm is the frequency of the maximum of Im(Z).The variation of  with T obeys an Arrhenius law given by [73]: where 0 is the pre-exponential factor and Wa the activation energy.Figure 6c shows the temperature dependence of the relaxation time of LTO sample in the range 320-500 °C.The mean relaxation time of the process is measured in fractions of milliseconds that does not implies electronic and ionic lattice polarization but slow relaxation can be imposed by permanent molecular dipoles, ion defects of a dipolar type, or mobile hopping charge carriers [74].The activation energy estimated from the linear fit is found to be ~0.66 eV, which indicates a quasi-Debye behavior of the relaxation process of charge carriers in the LTO lattice.The mechanism of ionic motion has been discussed by several workers [23,74,75].Li2TiO3 has a three-dimensional path for Li + ion diffusion, in which the ionic migration can occur in the (00l) plane, that is, LiTi2 layer, and along the c axis [74].The conductivity occurs with the hopping of Li + from tetrahedral sites to adjacent octahedral sites.At low temperatures, defects are created by surface modification.At high temperature a drift of large number of Li + ions released from tetrahedral sites (LiTi2 layer) then occupied octahedral sites (Li layer), creating interstitial site vacancies that are thermally activated and some structural disorder possibly occurred that facilitate ion transport induced by low activation energy.

Li + -ion Diffusivity
Investigations of the diffusivity of Li + ions in the LTO lattice were carried out by cyclic voltammetry (CV) at sweep rate in the range 1-50 mV s −1 and by electrochemical impedance spectroscopy (EIS) measurements in the frequency range 1-10 6 Hz for Pt/saturated Li2SO4 aqueous cells.Cyclic voltammograms display one set of well-defined current peaks (see Figure 7 in Ref. [53]) corresponding to the redox reaction in Li//Li2TiO3 cell, according the (de)insertion reaction: As the starting electrode material is Li2 + Ti 4+ O3, the insertion of the faction x of Li + ions in Li2+xTiO3 implies the reduction of tetravalent to trivalent titanium [45].At sweep rate of 10 mV s −1 , the reduction peak occurred at 0.338 V during cathodic sweep corresponding to insertion of lithium into interstitial sites of Li2+xTiO3 (x equals to 0.5), while the oxidation peak occurred at 0.643 V during anodic sweep.Thus, a peak separation of 0.305 V for Li2TiO3 is ascribed to the Li + ion storage at the solid-electrolyte interface during charge-discharge process [76].As shown in Figure 5c, Z" = Im(Z(ω)) exhibits a peak at the particular frequency, i.e., the relaxation frequency, which corresponds to a single relaxation time that fulfils the relation 2πf m τ m = 1, where f m is the frequency of the maximum of Im(Z).The variation of τ with T obeys an Arrhenius law given by [73]: where τ 0 is the pre-exponential factor and W a the activation energy.Figure 6c shows the temperature dependence of the relaxation time of LTO sample in the range 320-500 • C. The mean relaxation time of the process is measured in fractions of milliseconds that does not implies electronic and ionic lattice polarization but slow relaxation can be imposed by permanent molecular dipoles, ion defects of a dipolar type, or mobile hopping charge carriers [74].The activation energy estimated from the linear fit is found to be ~0.66 eV, which indicates a quasi-Debye behavior of the relaxation process of charge carriers in the LTO lattice.The mechanism of ionic motion has been discussed by several workers [23, 74,75].Li 2 TiO 3 has a three-dimensional path for Li + ion diffusion, in which the ionic migration can occur in the (00l) plane, that is, LiTi 2 layer, and along the c axis [74].The conductivity occurs with the hopping of Li + ions from tetrahedral sites to adjacent octahedral sites.At low temperatures, defects are created by surface modification.At high temperature a drift of large number of Li + ions released from tetrahedral sites (LiTi 2 layer) then occupied octahedral sites (Li layer), creating interstitial site vacancies that are thermally activated and some structural disorder possibly occurred that facilitate ion transport induced by low activation energy.

