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Amorphization as a pathway to fast charging kinetics in atomic layer deposition-derived titania films for lithium ion batteries Jianchao Ye, Patrick Shea, Andreas C. Baumgaertel, Stanimir A. Bonev, Monika M. Biener, Michael Bagge-Hansen, Y. Morris Wang, Juergen Biener, and Brandon C. Wood Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b04002 • Publication Date (Web): 29 Nov 2018 Downloaded from http://pubs.acs.org on December 2, 2018

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Chemistry of Materials

Amorphization as a pathway to fast charging kinetics in atomic layer deposition-derived titania films for lithium ion batteries Jianchao Ye*,†, Patrick Shea†, Andreas C. Baumgaertel, Stanimir A. Bonev, Monika M. Biener, Michael Bagge-Hansen, Y. Morris Wang, Juergen Biener, Brandon C. Wood* Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA ABSTRACT: Safe, reliable materials with fast charging kinetics are required to increase the power density of batteries in electric vehicles. One potential avenue for improving kinetics involves disturbing the electrode crystalline structure to alter diffusion properties. However, it remains controversial whether amorphization universally benefits intercalation kinetics, and the specific enhancement mechanisms with respect to the crystalline counterpart are often unclear. In this work, we systematically explore the effects of amorphization on Li+ intercalation kinetics using variable-thickness TiO2 films derived from atomic layer deposition. The amorphous films exhibit an order-of-magnitude faster Li+ diffusivity and > 0.3 eV reduction in the effective Li+ migration barrier with respect to the crystalline anatase phase, resulting in superior high-rate capacity. To investigate the origin of this improvement, we perform a detailed analysis of the energy landscape, migration barriers, and diffusion rates in validated models of amorphous TiO2 using multiscale simulations. The range of site energies produced by the intrinsic structural disorder of amorphous TiO2 is found to generate low-barrier pathways for Li+ migration that penetrate some distance into the material, resulting in defined regions with faster diffusion behavior. We propose that the formation of these fast ion transport “highways” improves accessibility to interior sites, leading to significantly improved overall rate performance in the amorphous films. In addition to confirming the viability of amorphous TiO2 films as an alternative to crystalline layered materials for high-rate-performance energy storage, this work outlines a strategy for determining the conditions under which such performance might be realized in other similar materials.

1.

In parallel with these efforts on crystalline ordered materials, there has been growing interest in exploring disordered and amorphous materials for fast charging purposes. For example, the presence of a thin amorphous non-stoichiometric surface layer has been shown to dramatically enhance the rate performance of LiFePO49. Disorder at the atomic scale also appears to assist diffusion in certain materials. For instance, it has been shown that cation-disordered Li1.211Mn0.467Cr0.3O2 exhibits a high Li cycling capability due to percolation of active transition-metal-poor channels that allow facile Li+ diffusion10. Disordering of anions has also been linked to fast diffusion in certain ionic conductors, such as loosely packed Li/Na closo-borate salts11, 12. These studies point to possible benefits of introducing diversity in the local structural environments as a means of enhancing diffusion kinetics.

Introduction

Extreme fast-charging batteries are in urgent demand for electrical vehicles, portable electronics, and grid-scale energy storage. Current electric vehicles can require hours to attain full capacity, significantly limiting their appeal compared with gasoline vehicles. The slow charging issues can be traced to sluggish Li+ insertion owing to low diffusivity and long diffusion pathways, as well as a mismatched electrochemical window resulting in Li plating during charging. The development of fastcharging materials—especially anodes—are therefore desperately needed. Several strategies have been reported to achieve fast charging. For example, layered materials such as MoS21, Nb2O52, Li4Ti5O123, have shown high rate performance thanks to low Li+ diffusion barriers through the interlayer spaces. Rate performance can also be improved via nanostructuring, which is beneficial not only for intrinsic intercalation-based Li+ storage materials, but also for conversion and alloying materials such as Fe3O44 and Si5. A carbon coating6-8 is often adopted to improve the surface integrity and maintain high ion diffusion through oxide-based materials, while simultaneously enhancing electrical conductivity. Surface coatings can also be used to adjust interface properties in order to create a stable interphase region with relatively fast ion diffusion (e.g., Si with Al2O3 coating).

In general, the effects of disorder and amorphization on diffusion are poorly understood, since amorphous materials lack well-defined ion transport channels. However, their lower densities imply more open space inside the material that could reduce the Li+ diffusion barrier. Nevertheless, improvements in rate performance of amorphous materials do not appear to be universal. For example, while some studies have concluded that amorphous metal oxides such as MoO313 and Nb2O514 have lower capacity compared to their crystalline counterparts, contrary observations have been shown in other amorphous systems. Furthermore, several groups have discovered that

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amorphous TiO2 exhibits much higher rate performance than crystalline anatase counterparts15-20; however, these studies use different synthetic approaches that likely result in different structures, morphologies, and compositions, and the mechanisms for the enhanced performance are still debatable. For example, an amorphous-to-cubic phase transition was proposed to explain the superior Li storage capability of anodic oxidationprepared nanotubular TiO2 anode17. However, this phase transition has not been reported in other amorphous TiO2 materials, including several derived from atomic layer deposition (ALD)20-23.

selected area diffraction (SAD) patterns were collected using an aperture diameter of 2 µm. Raman spectra were collected using Almega system (Thermo Electron Corporation, Madison, WI, USA) to confirm the titania phase. A 633-nm laser source with beam power as low as 0.67 mW and spot size of 1.3 µm was set to avoid in situ crystallization of TiO2. The electronic structures of the TiO2/nanoporous Au samples were assessed by total electron yield (TEY) near-edge x-ray absorption fine structure (NEXAFS). The Ti L2,3-edge NEXAFS measurements were performed at beamline 8.2 of the SSRL, Stanford using an angle of incidence of ~ 45°. The data were normalized to the incident x-ray flux (measured simultaneously using the drain current to an upstream gold-coated mesh inserted into the beam path), background corrected by subtraction of the pre-edge intensity, and further normalized to the magnitude of both the integrated intensity across the edge and to the absorption step. Reference anatase TiO2 (powder, 10-30 nm, 99.5%, SkySpring Nanomaterials, Inc.) was measured and correlated with literature values. High-energy X-ray diffraction (HE-XRD) was conducted at beamline 11-ID-C (beam energy of 105.6 keV, wavelength of 0.1174 Å, beam size of 0.5 mm × 0.5 mm) in Advanced Photon Source, Argonne National Laboratory (APS-ANL, Argonne, IL). An amorphous Si area detector (Perkin Elmer) was used for data collection. System calibration was carried out using a standard CeO2 sample. The TiO2 Sample loaded in 1 mm Kapton capillary was prepared by first etching away Au using KI/I2 aqueous solution followed by super critical drying. Data integration was performed using Fit2D software, and structure factor was obtained using PDFgetX3 software24.

