Accordion Strain Accommodation Mechanism Within the Epitaxially

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Accordion Strain Accommodation Mechanism Within the Epitaxially Constrained Electrode Sung Joo Kim, Donghee Chang, Kui Zhang, George W. Graham, Anton Van der Ven, and Xiaoqing Pan ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.8b00829 • Publication Date (Web): 09 Jul 2018 Downloaded from http://pubs.acs.org on July 11, 2018

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ACS Energy Letters

Accordion Strain Accommodation Mechanism within the Epitaxially Constrained Electrode Sung Joo Kim†‡, Donghee Chang§, Kui Zhang†, George Graham†‡, Anton Van der Ven§*, Xiaoqing Pan†¶* †

Department of Chemical Engineering and Materials Science, University of California-Irvine,

Irvine, California, 92697, USA. ‡

Department of Materials Science and Engineering, University of Michigan, 2300 Hayward

Street, Ann Arbor, Michigan, 48109, USA. §

Materials Department, University of California, Santa Barbara, 1361A, Engineering II, Santa

Barbara, CA, 93106, USA. ¶

Department of Physics and Astronomy, University of California-Irvine, Irvine, California,

92697, USA.

S.J.K. and D.C. contributed equally to this work.

ACS Paragon Plus Environment

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ABSTRACT The tremendous benefits of all-solid-state Li-ion batteries will only be reaped if the cycle-induced strain mismatch across the electrode/electrolyte interfaces can be managed at the atomic scale to ensure that structural coherency is maintained over the lifetime of the battery. We have discovered a unique strain accommodation mechanism within an epitaxially constrained high-performance bronze TiO2 (TiO2-B) electrode that relieves coherency stresses that arise upon Li insertion. In-situ transmission electron microscopy observation reveals the formation of anatase shear bands within the TiO2-B crystal that play the same role that interface dislocations do to relieve growth stresses. While first-principles calculations indicate that anatase is the favored crystal structure of TiO2 in the lithiated state, its continued propagation is suppressed by the epitaxial constraints of the substrate. This discovery reveals an accordion-like mechanism relying on an otherwise undesirable structural transformation that can be exploited to manage the cyclic strain mismatch across the electrode/electrolyte interfaces that plague all solid-state batteries.

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High capacity and cycling stability are becoming increasingly important for next-generation Liion batteries, especially for large-scale applications like electric vehicles (EVs) and energy storage for static grids.1-3 However, electrodes of high-performance Li-ion batteries undergo large variations in Li concentration that often take the electroactive material into a state where its crystal structure becomes metastable and susceptible to phase transformations to less favorable crystal structures.4,5 Even in the absence of undesirable phase transformations, most electrode chemistries still undergo significant volumetric changes during each charge and discharge cycle that can cause mechanical degradation.6-12 The increasing trend towards all solid-state batteries introduces additional challenges in the management of mechanical degradation and phase transformations.13 The requirement that the electrode and electrolyte materials must maintain intimate contact during each charge and discharge cycle imposes severe constraints on their mechanical properties.14 While solid electrolytes do not undergo volume changes, as their Li concentration remains constant, the electrodes in contrast swell and contract with each charge/discharge cycle.15 Maintaining coherency in all-solid-state batteries will therefore require new strategies to accommodate large strain fluctuations reversibly. In this communication, we report on the discovery of a novel strain accommodation mechanism that exploits an otherwise undesirable phase transformation. We focus on the relaxation mechanism of an epitaxially strained high-performance bronze TiO2 (TiO2-B) film upon Li insertion by fabricating a highly crystalline TiO2-B thin film and conducting in-situ high-resolution transmission electron microscopy (HRTEM) during electrochemical Li insertion. Various polymorphs of TiO2 are being actively investigated as Li-ion intercalation anode materials due to their superior safety and high rate capability when compared with graphite. While the well-known anatase and rutile polymorphs suffer from sluggish Li diffusion16-21 and


