Microscopic Magnetic Study on the Nominal Composition Li[Li1

Microscopic Magnetic Study on the Nominal Composition Li[Li1/3Mn5/3]O4 by ... Romania, Laboratory for Neutron Scattering, ETH Zürich and Paul Scherre...
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J. Phys. Chem. C 2010, 114, 11320–11327

Microscopic Magnetic Study on the Nominal Composition Li[Li1/3Mn5/3]O4 by Muon-Spin Rotation/Relaxation Measurements Kazuhiko Mukai,*,† Jun Sugiyama,† Yutaka Ikedo,†,O Hiroshi Nozaki,† Kazuya Kamazawa,† Daniel Andreica,‡,§ Alex Amato,‡ Martin Månsson,| Jess H. Brewer,⊥ Eduardo J. Ansaldo,# and Kim H. Chow∇ Toyota Central Research and DeVelopment Laboratories, Inc., 41-1 Yokomichi, Nagakute, Aichi 480-1192, Japan, Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, PSI Villigen CH-5232, Switzerland, Faculty of Physics, Babes-Bolyai UniVersity, 400084 Cluj-Napoca, Romania, Laboratory for Neutron Scattering, ETH Zu¨rich and Paul Scherrer Institut, PSI Villigen CH-5232, Switzerland, TRIUMF, CIfAR, and Department of Physics and Astronomy, UniVersity of British Columbia, VancouVer, British Columbia V6T 1Z1, Canada, TRIUMF, 4004 Wesbrook Mall, VancouVer, British Canada V6T 2A3, Canada, and Department of Physics, UniVersity of Alberta, Edmonton, Alberta T6G 2G7, Canada ReceiVed: March 18, 2010; ReVised Manuscript ReceiVed: May 24, 2010

In order to elucidate the structural and physical properties of the nominal composition Li[Li1/3Mn5/3]O4 compound, we have investigated the nature of polycrystalline Li[LixMn2-x]O4 (LMO) with 0 e x e 1/3 and Li2MnO3 samples by electrochemical charge and discharge analysis, X-ray diffraction (XRD), magnetic susceptibility (χ), and muon-spin rotation/relaxation (µSR) measurements. Here, µSR signal roughly corresponds to the volume fraction of the local magnetic phases in the sample. The Rietveld analysis suggested that the x ) 1/3 sample contains ∼11 weight% Li2MnO3 phase. This was also supported by electrochemical charge and discharge analysis and zero-field (ZF-) µSR measurements. If we follow the past reported relation for the x ) 1/3 compound, i.e. Li[Li1/3Mn5/3]O4 consists of a (1 - z)Li[Li1/3-ωMn5/3+ω]O4 phase and a zLi2MnO3 phase, the average chemical formula of the former spinel phase is represented as Li[Li0.21Mn1.79]O4. However, weak-transverse-field µSR measurements demonstrated that the spinel phase undergoes a spin-glass-like transition at 21 K with a large transition width (∆T ) 28 K). Since both x ) 0.2 and Li2MnO3 samples exhibit a very sharp magnetic transition at 24 and 36 K, respectively, the spinel phase in the x ) 1/3 sample is found to be magnetically inhomogeneous in a microscopic scale. This indicates that the distribution of Li ions is microscopically inhomogeneous in the spinel lattice, although Li[Li1/3-ωMn5/3+ω]O4 has been assigned as a single-phase by macroscopic analyses such as XRD. Li[LixMn1-3x3+Mn1+2x4+]O4 f yLi+ + ye- +

Introduction In the (Li)8a[LixMn2-x]16dO4 (LMO) spinel lattice with space group of Fd3jm, the tetrahedral 8a site is occupied by Li ions, while the octahedral 16d site is occupied by both Li and Mn ions. Since the Li ions at the 8a site are extracted/inserted reversibly by an electrochemical oxidation/reduction reaction in a nonaqueous electrolyte, LMO has been heavily studied as a positive electrode material for Li-ion batteries.1 In spite of the extensive studies on LMO, structural and physical properties for the LMO compound with x ) 1/3 are not fully understood. For instance, if we assume that the theoretical charge/discharge capacity [Qtheo(x)] of LMO is determined by the amount of Mn3+ ions, more correctly, the electrochemical reaction of LMO is formulated as * To whom correspondence should be addressed. E-mail: e1089@ mosk.tytlabs.co.jp. Tel: +81-561-71-7698. Fax: +81-561-63-6137. † Toyota Central Research and Development Laboratories, Inc. ‡ Paul Scherrer Institut. § Babes-Bolyai University. | ETH Zu¨rich and Paul Scherrer Institut. ⊥ University of British Columbia. # TRIUMF. ∇ University of Alberta. O Present address: Muon Science Laboratory, Institute of Materials Structure Science, KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.

