Paramagnetic electrodes and bulk magnetic susceptibility effects in the in situ NMR studies of batteries: Application to Li1.08Mn1.92O4 spinels

Journal of Magnetic Resonance 234 (2013) 44–57

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Paramagnetic electrodes and bulk magnetic susceptibility effects in the in situ NMR studies of batteries: Application to Li1.08Mn1.92O4 spinels Lina Zhou a,b, Michal Leskes a, Andrew J. Ilott b, Nicole M. Trease b, Clare P. Grey a,b,⇑ a b

University of Cambridge, Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, United Kingdom Stony Brook University, Department of Chemistry, Stony Brook, NY 11794-3400, United States

a r t i c l e

i n f o

Article history: Received 10 February 2013 Revised 24 May 2013 Available online 12 June 2013 Keywords: In situ NMR Lithium ion battery Paramagnetism Li1.08Mn1.92O4 Bulk magnetic susceptibility

a b s t r a c t To date, in situ nuclear magnetic resonance (NMR) studies of working batteries have been performed in static mode, i.e., in the absence of magic angle spinning (MAS). Thus, it is extremely challenging to apply the method to paramagnetic systems such as the cathodes spinels Li1+xMn2xO4 primarily due to three factors: (1) the resonance lines are broadened severely; (2) spectral analysis is made more complicated by bulk magnetic susceptibility (BMS) effects, which depend on the orientation and shape of the object under investigation; (3) the difficulty in untangling the BMS effects induced by the paramagnetic and metallic components on other (often diamagnetic) components in the system, which result in additional shifts and line broadening. Here we evaluate the orientation-dependence of the BMS effect of Li1.08Mn1.92O4, analyzing the experimental results by using a simple long-distance Li-electron dipolar coupling model. In addition, we discuss the shape and packing density dependence of the BMS effect and its influence on the observed frequencies of other components, such as the Li metal and the electrolyte in the battery. Finally, we show that by taking these effects into account we are able to minimize the BMS induced shift by orienting the cell at a rotation angle, ai = 54.7° which facilitates the interpretation of the in situ NMR spectra of a working battery with the paramagnetic Li1.08Mn1.92O4 cathode. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction NMR spectroscopy is a powerful technique with which to study the structural and electronic properties of electrode materials during electrochemical cycling [1,2]. Most of the NMR studies of lithium-ion batteries (LIBs) are performed ex situ, that is, NMR spectra are acquired on an electrode extracted from a cycled battery. This method has been successfully and widely used since it combines fast magic angle spinning (MAS) with modern pulsed NMR techniques to probe structural and dynamical processes that occur at various charge/discharge states of the electrode. However, this method does not always allow the metastable/transient phases, which may form in batteries during real time operation, to be captured [3]. By contrast, in situ experiments can probe these structural and dynamic changes, as the acquisition of the NMR spectra is performed in parallel with the battery cycling. To date, most of the in situ NMR studies of Li-ion batteries have been performed on either diamagnetic or metallic systems [3–7]. The next challenge is to apply in situ NMR to paramagnetic systems. The difficulties stem from the effect of the magnetic properties of the paramagnetic electrode material on the NMR spectra of ⇑ Corresponding author at: University of Cambridge, Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, United Kingdom. Fax: +44 1223336300. E-mail address: [email protected] (C.P. Grey). 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.05.011

the whole battery. A paramagnetic material can cause shifts and severe broadening of the NMR resonances via two possible mechanisms—the electron–nuclear hyperfine interaction [8] and the bulk magnetic susceptibility (BMS) [9,10], the effects being additive. The hyperfine or Fermi-contact mechanism, which results from electron–nuclear interactions that are mediated by the covalent bonds in the material, can result in significant shifts of the isotropic resonances, while the electron–nuclear dipolar coupling through-space interaction generally causes line-broadening. Further isotropic (pseudo-contact) shifts can result from the through-space dipolar interactions but only when the electronic magnetic moments of the paramagnetic ions are anisotropic [2,11]. The chemical shifts of paramagnetic compounds can often be neglected since they are small in comparison to the hyperfine shifts. The BMS mechanism is a macroscopic effect, which can vary in space throughout a particle and the whole sample. It also has its origin in the dipolar couplings between nuclear spins and electron magnetic moments, and arises if the sample shape is not spherical and/or if the distribution of paramagnetic spins within the sample is not homogeneous. Lithium manganese oxide (LiMn2O4), the material class studied in this work, is a promising cathode material for commercial Li-ion batteries because it is cheap and has low toxicity. Its electrochemical properties can be improved by introducing excess lithium into the structure (to form Li1+xMn2xO4,), raising the average Mn

