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# Study of the lithium diffusion properties and high rate performance of TiNb6O17 as an anode in lithium secondary battery

## Abstract

TiNb6O17 and TiNb2O7 were synthesized using a solid-state method. The techniques were used to assess the electrochemical performance and lithium diffusion kinetics of TiNb6O17 related to the unit cell volume with TiNb2O7. The charge-discharge curves and cyclic voltammetry revealed TiNb6O17 to have a similar redox potential to TiNb2O7 as well as a high discharge capacity. The rate performance of TiNb6O17 was measured using a rate capability test. SSCV and EIS showed that TiNb6O17 had higher lithium diffusion coefficients during the charging. From GITT, the lithium diffusion coefficients at the phase transition region showed the largest increase from TiNb2O7 to TiNb6O17.

## Introduction

Lithium secondary batteries have been studied for large scale energy devices, such as electric vehicles (EVs) and energy storage systems (ESSs), requiring high energy density and superior rate performance. The development of anode materials has been investigated due to importance of the charge rate and good reversibility for lithium secondary batteries. Commercial anode materials for batteries, such as graphite, have high capacities (370mAh/g). On the other hand, the active material has some problems, such as irreversible capacity loss, due to solid electrolyte interface (SEI) layer and lithium dendrite formation due to the low working voltage window at 0.8 V1. In particular, lithium dendrite formation leads to the safety hazard of lithium secondary batteries and the unsuitability of the active materials for batteries1,2,3. The Si based materials such as SiO2 showed also high capacity but could not be used to high volume expansion4. In contrast, titanium-based anode materials allow lithium batteries to avoid SEI and lithium dendrite formation due to their safe working voltage area using the Ti4+/Ti3+ redox reaction (~1.5 V vs. Li/Li+)2. Typically, Li4Ti5O12 has been studied because of its working voltage area and zero strain properties, resulting in good rate performance due to its strong Ti-O covalent bond3. Despite this, the material has a low theoretical capacity (175mAh/g) and is unsuitable for large-scale devices.

Recently, titanium niobium oxide (TNO) materials, such as TiNb2O7 and Ti2Nb10O29, have been introduced as promising titanium-based anode materials owing to their nontoxic, good rate performance, low volume change, stable working voltage window (1–2.5 V), and high theoretical capacity (387~390mAh/g). The capacities of TNO materials are influenced by many redox reactions, such as one Ti (Ti3+/Ti4+) and two Nb reactions (Nb3+/Nb4+ and Nb4+/Nb5+)5,6. On the other hand, they have lower capacity and reversibility than their theoretical capacities due to the low electric conductivity and lithium diffusion properties into the structure called Wesley-Roth 2D structure7,8,9. To solve these problems, many studies have been conducted to achieve TNO materials with high reversible capacity and improved rate performance, such as doping with other metals (Ru, Mo, etc.) to achieve high ionic conductivity and electrical conductivity and controlling the particle shape and size1,2,3,6,7,8,9,10,11,12. Chunfu Lin et al. examined TiNb6O17, which is a new TNO material. The material is composed a large number of Nb ions and has a higher theoretical capacity (397 mA/g) than TiNb2O7 and Ti2Nb10O29. Moreover, the material has the same Wisely-Roth structure (monoclinic) but larger lattice parameters and unit cell volume than TiNb2O7 and Ti2Nb10O29 (1122.541 Å vs. 803.21 Å, 1118.512 Å) due to the larger number of Nb5+ ions with a larger size (0.64 Å) than that of Ti4+ ions (0.605 Å)13,14,15. This causes a more open lithium insertion/insertion site and improved rate performance; the schema of this theory is listed in Fig. 1. The material showed a higher discharge capacity and better lithium diffusion coefficients by charge-discharge, rate capability, and slow scan cyclic voltammetry (SSCV) than Ti2Nb10O29 in Chunfu’s study13.

Therefore, this study examined the accurate lithium diffusion kinetics and electrochemical performance of TiNb6O17 compared to TiNb2O7 which has the smallest unit cell volume among the TNO materials and can clearly be compared with TiNb6O17. The materials were synthesized using a solid-state method. For electrochemical analysis, the charge-discharge curves and rate capability tests were conducted to determine their electrochemical performance. To examine the lithium diffusion kinetics, SSCV, electrochemical impedance spectroscopy (EIS), and a galvanostatic intermittent titration technique (GITT) were used. As a result, TiNb6O17 showed higher discharge capacity (284mAh/g vs. 264mAh/g) and better rate performance than TiNb2O7 (82mAh/g vs. 20mAh/g at 30 C). In addition, TiNb6O17 showed higher lithium diffusion coefficients than TiNb2O7 (mean value 10–12 S2/m vs. 10–13 S2/m).

