Nano/crystal structures of the as-prepared LTO model electrodeThe LTO/Pt/Ti/SiO2/Si thin film electrodes were prepared by layer-by-layer magnetron sputtering. As shown in the cross-section SEM image in Fig. 1a, the thickness of Ti, Pt and LTO layers is controlled at about 45 nm, 130 nm and 130 nm, respectively. We systematically explored the materials, including Cu, Au, Ag and Pt, as the optical reflector and current collector layer, and found that Pt is the most suitable material for the electrochemical and optical characterizations (see SI, Supplementary Note 1). Figure 1b shows the scanning electron microscopy (SEM) for the surface of the as-prepared LTO thin film electrode. The LTO thin film consists of many tightly stacked grains with an average size of about 48 nm. This polycrystalline structure was also confirmed in the cross-section SEM image in Supplementary Fig. 1a. The High-resolution TEM image in Fig. 1c shows the lattice fringe of LTO (111) faces. The crystallinity was also confirmed by XRD spectra in Fig. 1d, in which the diffraction peaks of LTO, (111), (311) and (400) at around 2θ = 18.3, 35.7, and 42.9 degrees are observed, with a good match with the standard card (PDF#-040802), confirming the crystal structure with the space group of \({Fd}\bar{3}m\). In addition, the Raman spectrum of the as-prepared LTO thin film is shown in Fig. 1e. It is worth noting that the phase purity of the as-prepared LTO thin films should be optimized by tuning the ratio of Li: Ti in the sputtering target (see Supplementary Fig. 1b). The peak at the wavenumber of around 233 cm-1 is the F2g vibration mode of Ti-O bonds37, which corresponds to the asymmetric bending vibration of TiO6 octahedrons. The peaks at around the wavenumbers of about 335 cm-1 and 432 cm-1 can be attributed to the Eg and A1 mode of Li-O bonds, deriving from the stretching and bending vibration of LiO6 octahedrons and LiO4 tetrahedrons, respectively47,48. In the as-prepared LTO thin film, about 1/5 of 16d sites in the Li4Ti5O12 lattice are occupied by Li+, forming LiO6 octahedrons (Eg band), meanwhile, all lithium ions occupy at 8a sites, forming LiO4 tetrahedrons (A1 band). During the intercalation and de-intercalation, Li+ will reversibly insert and extract to the 16c sites (also forming the LiO6 octahedrons) and 8a sites. Therefore, the ratio of these two peaks is an indicator of lithium-ion occupation states in LiO6 octahedra and LiO4 tetrahedra47. The strong peak at the high wave number region (around 674 cm-1) is the A1g vibration band of Ti-O bonds, corresponding to the symmetric stretching vibration of the TiO6 octahedron in the crystal structure37. These Raman peaks, together with the above crystal/nano-structure characterization results, support that the as-prepared LTO has a \({Fd}\bar{3}m\) crystal structure. As a result, the as-prepared LTO thin film with stable spinel structure shows excellent charge/discharge cycle stability, with only about 15% capacity loss after 1500 lithiation/de-lithiation cycles (Supplementary Information, Fig. S2a and S2b).Fig. 1: Micro/Nano-structures of the as-prepared LTO thin film electrodes.a Argon-ion polished cross-sectional SEM image of Li4Ti5O12 deposed on the Pt/Ti reflector/current collector on the SiO2/Si substrate. b Surface SEM image of Li4Ti5O12 thin film electrode. Inset is the statistical result of the average grain size. c TEM lattice fringe of a Li4Ti5O12 grain inside the thin film electrode. d XRD pattern of SiO2/Si substrate and LTO/Pt/Ti/SiO2/Si model electrode. e Raman spectra of the as-prepared Li4Ti5O12 thin film electrode. The vibration mode of each peak and the corresponding schematic diagram are shown in the insets.Lithium occupation states inside LTO lattice during quasi-equilibrium and non-equilibrium lithiationWe assembled the as-prepared LTO film into coin cells and conducted electrochemical performance tests, including rate capability tests (Fig. 2a), cycling tests (Supplementary In formation Fig. S2a and S2b), and CV tests (Supplementary Fig. 2c). Before the rate performance tests, the LTO cell was activated by cycling at 0.1 C to form a stable electrode surface