Li1-y[LixMn1-3x-y3+Mn1+2x+y4+]O4

(0 e y e 1 - 3x) (1)

Qtheo(x) in mAh · g-1 should be given by

Qtheo(x) ) Qtheo(LiMn2O4) × (1 - 3x) × M(LiMn2O4)/M(x)

(2)

where Qtheo(LiMn2O4) and M(LiMn2O4) is the theoretical charge/ discharge capacity () 148 mAh · g-1) and the molecular weight () 180.81) for the LiMn2O4 phase, respectively, and M(x) is the molecular weight of LMO with x > 0. This means that the e4.5 V ), which is rechargeable capacity below 4.5 V vs Li+/Li (Qrecha equivalent to Qtheo(x) for the reversible extraction/insertion of the Li ions at the 8a site, decreases monotonically with increasing x, and finally reaches 0 mAh · g-1 at x ) 1/3. e4.5 V However, it is widely reported that Qrecha ∼ 60 mAh · g-1 for the x ) 1/3 compounds regardless of the synthesis temperature (T) between 400 and 750 °C.2-4 The discrepancy between Qtheo e4.5 V and Qrecha was initially thought to be caused by the oxygen deficiency (δ) in the x ) 1/3 samples (δ e 0.2).5 However, in e4.5 V ∼ 60 mAh · g-1, the order to explain the fact that Qrecha

10.1021/jp102453r  2010 American Chemical Society Published on Web 06/07/2010

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composition of the samples should be Li[Li1/3Mn5/3]O4-δ with e4.5 V is independent of the δ ) 0.3. Furthermore, since Qrecha synthesis T, we require an other mechanism to explain the value e4.5 V for the x ) 1/3 samples. In fact, Paulsen and Dahn of Qrecha clarified that δ is negligibly small (less than 0.025) for Li[LixMn2-x]O4 by solid electrolyte coulometry analyses.6 On the contrary, a complex phase relation among the Li[LixMn2-x]O4 and Li2MnO3 phases was reported below 1000 °C.6-9 Thus, the x ) 1/3 compounds have been assigned as a mixture of a Li[LixMn2-x]O4 phase and a Li2MnO3 phase.10-12 Since the Mn ions are in the 4+ state in Li2MnO3, the formation of the Li2MnO3 phase naturally reduces the average valence of the Mn ions in the spinel phase. Here, the weight fraction of the Li2MnO3 phase is reported as ∼10% for the x ) 1/3 sample prepared at 750 °C.11,12 The chemical formula for the spinel phase in this sample is, thus, represented by Li[Li0.23Mn1.77]O4, based on the following relation:13

Li[LixMn2-x]O4 T (1 - z)Li[Lix-ωMn2-x+ω]O4 + zLi2MnO3 + z/2O2

(3)

where

ω ) (x - z)/(1 - z)

(4)

e4.5 V However, the observed Qrecha for the x ) 1/3 samples (∼60 -1 2-4 mAh · g ) is slightly larger than Qtheo for the x ) 0.23 phase (∼46 mAh · g-1). Moreover, the x ) 1/3 sample synthesized at V -1 4 400 °C still exhibits Qe4.5 recha ∼ 54 mAh · g , although the weight fraction of the Li2MnO3 phase is almost 0% by XRD analyses.12 e4.5 V This implies that there is another factor to govern Qrecha for the x ) 1/3 sample. Recently, we examined the microscopic magnetism for a zigzag chain compound Li0.92Mn2O4 and clarified the volume fraction of the coexisting Li2MnO3 phase in the sample by muon-spin rotation/relaxation (µSR) measurements.14 Here, µSR is a powerful technique to detect local magnetic fields caused by both nuclear and electronic origin.15 Moreover, µSR signal roughly corresponds to the volume fraction of the magnetic phases in the sample.15 We have, therefore, performed µSR measurements for the LMO with 0 e x e 1/3 and Li2MnO3 samples, in order to elucidate the homogeneity/inhomogeneity of the samples through their microscopic magnetism. In this paper, we report the structural and microscopic magnetic nature for the nominal composition Li[Li1/3Mn5/3]O4 sample.

Experimental Section It is known that the decomposition reaction in eq 3 is accelerated above 850 °C.6,7 However, if we decrease the reaction T below 850 °C, both the solid state diffusion of each element and the grain growth of LMO are suppressed, resulting in an inhomogeneous compositional distribution in the obtained sample. Fortunately, highly crystallized LMO compounds with x e 0.1516,17 are recently available by a “two-step solid-state reaction” technique, which was originally used in Li[Ni1/2Mn3/2]O4 (P4332).18,19 That is, in the first step, a crystallization process is completed at high T (∼1000 °C), then in the second step, a chemical composition is controlled precisely below ∼700 °C. This technique is, in principle, applicable for the preparation of the x ) 1/3 sample. Therefore, powder samples of LMO with x ) 0, 0.1, 0.2, and 1/3 were prepared by the two-step solid-state reaction technique as reported previously.16,17 The reaction mixture of LiOH · H2O and MnOOH (Manganite) was well mixed with a mortar and