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anisotropic lattice expansion,22,23 the TiO2-B polymorph has large open channels that facilitate rapid Li ion diffusion.24 TiO2-B is a low-density lithium intercalation host that can accommodate more Li than any of the other TiO2 polymorphs,25-28 with intercalation capacities as a high as 0.8 Li per TiO2 unit in bulk and 0.91 in nanowire form.29-32 In this study, we deposited a TiO2-B thin film on a (100) STO substrate, which hinged on the use of CaTi5O11 (Ca:TiO2-B), a new variant of TiO2-B via Ca doping, as an interposed template layer. The lattice mismatch between regular TiO2-B and Ca:TiO2-B is very small, being less than 1% as calculated by geometric phase analysis (GPA).33,34 The thin film was grown along the [001] direction as shown in a high-resolution scanning TEM (HRSTEM) image and the atomic model schematics in Figures s1a and b. The film contains large defect-free regions where the Li ion source can make local contact and hence minimize any structural influence of defects in the film on lithiation. The coherently strained film serves as an ideal platform to study the chemomechanics associated with the lithiation-driven misfit strain relaxation and accompanying morphological evolution of TiO2-B. By loading this electrode film on an in-situ TEM-STM holder, we constructed a nano-sized electrochemical cell inside a TEM (Figure s2a). As schematically illustrated in Figure s2b, a cell was assembled and run with an external voltage source-meter by contacting the top surface of the film with the Li-metal coated STM tip. Figure s2c shows the electron energy loss spectroscopy (EELS) spectra of the Li-K edge and the O-K edge in a naturally formed Li2O layer on the STM tip surface that serves as a solid electrolyte. The peaks shown in both near-edge spectra match well with those measured for Li2O.35 Electrochemical Li insertion of the TiO2-B structure was conducted under a potentiostatic mode at room temperature. Assuming that a sudden conductance change, observed at -3V (relative to Li metal) as the voltage was swept from -5 to


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ACS Energy Letters

0V, is the threshold for Li ion transport through Li2O into the lattice, we used the higher lithiation voltage of -4V in order to expedite Li ion migration into the film. This voltage deviates significantly from the 1-3 V window relative to a metallic Li-anode (with Li insertion potentials of TiO2-B starting at 1.6-1.7 V vs. Li/Li+) because a large negative over potential is required to drive ionic transport through the Li2O layer, which has low Li+ ion conductivity at room temperature.36 No analysis of electrochemical Li removal from the film was attempted due to the difficulty of extracting Li from the film after lithiation. Rapid surface wetting by Li metal occurred instantly across a wide region of the film, including the surfaces of the cross-section of the film (i.e., two sides of the TEM grid) upon lithiation under a constant bias. This was followed by a slow increase of the wetting layer thickness as lithiation proceeded (see Figure 1a and b and also Figure s2a). Ultimately, this wetting layer developed into a thin layer of a sub-crystalline material, 2-3 nm in thickness, with a distinct cubic lattice. Using fast Fourier transform (FFT), this layer was found to be c-LixO (space group: Fm3തm). The formation of c-LixO was previously observed as a reaction product of Li and a nano-structured TiO2 electrode during in-situ lithiation.37,38 Under a cross-sectional projection inside the TEM, the thin c-LixO layer could only be visualized at the top most surface of the thin film. We speculate that LixO formation is likely because of the oxidation of Li driven by the residue oxygen existing inside the TEM column. Structural changes occurred in the TiO2-B film during lithiation soon after the formation of the LixO surface layer. Movie s1 shows a clear change in image contrast as Li appears to migrate across the cross-sectional surfaces of the film. The dynamic change in image contrast was accompanied by the formation of nano-scale shear bands, marked by a linear contrast, that cut through the TiO2-B layer from the top surface down to the interface between TiO2-B and


