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[Gen Hasegawa](https://orcid.org/0000-0002-9297-6902), [Naoaki Kuwata](https://orcid.org/0000-0002-0736-6967), [Tsuyoshi Ohnishi](https://orcid.org/0000-0002-2333-7752), [Kazunori Takada](https://orcid.org/0000-0001-7568-1806)
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[Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometry](https://mdr.nims.go.jp/datasets/112f1dc3-aafd-4fc7-ba86-bd2f7b9fee7b)
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Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryJournal of Materials Chemistry AMaterials for energy and sustainabilityrsc.li/materials-aISSN 2050-7488Volume 12Number 214 January 2024Pages 525–1324PAPERNaoaki Kuwata et al.Visualization and evaluation of lithium diff usion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryJournal ofMaterials Chemistry APAPEROpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journal | View IssueVisualization andResearch Center for Energy and Environmenfor Materials Science (NIMS), 1-1 Namiki, TKUAWATA.Naoaki@nims.go.jp† Electronic supplementary informahttps://doi.org/10.1039/d3ta05012bCite this: J. Mater. Chem. A, 2024, 12,731Received 21st August 2023Accepted 4th November 2023DOI: 10.1039/d3ta05012brsc.li/materials-aThis journal is © The Royal Society oevaluation of lithium diffusion atgrain boundaries in Li0.29La0.57TiO3 solidelectrolytes using secondary ion massspectrometry†Gen Hasegawa, Naoaki Kuwata, * Tsuyoshi Ohnishi and Kazunori TakadaUnderstanding Li diffusion at interfaces in solid-state Li batteries is essential to improving their performance(e.g., rate capabilities and energy densities). However, the visualization of Li diffusion at grain boundaries hasbeen impossible due to the lack of experimental techniques. In this study, we visualize Li-ion diffusion atgrain boundaries via secondary ion mass spectrometry at low temperatures (z−110 °C) using an isotopeexchange technique for perovskite-type Li0.29La0.57TiO3 as a model solid electrolyte. The grain boundarydiffusion coefficient obtained in this study is 1.4 × 10−13 cm2 s−1 at 25 °C, which is much smaller thanthe bulk diffusion coefficient of 2.6 × 10−8 cm2 s−1. The long-range effective diffusion coefficients canbe explained well by a 1D model based on a series of bulk and grain boundaries. The Haven ratio of grainboundary diffusion suggests that correlation between the Li+ ions is crucial for grain boundary diffusion.IntroductionSolid-state Li batteries are expected to serve as next-generationenergy storage systems due to their safety, reliability, andhigh energy densities.1 However, a signicant challenge lies inthe ion dynamics at the grain boundaries and the interfacesbetween the active materials and electrolytes.2–4 High resistanceat the cathode/electrolyte interface leads to poor power densityof solid-state batteries with sulde-based solid electrolytes, andit has been successfully lowered by interposition of thin lms atthe interface.5 Now, sulde-based solid-state batteries showpractical performance, and they are under development aimingat application to electric vehicles.6 One of the disadvantages ofsulde-based solid-state batteries is the instability of the solidelectrolytes. Sulde electrolytes are easily decomposed ina humid atmosphere and release harmful hydrogen suldeupon the decomposition.7 This concern has brought about a lotof efforts to replace the sulde electrolytes with oxides.However, oxide-based solid electrolyte batteries also show highinterfacial resistance at grain boundaries.2,8 Therefore,although oxide-based solid electrolytes have achieved ionicconductivities of the order of 10−3 S cm−1, the internal resis-tance of oxide-based solid-state batteries is still high, resultingin poor battery performance. In order to achieve practicalbattery performance, it is necessary to elucidate the origin oftal Materials (GREEN), National Institutesukuba, Ibaraki 305-0044, Japan. E-mail:tion (ESI) available. See DOI:f Chemistry 2024grain boundary resistance and nd a way to reduce it, for whichtechniques to evaluate the interfacial ion dynamics areessential.The analysis of ion dynamics in solid-state Li battery mate-rials has focused mainly on the average ionic conductivity ob-tained using impedance spectroscopy (IS), the bulk diffusioncoefficient obtained using pulsed-eld gradient nuclearmagnetic resonance (PFG-NMR) spectroscopy, and relaxationtime