passivation layer. The rate performance in Fig. 2a shows that the battery delivers a high discharge capacity (~160 mAh/g), but insufficient Coulombic efficiency (~93%) at small charge/discharge C-rates (0.2 C). As the rate increased to 10 C, the battery capacity dropped to about 50% of the capacity at 0.2 C. However, at this rate, the average Coulombic efficiency of the battery improved to about 99%. Figure 2b illustrates the charge/discharge curves of the battery during the rate tests. At 10 C rate, despite only about half of the specific capacity being achieved, the discharge curve still showed a voltage plateau below 1.5 V vs Li+/Li, manifesting the two-phase transition/co-existence inside the LTO thin film.Fig. 2: Electrochemical performance and phase transition mechanisms of LTO thin film electrodes captured by in situ Raman spectroscopy.a Rate performance of LTO thin film electrode. b Charge-discharge curves at different C-rates. c In situ Raman spectra at different voltages during 0.5 C lithiation cycles. d The charge/discharge curves of the LTO thin film electrode at about 0.5 C (quasi-equilibrium) and 10 C (non-equilibrium conditions). The blue color and orange color represent quasi-equilibrium and non-equilibrium lithiation, respectively. Insets are the Raman spectra of LTO Eg mode and A1g mode at the initial state (I sate), quasi-equilibrium half-lithiation state (H sate), quasi-equilibrium end-lithiation state (EE sate) and non-equilibrium end-lithiation state (NE state).To reveal the differences in lithium-ion diffusion kinetics under fast and slow charging conditions, we conducted in situ Raman spectroscopy measurements using the electrochemical cell as shown in Fig. 2c, aiming to comprehend the capacity decay, Coulombic efficiency and diffusion pathways of LTO films during fast and slow charge/discharge processes. Here, our LTO thin film electrode shows prominent capacity decay (20%) and discharge voltage platform dropping when the C-rate is >0.5 (Fig. 2b), we therefore denote 0.5 C as the quasi-equilibrium and 10 C as the non-equilibrium lithiation process for the discussions and comparations. As shown in the in situ Raman spectra of LTO during the 0.5 C lithiation (Fig. 2c), the variations in the peak intensity of F2g, Eg, A1 and A1g were used to infer the changes in lithium-ion occupation states. As mentioned above, the F2g peak represents the twisting vibration of TiO6 octahedra and the A1g peak corresponds to the symmetric stretching vibrations of TiO6 octahedra. Therefore, the occupation of lithium at 16c sites will enhance the twisting vibration of TiO6 octahedra49 but greatly suppress the symmetric vibrations of TiO6 octahedra.As shown in Fig. 2c, we observed the peak intensity decrease of A1g and increase of F2g during the lithiation, and vice versa during the de-lithiation (Supplementary Fig. 3). This is consistent with previous assumptions that, the intercalated lithium ions, together with the original lithium ions sitting at the 8a site, all move to the 16c sites during the lithiation20. We noticed that the A1g peak intensity stays until the end of the discharge platform, and only suddenly decreases at around 1.39 V when the LTO leaves the Li4/Li7 two-phase co-existence region. This indicates the 16c sites are not massively occupied by lithium-ions before leaving the two-phase co-existence region. When discharged at ~1.32 V, the disappearing A1g peak, together with the enhanced F2g indicated the long-range ordering of a nearly full-occupied 16c and full-emptied 8a lithium occupation states. The emptied 8a sites are due to the Coulombic repulsive force derived from the lithium ions at the coplanar 16c site20. Figure 2d shows the typical charge/discharge curves and Raman spectrum at different lithiation states during ~0.5 C (quasi-equilibrium) and ~10 C (non-equilibrium). Importantly, we found that the Raman spectra under non-equilibrium lithiation processes are different from the quasi-equilibrium lithiation process. The four Raman spectra of LTO at initial state (I sate), quasi-equilibrium half-lithiation state (H sate), quasi-equilibrium end-lithiation state (EE sate) and non-equilibrium