Ion Diffusion in Solids Detected with Muon-Spin Spectroscopy

R&D Review of Toyota CRDL, Vol.46 No.2 (2015) 29-36 29

Special Feature: Materials Analysis using Quantum Beams

Review Ion Diffusion in Solids Detected with Muon-spin Spectroscopy

Jun Sugiyama, Kazuhiko Mukai, Hiroshi Nozaki, Masashi Harada and Izumi Umegaki

Report received on Apr. 16, 2015

In this paper, we will give an introduction to the method itself but also summary of our muon-spin rotation and relaxation (µ+SR) work on Li-diffusion in battery positive electrode materials. Furthermore, we will show that the method is not limited to studying only Li-diffusion but can also be extended to other physical and/or electrochemical properties in transition metal oxides. Finally, we will compare our method to other available macroscopic and microscopic techniques that are able to study ion diffusion in solids, and provide an outlook towards future developments.

Muon-spin Relaxation, Nuclear Magnetic Field, Diffusion, Li, Na

1. Introduction ˜ DLi = ΘDLi, (2) In order to store electric energy in a compact package, huge number of batteries have been under where Θ is a thermodynamic factor. However, for intense investigation since 1800, i.e. the discovery of materials containing magnetic ions, Li-NMR provides a voltaic cell. Among them, Li-ion batteries are thought very limited information on DLi, because of the effect to be the most promising one,(1-4) particularly for the of electron spins on the spin-lattice relaxation rate (6) energy storage device for electric vehicles mainly due (1/T1). Hence, there is no optimal way to correctly to its high energy density. Back to the basic principle determine DLi for positive electrode materials of behind the operation of such batteries, ion-diffusion in Li-ion batteries, since they all include transition metal solids is one of the essential factors to govern the total ions to compensate charge neutrality during the Li+ performance of batteries, because the charge carrier in intercalation and deintercalation reaction. This is batteries should be ion. And, the speed and density of a highly unsatisfactory situation, since DLi is one of an ion flow provide the overall current. the primary parameters that govern the charge and According to Fick’s first law, a diffusion behavior of discharge rate of a Li-ion battery, particularly in the ions in solids is expressed by; case of future solid state batteries.

We have, therefore, attempted to measure DLi J = – D˜ × ∂f/∂x, (1) for lithium-transition-metal-oxides (LiMO) with muon-spin rotation and relaxation (µ+SR) since ˜ (7-16) where J is the diffusion flux, D is the chemical 2005. The other group also measured DLi for Li diffusion coefficient, f is the concentration, and x ionic conductors with µ+SR.(17,18) More correctly, the is the position. Although D˜ is usually determined by first µ+SR work for studying dynamics in battery electrochemical measurements, it is very difficult to materials was, to author’s knowledge, reported in ˜ (19) estimate DLi accurately due to absence of knowledge 2000 for Lix(Mn1.96Li0.04)O4, in which the authors on the reactive surface area of a porous electrode in a concentrated the change in the average nuclear liquid electrolyte.(1) magnetic field (the field distribution width) with On the other hand, a self diffusion coefficient or temperature. A similar experimental approach was + (20) a jump diffusion coefficient (D) of Li ions (DLi) in also reported for Li0.6TiO2, although DLi was not 7 (5) solids is usually evaluated by Li-NMR. Here, DLi is obtained in these work. ˜ connencted with DLi by the relationship; Muons do not feel fluctuating magnetic moments at

high T, but instead sense the change in nuclear dipole Here, PZF (t) is the muon-spin depolarization function field due to Li diffusion. Even if magnetic moments in ZF and Δ is the static width of the local field still affect the muon-spin depolarization rate, such distribution at the muon site. Note that Δ corresponds an effect is, in principle, distinguishable from that of to the linewidth of Li-NMR, while v corresponds to nuclear dipole fields. In particular, a weak longitudinal 1/T1. field can be applied that decouples the magnetic and When the muon sees a local field that fluctuates nuclear dipole interactions.(21) Here, we summarize randomly with an average rate, i.e. the field fluctuation + + KT our µ SR work on Li diffusion and compare the µ SR rate (v) due to Li-diffusion, Gzz is replaced by a DGKT method to other available experimental techniques in dynamic Gaussian KT function (Gzz (Δ, v, t)). DGKT terms of accuracy, flexibility as well as time window. Although the strict analytical expression for Gzz is unavailable, the variation of the µ+SR spectrum with 2. Basic Principle v/Δ is given by numerical calculations (see Fig. 1). If Li+ ions start to diffuse above a certain temperature