measurements using NMR spectroscopy (Fig. 1). Theinterfaces of solid-state Li batteries are observed using scanningtransmission electron and scanning electron microscopy(SEM).The chemical diffusion of Li+ ions at the grain bound-aries of LiNi0.8Co0.15Al0.05O2 cathode materials has beenanalyzed using electron energy-loss spectroscopy.9 Additionally,Kimura et al. used computed tomography combined with X-rayabsorption near-edge structure spectroscopy to visualize thedistribution of the chemical diffusion in LiCoO2 particles.10However, these methods observe chemical diffusion with Liconcentration change and cannot measure ion dynamics insolid electrolytes or at the interface between the electrolyte andactive material without Li concentration change. Electro-chemical strain microscopy is a technique for visualizing thebulk and grain boundary conductivities of solid electrolytes,although several assumptions are required.11Tracer diffusion analysis based on secondary ion massspectrometry (SIMS) is an effective tool for quantitativelyanalyzing ion diffusion in solid electrolytes and activematerials.12–23 Additionally, SIMS enables a wide range of ionicdiffusion measurements from the nanometer to the millimeterscale, but it is limited in analyzing fast ionic conductorsJ. Mater. Chem. A, 2024, 12, 731–738 | 731http://crossmark.crossref.org/dialog/?doi=10.1039/d3ta05012b&domain=pdf&date_stamp=2023-12-22http://orcid.org/0000-0002-9297-6902http://orcid.org/0000-0002-0736-6967http://orcid.org/0000-0002-2333-7752http://orcid.org/0000-0001-7568-1806https://doi.org/10.1039/d3ta05012bhttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bhttps://pubs.rsc.org/en/journals/journal/TAhttps://pubs.rsc.org/en/journals/journal/TA?issueid=TA012002Fig. 1 Multiscale ion dynamics in solid-state batteries and their measurement techniques. The average ionic conductivity can bemeasured by IS.PFG-NMR spectroscopy measures ion diffusion on the micrometer scale, and secondary ion mass spectrometry (SIMS) can determine the iondiffusion coefficients over a wide spatial range from millimeters to tens of nanometers.Journal of Materials Chemistry A PaperOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinebecause the primary ion beam disrupts the ion distributions insolid electrolytes.24 Téllez et al. suggested that the Li distribu-tion is maintained via analysis at low temperatures, even in fastionic conductors, such as perovskite-type solid electrolytes.24SIMS at low temperatures is known as cryo-SIMS, because itsuppresses sample damage.25,26In this study, perovskite-type solid electrolytes are analyzedusing SIMS. We have established high-resolution SIMS tech-niques for imaging the isotope distributions in polycrystallinesolid electrolytes and succeeded in quantitatively evaluating thetracer diffusion coefficients of bulk and grain boundaries.Furthermore, we quantify the grain boundary diffusion coeffi-cient, which indicated that the grain boundaries are the rate-limiting factors in the total conductivity. We use Li0.29La0.57-TiO3 (LLTO), which is a fast Li-ion conductor with an ionicconductivity of 10−3 S cm−1 at 27 °C,27–30 as the model material.Fig. 2 Schematic diagram of the 6Li isotope exchange study usingLLTO. The edge of the LLTO is immersed in the aqueous 6LiNO3solution for exchange. The sample is immediately cooled to −110 °Cand SIMS is performed to observe the 6Li isotope ratio. The sample isthen annealed at 22–400 °C for further diffusion. The sample is againcooled to−110 °C, and the 6Li isotope ratio is measured. Repeating thisprocedure enables the determination of the temperature dependenceof the diffusion coefficient.ExperimentalSample preparationLLTO polycrystals sintered at 1450 °C were purchased fromToho Titanium (Yokohama, Japan). The samples were cut into 5× 10 × 0.5 mm3 pieces using a pen-type diamond glass cutterand ground using 800, 1200, and 2500 grit sandpaper, followedby 2 and 0.5 mm diamond lapping lms. The specimens werepolished using Baikalox 0.1CR agglomerate-free alumina andcolloidal silica in deionized water. The polished samplesurfaces were etched at 1100 °C for 1 h in air to visualize thegrain boundaries. Surface observations were performed usinglaser microscopy (VK-9710, Keyence, Osaka, Japan). A 6LiNO3solution (5 mol L−1) was used in the isotope exchange studies.6LiNO3 was prepared by mixing 6Li2CO3 (95% 6Li, 5% 7Li,732 | J. Mater. Chem. A, 2024, 12, 731–738Cambridge Isotope