end-lithiation state (NE state) are compared in the insets. Comparing the Raman spectra at the NE state and EE state, one can find that, under large lithiation current density (NE state), the peak intensity of A1g mode did not completely disappear, suggesting that the 16c sites are not fully occupied by lithium-ions under fast discharging conditions (the remaining of unreacted electrode materials). This is consistent with the capacity loss at high-rate charging/discharging as observed in Fig. 2a. Surprisingly, we also noticed that, when about half of the specific capacity of lithium ions is intercalated into LTO, the NE state shows a much weaker A1g peak intensity compared with the quasi-equilibrium lithiation at the H state, indicating a different lithium occupation state (more 16c Li+) within LTO lattice during the non-equilibrium lithiation process. This implies the different paths of lithium-ion embedding and migration in the quasi-equilibrium (slow discharging) and non-equilibrium (fast discharging) processes.Based on the Raman spectra results, we can infer the lithium-ion migration and occupation states as depicted in Fig. 3a. At the initial state, lithium-ions exclusively occupy the 8a sites in the LTO lattice. During the quasi-equilibrium lithium insertion process, lithium ions from outside begin to insert into the 16c sites, meanwhile, the lithium-ions in the 8a positions, influenced by the Coulombic repulsion from embedded lithium ions, begin to move to adjacent coplanar 16c sites, creating a “8a-16c” rapid channel20. With the continued insertion of lithium ions into the 16c sites of LTO, more 8a-site lithium ions are moving to the 16c sites until the Li4 phase fully changes to the Li7 phase. At the end of quasi-equilibrium lithiation discharge (EE state), the charge order was achieved in LTO crystal with fully occupied 16c sharing vertices and fully emptied 8a sites. By contrast, during the non-equilibrium process, the overpotential applied on the LTO electrode may reduce the nucleation energy barriers27, therefore forming more nucleation sites of the Li7 phase inside the LTO crystal lattice. The dispersed nucleation sites result in more Li4/L7 interfaces50, indicating more lithium-ions in 8a sites can be repelled to the 16c sites (more 8a → 16c migrations). As a result, when about 50% Lithium-ions of full-capacity were intercalated into the LTO crystal lattice, the non-equilibrium NE state showed a much higher ratio of 16c site occupation compared with the H sate during the quasi-equilibrium lithiation.Fig. 3: The proposed phase transition models in the LTO electrodes and the formation energy calculations for the difference phase transition products.a Schematic of lithium occupation states and diffusion paths in LTO during the quasi-equilibrium and non-equilibrium lithiation process. The yellow tetrahedra represent the 8a sites in the lattice, and the octahedra represent the 16c sites. I, H, EE and NE states represent the initial state, quasi-equilibrium half-lithiation state, quasi-equilibrium end-lithiation state and non-equilibrium end-lithiation state, respectively. At the EE state crystal structure sketch, the purple arrows indicate the migration of lithium-ions into 16c sites, and the red rows indicate the migration of each sub-step (8a → 16c). b The formation energy and corresponding Density Functional Theory (DFT) calculation model of I state, EE state and NE states.These lithium occupation states are further verified by the formation energy using Density Functional Theory (DFT) calculations. As shown in Fig. 3b, according to the Raman characterizations, we constructed three crystal structures with stoichiometric ratios of (Li3)8a(Li1Ti5)16d(O12)32e, (Li6)16c(Li1Ti5)16d(O12)32e and (Li1.5)8a(Li3)16c(Li1Ti5)16d(O12)32e to represent the I state, EE state and NE state, respectively. The initial spinel LTO at I state, with all lithium-ions occupying 8a sites, has a formation energy of about −3.36 eV. At the EE state, when the lithium-ions fully occupy the 16c sites, the LTO shows an increased formation energy of about −3.21 eV. Interestingly, we noticed that, at the NE state, in which ½ of the 8a sites are emptied and ½ of the 16c sites are filled, the structure shows a lower formation energy of −3.26 eV compared with the EE state, indicating the energetically favorable of forming an 8a/16c co-occupied state under non-equilibrium lithiation process. It is also worth noticing that, unlike the EE state, the NE state still contains lithium ions in the 8a sites, indicating the presence of the face-sharing Li-polyhedra “rapid diffusion channels”51. In the quasi-equilibrium condition, the fully discharged EE state of LTO consists only of 16c sites sharing vertices, leading to slower ion migration kinetics, therefore, the Coulombic efficiency is low during the de-intercalation process. In contrast, at the end of the discharged NE state, the “8a-16c” rapid channel persists, allowing lithium ions to quickly extract through these channels, thereby enhancing the Coulombic efficiency during charge processes.Lithium transportation kinetics during the quasi-equilibrium and non-equilibrium lithiationTo better understand the impact of lithium-ion occupation states on the charge transfer and ion migration of LTO, we employed dynamic electrochemical impedance spectroscopy and distribution of relaxation times (DRT) analysis to study the impedance of LTO electrodes during quasi-equilibrium and non-equilibrium processes. In LTO cells, lithium-ion transportations typically contain three steps as they migrate from the electrolyte to the LTO lattice (Fig. 4a). The first step (Step 1) involves the diffusion of lithium ions and lithium solvation complexes in the electrolyte bulk, allowing them to move to the surface of the LTO electrode. The second step (Step 2) is the interfacial-related processes, during which lithium ions strip off the solvent molecules and traverse the electrode-electrolyte interface. The final step (Step 3) is the diffusion of lithium ions within the LTO lattice structure. These kinetic steps can be de-convoluted by using DRT analysis which converts the complex electrochemical impedance data to a series of relaxation time distribution functions, providing detailed insights into the electrochemical processes at various time scales within the cell52.Fig. 4: Lithium-ion transportation kinetics revealed by the distribution of relaxation time constant spectra.a The schematic lithium migration process in an LTO cell. b Temperature dependency of the transfer resistance of LTO cell at the initial state measured at OCP. The red dotted line is the linear fitting curve with a fitting coefficient of ~0.975. c Dynamic distribution of relaxation time (DRT) spectra of initial LTO-Li battery at 25 °C, 30 °C, 40 °C, 50 °C, 60 °C,70 °C and 80 °C measured at OCP. Dynamic DRT spectra of (d) quasi-equilibrium lithiation process and (g) non-equilibrium lithiation process measured at 25 °C. 3D DRT peak map of LTO cell during the (e, f) quasi-equilibrium and (h, i) non-equilibrium lithiation process at the time constant region of interest. The expanded plot in the high-frequency region can be found in Supplementary Fig. 4.Step 1 is generally considered to be a faster transportation process than the de-solvation/charge transfer process (Step 2) and bulk diffusion (Step 3), we therefore focused on characterization of Step 2 and Step 3. Temperature dependencies Arrhenius plots of the charge-transfer resistance were plotted in Fig. 4b to understand the kinetics of lithium-ion transfer in the LTO electrode-electrolyte interface (Step 2). The charge transfer resistance (Rct) increased with decreasing temperature following an Arrhenius-type behavior showing a thermally activated process53:$$\frac{1}{{R}_{{ct}}}={A}_{0}{e}^{-\frac{{E}_{a}}{{RT}}}$$
(1)