Li + -ion Diffusivity
Investigations of the diffusivity of Li + ions in the LTO lattice were carried out by cyclic voltammetry (CV) at sweep rate in the range 1-50 mV s −1 and by electrochemical impedance spectroscopy (EIS) measurements in the frequency range 1-10 6 Hz for Pt/saturated Li 2 SO 4 aqueous solution/Li 2 TiO 3 cells.Cyclic voltammograms display one set of well-defined current peaks (see Figure 7 in Ref. [53]) corresponding to the redox reaction in Li//Li 2 TiO 3 cell, according the (de)insertion reaction: As the starting electrode material is Li 2 + Ti 4+ O 3 , the insertion of the faction x of Li + ions in Li 2+x TiO 3 implies the reduction of tetravalent to trivalent titanium [45].At sweep rate of 10 mV s −1 , the reduction peak occurred at 0.338 V during cathodic sweep corresponding to insertion of lithium into interstitial sites of Li 2+x TiO 3 (x equals to 0.5), while the oxidation peak occurred at 0.643 V during anodic sweep.Thus, a peak separation of 0.305 V for Li 2 TiO 3 is ascribed to the Li + ion storage at the solid-electrolyte interface during charge-discharge process [76].Figure 7a displays the dependency of the peak current Ip for the redox peaks as a function of scan rate ν in CV measurements (typical CV response at ν = 10 mV s −1 is shown in the inset of Figure 7a).
For cathodic and anodic reactions, the plots in double logarithmic scale show mutual linear behavior over the entire measurement range with a slope of 0.511 and 0.497, respectively.These values are very close to 0.5, which characterizes the conventional diffusion-controlled faradaic reaction, i.e., the lithium insertion/extraction reaction in LTO.The classical Randles-Sevcik equation for a semi-infinite diffusion of Li-ion into Li 2 TiO 2 layer can be applied [77]: where I p is the peak current, n the charge-transfer number, A the surface area in cm 2 of the electrode, D Li the chemical diffusion coefficient, ν the scan rate, C Li the bulk concentration of Li-ion in electrode (~1.8 × 10 −3 mol cm −3 calculated from the volume of Li 2 TiO 3 (429.1 Å 3 )), F is Faraday constant, R the gas constant and T the absolute temperature.Based on Equation ( 9), the apparent diffusion coefficient of Li-ion in the nanostructured Li 2 TiO 2 sample was calculated to be 9.2 × 10 −12 cm 2 s −1 .
Sci 2019, 2, x FOR PEER REVIEW 10 of 17 Figure 7a displays the dependency of the peak current Ip for the redox peaks as a function of scan rate ν in CV measurements (typical CV response at ν = 10 mV s −1 is shown in the inset of Figure 7a).For cathodic and anodic reactions, the plots in double logarithmic scale show mutual linear behavior over the entire measurement range with a slope of 0.511 and 0.497, respectively.These values are very close to 0.5, which characterizes the conventional diffusion-controlled faradaic reaction, i.e., the lithium insertion/extraction reaction in LTO.The classical Randles-Sevcik equation for a semi-infinite diffusion of Li-ion into Li2TiO2 layer can be applied [77]: where Ip is the peak current, n the charge-transfer number, A the surface area in cm 2 of the electrode, DLi the chemical diffusion coefficient, ν the scan rate, CLi the bulk concentration of Li-ion in electrode (~1.8 × 10 −3 mol cm −3 calculated from the volume of Li2TiO3 (429.1 Å 3 )), F is Faraday constant, R the gas constant and T the absolute temperature.Based on Equation ( 9), the apparent diffusion coefficient of Li-ion in the nanostructured Li2TiO2 sample was calculated to be 9.2 × 10 −12 cm 2 s −1 .Electrochemical impedance spectroscopy (EIS) was carried out over the frequency range from 1 Hz to 1 MHz for Li2+xTiO3 electrode in the fully charged state, i.e., x (Li) = 0.The Nyquist plot consists of a depressed semicircle in high frequency and straight line at low frequency region.The interception of Z′ axis at high frequency indicating electrode/electrolyte contact resistance corresponds to the solution resistance (Rs).The depressed semicircle in the middle frequency region denotes the charge transfer resistance Rct related to electrochemical reaction at electrode/electrolyte interface.At low frequency, the observed straight line that is the response of the Warburg impedance Zw, which is related to solid-state diffusion of Li + ions.The impedance spectrum was fitted using the Randles equivalent circuit