## Experimental

### Synthesis of the active materials and characterization

TiNb2O7 and TiNb6O17 were synthesized by a solid-state reaction method using TiO2 (99.9%, Rare Metallic) and Nb2O5 (99.99%, Sigma-Aldrich) powders as the starting materials. TiO2 and Nb2O5 were mixed by ball milling at a stoichiometric molar ratio for 4 h at 300 rpm. The mixed powder was pressed into pellets and calcined in air 1300 °C for 12 h (5 °C/min). The morphology and Ti and Nb content in the two TNO materials were observed by field-emission scanning electron microscopy (FE-SEM, Jeol JSM6500F) and energy dispersion spectroscopy (EDS) attached to FE-SEM. The crystalline structures of the materials were analyzed by X-ray powder diffraction (XRD, Rigaku, Ultima4) was conducted using Ka1 radiation at 45KV/40 mA in the range, 10–100° (2θ). Fourier-transform infrared spectroscopy (FT-IR, Shimadzu IR AFFInity-1S) and X-ray photoelectron spectroscopy (XPS, ThermoFisher K-alpha) were used to examine the chemical bonding and oxidation state of the TNO materials, respectively.

### Coin cell assembly and electrochemical analysis

The composition of the TNO anodes was a mixture of active material (TiNb2O7 or TiNb6O17, 70 wt. %), conducting agent (Super-P, 20 wt. %), and polyvinylidene fluoride binder (PVdF 5130, 10 wt. %). The materials were mixed by ball-milling in 1-methyl-2-pyrrolidinone (NMP) until a viscous slurry formed and cast on Cu foil. The electrochemical properties were tested in CR2032-type coin cells. The cells were assembled with a TNO electrode as the working electrode and lithium metal as the counter electrode separated by a membrane with polypropylene in an Ar-filled glove box. The electrolyte was 1 M LiPF6 dissolved in a mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) with a volume ratio 1:2. Cyclic voltammetry (CV) was conducted using a battery cycler (Won A tech, WBCS3000) at a scan rate of 0.1mVs−1 and ranging from 0.05–0.3 mVs−1 from 3.0 to 1.0 V (versus Li/Li+). Galvanostatic charge-discharge tests were performed using the battery cycles at 0.1 C (38.7mAg−1 of TiNb2O7 and 39.7mAg−1 of TiNb6O17) from 3.0 to 1.0 V. The rate capabilities were conducted over the voltage range of 3.0–1.0 V with a current density range 1.0 C to 30 C at room temperature. EIS was carried out by applying an AC signal of 5 mV amplitude over the frequency range from 100KHz to 10mHz using an electrochemical analyzer (NeoSience, SP-300). GITT was tested at a current density of 0.1 C over the voltage range of 3.0–1.0 V using the electrochemical analyzer. The procedure of GITT consisted of galvanostatic charge pulses for each duration time (15 min), followed by a relaxation time (30 min).

## Results and Discussion

### Characterization

Figure 2(a),(b) shows SEM images (magnification ×20,000) of TiNb2O7 and TiNb6O17. A comparison of the particle size and morphology was not accurate due to irregular particle formation by solid state synthesis. On the other hand, the morphologies of the two materials were similar in principle. The mean particle size of the two samples was approximately 1–3 μm. Figure 2(c)~(f) and (g)~(j) present SEM images of (c) TiNb2O7 and (g) TiNb6O17 (magnification ×5,000) and EDS mapping images of (d) oxygen, (e) titanium, and (f) niobium in TiNb2O7 and (h) oxygen, (i) titanium, and (j) niobium in TiN6O17. The calculated atomic percentages of the two materials by EDS are presented in Fig. 2(k) TiNb2O7 and (l) TiNb6O17. The mapping images of Ti and Nb of the two materials exhibited similar dispersion. On the other hand, the images of Ti in TiNb2O7 and TiNb6O17 showed different dispersion and brightness. Ti in TiNb6O17 was darker than that of TiNb2O7. The brightness means that the Ti content in TiNb6O17 is lower than that of TiNb2O7. These results correspond to atomic percentages of Ti and Nb in the two materials. The atomic percentage ratio of Nb and Ti in TiNb2O7 was 1:2 (Ti:Nb = 9.06:18.46), whereas the Nb: Ti ratio in TiNb6O17 was approximately 1:7 (Ti:Nb = 3.48:25.02). These results show that the molar ratio of Nb and Ti is different in the two TNO materials.