where A0, Ea, R, and T are the frequency factor, the activation energy [kJ mol-1], the gas constant (8.3145 Jmol−1 K−1), and the temperature [K], respectively. The activation energy, Ea, can be obtained from the slope of a log(1/Rct) versus the inverse of temperature 1000/T plot, as shown in Fig. 4b, the activation energy is about 49.3 kJ mol-1, which is close to the previously reported lithium ion de-solvation energy54. These temperature-dependent impedance spectra were further converted to DRT spectra (Fig. 4c) to find the relaxation time domains of Steps 2 and Step 3. By comparing the DRT of the battery from 25 °C, 30 °C, 40 °C, 50 °C, 60 °C, 70 °C and 80 °C, it can be seen from the relaxation time spectra that the peak position at relaxation time (τ) range from ~0.1 to 1.0 s is slightly increased with the increased temperature, while the peak of relaxation time at about 10 s is unchanged. The mid-frequency peak (τ ~ 0.1−1.0 s) can be attributed to the lithium transfer across the LTO-electrolyte interface, such as the de-solvation processes. It shows an increased time constant due to the effects of solid-electrolyte interphase (SEI) formed at elevated temperatures44. While the intensity of the low-frequency relaxation time peak (τ ~ 1−10 s) significantly decreased at high temperatures should be attributed to the thermal activation of lithium migration inside the LTO lattice (Step 3, bulk diffusion). At the frequency of about τ ~ 0.001 s, we also observe the relatively stable SEI-related peaks that do not change upon the charge/discharge cycles (Supplementary Fig. 4), demonstrating the SEI-free characteristic of the LTO anode. Overall, the time scale of lithium transport through the LTO-electrolyte interface and diffusion inside the LTO thin film bulk are consistent with the previously reported values55,56,57.Based on these characteristic time constants, we conduct the dynamic DRT tests for the LTO battery during the (Fig. 4d–f) quasi-equilibrium and (Fig. 4g–i) non-equilibrium lithiation processes. The Nyquist plots can be found in Supplementary Fig. 5. At the time scale of crossing interfacial diffusions (Fig. 4e), there are two peaks. The peaks are related to the de-solvation of lithium ions on the LTO surface. During the lithium intercalation, the de-solvation-related peaks reduce at the two-phase co-existence region and then increase at the end of lithiation. A similar trend was observed in the DRT peak of bulk diffusion (τ = 1–10 s region) as shown in Fig. 4f. The DRT peak intensity at around τ = 5 s is greatly reduced when discharged to the Li4/Li7 two-phase co-existence region due to the formation of the “8a⇋16c” fast channel as discussed above. However, at the end of the lithiation state, when the 16c sites are fully occupied by lithium ions, the peak intensity almost increases to the original impedance value due to the disappearance of the 8a⇋16c” fast channels. This is consistent with the Raman characterization results in Fig. 2. However, during the initial non-equilibrium lithiation process (Fig. 4g–i), it can be found that at the cut-off discharge state, the intensity of the de-solvation and bulk diffusion-related DRT peaks are both very weak. This indicates that at the NE state, the impedance of lithium transportation at the LTO-electrolyte interface or LTO bulk are both very small. The low impedance value is a result of the co-existence of lithium-ions at 8a and 16c sites in the LTO lattice (as well as the small amount of the unreacted Li4 phase in the electrode), which also proves the lithium-ion migration mechanism and occupation states as shown in Fig. 3.Mesoscopic scale phase distribution patterns inside LTO thin film electrodesTo further investigate the mesoscopic phase distribution of Li4 and Li7 phases inside the LTO thin film during the quasi-equilibrium and non-equilibrium lithiation process, we conducted in situ UV spectroscopy tests in a reflective geometry as shown in Fig. 5a. In this geometry, the top LTO layer is a wide-bandgap semiconductor with a bandgap of approximately 2.5–3.55 eV37,58, when visible light is vertically incident, due to the wide bandgap characteristic, the light with energy smaller than 2.5–3.55 eV, corresponding to the wavelength λ > 350–496 nm, will pass through the LTO layer to reach the Pt surface. Because of the high reflectivity of the Pt layer (see the reflection spectrum of Pt in Supplementary Note 1), the light will be reflected on the Pt surface, resulting in a high reflectance in the obtained spectrum. When lithium ions are inserted into the LTO lattice, a donor energy level appears close to the conductance