shown in the inset of Figure 7b.Resistance RS of the electrode is 38 Ω; Rct is ≈250 Ω and slope of the Warburg impedance (≈ 45º) indicates that the electrode is controlled by a diffusion process.In the Warburg regime, the impedance varies with the angular frequency ω according to the law [78]: (10) in which the Warburg impedance σw is obtained from the slope of Z' vs. ω −1/2 in the low-frequency range (Figure 7b).The apparent diffusion coefficient Li + ions can be quantified from the low-frequency Warburg impedance according the equation [78]: Electrochemical impedance spectroscopy (EIS) was carried out over the frequency range from 1 Hz to 1 MHz for Li 2+x TiO 3 electrode in the fully charged state, i.e., x (Li) = 0.The Nyquist plot consists of a depressed semicircle in high frequency and straight line at low frequency region.The interception of Z axis at high frequency indicating electrode/electrolyte contact resistance corresponds to the solution resistance (R s ).The depressed semicircle in the middle frequency region denotes the charge transfer resistance R ct related to electrochemical reaction at electrode/electrolyte interface.At low frequency, the observed straight line that is the response of the Warburg impedance Z w , which is related to solid-state diffusion of Li + ions.The impedance spectrum was fitted using the Randles equivalent circuit shown in the inset of Figure 7b.Resistance R S of the electrode is 38 Ω; R ct is ≈250 Ω and slope of the Warburg impedance (θ ≈ 45 • ) indicates that the electrode is controlled by a diffusion process.In the Warburg regime, the impedance varies with the angular frequency ω according to the law [78]: (10) in which the Warburg impedance σ w is obtained from the slope of Z vs. ω −1/2 in the low-frequency range (Figure 7b).The apparent diffusion coefficient Li + ions can be quantified from the low-frequency Warburg impedance according the equation [78]: (11) where R, T and F are the usual constants, A the surface area of the electrode-electrolyte interface and C Li the lithium-ion concentration in the electrode.Linear fit of data in Figure 7b gives σ w = 9.36 V s −1/2 and D Li+ = 2.1 × 10 −11 cm 2 s −1 .Note that the D Li+ (EIS) value is larger by a factor of 2 in comparison to that obtained by CV.Similar difference in D Li+ for the same cathode material by two different techniques is commonly observed [79,80].The capacity retention is about 94%.In this figure the present results are compared with those of literature [41,43,46,47].
Sci 2019, 2, x FOR PEER REVIEW 11 of 17 where R, T and F are the usual constants, A the surface area of the electrode-electrolyte interface and CLi the lithium-ion concentration in the electrode.Linear fit of data in Figure 7b gives σw = 9.36 V s −1/2 and DLi+ = 2.1 × 10 −11 cm 2 s −1 .Note that the DLi+(EIS) value is larger by a factor of 2 in comparison to that obtained by CV.Similar difference in DLi+ for the same cathode material by two different techniques is commonly observed [79,80].Figure 8a,b present the cyclability of the Li2.55TiO3 electrode (discharge state).The XRD patterns of the starting Li2TiO3 and final Li2.55TiO3 phase after cycling process are displayed in Figure 8a displays.These results show that the structure has retained after 30 insertion-extraction cycles with the C2/c monoclinic symmetry.This insertion process is in good agreement with the model of Bian and Dong [59] who demonstrated the formation of a non-stoichiometric Li2+xTiO3 with x = 0.2 that retains the initial rock-salt structure.These authors have proposed three possible occupation mechanisms in Li-rich Li2TiO3: (i) excess of Li + ions occupied the tetrahedral interstitial sites, which took the composition Li2+4yTi1−yO3; (ii) the Li + ions are located on the Ti sites formed as antisite defects (2Li″Ti = 3VO •• ); and (iii) excess of Li + ions occupied itself site and Ti 4+ and O 2− site vacancies formed simultaneously.The plot of the specific discharge capacity vs. cycle number for the Li2TiO3 electrode over 30 cycles in the voltage range 0.0-1.0V is shown in Figure 5b.The Li2TiO3 anode exhibited an initial discharge capacity of ≈122 mAh g −1 that is retained up to ≈114 mAh g −1 after 30 cycles.The capacity retention is about 94%.In this figure the present results are compared with those of literature [41,43,46,47].