Figure 3 (a) TiNb2O7 and (b) TiNb6O17 present XRD patterns of the two TNO materials. The pattern of TiNb2O7 was well indexed to the calculated patterns according to the monoclinic symmetry of TiNb2O7 with the monoclinic ReO3 shear structure with the space group C2/m (JCPDS card No. 70–2009);6 however, there have been no studies of TiNb6O17. Therefore, there is no calculated structural data for TiNb6O17. On the other hand, the XRD patterns of Ti2Nb10O29 have been reported in many studies, which is similar to that of TiNb6O17 13. Therefore, TiNb6O17 has a similar crystal structure to Ti2Nb2O29, which is a Wadsley-Roth shear structure with an A2/m space group. Compared to the XRD patterns of calculated Ti2Nb10O29 and TiNb6O17 synthesized in this study, most peak positions and intensities were in good agreement except for two main peak intensities, which coincides with the XRD patterns reported by Chunfu Lin. The powder XRD patterns of TiNb6O17 was refined with the fullprof software and the rietveld parameters are a = 15.48089 Å, b = 3.81501 Å, c = 20.62921 Å, α&γ = 90°, β = 113.106°, and V= 1218.356 Å3. The calculated rietveld refinement parameters of TiNb6O17 is well matched the with the crystalline parameters of Ti2Nb10O29 13.

FT-IR spectroscopy was conducted to characterize the Ti-O and Nb-O bond of TiNb2O7 and TiNb6O17. Figure 4(a) presents the FT-IR spectra of two samples. The peaks at 924 cm−1 and 520 cm−1 correspond to the stretching vibrations of the Nb-O bonds and Nb-O-Nb bridging bonds and the stretching vibration of at 694 cm−1 and 839 cm−1 are Ti-O-Ti bonds12. The BET specific surface area and volume of the TNO materials were studied by nitrogen adsorption techniques; Fig. 4(b) shows the corresponding isotherm. The specific surface area of TiNb2O7 and TiNb6O17 is 2.66 m2/g and 2.36 m2/g; the mean pore volume of the materials is 0.11 cm3/g and 0.10 cm3/g respectively. As the measurement was conducted by using standard multi point BET, the specific surface area of two materials is almost same. The results are corresponded to the SEM images showing similar particle size of two materials. Therefore, the surface area of the electrodes made by two TNO materials is also same and have not an effect on the electrochemical analysis such as lithium diffusion analysis.

XPS was used to analyze the chemical oxidation state of Ti and Nb in the samples, as shown in Fig. 5. Figure 5(a) TiNb2O7 and (c) TiNb6O17 showed Ti 2p1/2 and 2p3/2 peaks at 464.18 eV & 458.38 eV (TiNb2O7), and 464.18 eV & 458.18 eV (TiNb6O17), respectively. These binding energies were similar and corresponded to the binding energies of Ti4+ in TiO2 3,5,6,8. The noise of the Ti spectra was attributed to the smaller content than Nb. In particular, the spectra of Ti in TiNb6O17 showed more noise than that of TiNb6O17. This may be because TiNb6O17 is composed of a lower Ti content than TiNb2O7. These results match the results of EDS analysis and the mapping images. Figure 5(b) TiNb2O7 and (d) TiNb6O17 present the spectra of Nb5+ in Nb2O5.The Nb 3d3/2 and Nb 3d5/2 peaks were located at (b) 209.88 & 207.18 and (c) 209.68 & 206.98. These values agree with the binding energies of Nb5+ in Nb2O5 3,5,10. Therefore, FT-IR spectroscopy and XPS shows that the two TNO materials are composed with Ti4+ in TiO2 and Nb5+ in Nb2O5.