band (Fig. 5a), allowing the LTO to largely absorb the light with certain wavelengths (about 500–900 nm), and reducing the reflectance at these wavelengths of the testing system. This will cause the so-called electrochromism (Supplementary Fig. 5). Therefore, the reflectance can quantitatively represent the amount of lithium insertion into the material. Figures 5c, d are the in situ UV reflection spectra of LTO during the quasi-equilibrium (~0.5 C) and non-equilibrium (~10 C) lithiation processes. Overall, the changes in the two sets of spectra align with the proposed assumption that the reflectance at the high-wavelength region (λ > 500 nm) is decreasing during the lithium intercalation, indicating a narrowed band gap of LTO. A closer scrutiny of the spectra reveals that in the non-equilibrium process, the change in reflectance from the initial to the cutoff state is smaller than that in the quasi-equilibrium process, indicating a smaller amount of lithium-ion insertion. Moreover, by fitting the full reflective spectra of LTO, we can further quantify the mesoscopic Li4 and Li7 distribution patterns during the quasi-equilibrium and non-equilibrium processes using the effective dielectric constant model.Fig. 5: Electrode-scale phase transition and distribution patterns studied by in situ optical microscopy.a Schematic diagram of the electrochemical cells using LTO model electrode for the reflective UV spectroscopy measurements. b Schematic diagram of the LTO electron band structure change during lithium intercalation. In situ UV spectra of LTO thin film model electrode during the (c) quasi-equilibrium and (d) non-equilibrium lithiation processes. e The simulation and experiment results of LTO reflectance (at λ = 780 nm) changes vs the amount of lithium insertion during the lithium intercalation. Insets show the schematic diagram of the parallel and series dielectric constant models for the reflectance fitting for different phase distribution patterns. The error bars represent the standard deviations of the measured reflectance at each lithium concentration, based on three separate lithiation/de-lithiation measurements. f Numerical simulation results of the reflectance changes during the lithium intercalation with different volumetric ratios (α) of the 8a → 16c migration-induced Li7. The more nucleation sites in the LTO thin film, the larger number of interfaces were formed, and the larger α value was achieved. g Schematic diagram of the phase distribution of Li4 and Li7 phases in LTO thin film during the quasi-equilibrium and non-equilibrium lithiation processes. The blue color regions and wheat color regions represent the Li7 and Li4 phases, respectively.First of all, it is worth mentioning that the changes in reflectance are a result of the changed optical refractive index of the LTO layer, which can strictly be described by the model of an incident light reflected by the electrolyte/LTO/Pt model sample (also see Supplementary Information, Supplementary Note 2)59,60,$$R={\left(\left|\frac{{r}_{1}+{r}_{2}{e}^{i\frac{2\pi }{\lambda }\cdot 2{n}_{LTO}^{ * }h}}{1+{r}_{1}{r}_{2}{e}^{i\frac{2\pi }{\lambda }\cdot 2{n}_{LTO}^{ * }h}}/{r}_{2}\right|\right)}^{2}$$
(2)
Where R is the total reflectance of the system, r1 and r2 are the reflection coefficients for the two interfaces, \({n}_{{LTO}}^{* }\) and h are the complex refractive index and thickness of LTO thin film, respectively, and λ is the wavelength of incident light. The real-time reflective spectra can yield the effective optical dielectric constant of LTO by using Eq. (3):$${\varepsilon }_{{eff}}={\varepsilon }_{{eff}}^{{\prime} }-i{\varepsilon }_{{eff}}^{{\prime} {\prime} }={({n}_{{LTO}}^{* })}^{2}$$
(3)
Where \({\varepsilon }_{{eff}}\) is the effective dielectric constant of the LTO, \({\varepsilon }_{{eff}}^{{\prime} }\) is the real part and \({\varepsilon }_{{eff}}^{{\prime} {\prime} }\) is the imaginary part of \({\varepsilon }_{{eff}}\). Schmitz et al. 19,46 have proposed that if a thin film’s phase transition progresses gradually from the surface towards the interior (as the inset depicted Multilayer propulsion (MP) model in Fig. 5e), then the relationship between the material’s effective dielectric constant (\({\varepsilon }_{{eff}}\)) and the dielectric constants of the two phases can be expressed by,$${\varepsilon }_{{eff}}={f}_{\!\!1}{\varepsilon }_{1}+{f}_{\!\!2}{\varepsilon }_{2}$$