Discussion
view of these previous results reported in Figure 8b, one understands why Li2TiO3 not considered as a possible anode element.Indeed, the material in these works were not investigated as an anode for itself, but was used as an element entering in the composition of a composite with another anode material, usually Li4Ti5O12 [46,47], or LiFeO2 [41,43].Coating lamellar cathode element with Li2TiO3 has also been made [81].In any case, the voltage range used for electrochemical investigation was 1-3 V, since Li4Ti5O12 or LiFeO2 or the lamellar compounds are active only at voltage higher than 1 volt.However, in the range 1-3 V, Li2TiO3 is simply electrochemically inactive.The purpose of the addition of Li2TiO3 in the composite was to increase the ionic conductivity and stabilize the structure of the electrode materials [46,48,81] by taking advantage of the strong Ti-O bond in Li2TiO3 [82][83][84].In addition, Li2TiO3 is known to be a fast Li + conductor when it is doped [85,86].Here, no doping has been made, but the conductivity has been improved owing to the nano-size of the particles.In the present work, we have shown that nanostructured Li2TiO3 has

Discussion
In view of these previous results reported in Figure 8b, one understands why Li 2 TiO 3 was not considered as a possible anode element.Indeed, the material in these works were not investigated as an anode for itself, but was used as an element entering in the composition of a composite with another anode material, usually Li 4 Ti 5 O 12 [46,47], or LiFeO 2 [41,43].Coating lamellar cathode element with Li 2 TiO 3 has also been made [81].In any case, the voltage range used for electrochemical investigation was 1-3 V, since Li 4 Ti 5 O 12 or LiFeO 2 or the lamellar compounds are active only at voltage higher than 1 volt.However, in the range 1-3 V, Li 2 TiO 3 is simply electrochemically inactive.The purpose of the addition of Li 2 TiO 3 in the composite was to increase the ionic conductivity and stabilize the structure of the electrode materials [46,48,81] by taking advantage of the strong Ti-O bond in Li 2 TiO 3 [82][83][84].In addition, Li 2 TiO 3 is known to be a fast Li + conductor when it is doped [85,86].Here, no doping has been made, but the conductivity has been improved owing to the nano-size of the particles.In the present work, we have shown that nanostructured Li 2 TiO 3 has interesting electrochemical properties at low voltage (<1 V).This result can also explain former results obtained on Li 4 Ti 5 O 12 /Li 2 TiO 3 composite.In Ref. [47], the authors noticed an increased capacity of this composite, associated to a sloping discharge in the range 1.25-0 V with respect to the results observed when cycling with a lower cut-off of 1.25 V.Although this effect was attributed to an intrinsic property of Li 4 Ti 5 O 12 since an increased capacity in this voltage range has been reported by one group with Li 4 Ti 5 O 12 alone [87], the present work suggests that at least part of this effect can be attributed to Li 2 TiO 3 .In addition, the enhanced conductivity and the correlated improved Li-diffusion by reduction of the Li