pestle, and pressed into a pellet of 23 mm diameter and ∼5 mm thickness. The pellet was heated at 1000 °C under air for 12 h in order to develop crystallites. Indeed, the morphology of the primary particle for all the samples showed an octahedral shape with smooth (111) facets. The obtained powder was crushed, repressed into a pellet, then oxidized at 700 °C for x ) 0, 600 °C for x ) 0.1, and 550 °C for x ) 0.2 under air for 24 h. For the x ) 1/3 sample, the pellet was oxidized at 650, 600, 550, and 500 °C under air for 24 h successively without cooling down to room T. For comparison, a powder sample of Li2MnO3 was also synthesized by heating the reaction mixture of LiOH · H2O and MnOOH (Li/Mn ) 2.00/1.00) at 900 °C under air for 12 h. The lattice parameters of the samples was determined by a powder X-ray diffraction (XRD, type XD-3A, Shimadzu Co. Ltd., Japan) analysis with an Fe KR radiation equipped with a graphite monochromator. For the x ) 1/3 sample, XRD measurement was performed with a synchrotron radiation using the large Debye-Scherrer camera installed at BL19B2 in SPring-8. The wavelength of the X-ray was estimated to be 0.99772(1) Å by the XRD measurement on NIST CeO2 standard (674a). Note that the actual chemical formula for the x ) 1/3 sample is no longer Li[Li1/3Mn5/3]O4, since the x ) 1/3 sample segregates into the Li[Li1/3-ωMn5/3+ω]O4 phase with ω ) 0.124 and Li2MnO3 phase. According to an inductively coupled plasma-atomic emission spectral (ICP-AES, CIROS 120, Rigaku Co. Ltd., Japan) analysis, the Li/Mn ratios for the x ) 0, 0.1, 0.2, and 1/3 samples were determined to be 1.00/2.00, 1.09/ 1.90, 1.20/1.80, and 1.33/1.67, respectively. The electrochemical properties were examined by a charge and discharge test in nonaqueous lithium cells. The LMO electrodes for the electrochemical measurements were prepared as follows. Polyvinylidene fluoride (PVdF) dissolved in N-methyl-2-pyrrolidone (NMP) solution was used as a binder for preparing the electrodes. The black viscous slurry, which consists of 88 wt % LMO, 6 wt % acetylene black, and 6 wt % PVdF, was cast onto an aluminum foil (thickness 20 µm) using a conventional doctor-blade method with a blade gap 0.35 mm. Then, NMP was evaporated at 120 °C for 30 min, and finally the electrodes (1.5 cm × 2.0 cm) were dried under vacuum at 150 °C for 12 h. For the electrochemical tests, the counter electrode was prepared by pressing a Li metal sheet onto a stainless steel substrate. Two sheets of porous polypropylene membrane (Celgard 2500) were used for a separator, and 1 M LiPF6 dissolved in ethylene carbonate (EC)/dimethyl carbonate (DMC) (3/7 v/v) solution was used for an electrolyte. Magnetic susceptibility (χ) was measured using a superconducting quantum interference device magnetometer (MPMS, Quantum Design) in the T range between 5 and 400 K under magnetic field H e 10 kOe. µSR experiments were performed at PSI in Switzerland and TRIUMF in Canada. µSR technique is particularly sensitive to the local magnetism, because the muon detects the magnetism due to nearest neighbors. It is, therefore, sensitive to short-range magnetic order, which sometimes appears in frustrated systems, while both neutron scattering and χ measurements mainly detect long-range magnetic order. Here, zero-field (ZF-) µSR is useful to detect a weak local magnetic [dis]order produced by quasi-static paramagnetic moments. On the contrary, weak (relative to the spontaneous internal fields in the ordered state) transverse field (wTF-) µSR is effective to study the volume fraction of paramagnetic phases in the sample. The powder samples were pressed into a disk of about 15 mm diameter and 1 mm thickness, and subsequently

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Nµeff2 χ) + χ0 3kB(T - Θp)

Figure 1. Temperature dependence of (a) magnetic susceptibility (χ) and (b) inverse susceptibility (χ-1) for the Li2MnO3 sample measured in field-cooling (FC) mode with H ) 10 kOe. The inset in (a) shows the temperature (T) dependence of the dχ/dT slope. The χ(T) curves in zero-field-cooling (ZFC) and FC modes with H ) 100 Oe are also shown in (a). The effective magnetic moment (µeff) and Weiss temperature (Θp) are estimated by fitting the χ(T) curve in the temperature range between 200 and 400 K [red line in (a)] with the Curie-Weiss relation described in eq 5.

placed in a muon-veto sample holder. The experimental setup and technique are described more detail in elsewhere.15 Results and Discussion 3.1. Magnetism of Li2MnO3. Since Li2MnO3 coexists in the x ) 1/3 sample as a second phase,3,10-12 we have, at first, investigated its macro- and microscopic magnetism by χ and µSR measurements. The past neutron scattering measurements on a single crystal sample indicated that the crystal structure belongs to a monoclinic symmetry with space group of C2/ m.20 Li2MnO3, more specifically, Li[Li1/3Mn2/3]O2 has a layered structure with stacking alternatively by the Li1/3Mn2/3 and Li layers. The Mn4+ ions in the Li1/3Mn2/3 layer are surrounded by three Li+ ions, and consequently, form a honeycomb sublattice. However, the other structural model with space group C2/c was reported by the XRD study using a polycrystalline sample.21 The difference between C2/m and C2/c is caused by a different stacking sequence along the cm axis.22,23 The crystal structure of the present Li2MnO3 sample can be indexed by a monoclinic setting, although the details of the crystal structure is currently unknown. The lattice parameters, which are calculated by a leastsquared method using 13 diffraction lines, are am ) 4.928 Å, bm ) 8.527 Å, cm ) 5.021 Å, and βm ) 109.27°. Figure 1 shows the T dependence of (a) χ and (b) χ-1 for the Li2MnO3 sample measured in field-cooling (FC) mode with H ) 10 kOe. The χ(T) curves in zero-field-cooling (ZFC) and FC modes with H ) 100 Oe are also shown in Figure 1a. As T increases from ∼100 K, χ-1 increases monotonically with increasing T. The Curie-Weiss parameters are, hence, estimated by the following relation:

(5)

where N is the number density of Mn ions, µeff is the effective magnetic moment of Mn ions, kB is the Boltzmann’s constant, T is the absolute temperature, Θp is the Weiss temperature, and χ0 is the T-independent susceptibility. Using eq 5 in the T range between 200 and 400 K, we obtained µeff ) 3.787(2) µB and Θp ) -25.3(2) K. These values are comparable to the past result by Jansen and Hoppe (µeff ) 3.83 µB and Θp ) -33 K), although they assigned the crystal structure of Li2MnO3 as C2/c space group.21 Here, the spin-only effective magnetic moment pre is calculated as 3.873 µB, by assuming that Mn4+ ions are µeff 3 and gyromagnetic factor g is 2. in the S ) 3/2 state with t2g pre . As T Therefore, the observed µeff is almost consistent with µeff decreases from 100 K, χ increases with decreasing T. The χ(T) curve with H ) 10 kOe exhibits a broad maximum around 47 K as reported previously for a polycrystalline sample () 50 K),21 whereas the dχ/dT(T) curve shows a sharp peak at 35 K χ () T N) (see the inset in Figure 1a). This indicates the presence of an antiferromagnetic (AF) transition in the sample. Note that the χ(T) curves in both ZFC and FC modes show a broad maximum around 47 K (Figure 1a). In order to confirm the existence of static AF order in χ Li2MnO3 below T N, µSR measurements were performed. Figure 2 shows the T dependence of ZF-µSR spectra for the Li2MnO3 sample in the time domain below 0.3 µs. The ZF-µSR spectrum above 38 K shows a typical Kubo-Toyabe24 behavior, indicating that muon-spins are depolarized by randomly oriented nuclear magnetic moments of 6Li, 7Li, and 55Mn. However, as T decreases from 38 K, the ZF-µSR spectrum clearly exhibits an oscillation. This unambiguously shows the formation of static AF order in the sample. Indeed, the ZF-µSR spectra were well fitted by a combination of the oscillatory signal and a nonoscillatory relaxing signal, which corresponds to a “tail” caused by the AF component parallel to the initial muon-spin polarization

A0PZF(t) ) AAF exp(-λAFt) cos(ωµAFt + φAF) + Atail exp(-λtailt)

(6)

where A0 is the initial asymmetry, AAF and Atail are the asymmetries for the two signals, λAF and λtail are their relaxation rate, ωµAF is the Larmor frequency due to the AF internal field at the muon site, and φAF is the initial phase of the oscillatory signal. Although the wTF-µSR measurements (described later) showed that the whole Li2MnO3 sample enters into the magnetic phase below TN, the AAF/A0 ratio is limited to be ∼0.42(2) even at 1.8 K. Here, the value of A0 is determined to be ∼0.23 from the ZF-µSR spectra far above TN. Thus, the large internal magnetic field which exceeds the muon time scale partially exists in the sample. It should be noted that the value of φAF ranges -15 ( 3° below 35 K. This indicates that the period of AF order is commensurate with the lattice. Figure 3a shows the T dependence of the muon precession frequency fAF () ωµAF/2π) for the Li2MnO3 sample. As T decreases from 38 K, fAF increases with decreasing the slope (dfAF/dT) and then reaches 42.2(1) MHz at 1.8 K. Here, the fAF(T) curve is well fitted by the following expression

( )

fAF(T) ) fAF(0 K)

TNµ - T TNµ

β

(7)

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Figure 4. Rietveld analysis for the Li[LixMn2-x]O4 sample with x ) 1/3. The observed (Iobs) and calculated (Icalc) intensity data are plotted as points and solid line. The bar-code type indications show all the possible Bragg reflections from both Li[Li1/3-ωMn5/3+ω]O4 (upper) and Li2MnO3 (lower) phases. The difference between Iobs and Icalc (∆I) is also shown.

Figure 2. Temperature dependence of ZF-µSR spectra for the Li2MnO3 sample in the time domain below 0.3 µs. The top of four ZF-µSR spectra are shifted by +0.2 for clarity of display. The solid line is the fitting result with eq 6.

Figure 3. Temperature dependence of (a) oscillation frequency (fAF) of the antiferromagnetic (AF) phase and (b) normalized wTF-asymmetry (NATF) determined by the wTF-µSR measurements for the Li2MnO3 sample. fAF was obtained by fitting the ZF-µSR spectra with eq 6. Note that NATF roughly corresponds to the volume fraction of paramagnetic phases in the sample. The magnetic transition TNmid was determined as the temperature, at which NATF ) 0.5. fAF for the Li[LixMn2-x]O4 sample with x ) 1/3 is also shown in (a) for comparison. Here, due to a small volume fraction of the Li2MnO3 phase in the x ) 1/3 sample (∼10%), fAF was clearly determined only below 15 K.