Among several methods to detect ion diffusion in solids, (≡ Tdiffu), such diffusive motion induces additional the muon-spin relaxation (µ+SR) technique provides fluctuation in the local field, resulting in the increase unique information on Li diffusion, mainly because of of v with temperature above Tdiffu, and we can know its characteristic time and spatial resolutions.(22) Muons the change in v from the ZF-µ+SR measurements, are S = 1/2 particles with a very large gyromagnetic and, as a result, evaluate DLi, if we assume that v ratio γ/2π = 13.553 kHz/Oe. Therefore, the implanted corresponds to the jump rate of the Li+ ions between muons into a material act as an extremely sensitive the neighboring sites. This is the basic principle how + and local probe of static as well as dynamic to measure DLi in solids by µ SR. DGKT magnetic/dipole fields. Furthermore, when using Note that, when v >> Δ, Gzz (Δ, v, t) is equivalent nu nu muons with momentum pµ = 29.8 MeV/c and kinetic to exp(–λ t) (see Fig. 1 with ν /∆ = 10). Here, λ is the energy Kµ = 4.1 MeV, – i.e. surface muons, the initial exponential relaxation rate due to fluctuating nuclear muon-spin direction is perfectly antiparallel to its magnetic moments. For such situation, we can not momentum due to parity violation. This is a significant extract v from the µ+SR data. This leads to the upper advantage over NMR and other resonance techniques, limit for detecting Li-diffusion in solids with µ+SR, as since such 100% spin polarized muons sense the local shown in Section 5. magnetic field under zero applied field (ZF).

2. 1 How to Detect Li-diffusion by µ+SR

Positive muons are identified as an ideal point charge with a positive elementary charge. Thus, the implanted v/ = 1 muons into LiMO are located in the vicinity of oxygen 10 anions, i.e. typically 1-1.2 Å away from O2– ions so as 2.5 to make a stable µ+-O2– bond. In other words, the muon 1 2– 0 in LiMO is stationary in the vicinity of O ions and ( t ) ZF is able to sense the local magnetic field of nuclear P 0.5 Nu origin (H int ), when LiMO is in a paramagnetic state. If we assume a static and isotropic Gaussian field distribution around the muon, the ZF-µ+SR time-spectrum is expressed by a static Gaussian (22) KT 0 Kubo-Toyabe (KT) function (Gzz (Δ, t), see the 0 5 10 15 20 curve with v/Δ = 0 in Fig. 1); Time (µs)

P (t) = G KT (Δ, t) Fig. 1 Muon-spin depolarization in ZF expressed by a ZF zz dynamic Gaussian Kubo-Toyabe function with four different ν /∆. Here, ∆ is fixed at 0.2 × 106 s−1, = 1 + 2 (1 – Δ2t 2) exp (– 1 Δ2t 2) (3) 3 3 2 . which corresponds to about 2.3 Oe.

2. 2 How to Separate Electronic Contribution from 4. Results Nuclear Contribution Figure 3 shows the ZF-µ+SR spectrum for the + For the case that the ZF-µ SR spectrum shows Li0.73CoO2 sample recorded at 100, 225, and 275 K. a KT-type relaxation, longitudinal field (LF) At 100 K, the ZF-spectrum exhibits a typical KT measurements are very useful to study Δ and v in detail.(21) Here, LF means the external field applied parallel to the initial muon-spin direction. When (a)

HLF > Δ, the nuclear field contribution is quenched DGKT 1 P0(t) = G LF by HLF. As a result, the muon-spin is held its original direction with increasing HLF, leading to a decrease LF = 10 Oe in relaxation (see Fig. 2(a)). Such behavior is called

“decoupling” with LF. Since Δ of nuclear origin ( t ) P 0.5 LF = 5 Oe usually ranges below 10 Oe in LiMO, the decoupling behavior is observed even with an LF of a few Oe. Nu ZF When the muon-spin is depolarized by both H int and H originated by electron (H Ele), the total int int 0 depolarization function is given by the product of the (b) two polarization functions (see Fig. 2(b)).(23) DGKT 1 P0(t) = G LF DGKT PZF(t) = Gzz (Δ, v, t) exp (–λt). (4)