### Electrochemical analysis

Figure 6 (a),(b) presents the charge and discharge curves of TiNb2O7 and TiNb6O17 at a current density of 0.1 C (38.7 mAg−1 and 39.7 mAg−1) over the voltage range of 3.0–1.0 V. The curves of the two TNO anodes showed three plateau regions. The regions 1 and 3 are the solid-solution region6,9. These regions mean the redox reaction of Ti4+ ↔ Ti5+ and Nb3+ ↔ Nb4+, respectively. Region 2 is a two-phase reaction, which means the reaction of Nb4+ ↔ Nb5+ 3,5,6,7,8,9,10,11,12,13. Compared to the initial discharge capacities, TiNb6O17 exhibited a larger discharge capacity (284 mAhg−1) than that of TiNb2O7 (264 mAhg−1). In addition, the irreversibility of TiNb6O17 was smaller than TiNb2O7 particularly from the 1st to 2nd cycles. CV of TiNb2O7 and TiNb6O17 was conducted at a scan rate of 0.1mVs−1 from 3.0 V to 1.0 V and from 3.0 and 1.0 V for 10 cycles. As shown in Fig. 6(c) TiNb2O7 and (d) TiNb6O17, both curves Fig. 6(a) TiNb2O7 and curve (b) TiNb6O17 showed three current peaks at the oxidation and reduction state, respectively. Each peak is expressed in the curves (Cp and Ap mean the cathodic peaks and anodic peaks). Although the reduction peaks were Cp1 (Ti4+ → Ti3+), Cp2 (Nb5+ → Nb4+), and Cp3 (Nb4+ → Nb3+), Ap1, Ap2, and Ap3 mean the oxidation reaction of Nb3+ → Nb4+, Nb4+ → Nb5+, and Ti3+ → Ti4+ 10,15. These potential regions of the current peaks were matched with the plateau regions in charge and discharge curves. These results show that the reaction mechanisms of the two TNO materials are the same. In addition, the reaction of Nb4+ ↔ Nb5+, which is corresponded to two-phase regions in the charge and discharge curves, showed the highest current peak area and is regarded as the main reaction. Compared to the CV curves of TiNb2O7 and TiNb6O17, TiNb6O17 exhibits higher reactivity and reversibility from the peak area at all cycles. In addition, the decrease in the peak intensity during the cycle, particularly Ap2 and Cp1, suggests that the reversibility of TiNb6O17 is better than TiNb2O7. This is in agreement with the results of the charge and discharge tests.

To understand the electrochemical performance of the lithium diffusion properties of TiNb2O7 and TiNb6O17, the rate capabilities were performed at various C-rates from 1 C to 30 C (discharge rate was fixed at 1 C). Figure 7 presents the rate performance of the two TNO materials. A comparison with the average capacities for the 5thcycle at each C-rate revealed TiNb6O17 to have charge capacities of 252, 230, 206, 187, 107, and 80 mAhg−1 at 1 C, 2 C, 5 C, 10 C, 20 C, and 30 C, respectively. These values are larger than that of TiNb2O7 (234, 210, 174, 152, 52, and 19 mAhg−1). In particular, the difference in the charge capacities at a high rate (20 C and 30 C) was distinct. When calculating the ratio of the average charge capacity, 30 C/1 C, the ratio was 8.12% for TiNb2O7 and 31.7% for TiNb6O17, which suggests that TiNb6O17 has better rate properties than TiNb2O7 13. In addition, a comparison of the cycling retention at 5 C to 30 C revealed TiNb6O17 to have better cycling properties, whereas TiNb2O7 exhibited a rapid decrease in capacity. This means the better electrochemical reversibility of the TiNb6O17. These studies including the results of the charge and discharge tests and CV indicated that lithium ion transport of TiNb6O17 is faster than the rate of TiNb2O7 due to the larger theoretical capacity and better lithium diffusion kinetics by larger lithium site.