(4)
Where ε1 and ε1 are the dielectric constants of the first and second phases, f1 and f2 are the proportionality coefficients (volumetric ratio) of the two phases, respectively. However, if the phase transition process spreads laterally along the thin film electrode through the grain boundaries/defect sites, which we denoted as the Nano-filament (NF) model61,62 as shown in the inset in Fig. 5e, then the relationship satisfies,$$\frac{1}{{\varepsilon }_{{eff}}}=\frac{{f}_{\!\!1}}{{\varepsilon }_{1}}+\frac{{f}_{\!\!2}}{{\varepsilon }_{2}}$$
(5)
Therefore, Eqs. (3–5) can be used to differentiate the phase distribution patterns inside the LTO thin film. Figure 5e shows the simulation and experiment result of reflectance changes during the lithium intercalation recorded at characteristic wavelength63. The lithium concentration is determined by the galvanostatic discharge capacity. From Fig. 5e, one can find that the quasi-equilibrium lithiation process well follows the NF model, while the non-equilibrium lithiation process shows unexpected faster reflectance dropping. This may be a result of a faster and higher ratio of Li7 phase formation at each lithium concentration during the non-equilibrium lithiation process. According to the Raman characterization in Fig. 2, under a non-equilibrium lithiation process, a larger amount of 16c lithium ions is formed due to the 8a → 16c migration-induced Li7 phase. The more nucleation sites inside the LTO, the higher the volumetric ratio of the interface, and the more 8a → 16c migration-induced Li7 phase was formed in the LTO thin film. Therefore, we introduced an interfacial coefficient (α) to modify the NF model under a non-equilibrium lithiation process,$$\frac{1}{{\varepsilon }_{{eff}}}=\frac{{f}_{\!\!1}-{{{\rm{\alpha }}}}}{{\varepsilon }_{1}}+\frac{{f}_{\!\!2}+{{{\rm{\alpha }}}}}{{\varepsilon }_{2}}$$
(6)
In this modified NF model, the interfacial coefficient α represents the effect of interface on the proportionality coefficients, f1 and f2. The more interfaces were formed, the higher the value of α is. In Fig. 5f, one can find from the numerical simulation result that the larger the value of α is, the faster the decrease of reflectance can be expected. Moreover, from the top view schematic of the two-phase mode in thin film electrode, we can easily obtain that, regardless of the vertical shape of nano-filaments, α is not a constant value but proportional to the proportionality coefficients of the nucleation phase (f2), indicating an even faster dropping of reflectance in a real scenario. The numerical simulation result of the NF model with different α explains the existence of this interface effect under the non-equilibrium state. Therefore, as sketched in Fig. 5g, we believed that the Li4/Li7 phase distribution inside the LTO thin film under quasi-equilibrium and non-equilibrium lithiation processes differs in the density of nucleation sites, which may result in the Li7 nanofilaments with different diameters. Under non-equilibrium conditions, the dense and fine Li7 nanofilaments in LTO have more nucleation interface, contributing to the larger ratio of 16c/8a occupation that is experimentally verified by in situ optical and DRT spectroscopy measurements. Importantly, this mesoscopic phase distribution pattern of Li4 and Li7 phases has also been proved by three-dimensional nano-tomography AFM64,65,66 as shown in Supplementary Fig. 6, where the nano-filament structure, the more conductive Li7 phases penetrating the LTO thin film, was observed in the partially lithiated LTO thin film under non-equilibrium condition. We, therefore, suggest that further optimizing the volumetric density of the Li4/Li7 interface, consisting of the sub-nanometre lithiated and unlithiated LTO domain interfaces, may improve the fast-charging performance in LTO thin film electrodes.
Nonequilibrium fast-lithiation of Li4Ti5O12 thin film anode for LIBs