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Ca:TiO2-B. Shear bands were generated over a wide region even at lateral distances far from the tip-film contact (Figure 1). A measurement of core-loss EELS spectra indicates that the shear bands appeared within regions that were fully lithiated, with Li presumably entering at the broad surfaces of the film’s cross-section. Figure 2c compares EELS plots of a TiO2-B film before and after full lithiation taken from different regions of the HRSTEM images of Figure 2a and b. Before lithiation, the Ti L2,3-edges split into t2g and eg peaks due to the second order Jahn-Teller distortion of the TiO68octahedron when Ti has a valence of +4.39 This splitting disappears in the lithiated film as the octahedral distortions are absent when the Ti valence shifts from 4+ to 3+ (Figure 2c and Figure s3b).18,40-42 The EELS study was performed on each of the three stacked layers (i.e. LixTiO2-B, Ca:TiO2-B, and SrTiO3) after full lithiation as shown in Figure s3a and b. The data clearly shows that lithium does not insert into the Ca:TiO2-B layer, consistent with our observations that the shear bands generated in the TiO2-B layer do not extend into the Ca:TiO2-B layer. A recent DFT study of Ca:TiO2-B showed that Li diffusion is more sluggish in Ca:TiO2-B than in TiO2-B due to the presence of two-dimensional CaTiO3 sheets in the Ca:TiO2-B crystal structure, which act as high barrier bottle-necks for long-range Li transport.43 Figures 3a and b show HRSTEM images of shear bands at different magnifications. The shear bands were only found to occur in lithiated regions of the film. The shear bands formed in single lithiated crystal TiO2-B grains that have their (010) planes parallel to the film’s cross section, as is evident from the FFT pattern taken from the HRTEM image of Figure 1a. Large open channels parallel to the b-axis that facilitate fast Li transport44,45 are therefore exposed at the large crosssectional surfaces of the film, giving these grains easy access to Li. The angle of the shear bands


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ACS Energy Letters

relative to the normal to the substrate was found to be 34o for all the defects of this type, everywhere throughout the film. Close inspection of the high resolution image in Figure 3b reveals that the local crystal structure within the shear band is no longer that of LixTiO2-B, but rather that of anatase LixTiO2 (LixTiO2-A). Shear band formation, therefore, seems to be accompanied by a local structural transition upon lithiation from the LixTiO2-B crystal structure to the LixTiO2-A crystal structure. However, this structural transformation is restricted to a thin region that is approximately one unit cell thick. Interestingly, even after continued lithium insertion, the band did not widen, but instead more thin shear bands were generated across the thin film (Figure s4). The irreversible formation of LixTiO2-A is detected by the post-mortem x-ray diffraction study of an after-cycled TiO2-B film by detection of new peaks (Figure s5). The formation of atomically thin LixTiO2-A along shear bands within TiO2-B during lithiation motivates several questions: Why does LixTiO2-B transform to LixTiO2-A during lithiation and why is this transformation only restricted to narrow shear bands? To help answer these questions, we calculated the free energies of the various polymorphs of TiO2 such as bronze, anatase, and spinel as a function of Li concentration to determine whether the relative stability among the three polymorphs changes significantly during lithiation. The free energies were calculated with Monte Carlo simulations applied to cluster expansions parameterized with density functional theory calculations using the CASM package.46-49 The calculated free energies are shown in Figure 4a. While LixTiO2-A and LixTiO2-B are close in energy in the absence of Li, Figure 4a clearly shows that the LixTiO2-A phase is predicted to become significantly more stable than LixTiO2-B above x=0.3. It also shows the free energy of spinel LixTiO2, which is even more stable than anatase at x=0.5.


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Free energies based on DFT calculation indicate that LixTiO2-B begins to experience a sizable thermodynamic driving force to transform to LixTiO2-A and spinel upon Li insertion. Whether or not TiO2-B actually transforms to either anatase or spinel during Li insertion depends on whether there are facile crystallographic and kinetic pathways that connect TiO2-B and one of the more stable phases. A continuous crystallographic pathway that connects the crystal structures of LixTiO2-B and LixTiO2-A certainly exists. The crystallographic model in Figure 3c, for example, illustrates how the Li0.5TiO2-B crystal structure can be converted to Li0.5TiO2-A by a simple shear of the angle between the a and c axes of the monoclinic unit cell of Li0.5TiO2-B and an internal rearrangement of Ti and O atoms within the unit cell of Li0.5TiO2-B. The above thermodynamic and crystallographic considerations suggest that the lithiation of TiO2-B should lead to a complete transformation to LixTiO2-A. Why then do the lithiated TiO2-B grains only transform to LixTiO2-A within thin shear bands? This peculiar behavior likely arises due to the epitaxial constraints of the Ca:TiO2-B substrate coupled with an expansion of the TiO2-B crystal upon lithiation. An XRD study by Armstrong et al.,29 showed that the a and b axes of the LixTiO2-B unit cell can expand by as much as 6% upon Li insertion. At x=0.5 in LixTiO2-B, where driving forces for transformation to Li0.5TiO2-A are especially large, both a and b axes were observed to increase by approximately 2.2%.30 Lithium addition will, therefore, swell the TiO2-B crystal parallel to the substrate setting up compressive stresses that can be relieved by buckling. The crystallography of the Li0.5TiO2-B to Li0.5TiO2-A transformation provides a mechanism with which such buckling can occur without having to generate highenergy cracks. Inspection of the crystallographic path between Li0.5TiO2-B to Li0.5TiO2-A shows that the macroscopic effect of transforming one unit cell of LixTiO2-B to LixTiO2-A, as occurs in the