Figure 8 presents the CV data of (a) TiNb2O7 and (b) TiNb6O17 at various scan rates in the range, 0.05–0.3 mVs−1. CV at various scan rates is usually used to study the oxidation and reduction properties in electrochemical reactions and obtain the apparent chemical diffusion coefficient of Li-ions16,17,18,19,20. With increasing scan rate, the anodic peaks move to a low potential and the cathodic peaks move to a high potential due to the increasing polarization. In addition, the peak intensities of anodic and cathodic reaction increase with increasing scan rate. The peak current density (I p) revealed a linear relationship with the square root of the scan rate (v −0.5), which is expected for a diffusion-controlled process in Fig. 8(c) TiNb2O7 and (d) TiNb6O17 20,21,22. Each color means the linearity of three anodic and cathodic peaks (Black: Ap1 and Cp1, Pink: Ap2 and Cp2, and Purple: Ap3 and Cp3). The relationship and chemical diffusion coefficient can be determined from the Randles-Sevcik equation (Eq. 1)16,17,23:

$$I{\rm{p}}=0.4463{{\rm{n}}}^{3/2}{{\rm{F}}}^{3/2}{{\rm{C}}}_{{\rm{Li}}}+{{\rm{SR}}}^{-1}{{\rm{T}}}^{-1}{{{\rm{D}}}_{({{\rm{Li}}}^{+})}}^{1/2}{v}^{1/2}$$
(1)

where n is the charge transfer number; F is Faraday’s constant; CLi + is the Li-ion concentration in TiNb2O7 and TiNb6O17; S is the surface area per weight of active materials; R is the gas constant; and T is the absolute temperature (K). $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ is the Li-ion diffusion coefficient, and v is the scan rate. In this study, $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ around three anodic and three cathodic peaks in Fig. 6(c) and (d) was calculated using the above equation. Table 1 lists the calculated $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$. As the results, TiNb2O7 showed the $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ value 10−14 cm2/s which is similar to the diffusion coefficient in the previous study (for phase transition region)24. Compared to $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ at the anodic peaks, $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ of TiNb6O17 was 20 times (Ap1), 12 times (Ap2), and 38 times (Ap3) higher than that of TiNb2O7. $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ of the peaks Ap1 (Nb4+→ Nb5+) and Ap3 (Ti3+→ Ti4+) of TiNb6O17 was particularly high. Although the gap of $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ at the Ap2 (Nb4+→ Nb5+) between TiNb2O7 and TiNb6O17 was smaller than those of Ap1 and Ap3, the difference was apparent. In the case of $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ at cathodic peaks, the values of TiNb6O17 were 5 times (Cp1, Nb4+→ Nb3+), 15 times (Cp2, Nb5+→ Nb4+), and 14 times (Cp3, Ti4+→ Ti3+) higher than those of TiNb2O7. A comparison of the gap of D between TiNb6O17 and TiNb2O7 at the anodic peaks revealed the difference in the DLi + values at the cathodic peaks to be low except for Cp2. On the other hand, the DLi + of TiNb6O17 at Ap2 and Cp2 meaning two phase transition in TNO materials were clearly higher than that of TiNb2O7(12 and 15 times). In addition, the anodic and cathodic reaction of the TNO anodes means the de-lithiation and lithiation process during oxidation and reduction, respectively. Therefore, the lithium diffusion properties of TiNb6O17 were better than those of TiNb2O7. The reason is that TiNb6O17 has a larger unit cell volume and more open Li-ion sites than TiNb2O7. The advanced crystal structure of TiNb6O17 leads to a larger size and number of Li-ion transport paths in the crystal structure, facilitating Li-ion transport during the de-lithiation and lithiation processes10,12,18.

Figure 9 presents the Nyquist plots of TiNb2O7 and TiNb6O17 by EIS. EIS has been used to examine electrode materials because it can reveal the relationship between the crystal lattice with the electrochemical properties24,25,26,27,28,29. This technique provides kinetic information that can be related to a specific state-of-charge or discharge (SOC, SOD), because the measurement is run by applying a low amplitude signal around an equilibrium state26,27,28,29. Figure 9(a) shows the Nyquist plot of TiNb2O7 and TiNb6O17 at the open circuit voltage (OCV) and an equivalent circuit (insert image). Each Nyquist plot was composed of a high-frequency semicircle and Warburg tail region followed by a steep sloping line in the low-frequency region27. The R1 and Cdl are the ohmic resistance between the electrolyte and surface of the electrode and double layer capacitance. The high-frequency semicircle means the charge-transfer resistance (Rct) relevant to the interfacial Li-ion transfer. The Zw is the Warburg impedance, which is related to Li-ion diffusion to the structure of the active materials and corresponds to the tail at a low frequency. Compared to Rct, the TiNb6O17 anode shows a smaller Rct (58Ω) than that of the TiNb2O7cell (85 Ω). This means that the TiNb6O17 anode has a faster Li insertion process in the surface area than TiNb2O7. Figure 9(b) presents a plot of the real part resistance with the inverse square root of the angular speed in the low-frequency range of TiNb2O7 and TiNb6O17 anodes at the OCV state. The Warburg factor ($${\rm{\sigma }}$$) is determined from the slope, and is substituted using equation (Eq. 2 and 3):