The interest in amorphous materials for high-rate batteries prompts the need for a more controlled diffusion study. To this end, we employ an ALD approach to obtain precisely controlled morphologies of TiO2 electrodes. The systematic thickness tunability afforded by ALD allows us to investigate the Li+ charge/discharge kinetics in detail. To avoid complications arising from carbon blacks and binders, nanoporous gold was used as a conductive substrate, since it is highly conductive and electrochemically inert within our voltage window of interest. Unambiguous experimental evidence is provided to support the intrinsically improved kinetics of amorphous TiO2, signaled by a significant reduction in the effective diffusion barrier. A multiscale theoretical investigation based on first-principles calculations and kinetic Monte Carlo simulations is applied to elucidate the mechanism for fast discharging/charging, which is attributed to the dispersion of site barriers and the formation of fast ion transport modes that improve accessibility of Li sites in amorphous films.

2.

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Cell assembly and electrochemical measurements. A threeelectrode setup was used for electrochemical characterizations. Cells were prepared inside Argon filled glovebox keeping moisture and oxygen levels below 1 ppm. 1 M LiPF6 in a 1/1/1 (vol.) mixture of EC/DEC/DMC (MTI, Cor.) was used as the electrolyte and polypropylene membrane (Celgard 3501) as the separator. Lithium metals were used as both counter and reference electrodes. Cells were rested for at least 5 h before any electrochemical measurements. Rate jump experiments were conducted using galvanostatic charge/discharge in a potential window between 1 and 3 V at varied rates from 1C up to 400C then back to 1C on a Maccor Model 4304 battery tester or a MTI 8 Channel Battery Analyzer. After that, cyclic voltammetry experiments with voltage sweep rates from 0.1 mV/s to 500 mV/s were recorded on a BioLogic electrochemical workstation VMP 300. For galvanostatic intermittent titration techniques (GITT), a constant current of 17 mA/gTiO2 was applied between the working and counter electrodes for 7 min and then was interrupted for 10 min. The above steps were repeated until the cell voltage is beyond the voltage window of 1 V – 3 V. All the above electrochemical tests were performed at 25 °C. In order to measure the activation energy, GITT experiments were also carried out at elevated temperatures up to 50 °C.

Experimental section

Preparation of TiO2/nanoporous Au electrodes. The Ag70Au30 alloy discs with diameter of 5 mm and thickness of 200 µm were immersed in 72 ml concentrated nitric acid at room temperature. The color of the discs changed from silver to brown in just a few seconds. After dealloying for 48 hours, the discs were washed with DI water and dried in air. The weight change was checked every time to confirm the successful removal of Ag. The derived nanoporous Au templates were then annealed at 500 °C in air for 60 min to increase the pore size to 750 nm. The TiO2 film was coated on the porous gold scaffold using a warm wall reactor (wall temperature of 100 °C and stage temperature of 110 °C) on ALD-200L system (Kurt J. Lesker Company, PA, USA) with titanium tetrachloride (TiCl4) as the Ti source and H2O as the O source. Long dose exposure and purge time (20/200 s/200 s) were used to ensure the gas precursors penetrate through the nanoporous Au discs and achieve uniform coatings. Anatase TiO2 was obtained by annealing the as-deposited TiO2/nanoporous Au electrode at 600 °C in air for 60 min. The weight of TiO2 was directly measured using an ultra-microbalance (METTLER TOLEDO) with readability of 0.1 µg and repeatability of 0.15 µg.

Simulation methods. Density functional theory calculations were performed using the VASP software package25-27. Pseudopotentials with four, six, and one valence electrons were employed for Ti, O and Li atoms, respectively. A plane wave kinetic energy cutoff of 400 eV was used, and the Brillouin zone was sampled at the gamma point. Anatase structures were tested at two different Li concentrations (LixTiO2 with x = 0.0625 and x = 0.5). For x = 0.0625, the structure is found to be tetragonal

Physical characterization. The morphology of the nanoporous Au/TiO2 samples was characterized by field emission scanning electron microscope (FE-SEM, JEOL 7401-F) at 20 keV (20 mA) in secondary electron imaging mode with a working distance of 5-8 mm. The morphology and the phase information were further analyzed using a Philips CM300-FEG microscope. Standard bright-field imaging technique was applied and the


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with a = b, and c/a = 2.53. For x = 0.5, the orthorhombic phase becomes preferred, with b/a = 1.06, and c/a = 2.40.

An estimate of the effect of polaron formation on the energy barrier for Li migration was obtained by considering how the barrier differs between a unit cell with a charge of +1e (i.e., the excess electron coming from the ionized Li atom is removed) and a neutral unit cell. PBE predicts a systematic lowering of the energy barrier by 0.026 eV when going from a charged to a neutral unit cell, while DFT+U predicts a change in the barrier ranging from -0.035 to +0.034 eV, depending on the location of the polaron relative to the Li ion. The barriers predicted by DFT+U are higher by approximately 0.1 eV compared to those predicted by PBE, although this value depends on the chosen value of the U parameter. In any case, we are able to verify that the effect of polaron formation on the migration barriers is insignificant compared to the spread of the barriers in amorphous TiO2. Accordingly, PBE was employed for all calculations for simplicity.