where fAF(0 K) is the fAF at 0 K, TNµ is the transition T, and β is the critical exponent of the transition. The fitting with eq 5 provides fAF(0 K) ) 43.9(3) MHz, TNµ ) 35.4(5) K, and β ) 0.24(1), although we need accurate data in the vicinity of TNµ to determine β more precisely. But, the obtained β ranges between the predictions for the 2-dimentional and 3-dimensional Ising model (β ) 0.125 and 0.3125, respectively).25 Figure 3(b) shows the T dependence of the normalized weak TF asymmetry (NATF) for the Li2MnO3 sample. The applied magnetic field (HwTF) was 30 Oe. Here, NATF is defined by NATF ) ATF/ATF,max ∼ ATF/0.23, and is roughly proportional to the volume fraction of paramagnetic (PM) phases in the sample. In other words, when NATF ) 1, the whole sample is in the PM phase, while, when NATF ) 0, the whole sample is in the magnetic phase, such as, ferromagnetic (FM), AF, ferrimagnetic, or spin-glass-like phase. As T decreases from 70 K, the NATF(T) curve exhibits a step-like decrease from 1 to 0 at ∼36 K, demonstrating the presence of a sharp magnetic transition. Thus, the AF transition with TN ) 36 K is found to be intrinsic behavior of Li2MnO3. The magnetic transition TNmid at which NATF ) 0.5 is almost equivalent to TNχ , TNµ , and TN () 36.5 K) determined by neutron scattering measurements using a single crystal sample,20 but is ∼10 K lower than the broad maximum in the χ(T) curves (see Figure 1a). Such discrepancy is also reported on the AF transition for the Co3O4 compound;26 the χ(T) curve exhibits a broad maximum around 40 K, whereas the dχ/dT(T) curve, T dependence of heat capacity, and µSR measurements show a sharp transition at 30 K. 3.2. Structural and Electrochemical Properties for the x ) 1/3 Sample. According to XRD measurements, the present LMO samples with x ) 0, 0.1, and 0.2 are identified as a single phase of the spinel structure with space group of Fd3jm. The cubic lattice parameter (ac), which was calculated by a leastsquares method using 7 diffraction lines, is determined to be 8.240(1) Å for the x ) 0 sample, 8.203(1) Å for the x ) 0.1 sample, and 8.177(1) Å for the x ) 0.2 sample. On the other hand, weak diffraction peaks from the Li2MnO3 phase are observed for the x ) 1/3 sample, because the rate of the reverse reaction of eq 3 is very slow.6 In order to estimate the amount of the Li2MnO3 phase (z) and ω in eq 3, a Rietveld analysis was carried out for the XRD data of the x ) 1/3 sample by RIETAN2000.27 Figure 4 and Table 1 show the result of the

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TABLE 1: Structural Parameters Determined by the Rietveld Analysis for the Li[LixMn2-x]O4 Sample with x ) 1/3 phasea

space group Fd3jm

Li[Li1/3-ωMn5/3+ω]O4 (ω ) 0.124)

ac ) 8.1679(1) Å Li2MnO3

atom

Wyckoff position

g

Li11 Li12 Mn11 O11

8a 16d 16d 32e

1.0 0.105 0.895 1.0

1/8 1/2 1/2 0

1.0 1.0 1.0 1.0 1.0 1.0

0 0 0 0 0.252(6) 0.247(6)

C2/m

Li21 Li22 Li23 Mn21 O21 O22 am ) 4.9251(8) Å, bm ) 8.5215(7) Å, cm ) 4.9997(9) Å, and βm )

2b 2c 4h 4g 4i 8j 109.13(2)°

z

Bisob/Å2

1/8 1/2 1/2 0

1/8 1/2 1/2 0.259(2)

0.5(1) 0.1(2) 0.1(2) 1.1(1)

1/2 0 0.694(5) 0.168(1) 0 0.329(1)

0 1/2 1/2 0 0.178(4) 0.235(2)

0.1(2) 0.1(2) 0.1(2) 0.1(2) 1.1(1) 1.1(1)

x

y

Rwp ) 4.17%, RB ) 2.54%, and S ) 1.56. a The weight fraction of the Li2MnO3 phase in the x ) 1/3 sample was estimated to be 0.110. The value of ω in Li[Li1/3-ωMn5/3+ω]O4 is, thus, calculated to be 0.124 using the relation described in eq 3. b Constrains: B(Li12) ) B(Mn11) ) B(Li21) ) B(Li22) ) B(Li23) ) B(Mn21) and B(O11) ) B(O21) ) B(O22).

Rietveld analysis. Here, we assume that the crystal structure of Li2MnO3 is a monoclinic system with space group of C2/m, as proposed by the work using a single crystal.20 The weight fraction of the Li2MnO3 phase [W(Li2MnO3)] is calculated by n

Wp ) Sp(ZMV)p /

∑ Si(ZMV)i

(8)

i)1

where Wp is the relative weight fraction of the phase p in a mixture of the n phase, Sp the its Rietveld scale factor, Z the number of formula units per unit cell, M the mass of the formula unit, and V the unit cell volume, respectively. Here, it is difficult to determine both values of W(Li2MnO3), i.e., S(Li2MnO3) and ω in Li[Li1/3-ωMn5/3+ω]O4 simultaneously, because the constrains between the scale factor and cite occupancy among the different phases are currently not available in a conventional Rietveld analysis.27 This means that the value of ω is initially required to satisfy the Li/Mn ratio () 1.33/1.67). Therefore, we first assume that W(Li2MnO3) ) 0.1 (ω ) 0.125) by the peak intensities at 2θ ∼ 12°, and repeat the refinements step by step. The W(Li2MnO3) and ω were finally determined to be 0.11 and 0.124, respectively, by minimizing the “goodness-offit” parameters such as R-weighted pattern factor (Rwp), R-Bragg factor (RB), and goodness-of-fit indicator (S) (Table 1). The chemical formula for the present spinel phase in the x ) 1/3 sample is, thus, estimated as Li[Li0.21Mn1.79]O4. Figure 5a shows the charge and discharge curves of the lithium cell with the x ) 1/3 sample for the first five cycles. The cell was operated with a constant current mode at a rate of 0.17 mA · cm-2 in the voltage range between 3 and 5 V at 25 °C. Assuming a simple electrochemical reaction described in eq 1, Qtheo for the ideal x ) 1/3 phase is calculated to be 0 mAh · g-1. However, since Qrecha ∼ 46 mAh · g-1 for the x ) 1/3 sample, x is estimated as 0.23, being almost consistent with the result of the Rietveld analysis (x ) 0.21). 3.3. Microscopic Magnetism for the x ) 1/3 Sample by µSR Measurements. The structural and electrochemical analyses indicated that the chemical formula of the spinel phase in the x ) 1/3 sample is Li[Li0.21Mn1.79]O4. According to our previous µSR study on the x e 0.15 samples, only a fast relaxing signal was observed in the ZF-µSR spectrum in the time domain below 0.1 µs even at lowest T measured (1.8 K).16 If the x ) 1/3 sample is a mixture of the Li[Li0.21Mn1.79]O4 and Li2MnO3 phases, the µSR spectrum should be the sum of the signals from the Li[Li0.21Mn1.79]O4 and Li2MnO3 phases. Furthermore, im-