Ele Nu Since H int >> H int , the electronic contribution is ( t ) distinguishable from the nuclear contribution by P 0.5 ZF LF measurements.(21) This is because a weak LF decouples the nuclear contribution but does not affect ZF the stronger electronic contribution (see Fig. 2(c)). ZF Nu As a result, we can know Δ and v originated by H int 0 Ele + under the coexistence of H int . This makes µ SR a (c) significant technique for detecting DLi in LiMO and DGKT other magnetic materials. We wish to emphasize that 1 P0(t) = G LF such characteristic feature is caused by the fact that the initial muon-spin is polarized even in ZF. ( t )

P 0.5 3. Experiment LF = 10 Oe LF = 5 Oe Powder samples of LiMO were used for the µ+SR measurements. Since some samples are unstable ZF 0 in air, the sample was usually packed into a sealed 0 5 10 15 20 + powder cell made of titanium. The µ SR spectra were Time ( µs) mainly measured at the surface muon beam lines Fig. 2 (a) Muon-spin depolarization in ZF and LF in pulsed-muon facilities, i.e., ISIS at Rutherford represented by a dynamic Kubo-Toyabe function Appleton Laboratory in UK and MUSE of Materials DGKT (Gzz ), which corresponds to the relaxation due and Life Science Facility at J-PARC in Japan, to a nuclear magnetic field, (b) the depolarization DGKT because of their higher counting rate than that of represented by Gzz , by an exponential relaxation continuous-muon facilities. function (exp(−λt)), and by a product of the two functions, and (c) the depolarization in ZF and DGKT LF represented by Gzz exp(−λt). In (a)-(c), ∆ = 2.8 Oe = 0.24 × 106 s−1 and ν = 0.08 × 106 s−1. In (b) and (c), λ = 0.2 × 106 s−1.

© Toyota Central R&D Labs., Inc. 2015 http://www.tytlabs.com/review/ 32 R&D Review of Toyota CRDL, Vol.46 No.2 (2015) 29-36 behavior, meaning that the implanted muons see v is likely to decrease down to 0.7 × 106 s–1 at about Nu 7 H int due to the nuclear magnetic moments of Li, 325 K, it is very difficult to estimate v accurately 6Li and 59Co. Although the ZF-spectrum still shows because of the fact that v >> Δ. The increase in v a KT behavior that at 225 K, the relaxation rate is between 150 and 275 K is well explained by a thermal smaller than that at 100 K. At 275 K, the spectrum activation process (not shown),(9) which signals the looks like an exponential relaxation behavior due to onset of diffusive motion of Li+. an increase in v/Δ with T, as expected from Fig. 1. Using a simple diffusion model through vacant Li (29) In order to estimate the KT parameters precisely, the sites, DLi was easily estimated as a function of the

ZF- and two LF-spectra recorded at 5 and 10 Oe Li content x (see Fig. 5(a)). And, such DLi is found were fitted simultaneously by a combination of Eq. (4) to be more consistent with the prediction from first (28) and an offset signal from the fraction of muons stopped principles calculations than DLi estimated from mainly in the sample cell. Li-NMR, as expected. A very similar experiment on (14,27) Lix(Co1/3Ni1/3Mn1/3)O2 demonstrated that DLi for DGKT A0 P(t) = AKTG (Δ, v, t) exp (–λt) + ABG , (5) Lix(Co1/3Ni1/3Mn1/3)O2 is lower than DLi for LixCoO2 by one order of magnitude in the whole x range measured (10) where A0 is the empirical maximum muon decay (Fig. 5(b)). We also estimated DLi for LiNiO2, (11) (12) (12) (13) asymmetry, AKT and ABG are the asymmetries LiFePO4, LiCoPO4, LiNiPO4, and Li2MnO3 associated with the two signals. with µ+SR. Figure 4 shows the T dependencies of Δ and v for Furthermore, the following properties have been + Li0.73CoO2. As T increases from 10 K, Δ slightly but obtained from DLi estimated with µ SR; linearly decreases until about 150 K, then decreases more rapidly up to 200 K, and levels off around (i) Reactive surface area(14)