Amorphous structures were obtained using the melt-andquench method. Starting from a 108-atom 3 × 3 × 1 supercell of anatase, the system was heated to 5000 K and equilibrated for 3 ps. Snapshots from the equilibrated melt at 5000 K were then randomly selected and cooled to 300 K over 8 ps and equilibrated for an additional 4.5 ps. Finally, the atomic positions and simulation box were fully relaxed to 0 K. A time step of 1.5 fs was used for molecular dynamics runs, and a force cutoff of 0.01 eV/Å was used for geometry optimizations. To search for stable interstitial sites for Li+ ions in amorphous TiO2, a Voronoi decomposition was performed. All Ti and O atoms in the amorphous structure were used as inputs, and the resulting Voronoi nodes were taken as candidate interstitial sites. Full geometry optimizations of the amorphous structures were then carried out with a Li atom initially placed at each of the Voronoi nodes. Voronoi decompositions were performed using the Qhull software28. Barriers were computed between neighboring sites identified by the Voronoi decomposition using the nudged elastic band algorithm29.

Diffusion of Li in TiO2 was modeled using kinetic Monte Carlo (KMC) simulations. Positions for lithium interstitial sites were taken from DFT-generated structural models, and jump rates were derived from energy barriers calculated with DFT. Slab models were created by taking randomly oriented 10 × 10 × 2 nm regions from the periodic DFT structures, and an initial density of 10 Li/nm3 was placed in a thin 0.05 nm layer at the surface of the slab to monitor diffusion of lithium into the bulk. The results were averaged over 100 randomly oriented slabs for both crystalline and amorphous TiO2.

All calculations were done using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional30. It is worth mentioning that the PBE functional is known to give an incorrect description of charge localization and polaron formation in TiO2 with excess electrons, as occurs upon lithiation of TiO2. However, it has been previously found31, and also verified by our calculations, that in the anatase structure, the correct description of the polaron (at the DFT+U level) gives only a small change in the energy barrier for Li migration, due in part to strong electrostatic screening in TiO2.

For crystalline TiO2, jump rates were estimated from transition state theory (TST): 𝑟# = 𝑟% 𝑒'()* ,

(1)

Figure 1. (a) TiO2 thickness as a function of ALD cycle number. Here 2-nm, 7-nm, and 20-nm thick TiO2 layers were coated on 750-nm pore-size nanoporous gold scaffold within 30, 100, and 300 cycles of ALD, respectively. The average growth rate is 0.07 nm per cycle. (b) and (c) SEM images of a 20-nm thick ALD TiO2 show a uniform and conformal coating. (d) and (e) TEM images of 2-nm thick TiO2 samples before (a-TiO2) and after (c-TiO2) 600°C annealing show the formation of the anatase phase. f) NEXAFS measurements of 7-nm thick TiO2 samples before and after annealing confirm the amorphous-to-anatase phase transition.



where 𝑟% is a constant prefactor, 𝐸# is the energy barrier for migration, and 𝛽 = 1/k0 𝑇 is the inverse temperature. The prefactor was chosen as 𝑟% = 103 s'6 to match the diffusion coefficient in anatase with the measured value in the dilute limit shown in Figure 5. For amorphous TiO2, in which there is a wide range of migration energy barriers for different pathways, TST-derived rates were modified by the empirical MeyerNeldel rule32, which gives a relationship between the energy barrier and prefactor, log 𝑟% = 𝑎𝐸 + 𝑏,

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Experimental Section and in Figure 1a; the morphology is shown in Figure 1b-c and the supporting information (SI) Figure S1. The large pore size and excellent electrical conductivity of gold ligaments allowed us to minimize both the electrical and liquid-phase ionic resistances and to focus mainly on the electrochemical behavior and size effects (the effect of the coating thickness) of the TiO2 film. Amorphous TiO2 can be converted into the anatase phase (without changing the morphology of coatings thicker than 2 nm; see below) by simply annealing for one hour at a temperature of 600 °C, thus providing a convenient and well-controlled material system for comparison.

(2)

where 𝑎 and 𝑏 are empirical constants. The constant 𝑏 was chosen to equate the jump rates in crystalline and amorphous TiO2 when the barriers are equal. The overall jump rate for the

High-resolution transmission electron microscopy (HRTEM) images of 2-nm thick samples are shown in Figure 1d-e. Asdeposited TiO2 has a uniform and conformal film thickness of

Figure 2. (a) Galvanostatic charge/discharge voltage profiles of 7-nm amorphous a-TiO2 and crystalline anatase c-TiO2 at 1C. (b-d) Rate performances of (b) 2-nm, (c) 7-nm, and (d) 20-nm thick ALD TiO2 samples. The square hollow symbols in (b) are the reported capacities of crystalline anatase TiO2 in References 15, 19, 35-45.

nth pathway in amorphous TiO2 is then given by 𝑟=> = 𝑟# 𝑒

'(('=)()AB ')* )

,

2 nm. After annealing, the amorphous film crystallized into the anatase phase, a process which was accompanied by some dewetting in the case of the thinnest coatings.33 As a consequence, the thickness of the porous TiO2 layer slightly increased to 2.8 ± 0.8 nm. However, the dewetting was only found in 2nm thick samples. Conformal morphology was maintained in the thicker samples (SEM images are shown in SI, Figure S1). The amorphous-to-anatase phase transition of the TiO2 ALD coating upon annealing at 600 °C was already observed in previous studies by Raman34 and near-edge x-ray absorption fine structure (NEXAFS) spectroscopy33. The characteristic NEXAFS spectra of both 7-nm thick amorphous and anatase TiO2 coatings are shown in Figure 1f. The increased energy gap between t2g and eg peaks, and the relative intensity of eg peaks indicate the formation of the anatase phase. In our previous work33, we also studied the content of residual amorphous phase

(3)

where 𝐸=> is the energy barrier associated with the nth migration pathway. The parameter 𝑎 therefore controls the extent to which the jump rates in the amorphous structure are modified by the spread of energy barriers. A value of a = 20 eV-1 was employed for results shown in the main text; tests of the sensitivity of the results to this value are shown in the SI.

3.