Figure 5. Charge and discharge curves of the lithium cell with the Li[LixMn2-x]O4 sample with x ) 1/3 for the first five cycles. The cell was operated at a current density of 0.17 mA · cm-2 in the voltage range between 3.0 and 5.0 V at 25 °C. The charge and discharge curves at the initial cycle (shown in red) significantly differs from those at the subsequent cycles, probably due to the decomposition reaction between the electrolyte and lithium metal.

planted muons are expected to sit in both phases with the same probability. Therefore, the asymmetries of the two signals are roughly proportional to their volumes in the sample. Here, Ariza et al.28,29 already reported the microscopic magnetism for the Li[Li1.33Mn1.67]O4 compound, which prepared by heating a reaction mixture at 400 °C. However, since they performed µSR measurements at the pulsed muon beam facility in Rutherford Appleton Laboratory (RAL),28,29 the muon-spin relaxation for LMO with x > 0.15 in the time domain below ∼0.5 µs was not still clarified. This is because the muon beams are distinguishable by their time structure:15 the pulsed muon beam facilities such as RAL and J-PARC are ideal for studying relatively slow relaxation, whereas the continuous muon beam facilities such as TRIUMF and PSI are suitable for the detection of larger magnetic fields and fast relaxing signals. Figure 6 shows the ZF-µSR spectra for the LMO samples with (a) x ) 0, (b) x ) 0.1, (c) x ) 0.2, and (d) x ) 1/3 at 1.8 K in the time domain below 0.1 µs. The ZF-µSR spectrum for the Li2MnO3 sample is also shown for comparison (e). The ZFµSR spectra for the samples with x e 0.2 lack an oscillatory signal even at 1.8 K but pose a first minimum at t ) 0.015 µs, indicating a spin-glass like freezing of the Mn moments at low T.16 On the contrary, a clear oscillation due to the Li2MnO3 phase is observed for the x ) 1/3 sample. The ZF-µSR spectrum was, hence, fitted by a combination of a dynamic Gaussian

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Figure 7. Temperature dependence of the normalized wTF-asymmetry (NATF) for the Li[LixMn2-x]O4 samples with x ) 0, 0.1, 0.2, and 1/3. The result for the Li2MnO3 sample is also shown. Note that NATF roughly corresponds to the volume fraction of a paramagnetic phase in the samples.

Figure 6. ZF-µSR spectra in the time domain below 0.1 µs for the Li[LixMn2-x]O4 samples with (a) x ) 0, (b) x ) 0.1, (c) x ) 0.2, and (d) x ) 1/3 at 1.8 K. The top of three ZF-µSR spectra are offset by +0.2 for clarity of display. The solid line represents the fitting result with eq 9. ZF-µSR spectrum for the Li2MnO3 sample is also shown for comparison.

Kubo-Toyabe24 (DGKT) signal (from the freezing phase), a fastrelaxing nonoscillatory signal (from the “tail”), and an oscillatory signal (from Li2MnO3) A0PZF(t) ) AKTGDGKT(t,∆,ν) exp(-λKTt) + Afast exp(-λfastt) + AAF exp(-λAFt) cos(ωµAFt + φAF) (9)

where AKT, Afast, and AAF are the asymmetries associated with the three signals, λKT, λfast, and λAF are their relaxation rates, ∆ is the static width of the local frequencies at the disordered sites, and ν is the field fluctuation rate. When ν ) 0, GDGKT(t, ∆, ν) is the static Gaussian Kubo-Toyabe function GKT zz (t, ∆) given by24

(

KT Gzz (t, ∆) ) 1/3 + 2/3(1 - ∆2t2) exp -

∆2t2 2

)

(10)

The magnitude of fAF for the x ) 1/3 sample is estimated as 42.3(3) MHz at 1.8 K, and is almost the same to that for the pure Li2MnO3 sample at 1.8 K, as expected. Moreover, the fAF(T) curve for the x ) 1/3 sample below ∼15 K traces that for the Li2MnO3 sample (see Figure 3a). Therefore, the oscillatory signal in the ZF-µSR spectrum for the x ) 1/3 sample is assigned to be caused by the AF order of the Li2MnO3 phase. Note that the volume fraction of the Li2MnO3 phase (AAF/A0) is ∼0.1 and is very consistent with the result of Rietveld analysis. Figure 7 shows the T dependence of the normalized wTF asymmetry (NATF) for the samples with x ) 0, 0.1, 0.2, and 1/3. Here, the NATF corresponds to the volume fraction of PM phases in the sample. A step-like decrease in NATF from 1 to 0

