#### 3.1. 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 2

θ = 18.48° along with other characteristic orientations (

$\overline{1}$31), (

$\overline{1}$33), (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 (

$\overline{1}$33) lattice plane. The strong intensity of (

$\overline{1}$33) 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 4

e sites, while the titanium ions occupy 2/3 other 4

e 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 together with their difference curve. The lattice parameters of the monoclinic structure (space group

C2/

c) are

a = 5.069(1) Å,

b = 8.799(1) Å,

c = 9.759(2) Å and β = 102°. The elementary unit volume (

V =

abc sinβ) is 429.1 Å

^{3}. These results match well with the literature data and confirm that the specimens are single Li

_{2}TiO

_{3} phase [

15,

16,

17]. The crystallite size of the prepared sample was estimated using Debye–Scherrer formula [

57]:

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.

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 (7

A_{g} + 8

B_{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

^{−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,

60,

61,

62,

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} [

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

^{−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].

#### 3.3. 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.

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 σ

T 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(ω)) exhibits a peak at the particular frequency, i.e., the relaxation frequency, which corresponds to a single relaxation time that fulfils the relation 2π

f_{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 (00

l) 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.

#### 3.4. 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}.

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]:

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]:

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].

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 0.0–1.0 V 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. The capacity retention is about 94%. In this figure the present results are compared with those of literature [

41,

43,

46,

47].