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shear bands, is similar to introducing an edge dislocation. Indeed, the crystallographic path of Figure 3c takes the Li0.5TiO2-B b lattice vector to the Li0.5TiO2-A c lattice vector. The Li0.5TiO2B b lattice vector is parallel to the substrate while the Li0.5TiO2-A c lattice vector is almost parallel to the substrate, having a slight tilt due to a local rigid rotation during shear band formation. The length of the Li0.5TiO2-A c lattice parameter, however, is shorter than the Li0.5TiO2-B b lattice parameter by almost 2.8 Å. Hence, shear band formation with local transformation from Li0.5TiO2-B to Li0.5TiO2-A has the same effect as introducing an edge dislocation having a Burger’s vector of approximately 2.8 Å with the missing half plane in the TiO2-B film. While the LixTiO2-A shear bands could serve as the nuclei for further transformation, the coherency between the LixTiO2-A shear band and the adjacent LixTiO2-B regions actually penalizes the LixTiO2-A crystal. Due to coherency constraints, the Li0.5TiO2-A crystal structure within the shear band cannot relax to its equilibrium lattice parameters, but is instead constrained to have lattice parameters that match those of the adjacent LixTiO2-B crystals within the [20-1] planes. Even more severe are the epitaxial constraints of the substrate. Transforming every LixTiO2-B unit cell to anatase while still maintaining epitaxial coherency with the Ca:TiO2-B substrate would require that the c-axis of LixTiO2-A must be stretched by close to 30%. The energy increase accompanying such a large strain is so severe that the LixTiO2-A crystal structure is no longer desirable compared to the strain-relieved LixTiO2-B crystal. In fact, as shown in Figure s6, DFT calculation of the strain energy as the anatase crystal (Li0.5TiO2-A) is stretched along its c axis (while maintaining its equilibrium a and b lattice parameters) shows that a mere strain of 0.07 (relative to fully relaxed Li0.5TiO2-A) is sufficient to make the epitaxial Li0.5TiO2-B crystal thermodynamically more favored. The coherency and epitaxial constraints of


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LixTiO2-A embedded between LixTiO2-B crystals, therefore, stop the thermodynamically favorable LixTiO2-B to LixTiO2-A transformation in its tracks. The calculated free energy curves of Figure 4a show that spinel LixTiO2 has an even lower free energy at x=0.5 than Li0.5TiO2-A. Nevertheless, it was not easy to detect the formation of a spinel phase, likely due to the more complex crystallographic pathway that links TiO2-B and spinel. A transition from TiO2-B to spinel requires not only a shape change of the monoclinic unit cell of TiO2-B to form Li0.5TiO2-A but also a reordering of Ti over the octahedral sites. As shown in Figure s7, both anatase and spinel phases share the same close-packed oxygen sublattice. However, half of the Ti atoms in each layer of anatase have to undergo re-ordering to form the spinel structure. Therefore, the transition from the anatase to the spinel phase is hampered by the requirement that Ti must reorder through diffusive hops. Careful examination using HRSTEM, however, did reveal its existence at the top surface of the TiO2-B film subjected to a constant bias (Figure s8). Interestingly however, under prolonged exposure of the film under an electron beam, we could promote a further reaction between the Li of the cross-section of the thin film and the underlying TiO2-B crystal, inducing a complete phase transformation to spinel LixTiO2 (Figure 4d). While we were unable to determine the Li composition of the spinel regions using Li K-edge EELS measurements under a spot mode in STEM due to further transformations to cubic LiTiO2, the observed structure is in good agreement with that obtained from DFT calculations (see structure information in Table s1). Nevertheless, the spinel regions were not in coherent contact with the TiO2-B crystals. In summary, we have discovered a relaxation mechanism of TiO2-B via in-situ TEM lithiation of a strained thin film. The relaxation follows a crystallographic route by topotactically shearing the TiO2-B crystal to create LixTiO2-A shear bands that are only a single unit cell thick.