Laboratories, Tewksbury, MA, USA) andHNO3 (65 wt%, FUJIFILM Wako Pure Chemical, Osaka, Japan)in a 1 : 2 molar ratio. Fig. 2 shows the process of 6Li exchangeand SIMSmeasurement. The edge of the LLTO was immersed inthe aqueous 6LiNO3 solution for 6Li isotope exchange for 59–110 h, and the sample was then cooled to −110 °C in a SIMSsystem and the surface 6Li isotope ratio was observed via SIMS.Aer SIMS, diffusion was further enhanced by annealing at 22–400 °C. The sample was again cooled to −110 °C and analyzedusing SIMS. This procedure enabled the measurement of thetemperature dependence of the diffusion coefficient.To prevent the potential effects of thermal etching on grainboundaries, the sample preparations and measurements wereproceeded in the following sequence: (i) polishing, (ii) isotopeexchange, (iii) SIMS, (iv) further diffusion (22–400 °C), (v) SIMS,(vi) thermal etching (1100 °C), and (vii) optical microscopy.This journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bPaper Journal of Materials Chemistry AOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineSIMS measurementTime-of-ight SIMS (TOF.SIMS 5, IONTOF, Münster, Germany)was used to measure the 6Li isotope distribution. During SIMS,the samples were cooled to −110 °C with liquid N2 to quenchthe 6Li diffusion. The primary ion source was a single charge ofBi+ with an acceleration voltage of 30 kV. An electron ood gunwas used for charge compensation. The surface impurities wereremoved using an Ar gas cluster ion beam with a raster size of700 × 700 mm2 and an acceleration voltage of 10 kV. The rastersize of the primary ion beam used in mapping measurementswas 500 × 200 mm2. The pixel resolution in SIMS imaging was512 × 206, and the spatial resolution was 1 × 1 mm2. Theprimary ion current was 0.5 pA and the signal was integrated for5 h to obtain one image. Line measurements were performedusing a Cs sputter gun (acceleration voltage of 2 kV) with a depthanalysis of approximately 500 nm to conrm uniformity in thedepth direction. The respective raster sizes of the sputter andprimary ion guns were set to 100 × 100 and 50 × 50 mm2.Results and discussionVisualization of the isotope distributions in solid electrolytesFig. 3a illustrates the results of 6Li isotope imaging using cryo-SIMS. LLTO was prepared via isotope exchange at 22 °C for 59 hFig. 3 (a) Imaging of the relative 6Li fraction of LLTO immediately afteatmosphere at 22 °C. (c) Laser microscope image of LLTO in the samobservation was performed after SIMS imaging. (d) 6Li isotopic profiles oopen circles respectively represent the profiles of the sample after 59 h aconcentration difference DCgb at the grain boundary.This journal is © The Royal Society of Chemistry 2024and introduced into the SIMS system immediately aer 6Liexchange. During cryo-SIMS, the temperature was maintainedat−110 °C to quench the Li diffusion. The relative 6Li fraction Cchanges from the bottom to the top of the LLTO owing to thediffusion of the 6Li isotope. C (=6Li/(6Li + 7Li)) is obtained basedon SIMS as follows:C ¼I6LiI6Li þ I7Li; (1)where I6Li and I7Li are the intensities of the peaks for6Li and 7Li,respectively. The SIMS image in Fig. 3a clearly reveals that Cchanges rapidly at the grain boundaries via comparison withthe laser microscope image taken from the same position inFig. 3c, and thus, Li diffusion in the LLTO polycrystals is rate-limiting at the grain boundaries. This grain boundary resis-tance is the main factor increasing the total resistance of thepolycrystalline solid electrolytes. Elucidating the origin of thegrain boundary resistance (i.e., grain boundary diffusivity) isone of the most important issues in the realization of solid-statebatteries. Atomic diffusion at the grain boundaries is usuallybelieved to be fast,31 and ionic conductivity increases at thegrain boundaries in ionic conductors such as ZrO2.32 However,in solid electrolytes with fast ionic conduction pathways in theircrystal structures, such as LLTO, diffusion at the grainr 6Li isotope exchange for 59 h and (b) after 16 d of storage in an Are position as that used in SIMS. Thermal etching for grain boundaryf the black and red lines shown in the SIMS images. The black and rednd 16 d of isotope exchange. (e) Gradient of the 6Li fraction vC/vy andJ. Mater. Chem. A, 2024, 12, 731–738 | 733http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bFig. 4 (a) Time evolution of the relative 6Li fraction of