Experimental results

We used low-temperature ALD to coat 3D nanoporous gold bulk samples (70% porosity and 500 nm diameter ligaments) with conformal layers of amorphous TiO2 with controlled thicknesses from 2 to 20 nm (the ALD parameters can be found in


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in the annealed samples by analyzing the NEXAFS spectra obtained from 2-nm to 7-nm thick TiO2 coatings. It was found that the 2-nm thick sample has ~20% amorphous phase left, whereas when the thickness increases to 7 nm, there is less < 5% amorphous phase remaining. It is assumed that the presence of residual amorphous phase is associated with disordered surface atoms and grain boundaries; their fraction is expected to increase significantly with decreasing coating thickness, especially when the latter is on the order of a few nm.

Figure 2c-d. Interestingly, the amorphous phase shows a much weaker thickness trend compared to the anatase phase, giving amorphous TiO2 a much higher rate capability for thicker samples. This high-rate performance of amorphous TiO2 is consistent with other reports17, 18, 21, although studies performed on TiO2 particles/films smaller than 3 nm are rare. Cyclic voltammetry results (Figure 3) show that anatase TiO2 behaves like a typical battery material, displaying sharp redox peaks with wide potential separation indicative of kinetic limitations. In contrast, amorphous TiO2 exhibits broad redox peaks with a nearly symmetric shape, implying much faster intercalation kinetics. A summary of the redox peak positions for 7-nm thick films of amorphous and anatase TiO2 are shown in SI, Figure S3. In the range from 0.1 mV/s to 2 mV/s, the redox peak separation for the amorphous sample increases from 0.05 V to 0.46 V. The anatase sample exhibits a similar increase in

The rate performance was characterized by galvanostatic rate jump experiments using a half-cell set up. Figure 2a shows typical charge/discharge curves of amorphous TiO2 with sloping voltage profiles suggesting solid solution reactions, and of anatase with plateaus implying two-phase reactions. The charge/discharge capacities at each step are shown in SI, Figure S2. Figures 2b-d summarize the charge (delithiation) capacity as a function of C-rate. The 2-nm thick samples (Figure 2b) exhibit high rate performance, specifically considering that the np-Au disks used as scaffold are 200 µm thick. At 1C, the capacity is close to, or even above, 200 mAh/g, corresponding to Li0.6-0.7TiO2. At 50C, 50% of the full capacity can still be retained. Our 2-nm thick samples only take ~ 30 s to achieve half of full capacity, which is six times faster than the average speed of ~ 3 min for anatase TiO2 electrodes prepared by the “doctorblade” technique15, 19, 35-45. The high rate performance of the TiO2/np-Au electrode is due to a combination of several effects, including ultrathin ALD coating thickness, large interconnected pores for fast Li+ supply from the electrolyte, and excellent electrical conductivity of gold ligaments. When the thickness increases, the rate performance decreases due to the increased Li+ and electron transportation lengths in solid TiO2, as shown in

Figure 3. Voltammetric responses at varied sweep rates (a-b) and for crystalline anatase (c-TiO2) and amorphous (a-TiO2) films of TiO2 with three different thicknesses (c-d).



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Figure 4. Logarithmic plots of the anodic peak current density as a function of the voltage sweep rate for (a) crystalline anatase and (b) amorphous TiO2 films. Two distinct regions can be identified. In Region I, anatase shows a gradually increasing slope with decreased coating thickness, while the amorphous samples exhibit size-independent behavior with a slope equal to unity. In Region II, the trend follows a slope of 0.5, indicating a transition from surface reaction-limited to diffusion-limited kinetics. The critical transition sweep rate between Regions I and II increases with decreased coating thickness for both amorphous and anatase cases.

the redox peak separation with increasing sweep rate but shifted towards higher values, namely, from 0.36 V at 0.1 mV/s to 0.80V at 2 mV/s. With decreasing ALD film thickness, the redox-peak separations of the anatase sample (Figure 3c) decrease, which facilitates Li+ insertion/extraction. However, such a trend is not apparent for the amorphous sample due to the broadening of the peaks, as shown in Figure 3d. Notably, the CV data from the 2-nm thick anatase TiO2 sample show a broad shoulder beside the Li+ extraction peak that contributes to the overall capacity. This broad oxidation peak with lower activation potential might be related to the residual disordered structure detected by NEXAFS.

hand, has significant diffusion limitations in this sweep range, particularly around the redox peak positions. Interestingly, we found that the size dependence of the charge/discharge behavior is quite different for amorphous and anatase TiO2. For simplicity, we analyzed the size dependence of the charge/discharge behavior by plotting the logarithmic response of the anodic peak current as a function of the voltage sweep rate (Figure 4). The slope curve fit then measures the constant 𝛽 in Equation (5) that reflects the Li+ storage mechanisms. In general, two distinct regions can be identified by their 𝛽 values: Region I with 𝛽~1 and Region II with 𝛽~0.5, corresponding to surface reaction-limited and diffusion-limited charge/discharge behavior, respectively. For amorphous TiO2, Region I is predominant over the range of tested sweep rates. Only at high sweep rates does the current response of amorphous TiO2 become diffusion limited (Region II) with a 𝛽 value of 0.5. Moreover, the amorphous material transitions sharply between the two regions, indicating well-separated kinetic regimes associated with diffusion and surface reaction limitations. The fact that the gravimetric current densities in Region I lie on top of each other for all three investigated coating thicknesses (2, 7, and 20 nm) suggests that Li+ ions can easily access the bulk and subsurface storage sites in amorphous TiO2. This size insensitivity, together with the broad redox peaks and small peak separations discussed above, serve as compelling evidence that the amorphous TiO2 film is an intrinsically fast charging/discharging material.

As suggested by Liu et al.46, one way to analyze the current response is to artificially separate it into two components: (1) a diffusion-limited contribution, proportional to the square root of sweep rate; and (2) a surface reaction (or charge transfer)limited contribution, which scales linearly with the sweep rate. Within this scheme, the current response can be described as: 𝑖(𝑉) = 𝛼6 𝜈6/G + 𝛼G 𝜈,

(4)

where 𝛼6 and 𝛼G are constants that determine the current contributions from the diffusion- and surface reaction-limited Li+ storage mechanisms, respectively, and ν is the sweep rate. Alternatively, the response can be fitted with the function: 𝑖(𝑉) = 𝛼𝜈 ( ,

(5)

where 𝛽 is a constant between 0.5 and 1. When 𝛽 = 0.5, the behavior exhibits classical diffusion-limited behavior, whereas for 𝛽 = 1 it has classical reaction-limited behavior.