2.3 Oe up to 250 K, then, finally rapidly decreases When DLi is clarified, a reactive surface area (A) of a again above 250 K. Making comparison with the positive electrode in a liquid electrolyte is obtained by (24) line width of Li-NMR for Li0.6CoO2 and neutron (25) diffraction measurements on Na0.7CoO2, it is found 1D 2D Tdiffu Tdiffu that Li+ ions start to diffuse along the a-axis above (a) 20 1D around 150 K(= T diffu), whereas in the ab-plane above 4 2D LixCoO2 275 K(= T diffu). In fact, the ZF spectrum above 275 K 15 shows a simple exponential decay (Fig. 3). On the 3 x = 0.73 W (kHz) other hand, the v(T ) curve is almost T-independent 10

(Oe) 2 up to 150 K, starts to increase at about 150 K, and exhibits a maximum at 275 K. Above 275 K, although 1 µSR x = 0.6 5 NMR 0 0 (b)

Li0.73CoO2 ZF-µSR 1.5 0.2

) Li CoO –1 0.73 2

s 1 6 ( t ) µSR ZF P v (10 0 0.5

A 0.1 275 K 0 225 K 0 100 200 300 400 100 K 0 Temperature (K) 0 5 10 15 20 Fig. 4 The temperature dependences of (a) the field Time (µs) distribution width (∆) and (b) the field fluctuation + rate (ν) obtained with µ+SR. In (a), the line width Fig. 3 ZF-µ SR spectra for Li0.73CoO2 measured at 100, 225, and 275 K. Solid lines represent the fit result (∆W) obtained by Li-NMR(24) is also plotted for using Eq. (5). comparison.

EC comparison with DLi extracted from electrochemical mobile ions. Therefore, if we measure DLi and σLi for EC + measurements in a liquid electrolyte. Namely, DLi Li ionic conductors, we can estimate the number is known to be proportional to A–2, although A was density of the mobile Li+ ions, as in the case for (30) not clarified so far. However, if we assume that garnet-type oxides, Li5+xLa3ZrxNb2–xO12 with x = 0-2. EC DLi = DLi , we obtain correct A, as in the case for (14) (13) Lix(Co1/3Ni1/3Mn1/3)O2. (iii) Diffusion pathway When Li+ ions start to diffuse very rapidly above (30) + (ii) Carrier density, i.e. mobile Li content Tdiffu, the nuclear magnetic field of such Li becomes For ionic conductors, the relationship between invisible by µ+SR, resulting in a step-like decrease

D and ionic conductivity (σ) is represented by a in Δ above Tdiffu, i.e. so-called a motional narrowing Nernst-Einstein equation; behavior (see Fig. 4(a)). When there are multiple Li sites in the lattice, and σRT D = , (6) some of them are diffusing, whereas the rest static, we nF 2z2 can determine the Li sites responsible for Li-diffusion. where R is the gas constant, F is the Faraday’s As a result, we could determine the diffusion pathway, (13) constant, z is ionic valence, and n is the density of as in the case for Li2MnO3.

(iv) Diffusion coefficient of Na D( )(16,31) (a) Na 10 –7 Not only Li-diffusion but also Na-diffusion is (16) (31) 400 K observed in NaxCoO2 and NaxFePO4, because 28 10 –9 calc Na has a nuclear magnetic moment as well as Li. /s) 2 10–11 300 K (v) Concentration of Li and Na (cm In a paramagnetic state, the field distribution width Li calc D at the muon site (Δ) is determined by the dipole field 10–13 created by nuclear magnetic moments, including 6Li 300 K, µSR; 400 K, NMR and 7Li. In fact, Δ increases with the Li content (x) 10–15 0 0.2 0.4 0.6 0.8 1 (8) in LixCoO2 (see Fig. 6). A very similar relationship x in Li CoO x 2 between Δ and x was also obtained for NaxCoO2. This (b) 10 –7 means that we could deduce the Li and Na content from Δ. Such measurements would become significant µSR –9 for the future solid state batteries, particularly at the 10 interface between electrode and electrolyte, when /s)

2 µ+SR has a good depth resolution (see Section 5). 10–11 (cm Li D –13 Li xCoO2 10 (14) 0.6 Li x (Co1/3Ni1/3Mn1/3)O2 (27) ZF- & LF-µSR Li x (Co1/3Ni1/3Mn1/3)O2 –15 at 1.8 K 10 0 0.2 0.4 0.6 0.8 1 0.4 x in LixMO2