LLTO at 22 °C.The black circles represent the SIMS profile immediately after 110 h of6Li isotope exchange, and the red and blue circles represent therespective SIMS profiles after 2 and 6 weeks of storage in an Aratmosphere. (b) Variation in the relative 6Li fraction of LLTO afterannealing at 200 °C. The black circles represent the SIMS profileimmediately after 6Li isotope exchange for 63 h, and the red circlesrepresent the profile after annealing at 200 °C.Journal of Materials Chemistry A PaperOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlineboundaries is slower than that in the bulk materials. Fig. 3bshows the SIMS images of C in LLTO aer diffusion at 22 °C foran additional 16 d. The 6Li distribution becomes homogeneousvia diffusion, but the 6Li concentration still changes stepwise atthe grain boundaries.Fig. 3d compares the proles of the C values along the blackand red lines shown in the SIMS images, which indicates that Cchanges abruptly at the grain boundary. The continuity of thediffusion ux across the interface between the bulk and grainboundaries is expressed as�D*bulkvCvy����bulk¼ �D*gbvCvy����gb; (2)where D*bulk and D*gb are the respective bulk and grain boundarydiffusion coefficients, vC/vyjbulk is the 6Li concentration gradientin the bulk nearby the boundary, and vC/vyjgb is the 6Li concen-tration gradient at the grain boundary. If the grain boundarythickness d is sufficiently thin, eqn (2) can be written as�D*bulkvCvy����bulk¼ �D*gbDCgbd; (3)where DCgb is the difference in the 6Li concentration at the grainboundary (Fig. 3e). When D*gb is much lower than D*bulk; DCgb/dmust be larger than vC/vyjbulk to satisfy eqn (3). Therefore, whenthe diffusion is rate-limiting at the grain boundaries, C variesstepwise at the grain boundaries. Based on Fig. 3e, the derivativecoefficient vC/vyjbulk is determined to be 1.1 cm−1 usinga quadratic function, and DCgb is 0.02. We assume that D*bulk isconsistent with the diffusion coefficient DNMR,bulk determined viaPFG-NMR spectroscopy,33 with DNMR,bulk representing the averagediffusion coefficient of randomly oriented LLTO crystals with 2Ddiffusion pathways. LLTO is known to have a 90° domainboundary microstructure,34,35 which is a 90° rotation of thealignment of La-rich and La-poor layers in the perovskite struc-ture. This domain boundary may affect the diffusion behaviorbecause LLTO has a two-dimensional diffusion pathway. TheLLTO sample used in this study also contains 90° domains witha size of several hundreds of nanometers.33 Despite the presenceof such 90° domains, the SIMS image shown in Fig. 3a revealsuniform isotope concentrations within the grains and thereforeuniform diffusion coefficients. This the bulk diffusion coefficientwill be the value averaged throughmultiple domain boundaries. Ifa DNMR,bulk of 2.6 × 10−8 cm2 s−1 at 22 °C33 is used, thenD*gb=d ¼ 1:5� 10�6 cm2 s�1: Assuming that the typical thicknessd = 0.5 nm,36,37 then D*gb ¼ 7:6� 10�14 cm2 s�1; and the calcu-lated D*gb is ve orders of magnitude lower than DNMR,bulk. Simi-larly, the SIMS prole aer 16 d, as indicated by the red lineshown in Fig. 3d, is analyzed, and vC/vyjbulk and DCgb are0.65 cm−1 and 0.009, respectively. D*gb ¼ 9:2� 10�14 cm2 s�1;which is consistent with the D*gb determined immediately aer 6Liexchange. Similar line analyses are performed at other grainboundaries. The results are shown in the ESI (Fig. S3 and TableS2†). The D*gb values for each grain boundary are in the range of2.6 × 10−14 to 1.5 × 10−13 cm2 s−1. The average value is 6.8 ×10−14 cm2 s−1, which agrees with the D*gb value obtained fromFig. 3e. The above analysis reveals that D*gb values are low at mostgrain boundaries in LLTO.734 | J. Mater. Chem. A, 2024, 12, 731–738Measurements of the long-range (effective) diffusioncoefficientsThe long-range diffusion coefficients are then measured usingSIMS line analysis. Long-range diffusion in polycrystalscomprising bulks and grain boundaries exhibits a single effec-tive diffusion coefficient ðD*gbÞ on the macroscopic scale.38–40Fig. 4a shows the time evolution of the C of LLTO, as measuredvia SIMS line analysis. The black circles shown in Fig. 4arepresent the 6Li prole aer 110 h of isotope exchange incontact with a 6LiNO3 solution. C is constant in the regionimmersed in the solution (−1 to 0 mm, as shown in Fig. 4a),whereas above the liquid level (0–6 mm, as shown in Fig. 4a),a 6Li concentration distribution is observed due to