$$Z^{\prime} ={R}_{{1}}+{R}_{ct}+\sigma {\omega }^{(-1/2)}$$
(2)
$${D}_{Li}=\frac{{R}^{2}{T}^{2}}{2{A}^{2}{n}^{2}{F}^{4}{C}^{2}{\sigma }^{2}}$$
(3)

where Z’ is the real part resistance; $$\omega$$ is the angular frequency; R is the gas constant; T is the absolute temperature; A is the surface area of the electrode; F is the Faraday constant; and C is the molar concentration of Li ion in an active material. Equations (2) and (3) were used to calculate the Warburg factor and lithium diffusion coefficient, respectively. Table 2 lists the calculated $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ from the obtained $${\rm{\sigma }}$$. The $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ value of TiNb2O7 and TiNb6O17 anodes at the OCV state was 4.57 × 10–14 cm2s−1 and 1.27 × 10–13 cm2s−1, respectively. As a result, the TiNb6O17 anode has a better lithium diffusion process than the TiNb2O7 anode. Although it is not the charge/discharge state, the results revealed the improved lithium diffusion kinetics of TiNb6O17 at the equilibrium state because the more open Li ion insertion site of TiNb6O17 than that of TiNb2O7 affects the barrier energy and electrostatic interaction regarding the Li+ insertion mechanism.

To investigate the Li-ion diffusion properties of two TNO materials at the charge state, ex-situ EIS experiments were performed on TiNb2O7 and TiNb6O17 anodes at three oxidation reaction potentials of Nb3+→ Nb4+(1.36 V), Nb4+→ Nb5+(1.68 V), and Ti3+→ Ti4+(1.98 V) in Fig. 6 (c),(d). Before the EIS experiments, the discharge and charge were processed during 1 cycle and the discharge was then conducted to the cut off potential of 1.0 V. Figure 9(c) TiNb2O7 and (d) TiNb6O17 present Nyquist plots of the two anodes from EIS (Inert images: plot of the real part resistance with the inverse square root of angular speed in the low-frequency range at three oxidation potential). The calculated $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ value is listed in Table 2 with a value at the OCV state. Compared to $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ of two TNO anodes from EIS, TiNb6O17 showed higher $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ values of 2.94 × 10−13 cm2s−1, 1.12 × 10−11 cm2s−1, and 1.85 × 10−12 cm2s−1 at 1.36 V, 1.68 V, and 1.98 V, respectively, than those of TiNb2O7 (6.64 × 10−14 cm2s−1, 1.12 × 10−11 cm2s−1, and 4.57 × 10−11cm2s−1). The $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ values of TiNb6O17 were 4.4 times (1.36 V), 14 times (1.68 V), and 25 times (1.98 V) higher than those of TiNb2O7. Compared to the SSCV results, the $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ values of TiNb6O17 showed different multiples except for the value at 1.68 V (20, 12, and 38 times at Ap1-1.36 V, Ap2-1.68 V, and Ap3-1.98 V, respectively, from SSCV) but exhibited similar tendency showing higher $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ at all redox potentials than TiNb2O7. In particular, the gap of $${{\rm{D}}}_{{{\rm{Li}}}^{+}}$$ at 1.68 V (Ap2 peak at CV) meaning that the two phase regions coincide well with the results of SSCV (14 and 12 fold, respectively.) Therefore, TiNb6O17 has better lithium diffusion properties than TiNb2O7 due to its structure inducing a larger open lithium site and a number of Li-ion transport paths during the charge processes.