Fig. 5 The relationship between DLi and x in (a) + (9) (24,26) 0.2 LixCoO2 estimated by µ SR and Li-NMR (9) (14,27) and (b) LixCoO2 and Lix(Co1/3Ni1/3Mn1/3)O2 estimated by µ+SR. In (a), solid line represents the predictions by µ+SR. In (a), solid line represents 0 0 0.2 0.4 0.6 0.8 1 the predictions by first-principles calculations(28) x in LixCoO2 at T = 300 K for LixCoO2, when the effective 13 −1 vibration frequency is a typical value (10 s ). Fig. 6 The relationship between ∆ and x in LixCoO2 at Sharp minima in the predicted curve (at x = 1/3 and 1.8 K.(8) A solid line represents the prediction by 1/2) are caused by Li-ordering. dipole field calculations.

5. Summary and Future Acknowledgement

We wish to compare µ+SR with the other techniques We thank the staff of J-PARC and ISIS for help (5) + for detecting DLi from a viewpoint of time window with the µ SR experiments. We also appreciate

(see Fig. 7). Here, DLi for positive and negative Asst. Prof. M. M˚ansson of KTH, Dr. I. Watanabe electrode materials of the Li-ion battery are expected of Riken-RAL, Dr. Y. Ikedo and Prof. Y. Miyake of to range between 10–12 and 10–9 cm2/s. Furthermore, J-PARC-muon, Dr. K. Kamazawa of CROSS, as well it is extremely difficult to measure DLi by Li-NMR Dr. J. Lord and Dr. A. Hillier of ISIS and Dr. S. Giblin in the materials containing magnetic ions. Therefore, of Univ. of Cardiff for their valuable collaboration and µ+SR is a very good complementary technique to contributions. This work was supported by MEXT quasi-elastic neutron scattering (QENS) in the research KAKENHI Grant No. 23108003 and JSPS KAKENHI of Li-diffusion in solids. Grant No. 19340107 and 26286084. For future investigations, we find a particularly interesting and versatile development using a µ+SR References technique in combination with the unique low-energy muon available at the Paul Scherrer Institute (PSI) (1) Tarascon, J.-M. and Armand, M., “Issues and in Switzerland(32) or the upcoming ultra-slow muon Challenges Facing Rechargeable Lithium Batteries”, Nature, Vol. 414, No. 6861 (2001), pp. 359-367. (USM) at J-PARC in Japan.(33) With this technique, (2) Goodenough, J. B. and Kim, Y., “Challenges for it is possible to tune the kinetic energy of the muons Rechargeable Li Batteries”, Chemistry of Materials, i.e. their implantation depth (1-250 nm) into the Vol. 22, No. 3 (2010), pp. 587-603. sample. As a result, it is possible to perform depth (3) Marom, R., Amalraj, S. F., Leifer, N., Jacob, D. and resolved studies of ion diffusion and to clarify both Aurbach, D., “A Review of Advanced and Practical the effects of reduced dimensionality (nano) in the Lithium Battery Materials”, J. Mater. Chem., Vol. 21, No. 27 (2011), pp. 9938-9954. form of ultra-thin films, but also to study each of the (4) Goodenough, J. B. and Park, K.-S., “The Li-ion individual components as well as their interfaces of Rechargeable Battery: A Perspective”, J. Am. Chem. an operational thin film solid state battery. There is no Soc., Vol. 135, No. 4 (2013), pp. 1167-1176. other technique currently available that allows for such (5) Heitjans, P. and Indris, S., “Diffusion and Ionic studies and it is our estimate that µ+SR/LEM/USM Conduction in Nanocrystalline Ceramics”, will become crucial tools for materials development J. Phys.: Condens. Matter, Vol. 15, No. 30 (2003), pp. R1257-R1286. of future solid state energy devices. (6) Grey, C. P. and Dupr´e, N., “NMR Studies of Cathode Materials for Lithium-ion Rechargeable Batteries”, Chem. Rev., Vol. 104, No. 10 (2004), pp. 4493-4512. (7) Sugiyama, J., Nozaki, H., Brewer, J. H., Ansaldo, E. J., Morris, G. D. and Delmas, C., “Frustrated Magnetism

in the Two-dimensional Triangular Lattice of LixCoO2”, Phys. Rev. B, Vol. 72, No. 14 (2005), 144424. (8) Mukai, K., Ikedo, Y., Nozaki, H., Sugiyama, J., Nishiyama, K., Andreica, D., Amato, A., Russo, P. L., Ansaldo, E. J. and Brewer, J. H., “Magnetic Phase