diffusion.When the origin of position x is the liquid surface, the 6Liconcentration C(x,t) at x = 0 is regarded as constant, regardlessof time t. The solution of the 1D diffusion equation is thenexpressed as41,42Cðx; tÞ � C0Cs � C0¼ erfc264 x2ffiffiffiffiffiffiffiffiffiffiD*eff tp375; (4)where Cs is the 6Li fraction in the aqueous solution, C0 is theinitial 6Li fraction in the LLTO polycrystal, and D*eff is theThis journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bPaper Journal of Materials Chemistry AOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlineeffective tracer diffusion coefficient. By tting eqn (4) to theexperimental data, as indicated by the solid black line shown inFig. 4a, D*eff is determined to be 8.0 × 10−9 cm2 s−1. The red andblue circles shown in Fig. 4a indicate the 6Li proles of LLTOaer storage in an Ar atmosphere for 2 and 6 weeks at 22 °C,respectively. During storage, the sample did not come intocontact with the 6LiNO3 solution, and the total amount of 6Lishould be maintained. D*eff is obtained based on the timeevolution of the 6Li prole using a 1D numerical simulation ofthe diffusion equation. The initial conditions are indicated bythe solid black line shown in Fig. 4a. The simulated results aerstorage for 2 and 6 weeks are shown as the red and blue solidlines, respectively, with a D*eff of 3.0× 10−9 cm2 s−1 at 22 °C. TheD*eff determined immediately aer 6Li exchange is slightly largerthan the D*eff of the stored sample. The D*eff immediately aerion exchange is likely overestimated due to the rise in the levelof the upper surface of the liquid caused by the meniscus andthe slight uctuation in the liquid level. The D*eff determinedusing the time evolution of the 6Li distribution is thus moreaccurate. Fig. 4b shows the effect of annealing at 200 °C for 3.8 haer 6Li exchange. The numerical simulations show thatD*eff ¼ 6:6� 10�6 cm�2 s�1 at 200 °C and the other D*eff values atdifferent temperatures from 22 to 400 °C were determined ina similar manner and used in the following discussion.Relationship between D*bulk;D*gb; and D*effWe analyze the relationship between D*gb;D*bulk; and D*eff basedon a simple model. The Fisher model,43 which is a well-knownmodel of grain boundary diffusion, is suitable when grainboundary diffusion is faster than bulk diffusion, e.g., in metals.However, in LLTO, Dbulk » Dgb, and the Fisher model is inap-propriate. The brick layer39 and Maxwell–Garnett models,38 asshown in Fig. 5a, are generally used inmodeling ion diffusion inpolycrystalline materials. These models include two types ofdiffusion pathways: along and across grain boundaries. InLLTO, Dbulk » Dgb, and thus, diffusion along the grain bound-aries is ignored. Therefore, the series model of the bulk andgrain boundaries provides a good approximation. If the diffu-sion length is sufficiently large relative to the grain diameter lðl �ffiffiffiffiffiffiffiffiffiffiD*eff tqÞ;D*eff can be expressed as44l þ dD*eff¼ lD*bulkþ dD*gb; (5)where d is the thickness of the grain boundary. This equationalso represents the 1D case of the Maxwell–Garnett equation forcalculating the diffusion coefficient in a two-phase material.38,39As l is much larger than d (l » d), D*eff is given byD*eff ¼1�D*bulk��1 þ�ldD*gb��1: (6)We use D*gb=d ¼ 2:8� 10�6 cm s�1; as determined by SIMSimaging, and we again assume that D*bulk is equal to DNMR,bulk =2.8 × 10−8 cm2 s−1.33 The average particle size l = 16 ± 11 mm isdetermined via electron backscatter diffraction,33 and theThis journal is © The Royal Society of Chemistry 2024results are shown in Supplementary Fig. S1 in the ESI.† Whenthese values are substituted into eqn (6), the effective diffusioncoefficient of the 1D model may be calculated asD*eff ¼ 2:3� 1:4� 10�9 cm2 s�1: This value is consistent withD*eff ¼ 3:0� 10�9 cm2 s�1 for long-range diffusion determinedexperimentally based on the time evolution of the SIMS lineanalysis, as compared in the Arrhenius plot in Fig. 5b. Althoughit is a coarse approximation, the 1D series model explains thelong-range Li diffusion in LLTO polycrystals very well. Extrap-olating the Arrhenius plot, the D*eff value at −110 °C is calcu-lated to be 1 × 10−14 cm2 s−1. Assuming the time of the SIMSimaging to be t = 5 h, the diffusion lengthffiffiffiffiffiffiffiffiffiffiffiffi2D*eff tqis 0.2 mm,which is smaller than the spatial resolution of SIMS imaging.The Li diffusion during the measurement is negligible. Weconrm that −110 °C is a suitable temperature for SIMSimaging measurements.Fig. 5b also demonstrates the temperature dependence ofDNMR,bulk33 and the conductivity diffusion coefficients of thebulk and total (Ds,bulk and Ds,total) obtained using IS.33 Here,Ds,bulk and Ds,total are calculated based on the Nernst–Einsteinequation using the bulk and total ionic conductivities, respec-tively, and the number density of Li (5.0 × 10−21 cm−3) inLLTO.45–47 The details of IS are provided in the ESI.