for the samples with x e 0.2 shows the existence of a sharp magnetic transition for these samples at TNmid; that is, TNmid ) 61 K for the x ) 0 sample, TNmid ) 29 K for x ) 0.1, and TNmid ) 24 K for x ) 0.2. Furthermore, since NATF reaches almost 0 below the vicinity of TNmid, the whole sample enters into the magnetic phase below TNmid for LMO with x e 0.2. On the contrary, as T decreases from 40 K, the NATF for the x ) 1/3 sample slightly drops around 36 K, then gradually decreases with further decreasing T, and finally approaches 0 at ∼10 K. Here, the NATF(T) curve for Li2MnO3 exhibits a step-like decrease around 36 K (see Figures 3b and 7). The small decrease in NATF for the x ) 1/3 sample around 36 K is, hence, attributed to the AF transition of the Li2MnO3 phase. Next, if the x ) 1/3 sample is a mixture of Li[Li0.21Mn1.79]O4 and Li2MnO3, the NATF(T) curve should show two step-like decreases at 36 and 24 K, as in the case for a zigzag chain compound Li0.92Mn2O4,14 since TNmid ) 36 K for Li2MnO3 and TNmid ) 24 K for the x ) 0.2 sample. However, as T decreases from 40 K, the magnitude of NATF for the x ) 1/3 sample slightly drops around 36 K and then decreases monotonically down to 0 at ∼10 K. For the spinel phase in the x ) 1/3 sample, TNmid ) 21 K with a large transition width (∆T ) 28 K). This could be explained by the presence of multiple magnetic phases with different TNmid in the x ) 1/3 sample. In other words, the x ) 1/3 sample is most likely to be magnetically inhomogeneous on a microscopic scale. Recently, Komaba et al. indicated that the crystallization process for the LMO compounds with x ) 0, 0.05, 0.1, and 0.2 by in situ high-T XRD measurements.9 That is, both x ) 0 and 0.05 compounds are thermodynamically stable up to 700 °C, whereas the x ) 0.1 and 0.2 compounds separate into the Li[Lix-ωMn2-x+ω]O4 phase with ω ≈ x and Li2MnO3 phase accompanying the release of O2 around 700 °C.9 They also reported that ac (∼8.28 Å) for the x ) 0.1 and 0.2 compounds are almost similar to that for the x ) 0 compound above 700 °C.9 This means that the LMO compound with x > 0 is formed by the LiMn2O4 and Li2MnO3 phases from the high-T above 700 °C

(1 - x)LiMn2O4 + xLi2MnO3 + x/O2 f Li[Li1+xMn2-x]O4

(11)

As seen in Figure 7, the spinel phase in the x ) 1/3 sample has a large transition width compared to those for the x ) 0,

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0.1, and 0.2 samples. This implies that the value of ω in Li[Lix-ωMn2-x+ω]O4 is microscopically different in the spinel lattice, although it has been widely believed that the Li[Lix-ωMn2-x+ω]O4 phase is a single-phase by X-ray diffraction and neutron scattering measurements.10-12 In other words, the Li ions at the 16d site distribute inhomogenously even in a muon-scale. As pointed out by Paulsen and Dahn,6 the number of phases that can coexist in the Li-Mn-O compound is estimated to be two, if we assume the Gibbs phase rule. However, such multiple phases in the x ) 1/3 sample indicate that the rate of the eq 11 reaction is too slow to reach the thermodynamically equilibrium state. It should be emphasized that the present x ) 1/3 sample was oxidized at 650, 600, 550, and 500 °C under air for 24 h, respectively, after heating at 1000 °C. Although the coexistence of multiple phases is inconsistent with the prediction by the Gibbs phase rule,6 nonequilibrium (or metastable) phases are also observed for the fully delithiated LixNiO2 compounds with x e 0.1;30-32 that is, there are at least four different phases in the both electrochemically30,31 and chemically31,32 delithiated LixNiO2 compounds. Finally, we wish to comment an application of µSR measurements on other lithium insertion materials. The composite compounds of yLi2MnO3 · (1 - y)LiMn2O44 and/or yLi2MnO3 · (1 - y)LiMO2 with M ) Co, Ni, and Mn33,34 have been recently promising as a positive electrode material for high-energy density L-ion batteries (LIB). The cation ordering between Li ions and Mn ions like the Li2MnO3 (Li[Li1/3Mn2/3]O2) phase coexists in theses compounds. On the other hand, the Li[Ni1/2Mn3/2]O4 compound18,19 with a space group of P4332 is attractive for high power density LIB. However, a “non-stoichiometric” Li[Ni1/2Mn3/2]O4 compound is easily formed depending on the reaction conditions, and its macroscopic magnetic properties are very different form those for the Li[Ni1/2Mn3/2]O4 (P4332).35 Since the µSR signal roughly corresponds to the volume fraction of each magnetic phase in the sample, µSR measurements can also be a powerful tool for investigating the local structural environment in these compounds. 4. Conclusion The microscopic magnetism for the Li[LixMn2-x]O4 sample with x ) 1/3 was investigated by muon-spin rotation/ relaxation (µSR) measurements. Since the Rietveld analysis indicated that the weight fraction of the Li2MnO3 impurity is estimated as 11%, the average chemical formula of the spinel phase is represented as Li[Li0.21Mn1.79]O4, if we assume that the relation between the (1 - z)Li[Lix-ωMn2-x+ω]O4 and zLi2MnO3 phases. However, the spinel phase in the x ) 1/3 sample is found to be magnetically inhomogeneous on a microscopic scale, indicating the inhomogeneous distribution of Li ions at 16d site in the spinel lattice. We arrive at theses conclusions because the temperature dependence of the normalized weak-transverse-field asymmetry for the spinel phase exhibits a large transition width (∆T ) 28 K), whereas both x ) 0.2 and Li2MnO3 samples show a sharp magnetic. Therefore, it is most likely that the distribution of Li ions at the 16d site correlates with the abnormal charge/discharge e4.5 V ) for the x ) 1/3 compound. capacity below 4.5 V (Qrecha Although we restrict present µSR measurements on the highly crystallized Li[LixMn2-x]O4 and Li2MnO3 samples, further µSR studies on the Li[LixMn2-x]O4 sample synthesized at low temperatures would provide crucial information for understanding the microscopic structural nature for lithium insertion materials.