In contrast, the charge/discharge behavior of anatase TiO2 is characterized with a 𝛽 value close to 0.5 (Region II) over a very broad range of sweep rates, meaning that the rate is largely limited by Li+ diffusion kinetics. Only in the case of the thinner anatase coatings and lower sweep rates does the slope gradually increase to 0.56 (7 nm) and 0.74 (nominally 2 nm; 2.8 nm as measured by TEM), indicating faster diffusion and an increased surface reaction-limited contribution. The observation that thinner anatase TiO2 films exhibit hybrid behavior (𝛽 up to 0.74)

By applying equation (4) to the current response of our 2-nm thick TiO2 system, we estimate that the reaction-limited contribution to the anodic peak current at ~ 2.2 V and 1 mV/s is only about 54% for the anatase sample (it increases to ~ 87% at the shoulder position near 1.8 V). In contrast, almost 100% of the peak current can be attributed to the reaction-limited mechanism for the amorphous sample. Anatase TiO2, on the other


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may be explained by the presence of residual amorphous phase along grain boundaries and surfaces, the contribution of which becomes more prominent with decreasing thickness. This residual amorphous phase is likely to induce a current response that averages the properties of the amorphous phase in Figure 4b with those of a diffusion-limited process, resulting in intermediate values of 𝛽. It may also reflect a multimodal particle size distribution, where smaller particles with enhanced solid solubility of Li contribute more to the fast intercalation behavior.47

The coulombic titration curve is shown in Figure 5a, where the Li+ insertion potential is plotted as a function of the stoichiometric composition of LixTiO2. During Li+ insertion, the quasiequilibrium potential of the anatase electrode (vs a Li/Li+ reference electrode) initially decreases with increasing Li+ uptake. This corresponds to the formation of a solid solution of Li+ in the interstitial sites of TiO248. Once the concentration of Li+ reaches the Li0.1TiO2 composition, a phase separation occurs, resulting in a potential plateau at 1.76 V, which remains until the Li0.4TiO2 composition is reached. Further charging to above 60% Li concentration (Li0.6-0.7TiO2) causes the potential to decrease again until it reaches 1 V. Amorphous TiO2, on the other hand, exhibits an almost linear potential profile, indicating that the Li+ ions are stored over the entire compositional range via a solid solution-based mechanism. The linear profile also reflects the dispersion of site energies in the amorphous sample, the effects of which will be explored further in the next section.

At higher voltage sweep rates, all samples have 𝛽 values of 0.5 owing to the onset of a diffusion-limited process. The sizedependent critical transition point that defines the boundary between surface reaction-limited (Region I) and diffusion-limited (Region II) behavior can be explained in terms of a comparison between the Li+ diffusion length and the sample thickness. Within the timescale of the charge/discharge process determined by the sweep rate, Li+ can access most of the sites in thinner samples but can only reach the near-surface region of the thicker samples. Consequently, the gravimetric current density generally decreases as the thickness increases. For the thickest samples (e.g., 20 nm), additional systematic decrease of the current density may arise from the large potential drop across the insulating TiO2 layer. However, as shown in SI, Figure S4, the areal current densities (normalized to the true surface area) become closer at higher sweep rates, further indicating that the Li+ ions are mainly stored in the near-surface regions.

The Li+ diffusion coefficient can be calculated by the following equation49: P

ST G

Z)

Z)

Q

UV

Z[

Z√]

OL 𝐷KLM = R N

W X𝐼% R W / R

G

W^ _𝑡 ≪

N bcde N

gd fcde

h,

(6)

N

where Vj is the molar volume of TiO2, S is the surface area of the 3D Au/TiO2 sample, F is the Faraday constant, I% is the no applied constant current, np is the slope of the coulometric titrano

tion curve shown in Figure 5a, and n√q is the slope of the potential change with the square root of time, t, in the limit of short transient times. Note that this equation is valid when the Li+ diffusion length is small compared to the TiO2 thickness. As shown in Figure 5b, a good linear fit of the electrode potential as a function of square root of time can be obtained in the first 15 s of the current flow period when the assumption of semi-infinite diffusion is still valid.

To explain the Li+ storage mechanisms, it is important to quantify the Li+ diffusion kinetics in both amorphous and anatase TiO2. The Li+ diffusion coefficient was measured using the galvanostatic intermittent titration techniques (GITT). In a GITT cycle, a constant current is first applied for a short period of time, followed by switching to open circuit to determine the corresponding equilibrium potential. During the transient time, the electrochemical process is limited by Li+ diffusion in the electrode. The latter is driven by a concentration gradient and can therefore can be treated as an infinite diffusion problem. By measuring the potential at the end of each rest period, a quasiequilibrium charge/discharge curve can be obtained.

The Li+ diffusion coefficients in amorphous and anatase TiO2 were calculated using Equation (6) as a function of the lithiation degree (Figure 5c). Amorphous TiO2 has a nearly constant diffusion coefficient of 0.5-2×10-14 cm2/s as a function of Li

Figure 5. Li+ diffusivity in amorphous (a-TiO2) and crystalline (c-TiO2) films of TiO2 measured using galvanostatic intermittent titration techniques (GITT). (a) Quasi-equilibrium potential of TiO2 electrode vs Li/Li+ reference electrode as a function of x in LixTiO2. The potential profile was derived by connecting the potential values of the last data point in the rest period. (b) Potential of TiO2 electrode as a function of square root of time after an injection of electrons in a sample with Li0.02TiO2 composition. (c) Li+ diffusion coefficients of amorphous and anatase TiO2 measured from GITT methods. Samples with 7-nm ALD layer thickness were selected for analysis in order to ensure long enough Li+ diffusion pathways for high-accuracy measurement.



concentration. In contrast, the diffusion coefficient of anatase TiO2 has a basin-shaped profile versus composition due to the phase separation taking place in the crystalline sample. Note that the values in the basin region for anatase are less reliable, since the model associated with Equation (3) is valid only in the solid-solution regime and does not apply across a phase transition. However, even in the initial solid-solution regime, the diffusion coefficient of anatase (1-3×10-15 cm2/s) remains an order of magnitude lower than that of amorphous TiO2. This suggests that there is an intrinsic difference between the diffusivities of the two systems, which we explore further below.

diffusion coefficient using Equation (6) at different temperatures. Here, Ea is defined by the Arrhenius equation: 𝐷 = 𝐷% 𝑒 ')A /~K ,

f{>|V 6/G }K

W

.