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Although the formation of this layer is thermodynamically favorable, it does not propagate laterally due to a strain energy penalty arising from coherency constraints of the anatase embedded between single crystal LixTiO2-B and epitaxially attached to a Ca:TiO2-B substrate. This unique finding suggests a non-destructive mechanism of strain relaxation that exploits deformations accompanying an otherwise unwelcome phase transformation. It may serve as a viable mechanism with which to manage strain mismatch between electrode and electrolytes in all solid-state batteries.

ASSOCIATED CONTENT AUTHOR INFORMATION Present Addresses †

(Sung Joo Kim) Department of Materials Science and Engineering, Seoul National University, 1

Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea §

(Donghee Chang) Department of Materials Science and Engineering, Seoul National University,

1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea

Author Contributions X.Q.P. and A.V.D.V. conceived and directed this project. S.J.K. performed the in-situ TEM on a thin film grown by K.Z.. D.C. performed theoretical calculations. S.J.K., D.C., G.W.G., A.V.D.V., and X.Q.P. prepared the manuscript.


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Corresponding Author *

Corresponding authors: [email protected], [email protected]

Notes The authors declare no competing financial interests.

Acknowledgment This worked was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences, the National Science Foundation(DMR-1436154) and Engineering, under Award DE-FG02-07ER46416. This work was also partially supported by Ford Motor Company under a University Research Proposal grant and the National Science Foundation through Grants CBET-1159240 and DMR-0723032 (thin-film growth and TEM). D.C. and A.V.D.V. were supported by an NSF DMREF grant: DMR1436154. Computational resource support was provided by the Center for Scientific Computing at the CNSI and MRL: an NSF MRSEC (DMR-1121053) and NSF CNS-0960316. D.C would like to acknowledge J. Goiri for a multi-shift code used for making a super cell with a specific surface as a basal plane of the super cell. S.J.K acknowledges J. R. Jokisaari for advice on handling of Li and transfer of the TEM-STM holder from a glove box to TEM.

Supporting Information.


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Description of experimental/computational methods. High-magnification TEM movie (mp4) showing lithiation-induced formation of an anatase shear band within a TiO2-B thin film. Morphology of a TiO2-B thin film and its set-up for the in-situ TEM lithiation cell test. Detailed posthumous HRSTEM and EELS analysis on a lithiated TEM specimen. Ex-situ diffraction pattern analysis of a TiO2-B thin film after electrochemical discharge. DFT calculation on crystallographic formation of Li0.5TiO2-A. This material is available free of charge via the Internet at http://pubs.acs.org.