Diagram of Layered Cobalt Dioxide LixCoO2” Phys. Rev. Lett., Vol. 99, No. 8 (2007), 087601. (9) Sugiyama, J., Mukai, K., Ikedo, Y., M˚ansson, M. and

Watanabe, I., “Li Diffusion in LixCoO2 Probed by Muon-spin Spectroscopy”, Phys. Rev. Lett., Vol. 103, No. 14 (2009), 147601. (10) Sugiyama, J., Ikedo, Y., Mukai, K., Nozaki, H., M˚ansson, M., Ofer, O., Harada, M., Kamazawa, K., Miyake, Y., Brewer, J. H., Ansaldo, E. J., Chow, K. H., Fig. 7 The time range of µ+SR is added to the typical Watanabe, I. and Ohzuku, T., “Low-temperature ranges of a diffusion coeffcient (D) and motional Magnetic Properties and High-temperature Diffusive Behavior of LiNiO Investigated by Muon-spin correlation time (τc) of some macroscopic and 2 microscopic methods.(5) Spectroscopy”, Phys. Rev. B, Vol. 82, No. 22 (2010),

224412. (22) Kalvius, G. M., Noakes, D. R. and Hartmann, O., (11) Sugiyama, J., Nozaki, H., Harada, M., Kamazawa, K., “SR Studies of Rare Earth and Actinide Magnetic Ofer, O., M˚ansson, M., Brewer, J. H., Ansaldo, E. J., Materials”, Handbook on the Physics and Chemistry of Chow, K. H., Ikedo, Y., Miyake, Y., Ohishi, K., Rare Earths, Vol. 32, Chap. 206 (2002), North-Holland. Watanabe, I., Kobayashi, G. and Kanno, R., (23) Matsuzaki, T., Nishiyama, K., Nagamine, K., Yamazaki, T.,

“Magnetic and Diffusive Nature of LiFePO4 Senba, M., Bailey, J. M. and Brewer, J. H., “Critical Investigated by Muon Spin Rotation and Relaxation”, Divergence of 55Mn Nuclear Spin Relaxation Rate in Phys. Rev. B, Vol. 84, No. 5 (2011), 054430. MnSi Revealed by Muon-nuclear-spin Double Relaxation”, (12) Sugiyama, J., Nozaki, H., Harada, M., Kamazawa, K., Phys. Lett. A, Vol. 123, No. 2 (1987), pp. 91-94. Ikedo, Y., Miyake, Y., Ofer, O., M˚ansson, M., (24) Nakamura, K., Ohno, H., Okamura, K., Michihiro, Y., Ansaldo, E. J., Chow, K. H., Kobayashi, G. and Moriga, T., Nakabayashi, I. and Kanashiro, T., 7 + Kanno, R., “Diffusive Behavior in LiMPO4 with “ Li NMR Study on Li Ionic Diffusion and Phase

M = Fe, Co, Ni Probed by Muon-spin Relaxation”, Transition in LixCoO2”, Solid State Ionics, Vol. 177, Phys. Rev. B, Vol. 85, No. 5 (2012), 054111. No. 9-10 (2006), pp. 821-826. (13) Sugiyama, J., Mukai, K., Nozaki, H., Harada, M., (25) Medarde, M., Mena, M., Gavilano, J. L., M˚ansson, M., Kamazawa, K., Andreica, D., Amato, A. Pomjakushina, E., Sugiyama, J., Kamazawa, K., and Hillier A., “Antiferromagnetic Spin Structure and Pomjakushin, V. Yu., Sheptyakov, D., Batlogg, B., + Lithium Ion Diffusion in Li2MnO3 Probed by µ SR”, Ott, H. R., M˚ansson, M. and Juranyi, F., “1D to 2D Phys. Rev. B, Vol. 87, No. 2 (2013), 024409. Na+ Ion Diffusion Inherently Linked to Structural