† As we re-ported previously, DNMR,bulk is consistent with Ds,bulk over theentire temperature range, and both display non-Arrheniusbehaviors at >177 °C.33 On the other hand, D*eff represents thelong-range diffusion including grain boundaries in LLTO, andthus it is comparable to Ds,total; however, Fig. 5b shows slightlysmaller values of D*eff than those of Ds,total. In order to clarify thetemperature dependence of D*eff and Ds,total, let us separate thebulk and grain boundary contributions according to eqn (6).Fig. 5c compares the Arrhenius plot of ðl=dÞD*gb; as calculatedusing eqn (6), assuming that D*bulk ¼ DNMR;bulk; with (l/d)Ds,gbcalculated from the grain boundary conductivity obtained viaIS.48 The activation energies of ðl=dÞD*gb and (l/d)Ds,gb showalmost the same value of 0.43 eV. Molecular dynamics (MD)simulations have been used to calculate the activation energiesof grain boundary diffusion in Li0.16La0.62TiO3.49 The activationenergy of the S5 grain boundary is predicted to be 0.36 eV,whereas that of D*gb in the experiment is 0.43 eV. The largeractivation energy can be attributed to the random nature of thegrain boundaries, with a low experimental consistency(Supplementary Fig. S1†). The relationship between the D*gbvalue and the type of grain boundary has been investigated onlyfor small S values. Sasano et al. reported that the ionicconductivity does not decrease at special grain boundaries,such as S2 grain boundaries in LLTO thin lms and S5 grainboundaries in polycrystalline LLTO.52,53 MD calculations alsosuggest a relationship between the type of grain boundary andthe diffusion coefficients.49 The polycrystalline LLTO used inthis study consists mostly of random grain boundaries(Fig. S1f†). Therefore, most grain boundaries had low D*gbvalues. A more detailed analysis will be performed in futurestudies.The respective pre-exponential factors of ðl=dÞD*gb and (l/d)Ds,gb are 0.048 and 0.20 cm2 s−1. The Haven ratio (HR h D*/Ds)J. Mater. Chem. A, 2024, 12, 731–738 | 735http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bFig. 5 (a) Ion diffusion modeling in polycrystals. The brick layer39 and Maxwell–Garnett models38 are generally used to model ion diffusion inpolycrystalline materials. These models include two types of diffusion pathways: along and across the grain boundaries. When Dbulk » Dgb,diffusion along the grain boundaries may be ignored. Therefore, the series model of bulk and grain boundaries provides a good approximation.(b) Temperature dependences of the diffusion coefficients determined using the bulk33 (Ds,bulk, filled squares) and total conductivities (Ds,total,open squares), PFG-NMR33 (DNMR,bulk, open circles), and SIMS line analysis (D*eff; open triangles). The D*eff calculated using the 1D model is alsoshown as a filled triangle. (c) Temperature dependences of (l/d)Dgb, as calculated using the grain boundary conductivity (open squares) and (l/d)Dgb, as determined via SIMS line and mapping analyses (open and filled triangles, respectively).Journal of Materials Chemistry A PaperOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinedetermined using the ratio of the pre-exponential factors is0.24, which is smaller than the bulk (HR z 1). Hence, we ndthat the separation of D*eff and Ds,total at low temperatures is dueto the smaller HR in the grain boundaries. There are twopossible reasons for the smaller HR of Dgb compared to that ofDbulk: the number of carriers at the grain boundary or thecorrelation effect is large.50,51 The grain boundaries of LLTOusing transmission electron microscopy and Li depletion at thegrain boundary were reported based on electron energy-lossspectra.36,52 Therefore, the possibility of increased carrierconcentration should be eliminated, and thus, the correlationbetween the Li+ ions is signicant at the grain boundaries.Understanding the correlation effect will be the key to futurebreakthroughs in reducing grain boundary resistance.ConclusionsWe