Method Used
Activation Energy (eV) Ref. 7 Li NMR, a.c.conductivity 0.47-0.80[89] a.c.conductivity 0.81-0.91[90] electrical conductivity 0.60-0.90[37] 6,7 Li NMR 0.27 [74] periodic quantum−chemical DFT 0.44-0.54[75] complex Few experimental works reported the kinetics of Li + ion in the LTO framework, while the Li ion dynamics is discussed controversially.Table 2 list the values of the activation energy for the charge carrier transport in Li 2 TiO 3 reported in the literature.Vijayakumar et al. utilized a combination of 6,7 Li nuclear magnetic resonance (NMR) and molecular dynamics (MD) simulations to predict that Li ions can be occupy a tetrahedral site if a Ti cationic defect is present in the LiTi 2 layer.They obtained a small activation energy of 0.27 eV for Li diffusion in β-Li 2 TiO 3 , which seems to be associated with impurities and stoichiometric deviation [74].Ruprecht et al. [89] reported a self-diffusion coefficient of 2 × 10 −13 cm 2 s −1 measured by 7Li NMR stimulated echoes at 160 • C and an extremely slow Li diffusion, i.e., D Li + = 3 × 10 −17 cm 2 s −1 at room temperature, evaluated from a.c.conductivity with the help of the Nernst-Einsten equation.Islam and Bredow [75] determined activation energies ranging between 0.44 and 0.55 eV for Li+ ion migrating along the ab plane and perpendicularly to the LiTi 2 layers as well.The early work by Vitins et al. [90] shows that the electrical conductivity of Li 2 TiO 3 is strongly dependent on the heat treatment conditions during sample preparation.Typical specimen mixed with 1.5 mol% Li

Conclusions
The nanocrystalline Li 2 TiO 3 phase has been successfully synthesized using a simple, low cost and scalable hydrothermal reaction.The structural analyses carried out using X-ray diffraction, Raman and FTIR spectroscopy show that β-Li 2 TiO 3 crystallizes with C2/c space group with crystallites 34 nm.FESEM image shows that the nanocrystalline β-Li 2 TiO 3 particles are homogeneously distributed as nearly spherical shaped grains with an average size of 150 nm.The Raman and FTIR spectroscopy confirm the impurity free monoclinic structure exhibiting well-defined vibrational modes Ti-O and Li-O stretching and O-Ti-O and O-Li-O bending modes.The electrical properties revealed a thermally activated conduction mechanism (Arrhenius-type behavior) with an activation energy of 0.71 eV.The conduction mechanism of the sample is greatly improved due to more charge carriers corresponding to nanoparticles.The electrochemical of β-Li 2 TiO 3 studies demonstrate that reduction of Ti 4+ /Ti 3+ (0.55 Li uptake) occurred in potential range 1.0-0.0V.The nanocrystalline β-Li 2 TiO 3 shows a specific discharge capacity of 114 mAh g −1 after 30 cycles at current density of 0.05 mAh cm -2 .These results suggest that nanocrystalline β-Li 2 TiO 3 nano particles have shortened the Li-ion diffusion lengths and enhanced the electrochemical kinetics of the sample, which are very important keys to high rate capacity.The electrode retains 94% of capacity even after 30 cycles with an excellent structural stability.

Figure 2 .
Figure 2. X-ray diffraction pattern of Li2TiO3 powders indexed in the monoclinic symmetry, C2/c space group of the -Li2TiO3 phase.The Rietveld refinement is shown with  2 = 5.21.

