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Ion Diffusion in Solids Detected with Muon-Spin Spectroscopy

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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 © Toyota Central R&D Labs., Inc. 2015 http://www.tytlabs.com/review/ 30 R&D Review of Toyota CRDL, Vol.46 No.2 (2015) 29-36 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– t 0 in LiMO is stationary in the vicinity of O ions and ( 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. © Toyota Central R&D Labs., Inc. 2015 http://www.tytlabs.com/review/ R&D Review of Toyota CRDL, Vol.46 No.2 (2015) 29-36 31 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 ) t “decoupling” with LF. Since Δ of nuclear origin ( 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.
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