GITT was conducted to determine the Li+ chemical diffusion coefficient and analyze the phase transition of the two TNO materials. The techniques developed by Weppner and Huggins assumed one-dimensional diffusion in a solid solution electrode and a uniform current distribution throughout the electrode and estimated the electrochemically active area from the structure of the active material particles not for the diffusion reaction between the electrode surface and electrolyte31,32,33,34,35,36,37. At the transitional GITT, a small constant current was applied to an electrode during a short time and the electrode was left to stand after reaching the OCV state31,32,33,34,35. In this study, GITT was performed on the TNO materials to determine the $${{\rm{D}}}_{{{Li}}^{+}}$$ at a single phase and two phase region as a function of the voltage for the cut off range of the charge/discharge cycle, 1.0–3.0 V. Figure 10 shows the GITT curves of (a) TiNb2O7 and (b) TiNb6O17 during the second cycle. The cells were first discharged at a constant current (0.1 C) for a duration time of 15 min and a rest time of 30 min. The curves showed a similar shape and exhibited three plateau regions meaning the solid-solution regions (Ti4+ ↔ Ti5+ and Nb3+ ↔ Nb4+) and two-phase reaction (Nb4+ ↔ Nb5+) with the charge-discharge curves. These regions also showed the cyclic voltammetry peaks of Cp1 (Ti4+ → Ti3+), Cp2 (Nb5+ → Nb4+), and Cp3 (Nb4+ → Nb3+); Ap1, Ap2, and Ap3 mean the oxidation reaction of Nb3+ → Nb4+, Nb4+ → Nb5+, and Ti3+ → Ti4+in Fig. 6(c),(d), Fig. 10 (c) TiNb2O7 and (d) TiNb6O17 present the single steps of GITT. The steps are the results measured at the 3th step during the charge state for the same duration and rest time. In Fig. 10(c) and (d), ΔEτ and ΔEs shows the change in the cell voltage during the duration time of 15 min from $${\tau }_{0}$$ to $${\tau }_{0+t}$$ and the variation of the cell voltage during the rest time of 30 min. The voltage changes from the steps are recorded as a function of time and the lithium diffusion coefficient were calculated using the following equation based on Fick’s second law32.

$${D}_{L{i}^{+}}=\frac{4}{\pi }{(\frac{{m}_{B}{V}_{M}}{{M}_{B}A})}^{2}{(\frac{{\rm{\Delta }}{E}_{S}}{\tau (d{E}_{\tau }/d\sqrt{\tau }})}^{2}({\rm{\tau }}\ll \frac{{L}^{2}}{{D}_{L{i}^{+}}})$$
(4)

where VM is the molar volume of the active material; MB is molecular weight of the materials; mB is the mass of the active materials in an electrode; L is the lithium diffusion distance (thickness of the electrode); A is the electrode area; and $$\tau$$ is the duration time. When the change in cell voltage with duration time exhibited a linear relationship on plotting against τ1/2, equation (4) can be changed to the following simple equation32

$${D}_{L{i}^{+}}=\frac{4}{\pi \tau }{(\frac{{m}_{B}{V}_{M}}{{M}_{B}A})}^{2}{(\frac{{\rm{\Delta }}{E}_{S}}{{\rm{\Delta }}{E}_{S}})}^{2}({\rm{\tau }}\ll \frac{{L}^{2}}{{D}_{L{i}^{+}}})$$
(5)