(14) Sugiyama, J., Mukai, K., Harada, M., Nozaki, H., Transitions in Na0.7CoO2”, Phys. Rev. Lett., Vol. 110, Miwa, K., Shiotsuki, T., Shindo, Y., Giblin, S. R. and No. 26 (2013), 266401. Lord, J. S., “Reactive Surface Area of the (26) Nakamura, K., Ohno, H., Okamura, K., Michihiro, Y., + Lix(Co1/3Ni1/3Mn1/3)O2 Electrode Determined by µ SR Nakabayashi, I. and Kanashiro, T., “On the Diffusion + and Electrochemical Measurements”, Phys. Chem. of Li Defects in LiCoO2 and LiNiO2”, Solid State Chem. Phys., Vol. 15, No. 25 (2013), pp. 10402-10412. Ionics, Vol. 135, No. 1-4 (2000), pp. 143-147. (15) Sugiyama, J., “Ion Diffusion in Solids Probed by (27) M˚ansson, M., Nozaki, H., Wikberg, J. M., Prsa, K., Muon-spin Spectroscopy”, J. Phys. Soc. Jpn., Vol. 82, Sassa, Y., Dahbi, M., Kamazawa, K., Sedlak, K., No. Suppl. A (2013), SA023. Watanabe, I. and Sugiyama, J., “Lithium Diffusion (16) M˚ansson, M. and Sugiyama, J., “Muon-spin & Magnetism in Battery Cathode Material

Relaxation Study on Li- and Na-diffusion in Solids”, LixNi1/3Co1/3Mn1/3O2”, J. Phys.: Conf. Ser., Vol. 551, Physica Scripta, Vol. 88, No. 6 (2013), 068509. No. 1 (2014), 012037. (17) Powell, A. S., Lord, J. S., Gregory, D. H. and (28) Van der Ven, A. and Ceder, G., “Lithium Diffusion in

Titman, J. J., “Muon Spin Relaxation Studies of Layered LixCoO2”, Electrochem. Solid-state Lett., Vol. Lithium Nitridometallate Battery Materials: Muon 3, No. 7 (2000), pp. 301-304. Trapping and Lithium Ion Diffusion”, J. Phys. Chem. (29) Borg, R. J. and Dienes, G. J., An Introduction to Solid C, Vol. 113, No. 48 (2009), pp. 20758-20763. State Diffusion (1988), 360p., Academic. (18) Powell, A. S., Stoeva, Z., Lord, J. S., Smith, R. I., (30) Nozaki, H., Harada, M., Ohta, S., Jalarvo, N. H., Gregory, D. H. and Titman, J. J., “Insight into Lithium Mamontov, E., Watanabe, I., Miyake, Y., Ikedo, Y. and Transport in Lithium Nitridometallate Battery Materials Sugiyama, J., “Diffusive Behavior of Li Ions in Garnet

from Muon Spin Relaxation”, Phys. Chem. Chem. Phys., Li5+xLa3ZrxNb2−xO12 (x = 0-2)”, J. Phys. Soc. Jpn., Vol. 15, No. 3 (2013), pp. 816-823. Vol. 82, No. Suppl. A (2013), SA004. (19) Kaiser, C. T., Verhoeven, V. W. J., Gubbens, P. C. M., (31) Sugiyama, J., Nozaki, H., Umegaki, I., Harada, M., Mulder, F. M., de Schepper, I., Yaouanc, A., Higuchi, Y., Ansaldo, E. J., Brewer, J. H., Miyake, Y., Dalmas de R´eotier, P., Cottrell, S. P., Kelder, E. M. Kobayashi, G. and Kanno, R., “Structural, Magnetic,

and Schoonman, J., “Li Mobility in the Battery and Diffusive Nature of Olivine-type NaxFePO4”,

Cathode Material Li x(Mn1.96Li0.04)O4 Studied by J. Phys.: Conf. Ser., Vol. 551, No. 1 (2014), 012012. Muon-spin Relaxation”, Phys. Rev. B, Vol. 62, No. 14 (32) Morenzoni, E., Kottmann, F., Maden, D., Matthias, B., (2000), pp. R9236-R9239. Meyberg, M., Prokscha, Th., Wutzke, Th. and (20) Gubbens, P. C. M., Wagemaker, M., Sakarya, S., Zimmermann, U., “Generation of Very Slow Polarized Blaauw, M., Yaouanc, A., Dalmas de R´eotier, P. and Positive Muons”, Phys. Rev. Lett., Vol. 72, No. 17