(8)

where we assume that the pre-exponential factor, D0, is temperature independent. Using measurements in the temperature range from 25 °C to 40 °C (SI, Figure S5), we find that Ea = 0.53 eV for anatase TiO2 in the low-concentration solid solution region. This value is also consistent with previous cyclic voltammetry50 and chronoamperometry51 measurements. This procedure is not reliable in the two-phase region of anatase because of the lack of strict Arrhenius behavior. However, if we apply Equation (8) to amorphous TiO2, we obtain an activation energy of only 0.21 eV for Li+ insertion and 0.17 eV for Li+ extraction—close to the values obtained from other 7Li MAS NMR studies16, 48 of microscopic diffusion of Li+ in TiO2. Although we caution that the structural heterogeneity of the amorphous material leads to some spread in the diffusion coefficient data, it is clear that the effective activation energy is lowered substantially upon amorphization, allowing for fast Li+ transportation in amorphous TiO2 films.

The diffusion coefficient of Li+ in anatase as determined based on Equation (6) was further validated using data from the CV scan method. In CV scans, the current component at the redox peak, ibp, can be expressed as50: 𝑖rs = 0.4958𝑛𝐹𝑆𝐶 R

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(7)

Here n is the number of electrons involved in the electrode reaction, F is the Faraday constant, S is the surface area, C is the maximum concentration of Ti3+ (0.024 mol/cm3 at x = 0.5), D is the Li+ diffusion coefficient, R is the molar gas constant, T is the temperature, α is the transfer coefficient (approximated here to 0.5), and ν is the voltage sweep rate. The Li+ diffusion coefficients for the 7-nm and 20-nm thick anatase samples obtained using Equation (7) are 2.8×10-15 cm2/s and 1.9×10-15 cm2/s, respectively. Note that this method for calculating diffusion rates is not applicable to amorphous TiO2, because the electrochemical process is limited by surface charge transfer instead of Li+ diffusion at finite scan rates.

We note that in TiO2 nanotube arrays prepared by anodic oxidation of Ti substrate, an amorphous-to-cubic phase transition was previously discovered after lithiation to 0.9 V vs. Li/Li+ 17. The cubic phase, which has a more open structure, was believed to contribute to the high rate performance. In our work, we do not observe such a phase transition when ALD-derived amorphous TiO2 is lithiated to 1 V; synchrotron XRD (Figure 6) shows that TiO2 remains amorphous even after 500 cycles of charge/discharge between 1 V and 3 V. Accordingly, the atomistic origin of the high diffusivity, low activation energy, and better rate performance of our amorphous films must instead lie in the existence of random Li+ diffusion pathways.

Next, we estimate the activation energy, Ea, for Li+ diffusion jumps in amorphous and anatase TiO2 by measuring the

4.

Theoretical results

To elucidate the physical origin of the faster intercalation kinetics of Li+ within amorphous TiO2 compared to anatase TiO2 and its connection to the material structure, we performed additional analysis of the Li+ mobility and energy landscape using density functional theory. Details of the computational methods and simulation parameters can be found in the Simulation Methods section. First, we examine the energy barriers in crystalline TiO2.. In the conventional anatase TiO2 structure, Ti and O atoms are packaged in an octahedral TiO6 unit, which are edge-shared in a tetragonal phase. Li+ ions can reside in the interstitial octahedral sites and diffuse along the a or b axis to adjacent vacant octahedral sites10. Using a dilute concentration of Li in anatase TiO2 in our model (x = 0.0625), we obtain a unique migration barrier of 0.51 eV for hopping between adjacent sites. This value is in good agreement with our experimental measurement of 0.53 eV, as well as with other previously reported results48, 50, 52 . We note that volume expansion of crystalline TiO2 during lithiation is known to induce a tetragonal-to-orthorhombic phase transition when the Li concentration exceeds x ~ 0.05, with the exact threshold being a function of particle size47 (reflected in Figure 5c). This phase transition is suppressed in our

Figure 6. Synchrotron X-ray diffraction (XRD) patterns of 7nm thick anatase c-TiO2 (black), amorphous a-TiO2 (red) before electrochemical testing, and amorphous a-TiO2 (green) after 500 cycles of charge/discharge at 10 C rate in voltage window of 1 V to 3 V vs Li/Li+. Nanoporous Au substrate was etched away prior to XRD.


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model to avoid complications with determining a unique energy barrier when the precise value depends on the distribution of interstitial Li atoms in the simulation cell. We therefore focus our further discussion on differences between anatase and amorphous TiO2 only in the low-concentration regime.

To generate structures representative of amorphous TiO2, we created a series of atomic configurations using the melt-andquench method within an ab initio molecular dynamics scheme. A typical example configuration is shown in Figure 7a. In order to verify that the amorphous structures generated in this way are a good representation for the experimental phase, we computed the static structure factor by averaging over equilibrated molecular dynamics trajectories at 300 K for several amorphous structures. A comparison with measured quantities from high-energy X-ray diffraction (HE-XRD) pair distribution function (PDF) analysis (SI, Figure S6) shows a good qualitative agreement in the main features associated with the short-range order, giving us confidence that the simulated amorphous structures can be used to study the experimental material.