This equation assumes that the molar volume (VM) is stable with the change in Li content in an active material. In this study, the Li+ diffusion coefficient of the two TNO materials could be calculated, as shown in Fig. 10. (c)–(e). Figure 10.(e) shows the linear relationship between the single steps in Fig. 10. (c),(d). The Li+ diffusion coefficients of the two TNO materials from the GITT results are presented as a function of SOC (%) vs. Log ($${D}_{{{Li}}^{+}})$$ during the charge state in Fig. 10. (f). The coefficients were calculated at all steps during the GITT measurements except for the 1st step and the end two steps of the end due to the large voltage variations. The two cells showed three minimum Li+ diffusion coefficient points in Fig. 10.(f) and the voltages representing the points are shown. These minimum diffusion coefficients suggest a phase transition for strong attractive interactions between the intercalation species and the host matrix or some order-disorder transition during cycling24,32. Compared to the SSCV and EIS results, the voltages are the three redox potentials of TNO materials, in which the cell voltages of TiNb2O7 and TiNb6O17 are 1.42 V~1.38 V (Nb3+ → Nb4+), 1.71~1.75 V (Nb4+ → Nb5+), and 2.01~2.03 V (Ti3+ → Ti4+) vs. 1.36 V, 1.68 V, and 1.98 V, respectively, from the SSCV and EIS measurements. This explains why the plot from GITT has an electrochemical reaction mechanism of two TNO materials with SSCV and EIS. The Li+ diffusion coefficients of TiNb2O7 and TiNb6O17 from three points were calculated to be 1.11 × 10−11 and 6.70 × 10−11 cm2s−1 (Nb3+ → Nb4+), 2.74 × 10−11 and 2.23 × 10−10 cm2s−1 (Nb4+ → Nb5+), and 1.03 × 10−10 and 7.47 × 10−10 cm2s−1 (Ti3+ → Ti4+). The coefficients of TiNb6O17 showed higher values than that of TiNb2O7 at all positions with the other Li+ diffusion measurements, which indicates that TiNb6O17 has superior Li+ diffusion kinetics than TiNb2O7 owing to its larger unit cell volume. Compared to the diffusion coefficients of each transition region, the values increased from the (Nb3+ → Nb4+) reaction to the (Ti3+ → Ti4+) reaction, which correspond to the EIS results in Table 2. Among the three diffusion values, the diffusion coefficients of the (Nb4+ → Nb5+) reaction showed the largest increase from TiNb2O7 to TiNb6O17 and also corresponds to the EIS results. These trends suggest that the oxidation reaction is a two phase transition region of TNO materials with the charge-discharge curves and cyclic voltammetry results (the most reaction region). In the event of SSCV, the measurements showed a different tendency with EIS and GITT. The coefficients of the (Nb4+ → Nb5+) reaction (Ap2) showed the largest values and the diffusion coefficients of the (Nb3+ → Nb4+) reaction showed the largest increase from TiNb2O7 to TiNb6O17. This may be due to the inaccuracy of the SSCV measurements in this study. Compared to Ap2, both Ap1 and Ap3 showed a small peak current and a broad shape. Therefore, the diffusion coefficients of the two peaks may be not precise values.

## Conclusions

Galvanostatic charge-discharge, cyclic voltammetry, and rate capability test were conducted to analyze the electrochemical performance and properties of TiNb6O17 and TiNb2O7. From the results, two TNO materials showed three similar plateau regions and three redox peaks corresponding to two Nb redox and one Ti redox reaction. TiNb6O17 showed higher capacities of 284mAh/g than that of TiNb2O7 264mAh/g. In the rate capability test, TiNb6O17 exhibited improved rate capacity of 80mAh/g at 30 C than 19mAh/g for TiNb2O7. SSCV, EIS, and GITT measurement were taken to investigate the performance and lithium diffusion properties related to the unit cell volume of the two TNO materials. The anodic and cathodic Li+ diffusion coefficients from SSCV were in the range of 10−14 to 10−15 cm2s−1 for TiNb2O7 and 10−13 to 10−14 cm2s−1 for TiNb6O17. The anodic diffusion coefficients of TiNb6O17 were 5 times (Nb3+ → Nb4+), 15 times (Nb4+ → Nb5+), and 14 times (Ti3+ → Ti4+). From the EIS measurement, the coefficients were in the range of 10−12 to 10−14cm2s−1 of TiNb2O7 and 10−11 to 10−13cm2s−1 of TiNb6O17 at the OCV state and three oxidation potential region of the two TNO materials during the charging process. The three minimum diffusion coefficients points were determined from the GITT measurement. The diffusion coefficients of the two phase transition region (Nb4+ → Nb5+) were improved 10 fold compared to that of TiNb2O7. CV, EIS, and GITT indicated that TiNb6O17 has better lithium diffusion kinetics and electrochemical performance than TiNb2O7 because of its large unit cell volume and more open Li+ insertion site.

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## Acknowledgements

This study was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (MEST) of the Korean government (2009–0093818).

## Author information

### Affiliations

1. #### Department of Chemistry, University of Ulsan, Ulsan, 680-749, Korea

• Yong-Seok Lee
•  & Kwang-Sun Ryu

### Contributions

Kwang-Sun Ryu decided the concept of the experiments, discussed the results and reviewed the manuscript. Yong-Seok Lee performed all experiments, analyzed the data and wrote the manuscript.

### Competing Interests

The authors declare that they have no competing interests.

### Corresponding author

Correspondence to Kwang-Sun Ryu.