visualized and quantied the bulk and grain boundarydiffusion of Li+ ions in LLTO solid electrolytes using cryo-SIMS.The visualized image has revealed that the grain boundaryimpedes the ionic diffusion because of the much lower D*gbrelative to D*bulk: The grain boundary diffusion coefficient, D*gb;has been determined to be 1.4 × 10−13 cm2 s−1 at 22 °C. Theeffective diffusion coefficient D*eff is explainable by D*gb and D*bulkby using a simple 1D model of bulk and grain boundaries. Theactivation energy of D*gb of 0.43 eV was consistent with the grain736 | J. Mater. Chem. A, 2024, 12, 731–738boundary conductivity. HR was small at the grain boundaries,suggesting enhanced correlation between the Li+ ions at thegrain boundaries. The SIMS method developed in this studyeffectively elucidates the bottleneck of ion transfer at the solid–solid interface, which limits the performance of charge/discharge rates and may contribute to improving the perfor-mance of solid-state lithium batteries.Author contributionsG. H. and N. K. conceived the work. G. H. prepared andanalyzed the samples. T. O. and K. T. helped with experimentaldesign and interpretation of data. G. H. draed the originalmanuscript. N. K., T. O. and K. T. revised the manuscriptdras.Conflicts of interestThere are no conicts to declare.AcknowledgementsThis study was supported by the Japan Science and TechnologyAgency ALCA-Specially Promoted Research for Innovative NextGeneration Batteries project (grant number JPMJAL1301). Thisstudy was also supported by the Japan Society for the PromotionThis journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bPaper Journal of Materials Chemistry AOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlineof Science KAKENHI Grant Numbers JP19H05814 (Grant-in-Aidfor Scientic Research on Innovative Areas “Interface IONICS”)and JP21H02033 (Grant-in-Aid for Scientic Research (B)). Wethank Dr Atsuko Nagataki, Mr Kyosuke Matsushita, and Ms.Makiko Oshida for their assistance with SIMS and SEM at theNIMS Battery Research Platform (Tsukuba, Japan).References1 T. Famprikis, P. Canepa, J. A. Dawson, M. S. Islam andC. Masquelier, Nat. Mater., 2019, 18, 1278–1291.2 K. Takada, J. Power Sources, 2018, 394, 74–85.3 L. Xu, S. Tang, Y. Cheng, K. Wang, J. Liang, C. Liu, Y.-C. Cao,F. Wei and L. Mai, Joule, 2018, 2, 1991–2015.4 M. Pasta, D. Armstrong, Z. L. Brown, J. Bu, M. R. Castell,P. Chen, A. Cocks, S. A. Corr, E. J. Cussen, E. Darnbrough,V. Deshpande, C. Doerrer, M. S. Dyer, H. El-Shinawi,N. Fleck, P. Grant, G. L. Gregory, C. Grovenor,L. J. Hardwick, J. T. S. Irvine, H. J. Lee, G. Li, E. Liberti,I. Mcclelland, C. Monroe, P. D. Nellist, P. R. Shearing,E. Shoko, W. Song, D. S. Jolly, C. I. Thomas, S. J. Turrell,M. Vestli, C. K. Williams, Y. Zhou and P. G. Bruce, J. Phys.Energy, 2020, 2, 32008.5 N. Ohta, K. Takada, L. Zhang, R. Ma, M. Osada and T. Sasaki,Adv. Mater., 2006, 18, 2226–2229.6 A. L. Robinson and J. Janek, MRS Bull., 2014, 39, 1046–1047.7 Y. Morino, H. Sano, T. Takahashi, N. Miyashita, A. Sakudaand A. Hayashi, J. Phys. Chem. C, 2023, 127, 13616–13622.8 J. F. Wu and X. Guo, Phys. Chem. Chem. Phys., 2017, 19, 5880–5887.9 Y. Nomura, K. Yamamoto, Y. Yamagishi and E. Igaki, ACSNano, 2021, 15, 19806–19814.10 Y. Kimura, A. Tomura, M. Fakkao, T. Nakamura, N. Ishiguro,O. Sekizawa, K. Nitta, T. Uruga, T. Okumura, M. Tada,Y. Uchimoto and K. Amezawa, J. Phys. Chem. Lett., 2020,11, 3629–3636.11 N. Schön, D. C. Gunduz, S. Yu, H. Tempel, R. Schierholz andF. Hausen, Beilstein J. Nanotechnol., 2018, 9, 1564–1572.12 B. Steele, J. Kilner, P. Dennis, A. Mchale, M. Van Hemert andA. Buggraaf, Solid State Ionics, 1986, 18–19, 1038–1044.13 M. Sase, K. Yashiro, K. Sato, J. Mizusaki, T. Kawada, N. Sakai,K. Yamaji, T. Horita and H. Yokokawa, Solid State Ionics,2008, 178, 1843–1852.14 D. Uxa, H. J. Holmes, K. Meyer, L. Dörrer and H. Schmidt,Phys. Chem. Chem. Phys., 2021, 23, 5992–5998.15 G. Hasegawa, N. Kuwata, Y. Tanaka, T. Miyazaki, N. Ishigaki,K. Takada and J. Kawamura, Phys. Chem. Chem. Phys., 2021,23, 2438–2448.16 K. Watanabe, I. Sakaguchi, S. Hishita, N. Ohashi andH. Haneda, Appl. Phys. Express, 2011, 4, 055801.17 J. Rahn, E. Hüger, L. Dörrer, B. Ruprecht, P. Heitjans andH. Schmidt, Z. Phys. Chem., 2012, 226, 439–448.18 N. Kuwata, X. Lu, T. Miyazaki, Y. Iwai, T. Tanabe andJ. Kawamura, Solid State Ionics, 2016, 294, 59–66.19 E. Navickas, Y. Chen, Q. Lu, W. Wallisch, T. M. Huber,J. Bernardi, M. Stöger-Pollach, G. Friedbacher, H. Hutter,B. Yildiz