Having established the validity of our theoretical methods for computing energy barriers, we now turn our attention to the amorphous phase. Amorphous TiO2 does not have well-defined, long-range structural order; however, it does have short-range order, consisting mostly of distorted octahedral TiO6 units that are similar to those in anatase53, 54. It is worth noting that in several studies, some fraction of Ti atoms was found to exhibit a lower coordination, which was attributed to the contraction of the Ti-O bond in the tightly bonded clusters, as well as to the truncation of the TiO6 octahedron at surfaces53, 55, 56. Nevertheless, it is reasonable to assume that the TiOx units remain intact and tightly bound. Surrounding these tightly bonded octahedrons are the loosely bonded free-volume zones, which play an important role in Li+ storage and transportation.

Figure 7a also shows the potential energy isosurface (computed at 1.5 eV above the global energy minimum) for a Li atom inserted into the amorphous TiO2 structure, based on the limit where the positions of all Ti and O atoms are held fixed. Although further relaxation of Ti and O atoms in response to the presence of the interstitial Li stabilizes the configurations, these

Figure 7. (a) Model amorphous TiO2 structure obtained by the melt-and-quench method. Also shown is a potential energy isosurface (yellow) at 1.5 eV above the global energy minimum for a single Li probe atom with fixed Ti and O positions. (b) Histogram of Li migration energy barriers between interstitial sites in the amorphous TiO2 model. (c) Energy barriers for escape from an interstitial site as a function of site energy. The solid line indicates the minimum escape energy (i.e., the lowest-energy migration path) for each site. (d) Maximum distance that can be traversed through the amorphous TiO2 model as a function of the highest barrier crossed. In (b) and (d), the vertical dashed line indicates the calculated energy barrier for Li diffusion in crystalline anatase.



simpler calculations (with fixed Ti and O) offer a visual representation of possible migration pathways and interconnected channels distributed throughout the amorphous structure. This picture generally confirms that Li coordinates with oxygen within the free-volume zones surrounding the TiOx groups, and that the connectivity of these sites determines the diffusion pathway.

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exhibit a minimum escape barrier that is lower than the migration barrier in anatase TiO2, with the minimum escape barrier generally being anticorrelated with the site energy. This anticorrelation is unsurprising, as high energy sites are expected to provide facile exit channels. Only the lowest-energy site in Figure 7c has a minimum escape barrier that is considerably higher than in anatase. Due to the high escape barrier and energetic stability, such a site will act as a trapping site for the migrating Li atoms; once a mobile Li atom enters one of these sites, it will remain trapped there on the time scales relevant for charge and discharge of the electrode. The presence of such trapping sites therefore should not affect significantly the measured Li mobility but rather result in a slight lowering of the usable capacity of amorphous TiO2 upon initial cycling. This prediction was verified by extracting the experimental Coulombic efficiency of our amorphous and anatase TiO2 samples from the first cycle (SI, Figure S7), from which it is clear that a higher fraction of Li is indeed irreversibly incorporated into amorphous TiO2. Nevertheless, we emphasize that according to our predictions, only a small fraction of sites should fall within this category.

For a more rigorous and quantitative comparison, we next computed energy barriers between selected stable interstitial sites using the nudged elastic band method29. Due to the complicated nature of the potential energy surface in amorphous TiO2, identifying stable interstitial sites for intercalated Li atoms is not trivial. To search for them, we implemented a procedure based on a Voronoi decomposition algorithm, which has the advantage of being agnostic to the structural input. This procedure (explained in detail in the Simulation Methods section) resulted in 23 unique interstitial sites for one of the melt-andquench amorphous structures (compared to 36 sites in the corresponding anatase unit cell with the same number of atoms). Energy barriers were calculated between pairs of sites within a cutoff distance of 5.0 Å. A histogram of all computed energy barriers from the simulated amorphous structures is shown in Figure 7b. The distribution of migration energy barriers is broad, with a long tail at high energies; this is expected given the heterogeneous nature of the amorphous structure. Nevertheless, the peak of the distribution lies below the corresponding barrier in anatase TiO2 (shown as a dashed line in Figure 7b), within a range of energies that generally agrees with the experimentally extracted barrier for amorphous TiO2 (~ 0.2 eV).

In crystalline TiO2, the energy barrier for migration of Li between equivalent interstitial sites can be directly related to the effective diffusion coefficient (in the dilute limit where interactions between lithium ions are not important). For amorphous TiO2, however, the presence of a complex network of interconnected sites with a distribution of energy barriers for migration prevents such a straightforward determination of the effective diffusion coefficient. We therefore employed KMC simulations to study diffusion in amorphous TiO2, making use of DFTderived energy barriers to determine jump rates between individual interstitial sites. Diffusion into a slab of TiO2 was modeled by placing an initial uniform density of lithium in a thin layer at the surface of the slab, then monitoring diffusion into the bulk as a function of time. Details of the KMC simulation setup can be found in the Simulation Methods section.

In addition to the distribution of energy barriers for Li migration, amorphous TiO2 also exhibits a distribution of site energies. Figure 7c shows the energy barriers to escape from each site as a function of the site energy relative to metallic lithium, with the lowest-energy migration pathway for each site highlighted with a solid line. Note that the range of site energies is consistent with the measured range of the voltage of the amorphous TiO2 electrode versus metallic lithium shown in Figure 5, giving support to the accuracy of our computational approach for representing the energetics of lithium intercalation in amorphous TiO2. Figure 7c shows that the vast majority of the sites

Figure 8a compares the planar-averaged density of lithium as a function of distance into the slab for crystalline and amorphous TiO2 based on the KMC results. Initially, diffusion into the amorphous slab is much faster than the crystalline slab (see dashed lines in Figure 8a). However, once the lithium reaches

Figure 8. (a) Plane-averaged density of Li in amorphous (a-TiO2) and crystalline anatase (c-TiO2) slabs of TiO2 along the direction perpendicular to surface after 0.9 ms (dashed lines) and 250 ms (solid lines) of KMC simulation time. (b) Mean-squared penetration depth of Li atoms in the slabs as a function of KMC simulation time.