Mukai et al. Acknowledgment. We appreciate T. Ohzuku, K. Ariyoshi, and H. Wakabayashi of Osaka City University for preparation and electrochemical characterization of Li[LixMn2-x]O4 and Y. Kondo of TCRDL for ICP-AES analysis. µSR measurements were made both at the Swiss Muon Source, Paul Scherrer Institut, Switzerland, and TRIUMF, Canada. We thank the staff of PSI and TRIUMF for help with the µSR measurements. The XRD measurements were performed at the SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal No. 2007A1917). We also thank the staff of SPring-8 for help with the XRD measurement. JHB is supported at UBC by CIfAR, NSERC of Canada, and at TRIUMF by NRC of Canada. KHC is supported by NSERC of Canada. DA acknowledges financial support from the Romanian CNCSIS-UEFISCU Project PNIIIDEI 2597/2009 (Contract No. 444). This work is partially supported by Grant-in-Aid for Scientific Research (B), 1934107, MEXT, Japan. Supporting Information Available: Temperature dependence of (a) initial phase of the oscillatory signal (φAF), (b) normalized asymmetries of ATF, AAF, and Atail, and (c) their relaxation rate for the Li2MnO3 sample. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Amatucci, G.; Tarascon, J.-M. J. Electrochem. Soc. 2002, 149, K31-K46 and references cited therein. (2) Ohzuku, T.; Kitano, S.; Iwanaga, M.; Matsuno, H.; Ueda, A. J. Power Sources 1997, 68, 646–651. (3) Iwata, E.; Takeda, S.; Iwanaga, M.; Ohzuku, T. Electrochemistry 2003, 71, 1187–1191. (4) Johnson, C. S.; Li, N.; Vaughey, J. T.; Hackney, S. A.; Thackeray, M. M. Electrochem. Commun. 2005, 7, 528–536. (5) Endres, P.; Fuchs, B.; Kemmler-Sack, S.; Brandt, K.; Faust-Becker, G.; Praas, H.-W. Solid State Ionics 1996, 89, 221–231. (6) Paulsen, J. M.; Dahn, J. R. Chem. Mater. 1999, 11, 3065–3079. (7) Gummow, R. J.; Kock, A de; Thackeray, M. M. Solid State Ionics 1994, 69, 59–67. (8) Thackeray, M. M.; Mansuetto, M. F.; Dees, D. W.; Visseres, D. R. Mater. Res. Bull. 1996, 21, 133–140. (9) Komaba, S.; Yabuuchi, N.; Ikemoto, S. J. Solid State Chem. 2010, 183, 234–241. (10) Takada, T.; Hayakawa, H.; Akiba, E. J. Solid State Chem. 1995, 115, 420–426. (11) Kopec, M.; Dygas, J. R.; Krok, F.; Mauger, A.; Gendron, F.; Julien, C. M. J. Phys. Chem. Solids 2008, 69, 955–966. (12) Takada, T.; Akiba, E.; Izumi, F.; Chakoumakos, B. C. J. Solid State Chem. 1997, 130, 74–80. (13) Gao, Y.; Dahn, J. R. J. Electrochem. Soc. 1996, 143, 1783–1788. (14) Sugiyama, J.; Ikedo, Y.; Ofer, O.; Månsson, M.; Ansaldo, E. J.; Brewer, J. H.; Chow, K. H.; Sakurai, H.; Takayama-Muromachi, E. J. Phys. Soc. Jpn. 2009, 78, 084715. (15) Schenck, A. In Muon Spin Rotation Spectroscopy; Adam Hilger: Bristol, 1985. (16) Sugiyama, J.; Mukai, K.; Ikedo, Y.; Russo, P. L.; Suzuki, T.; Watanabe, I.; Brewer, J. H.; Ansaldo, E. J.; Chow, K. H.; Ariyoshi, K.; Ohzuku, T. Phys. ReV. B 2007, 75, 174424. (17) Kitagawa, M.; Wakabayashi, H.; Ariyoshi, K.; Ohzuku, T. ITE Lett. 2007, 8, 119–123. (18) Ohzuku, T.; Ariyoshi, K.; Yamamoto, S. J. Ceram. Soc. Jpn. 2002, 110, 501–505. (19) Ariyoshi, K.; Iwakoshi, Y.; Nakayama, N.; Ohzuku, T. J. Electrochem. Soc. 2004, 151, A296–A303. (20) Storbel, P.; Lambert-Andron, B. J. Solid State Chem. 1988, 75, 90–98. (21) Jansen, V.; Hoppe, R. Z. Anorg. Allg. Chem. 1973, 397, 279–289. (22) Lang, G. Z. Anorg. Allg. Chem. 1966, 348, 246–256. (23) Bre´ger, J.; Jiang, M.; Dupe´, N.; Meng, Y. S.; Shao-Horn, Y.; Ceder, G.; Grey, C. P. J. Solid State Chem. 2005, 178, 2575–2685. (24) Hayano, R. S.; Uemura, Y. J.; Imazato, J.; Nishida, N.; Yamazaki, T.; Kubo, R. Phys. ReV. B 1979, 20, 850–859.

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