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(19) Wagemaker, M.; Borghols, W. J. H. ; Mulder, F. M. Large Impact of Particle Size on Insertion Reactions. A Case for Anatase LixTiO2. J. Am. Chem. Soc. 2007, 129, 4323-4327. (20) Wagemaker, M. ; Mulder, F. M. Properties and Promises of Nanosized Insertion Materials for Li-Ion Batteries. Acc. Chem. Res. 2013, 46, 1206-1215. (21) Liu, H. ; Grey, C. P. Influence of Particle Size, Cycling Rate and Temperature on the Lithiation Process of Anatase TiO2. J. Mater. Chem. A 2016, 4, 6433-6446. (22) Borghols, W. J. H.; Wagemaker, M.; Lafont, U.; Kelder, E. M. ; Mulder, F. M. Impact of Nanosizing on Lithiated Rutile TiO2. Chem. Mater. 2008, 20, 2949-2955. (23) Kim, S. J.; Noh, S.-Y.; Kargar, A.; Wang, D.; Graham, G. W. ; Pan, X. In situ TEM observation of the structural transformation of rutile TiO2 nanowire during electrochemical lithiation. Chem. Commun. 2014, 50, 9932-9935. (24) Hua, X.; Liu, Z.; Fischer, M. G.; Borkiewicz, O.; Chupas, P. J.; Chapman, K. W.; Steiner, U.; Bruce, P. G. ; Grey, C. P. Lithiation Thermodynamics and Kinetics of the TiO2 (B) Nanoparticles. J. Am. Chem. Soc. 2017, 139, 13330-13341. (25) Tournoux, M.; Marchand, R. ; Brohan, L. Layered K2Ti4O9 and the open metastable TiO2(B) structure. Prog. Solid State Chem. 1986, 17, 33-52. (26) Marchand, R.; Brohan, L. ; Tournoux, M. TiO2(B) a new form of titanium dioxide and the potassium octatitanate K2Ti8O17. Mater. Res. Bull. 1980, 15, 1129-1133. (27) Deng, D.; Kim, M. G.; Lee, J. Y. ; Cho, J. Green energy storage materials: Nanostructured TiO2 and Sn-based anodes for lithium-ion batteries. Energy Environ. Sci. 2009, 2, 818-837. (28) Zukalová, M.; Kalbáč, M.; Kavan, L.; Exnar, I. ; Graetzel, M. Pseudocapacitive Lithium Storage in TiO2(B). Chem. Mater. 2005, 17, 1248-1255. (29) Armstrong, A. R.; Armstrong, G.; Canales, J.; García, R. ; Bruce, P. G. Lithium-Ion Intercalation into TiO2-B Nanowires. Adv. Mater. 2005, 17, 862-865. (30) Armstrong, A. R.; Arrouvel, C.; Gentili, V.; Parker, S. C.; Islam, M. S. ; Bruce, P. G. Lithium Coordination Sites in LixTiO2(B): A Structural and Computational Study. Chem. Mater. 2010, 22, 6426-6432. (31) Zachau-Christiansen, B.; West, K.; Jacobsen, T. ; Atlung, S. Lithium insertion in different TiO2 modifications. Solid State Ionics 1988, 28–30, Part 2, 1176-1182.


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(44) Arrouvel, C.; Parker, S. C. ; Islam, M. S. Lithium Insertion and Transport in the TiO2−B Anode Material: A Computational Study. Chem. Mater. 2009, 21, 4778-4783. (45) Panduwinata, D. ; Gale, J. D. A first principles investigation of lithium intercalation in TiO2-B. J. Mater. Chem. 2009, 19, 3931-3940. (46) CASM Developers. CASMcode: v0. 2. 1. 2017, DOI: 10.5281/zenodo.546148. (47) Thomas, J. C. ; Ven, A. V. d. Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles. Phys. Rev. B 2013, 88, 214111. (48) Puchala, B. ; Van der Ven, A. Thermodynamics of the Zr-O system from first-principles calculations. Phys. Rev. B 2013, 88, 094108. (49) Van der Ven, A.; Thomas, J. C.; Xu, Q. ; Bhattacharya, J. Linking the electronic structure of solids to their thermodynamic and kinetic properties. Math. Comput. Simulat. 2010, 80, 13931410.


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Figure 1. HRTEM Image of a TiO2-B thin film (a) before and (b) after lithiation. Arrows indicate the structural changes observed in the structure during lithiation. The inset in (a) shows the FFT pattern of the region within a TiO2-B stack. (c) Schematics demonstrating sequence of defect generation upon lateral Li propagation on a cross-sectional surface of the film with [010] in-plane orientation.


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ACS Energy Letters

Figure 2. HRSTEM images demonstrating a TiO2-B film (a) before and (b) after full lithiation. (c) EELS Spectra on the regions marked with circles in both (a) and (b) demonstrate the shift from valence state of Ti from Ti4+ to Ti3+ upon full lithiation.


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Figure 3. (a) HRSTEM images demonstrating a TiO2-B film after full lithiation. (b) Magnified STEM image and a DFT-simulated schematic that show the shear accompanied with Li0.5TiO2B-to- Li0.5TiO2-A transition. (c) Schematic illustration of a crystallographic pathway to convert a TiO2-B crystal to Li0.5TiO2-A. Li atoms are omitted for clear demonstration of the configuration of Ti and O ordering upon structural transformation.


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ACS Energy Letters

Figure 4. (a) A graph illustrating free energy per formula TiO2 unit with increasing Li concentration in LixTiO2. Notice that the anatase phase (LixTiO2-A) formation becomes more favorable than that of LixTiO2-B as xLi > 0.2. (b-d) HRSTEM images of a thin film at different stages of lithiation from TiO2-B to spinel.


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Figure 1 55x38mm (300 x 300 DPI)


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Accordion Strain Accommodation Mechanism Within the Epitaxially

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