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Chemistry of Materials connected to the sharp transition to diffusion-limited behavior in the CV data in Figure 4b, assuming that the percolation of connected low-barrier pathways defines the extent of the easyto-access regions for every voltage sweep rate.

a distance of approximately 1 nm into the slab, diffusion slows considerably (the exact distance should depend on the chosen simulation parameters). At later times (solid lines in Figure 8a), lithium eventually penetrates deeper into the crystalline slab. This behavior is also seen clearly in Figure 8b, which compares the mean-squared penetration depth as a function of time for crystalline and amorphous slabs. As expected, the crystalline material shows a uniform diffusive behavior, while in the amorphous material a turnover in the rate of diffusion can be seen at later times. We point out that this behavior is very similar to general models for diffusion through networks with random barriers57. Moreover, the fact that a continuous distribution of barriers (Figure 7b) leads to defined length and time scales separating “fast” and “slow” regions is consistent with expectations from percolation diffusion.

5.

Conclusions

We have explored the effects of amorphization on the intercalation kinetics of thin TiO2 films by combining controlled ALD synthesis with theoretical analysis from multiscale simulations. We have demonstrated that ALD-derived amorphous TiO2 films exhibit fast ion intercalation kinetics, leading to rate behavior that is limited by charge transfer rather than diffusion. This is evidenced by: (1) high rate performance; (2) broad CV scan peaks; (3) small potential gaps; and (4) a linear relationship between peak current and voltage sweep rate. In contrast, under most cycling conditions, anatase TiO2 shows behavior expected from a standard diffusion-limited process, with kinetics that improve more gradually with reduction in film thickness. This more conventional behavior of anatase is evidenced by: (1) a quick drop in the rate performance as the sample thickness increases; (2) sharp anodic/cathodic peaks in CV scans and voltage plateau in galvanostatic charge/discharge processes; (3) large potential gaps; (4) a current that follows the square root of the voltage sweep rate for thicker samples and remains sublinear when thickness decreases to 2.8 nm.

The initial fast diffusion in the amorphous TiO2 simulations results from pathways through the material connected by low energy barriers, allowing for rapid transport of lithium along the path. The presence of these low-barrier pathways is further illustrated in Figure 7d, which shows the longest distance that can be traversed through our amorphous TiO2 model without crossing an energy barrier higher than a given height. It can be seen that pathways with no barriers higher than the crystalline TiO2 barrier of 0.5 eV extend to a distance of about 1 nm within our simulation.

The fast rate performance of amorphous TiO2 films is attributed to the low effective activation barrier for Li+ ion diffusivity, as measured from temperature-dependent GITT experiments. First-principles simulations further reveal that the intrinsic disorder in amorphous TiO2 creates a distribution of site energies and migration barriers. As a result, amorphous TiO2 has a high probability of providing connected pathways with lower Li migration barriers that percolate some defined distance within the material. Parameterized kinetic Monte Carlo simulations show that this results in a separation between “fast” and “slow” regions with intrinsically different timescales, whose collective effect produces the measured activation barrier. We suggest that the fast regions in amorphous TiO2 films form transport highways that aid accessibility of Li to the slower regions of the material, improving rate performance over crystalline anatase films of similar thickness. For the thinnest samples, these fast regions can dominate the overall material, resulting in facile intercalation kinetics over a wide range of cycling rates. On the other hand, the simulations suggest that the relative advantages of amorphization are unlikely to carry over to bulk samples, for which the comparatively short intrinsic length scale of the fast regions will become a limitation.

Collectively, the KMC simulations suggest that intercalation of Li into amorphous TiO2 films proceeds via fast migration along connected low-barrier pathways that percolate some threshold distance within the material. Although the predicted distance is parameter dependent, these fast transport pathways should penetrate no more than a few nm into the material. Diffusive transport within this region is considerably faster than in crystalline TiO2. We propose that the fast subsurface regions in amorphous TiO2 form natural Li migration highways, especially following the initial cycling period. These fast highways allow the slower interior regions of the films to more easily accessed, leading to high-rate advantages of amorphous TiO2 over anatase—particularly in regimes for which diffusion limitations are most prominent. Notably, because the percolation distance that separates “slow” and “fast” regions is an intrinsic property of the material, the overall volume fraction of easily accessible sites should depend on film thickness (in addition to the distribution of barriers). As a result, for amorphous films that are sufficiently thin, the fast highways can comprise a large fraction of the available Li sites, effectively eliminating diffusion limitations in the intercalation kinetics over a wide range of cycling conditions, as shown in Figure 4b. Conversely, as sample thickness increases, the rate advantages offered by amorphization will eventually vanish as the fast highways are no longer able to penetrate a significant fraction of the interior.

Although the findings presented here are specific to TiO2, there is reason to suppose that the results can be generalized to other amorphous films, for which the distribution of diffusion barriers is likely to be similarly broadened. Nevertheless, it is important to emphasize that the exact transition to fast intercalation behavior will be material dependent, with each material potentially exhibiting a different dependence on film thickness and cycling rate. Our investigation demonstrates that in principle, this dependence could be understood based on how diffusion barriers are distributed in the material, opening up the possibility of predicting fast rate performance in other amorphous films for energy storage.

The existence of two different diffusion timescales implied by the KMC simulations is reflected in the rate performances of the 7- and 20-nm amorphous samples in Figure 2, which demonstrate a capacity response that is initially faster before slowing beyond a threshold value of 5-10C. This behavior contrasts with the more regular rate performance of the anatase samples, which exhibit diffusion on only one characteristic timescale. The transition between distinct “fast” and “slow” diffusion timescales within the amorphous material may also be



ASSOCIATED CONTENT Supporting Information. SEM images of TiO2/np-Au samples. Galvanostatic charge/discharge capacity at varied rates. CV analysis. Diffusion coefficients at different temperatures. Structural factors. Initial coulombic efficiency. Functional dependence of KMC results on Meyer-Neldel parameters. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors * Email: [email protected] * Email: [email protected] † These authors contributed equally

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is supported by 13-LWD-031, 15-ERD-022, and 18-FS019 projects funded by the Laboratory Directed Research and Development (LDRD) program at LLNL. The work at LLNL was performed under the auspices of the U.S. Department of Energy under Contract DE-AC52-07NA27344. Use of the Stanford Synchrotron Radiation Light Source, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC0276SF00515. HE-XRD research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC0206CH11357. J. Ye acknowledges help from K. W. Chapman, O. J. Borkiewicz, and R. Yang for the HE-XRD experiments in ANL.


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