Figure 2 .
Figure 2. X-ray diffraction pattern of Li 2 TiO 3 powders indexed in the monoclinic symmetry, C2/c space group of the β-Li 2 TiO 3 phase.The Rietveld refinement is shown with χ 2 = 5.21.
−1 are assigned to the antisymmetric stretching vibrations of Ti-O bonds.The low-frequency bands in the range 350-450 cm −1 are a mixture of the O-Li-O and O-Ti-O bending modes due to the presence of Li ions in the LiTi 2 slabs.The band at 263 cm −1 is attributed to the stretching mode of Li-O bonds in LiO 6 octahedra.The shoulder of the higher intensity peak at 642 cm −1 should be related to the local distortion of the lattice that results in a decrease of the local structural symmetry generating additional infrared bands[66].Sci 2019, 2, x FOR PEER REVIEW 5 of 17 −1 are assigned to the antisymmetric stretching vibrations of Ti-O bonds.The low-frequency bands in the range 350-450 cm −1 are a mixture of the O-Li-O and O-Ti-O bending modes due to the presence of Li ions in the LiTi2 slabs.The band at 263 cm −1 is attributed to the stretching mode of Li-O bonds in LiO6 octahedra.The shoulder of the higher intensity peak at 642 cm −1 should be related to the local distortion of the lattice that results in a decrease of the local structural symmetry generating additional infrared bands[66].
show the HRTEM image, selected area diffraction pattern (SAED) and lattice fringes images of Li 2 TiO 3 , respectively.The corresponding selected-area electron diffraction (SAED) pattern of the microstructure (Figure4c) shows that the nanoparticles are well crystallized.The d-spacing values obtained from SAED patterns are indexed to the respective planes of (002), (131), (133) and (312) that agree well with XRD patterns of the monoclinic structure of Li 2 TiO 3 .Figure2dshows the layered structure with fringe spacing of 0.48 nm matching well with the d-spacing of the high intensity plane (002) of Li 2 TiO 3 and corresponding to LiTi 2 slab along the c-axis [67].
shows the layered structure with fringe spacing of 0.48 nm matching well with the d-spacing of the high intensity plane (002) of Li2TiO3 and corresponding to LiTi2 slab along the c-axis [67].

Figure 4 .
Figure 4. Morphology of nano Li2TiO3 (a) FESEM image showing spherical-like shaped grains with an average particle size of 150 nm.(b) HRTEM image, (c) selected area diffraction pattern (SAED) and (d) lattice fringes images of Li2TiO3.

Figure 4 .
Figure 4. Morphology of nano Li 2 TiO 3 (a) FESEM image showing spherical-like shaped grains with an average particle size of 150 nm.(b) HRTEM image, (c) selected area diffraction pattern (SAED) and (d) lattice fringes images of Li 2 TiO 3 .

Figure 5 .
Figure 5. Temperature dependence of the electrical properties of nano-Li2TiO3.Nyquist plots of nanocrystalline Li2TiO3 in the temperature range 320-420 °C (a) and 420-500 °C (b).Variation of real part of the impedance Z″ = Re (Z) vs. frequency (c).Variation of imaginary part of the impedance Z″ = Im(Z) vs. frequency (d).Plot of the ac conductivity ac versus frequency in the temperature range 360-500 °C (e).

Figure 5 .
Figure 5. Temperature dependence of the electrical properties of nano-Li 2 TiO 3 .Nyquist plots of nanocrystalline Li 2 TiO 3 in the temperature range 320-420 • C (a) and 420-500 • C (b). Variation of real part of the impedance Z = Re (Z) vs. frequency (c).Variation of imaginary part of the impedance Z = Im(Z) vs. frequency (d).Plot of the ac conductivity σ ac (ω) versus frequency in the temperature range 360-500 • C (e).

Figure 7 .
Figure 7. Determination of the Li + -ion transport in nano-Li2TiO3.(a) Plot of ln(Ip) vs. ln () from CV data.Inset shows the typical CV response at 10 mV s −1 .(b) Plot of Z' vs. ω −1/2 plots in the Warburg region of the EIS shown in the inset.

Figure 7 .
Figure 7. Determination of the Li + -ion transport in nano-Li 2 TiO 3 .(a) Plot of ln(I p ) vs. ln (ν) from CV data.Inset shows the typical CV response at 10 mV s −1 .(b) Plot of Z vs. ω −1/2 plots in the Warburg region of the EIS shown in the inset.
Figure 8a,b present the cyclability of the Li 2.55 TiO 3 electrode (discharge state).The XRD patterns of the starting Li 2 TiO 3 and final Li 2.55 TiO 3 phase after cycling process are displayed in Figure 8a displays.These results show that the structure has retained after 30 insertion-extraction cycles with the C2/c monoclinic symmetry.This insertion process is in good agreement with the model of Bian and Dong [59] who demonstrated the formation of a non-stoichiometric Li 2+x TiO 3 with x = 0.2 that retains the initial rock-salt structure.These authors have proposed three possible occupation mechanisms in Li-rich Li 2 TiO 3 : (i) excess of Li + ions occupied the tetrahedral interstitial sites, which took the composition Li 2+4y Ti 1−y O 3 ; (ii) the Li + ions are located on the Ti 4+ sites formed as antisite defects (2Li" Ti = 3V O •• ); and (iii) excess of Li + ions occupied itself site and Ti 4+ and O 2− site vacancies formed simultaneously.The plot of the specific discharge capacity vs. cycle number for the Li 2 TiO 3 electrode over 30 cycles in the voltage range 0.0-1.0V is shown in Figure 5b.The Li 2 TiO 3 anode exhibited an initial discharge capacity of ≈122 mAh g −1 that is retained up to ≈114 mAh g −1 after 30 cycles.