and J. Fleig, ACS Nano, 2017, 11, 11475–11487.This journal is © The Royal Society of Chemistry 202420 N. Kuwata, M. Nakane, T. Miyazaki, K. Mitsuishi andJ. Kawamura, Solid State Ionics, 2018, 320, 266–271.21 C. Schwab, A. Höweling, A. Windmüller, J. Gonzalez-Julian,S. Möller, J. R. Binder, S. Uhlenbruck, O. Guillon andM. Martin, Phys. Chem. Chem. Phys., 2019, 21, 26066–26076.22 N. Kuwata, G. Hasegawa, D. Maeda, N. Ishigaki, T. Miyazakiand J. Kawamura, J. Phys. Chem. C, 2020, 124, 22981–22992.23 R. H. Brugge, R. J. Chater, J. A. Kilner and A. Aguadero, J.Phys. Energy, 2021, 3, 034001.24 H. Téllez, A. Aguadero, J. Druce, M. Burriel, S. Fearn,T. Ishihara, D. S. McPhail and J. A. Kilner, J. Anal. At.Spectrom., 2014, 29, 1361–1370.25 R. Metzner, M. R. Thorpe, U. Breuer, P. Blümler, U. Schurr,H. U. Schneider and W. H. Schroeder, Plant. Cell Environ.,2010, 33, 1393–1407.26 J. Zhang, J. Brown, D. J. Scurr, A. Bullen, K. MacLellan-Gibson, P. Williams, M. R. Alexander, K. R. Hardie,I. S. Gilmore and P. D. Rakowska, Anal. Chem., 2020, 92,9008–9015.27 Y. Inaguma, C. Liquan, M. Itoh, T. Nakamura, T. Uchida,H. Ikuta and M. Wakihara, Solid State Commun., 1993, 86,689–693.28 S. Stramare, V. Thangadurai and W. Weppner, Chem. Mater.,2003, 15, 3974–3990.29 M. J. Wang, J. B. Wolfenstine and J. Sakamoto, Adv. Funct.Mater., 2020, 30, 1909140.30 L. Zhang, X. Zhang, G. Tian, Q. Zhang, M. Knapp,H. Ehrenberg, G. Chen, Z. Shen, G. Yang, L. Gu and F. Du,Nat. Commun., 2020, 11, 3490.31 Y. Mishin and C. Herzig,Mater. Sci. Eng. A, 1999, 260, 55–71.32 P. Heitjans and S. Indris, J. Phys.: Condens. Matter, 2003, 15,R1257–R1289.33 G. Hasegawa, N. Kuwata, K. Hashi, Y. Tanaka and K. Takada,Chem. Mater., 2023, 35, 3815–3824.34 Y. Inaguma, J. Ceram. Soc. Jpn, 2006, 114, 1103–1110.35 X. Gao, C. A. J. Fisher, T. Kimura, Y. H. Ikuhara, A. Kuwabara,H. Moriwake, H. Oki, T. Tojigamori, K. Kohama andY. Ikuhara, J. Mater. Chem. A, 2014, 2, 843–852.36 C. Ma, K. Chen, C. Liang, C.-W. Nan, R. Ishikawa, K. Moreand M. Chi, Energy Environ. Sci., 2014, 7, 1638–1642.37 H. Mehrer, Diffusion in Solids: Fundamentals, Methods,Materials, Diffusion-Controlled Processes, Springer Science &Business Media, 2007, ch. 32.38 J. R. Kalnin, E. A. Kotomin and J. Maier, J. Phys. Chem. Solids,2002, 63, 449–456.39 I. V. Belova and G. E. Murch, J. Phys. Chem. Solids, 2003, 64,873–878.40 H. Mehrer, Diffusion in Solids: Fundamentals, Methods,Materials, Diffusion-Controlled Processes, Springer Science &Business Media, 2007, ch. 34.41 J. Crank, The Mathematics of Diffusion, Clarendon Press,1975, ch. 3.42 H. Mehrer, Diffusion in Solids: Fundamentals, Methods,Materials, Diffusion-Controlled Processes, Springer Science &Business Media, 2007, ch. 3.43 J. C. Fisher, J. Appl. Phys., 1951, 22, 74–77.J. Mater. Chem. A, 2024, 12, 731–738 | 737http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012bJournal of Materials Chemistry A PaperOpen Access Article. Published on 18 December 2023. Downloaded on 1/3/2024 11:20:00 PM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Online44 J. Crank, The Mathematics of Diffusion, Clarendon Press,1975, ch. 12.45 T. Zinkevich, B. Schwarz, P. Braun, A. Weber, H. Ehrenbergand S. Indris, Solid State Ionics, 2020, 357, 115486.46 Y. Q. Cheng, Z. H. Bi, A. Huq, M. Feygenson, C. A. Bridges,M. P. Paranthaman and B. G. Sumpter, J. Mater. Chem. A,2014, 2, 2418–2426.47 A. Varez, M. T. Fernández-D́ıaz, J. A. Alonso and J. Sanz,Chem. Mater., 2005, 17, 2404–2412.48 T. van Dijk and A. J. Burggraaf, Phys. Status Solidi, 1981, 63,229–240.738 | J. Mater. Chem. A, 2024, 12, 731–73849 A. R. Symington, M. Molinari, J. A. Dawson, J. M. Statham,J. Purton, P. Canepa and S. C. Parker, J. Mater. Chem. A,2021, 9, 6487–6498.50 G. E. Murch, Solid State Ionics, 1982, 7, 177–198.51 A. Van der Ven, Z. Deng, S. Banerjee and S. P. Ong, Chem.Rev., 2020, 120, 6977–7019.52 S. Sasano, R. Ishikawa, G. Sánchez-Santolino, H. Ohta,N. Shibata and Y. Ikuhara, Nano Lett., 2021, 21, 6282–6288.53 S. Sasano, R. Ishikawa, K. Kawahara, T. Kimura,Y. H. Ikuhara, N. Shibata and Y. Ikuhara, Appl. Phys. Lett.,2020, 116, 043901.This journal is © The Royal Society of Chemistry 2024http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b Visualization and evaluation of lithium diffusion at grain boundaries in Li0.29La0.57TiO3 solid electrolytes using secondary ion mass spectrometryElectronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ta05012b