Cottrell, S. P., “Muon Spin Relaxation in Li0.6TiO2 (1994), pp. 2793-2796. Anode Material”, Solid State Ionics, Vol. 177, No. 1-2 (33) Miyake, Y., Nishiyama, K., Kawamura, N., Strasser, P., (2006), pp. 145-147. Makimura, S., Koda, A., Shimomura, K., Fujimori, H., (21) Hayano, R. S., Uemura, Y. J., Imazato, J., Nishida, N., Nakahara, K., Kadono, R., Kato, M., Takeshita, S., Yamazaki, T. and Kubo, R., “Zero- and Low-field Spin Higemoto, W., Ishida, K., Matsuzaki, T., Matsuda, Y. Relaxation Studied by Positive Muons”, Phys. Rev. B, and Nagamine, K., Nucl. Instrum. Methods Phys. Res. Vol. 20, No. 3 (1979), pp. 850-859. Sect. A, Vol. 600, No. 1 (2009), pp. 22-24.

Figs. 1, 2 and 7 Reprinted from J. Phys. Soc. Jpn., Vol. 82, No. Suppl. A Kazuhiko Mukai (2013), SA023, Sugiyama, J., Ion Diffusion in Solids Research Field: Probed by Muon-spin Spectroscopy, © 2013 The Physical - New Generation of Energy Conversion Society of Japan. Materials Academic Degree: Dr.Eng. Fig. 3 Academic Societies: Reprinted from Physica Scripta, Vol. 88, No. 6 (2013), - The Electrochemical Society of Japan 068509, M˚ansson, M. and Sugiyama, J., Muon-spin - Society of Muon and Meson Science of Japan Relaxation Study on Li- and Na-diffusion in Solids, © 2013 - American Chemical Society The Royal Swedish Academy of Sciences, with permission - The Electrochemical Society from IOP Publishing. Award: - Young Scientist Award of Society of Muon and Figs. 4 and 5(a) Meson Science of Japan, 2014 Reprinted and modified from Phys. Rev. Lett., Vol. 103, No. 14 (2009), 147601, Sugiyama, J., Mukai, K., Ikedo, Y.,

M˚ansson, M. and Watanabe, I., Li Diffusion in LixCoO2 Probed by Muon-spin Spectroscopy, © 2009 American Hiroshi Nozaki Physical Society. Research Field: - Materials Science for Inorganic Fig. 6 Materials Using X-rays, Neutrons and Reprinted and modified from Phys. Rev. Lett., Vol. 99, Muons Academic Degree: Dr.Eng. No. 8 (2007), 087601, Mukai, K., Ikedo, Y., Nozaki, H., Academic Societies: Sugiyama, J., Nishiyama, K., Andreica, D., Amato, A., - The Physical Society of Japan Russo, P. L., Ansaldo, E. J. and Brewer, J. H., Magnetic - The Japan Institute of Metals and Materials Phase Diagram of Layered Cobalt Dioxide LixCoO2, - The Japanese Society for Synchrotron Radiation © 2007 American Physical Society. Research - The Japanese Society for Neutron Science Sections 2 and 4 - Society of Muon and Meson Science of Japan Partially reprinted and modified from Physcia Scripta, Awards: Vol. 88, No. 6 (2013), 068509, M˚ansson, M. and - Best Poster Award of International Conference on Sugiyama, J., Muon-spin Relaxation Study on Li- and Neutron Scattering, 2013 Na-diffusion in Solids, © 2013 The Royal Swedish - Hamon President Choice, the Japanese Society for Academy of Sciences, with permission from IOP Publishing. Neutron Science, 2014

Masashi Harada Research Field: - Structure Analysis by Small-angle Scattering and Reflectivity Academic Degree: Dr.Eng. Jun Sugiyama Academic Societies: Research Field: - The Society of Polymer Science, Japan - Materials Science with Muons and - The Japanese Society for Neutron Science Neutrons - Society of Muon and Meson Science of Japan Academic Degree: Dr.Eng. Academic Societies: - Physical Society of Japan - Society of Muon and Meson Science of Japan Izumi Umegaki - The Japanese Society for Neutron Science Research Field: - American Physical Society - Materials Science with Muons and - International Society for Muon-spin Spectroscopy Neutrons Awards: Academic Degree: Ph.D. - Best Poster Award of International Conference on Academic Societies: Neutron Scattering, 2013 - Physical Society of Japan - World Young Fellow Meeting Presentation Award, - Society of Muon and Meson Science of Japan The Ceramics Society of Japan, 2004 - The Japanese Society for Neutron Science - International Society for Muon-spin Spectroscopy