Figure 8 .
Figure 8.(a) XRD patterns of the starting Li2TiO3 and final Li2.55TiO3 phase after cycling process.(b) Specific discharge capacity vs. cycle number for the Li2TiO3 electrode over 30 cycles at C/13 rate.

Figure 8 .
Figure 8.(a) XRD patterns of the starting Li 2 TiO 3 and final Li 2.55 TiO 3 phase after cycling process.(b) Specific discharge capacity vs. cycle number for the Li 2 TiO 3 electrode over 30 cycles at C/13 rate.

2
TiO 3 material to the nanosize observed in the present work explains the enhanced electrochemical performance of recent electrospun Li 4 Ti 5 O 12 /Li 2 TiO 3 composite nanofibers observed recently [88].
+ and annealed at 760 • C for 20 h exhibits a conductivity of σ 300 = 4 × 10 −6 S cm −1 and E a = 0.81 eV in the temperature range 187-424 • C. The authors suggested an excess TiO 2 incorporated in the lattice byTi Li  3+ defects charge compensated for by V Li −1 defects, which facilitates Li diffusion.Ruprecht et al.[89] reported a dc conductivity of 5 × 10 −13 and 4 × 10 −6 S cm −1 at room temperature and 250 • C, respectively (with E a = 0.8 eV for long-range Li transport above 100 • C), which is very close with the value 3 × 10 −6 S cm −1 at 300 • C obtained by Fehr and Schmidbauer[37].Employing atomistic simulations to study the point defect processes and lithium diffusion in LTO, Kuganathan et al. evaluated the activation energy of 0.51 eV for Li + migration along the ab plane and showed that the energetically favorable intrinsic defect is lithium Frenkel type with 1.25 eV per defect[92].More recently, Ki et al. considered three types of lithium vacancies to investigate the diffusion behavior of tritium in LTO using density functional theory (DFT) calculations and found a minimum energy barrier of 0.76 eV for the tritium atom to escape the Li vacancy well[93].
−1 (with very weak intensity) is due to the Li-O stretching modes in LiO 4 and LiO 6 are observed at 358 and 430 cm −1 , respectively.Frequency and intensity of Raman bands are listed in Table 1.Our data are in good agreement with the literature [21,36,59-63].Recently, Raman and infrared bands of Li 2 TiO 3 have been calculated by Wan et al. [36] from first-principles total energy calculations with a generalized gradient approximation and plane-wave pseudopotential model.Our experimental data are compared with calculated frequencies in Table 2.Note that similar situation has been shown in the Raman spectrum of monoclinic Li 2 MnO 3 [21,ith[59][60][61][62]sity) is due to the Li-O stretching modes in LiO4 and LiO6 are observed at 358 and 430 cm −1 , respectively.Frequency and intensity of Raman bands are listed in Table1.Our data are in good agreement with the literature[21,36,[59][60][61][62][63].Recently, Raman and infrared bands of Li2TiO3 have been calculated byWan et al. [36]from first-principles total energy calculations with a generalized gradient approximation and plane-wave pseudopotential model.Our experimental data are compared with calculated frequencies in Table

Table 2 .
Values of the activation energy for the charge carrier transport in Li 2 TiO 3 reported in the literature.