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L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

oxidation state of the as-prepared material, and suppressing the Jahn–Teller distortion on discharge below 4 V [12]. The structure of Li1.08Mn1.92O4, investigated here, belongs to cubic space group  Fd3m. It has a three dimensional structure formed by cubic close packing of oxygen atoms, in which lithium and manganese ions, along with the excess lithium ions, occupy tetrahedral (8a) and octahedral (16d) sites, respectively. As Li1.08Mn1.92O4 is a paramagnetic material, the two mechanisms described above dominate its NMR response. Large Fermi contact interactions are observed giving shifts of 500–700 ppm and approximately 2000 ppm for the ions in the tetrahedral and octahedral sites, respectively [1,2,13,14]. Although the 16d (Mn) site itself is slightly distorted, no pseudo-contact shift is expected for the Li ions on the tetrahedral site due to the site symmetry. The strong dipolar interaction between Li nuclei and the thermally averaged magnetic moments of the Mn ions, results in a series of spinning sidebands in the MAS spectrum [2,13,15] and will cause significant broadening of the 7Li resonances in the static in situ NMR spectrum. The situation is made more complex in the plastic batteries designed for in situ NMR studies because the BMS effects can cause additional shifts and/or broadening [1], due to the flat rectangular shape of the Li1.08Mn1.92O4 electrode films and the heterogeneous properties of the Li1.08Mn1.92O4 electrode. Furthermore, the shift caused by the BMS effect depends on the orientation of the battery in the magnetic field [1]. Therefore, in order to extract accurate isotropic NMR shifts from the in situ studies, the BMS effects must be taken into account. Additionally, BMS effects caused by the paramagnetic electrode will change the local fields experienced by other components in the plastic bag battery and will cause shifts in the signals of the Li metal and the electrolyte [1]. Thus the BMS effect makes it difficult to separate and to assign the resonances originating from the different components of the bag cell [1]. The above factors inevitably complicate the analysis and interpretation of in situ NMR spectra of batteries containing paramagnetic cathode materials. In this paper we aim to provide insight into the factors affecting in situ NMR spectra of batteries containing paramagnetic electrode materials. Following a general description of the BMS effect, we first perform simulations of the effect of sample shape, orientation and packing density dependence of the BMS shift in a large LiMn2O4 single crystal. We then explore the effect of the orientation dependence of the BMS shift for a flat film of Li1.08Mn1.92O4 using a long-distance dipolar coupling model as the basis for the analysis of the data. In addition, the effects of film shape and packing density on the static NMR resonances will be discussed and the BMS effect of the paramagnetic Li1.08Mn1.92O4 film on the shift of NMR resonances of other components in the bag cell will be investigated. Based on this analysis, we identify the conditions that minimize the BMS effect and demonstrate this via an in situ 7Li NMR experiment of a plastic bag cell with Li1.08Mn1.92O4 as the cathode material. We expect that these results will provide a deeper understanding of the BMS effects in paramagnetic cathode materials, a necessary requirement for the development of viable in situ NMR techniques for the real-time investigation of batteries.

2. Theory 2.1. The bulk magnetic susceptibility (BMS) effect When a sample is placed in a magnetic field, a demagnetizing field is induced that, depending on the magnetic properties of the material, either opposes or adds to the static magnetic field. This demagnetizing field results in an NMR shift in an ellipsoid sample, and for a sample of general shape can result in both

frequency shifts and line broadening [16,17]. The effect of the demagnetizing field on a nuclear spin within a crystallite can be separated into three contributions (Fig. 1), making use of the model proposed by Terao and coworkers [17]: (1) the intra dipolar field arising from all the paramagnetic ions (pk) within Lorentz sphere, SE; (2) the demagnetization field produced by a given crystallite, SO, which depends on the shape, orientation and bulk magnetic susceptibility of the crystallite; (3) the inter dipolar field obtained by summing up the contributions from all the crystallites i within the whole sample, which depends on the overall sample shape (i.e., the sample container). The first contribution is responsible for the nuclear–electron through space dipolar interaction, and will give rise to broadening in all cases, and a pseudocontact shift if there is an anisotropic component to the magnetic susceptibility of the paramagnetic ions. The second and the third contributions produce what is collectively referred to as the BMS shift and correspond to the local (crystallite/particle shape, S0) and macroscopic shape components, respectively. Considering the local phenomenon, the BMS effect can be simply evaluated as the sum of the dipolar interactions between a nucleus in a particle and the surrounding paramagnetic ions within the same particle (intra-particle effects) [1,16,18,19]. Although a BMS shift is induced for a nucleus within a single particle if the particle shape is non-spherical, for a powdered sample, the intraparticle (local) dipolar interaction will result in (inhomogeneous) broadening, but will not give rise to an orientation dependent BMS shift for the whole powdered sample, since the particles are randomly oriented. The induced broadening can be averaged under MAS, but it will contribute to the sideband intensity if the spinning frequency is not sufficient. In the static case described here, it produces line broadening. If the susceptibility of the magnetic ion is anisotropic, an additional effect, known as the anisotropic bulk magnetic susceptibility (ABMS) will occur [19,20], which will result in a shift of the isotropic resonance even under MAS. For a static sample, this effect is generally much smaller than the overall broadening of the resonance. Furthermore, for Li1.08Mn1.92O4, the ABMS shift can be neglected due to the cubic symmetry of the crystal. The macroscopic shape effect, by analogy with the intraparticle interaction, can be formulated as the sum now over all inter-particle, longer-range, dipolar interactions [1]. It results in a variation of the local field inside a non-spherical object, even in a continuous medium, which depends on the position of the particle (or probe nucleus) within the sample, the bulk magnetic susceptibility of the crystallite/particle and the orientation of the sample with respect to the magnetic field. The orientation dependence of the BMS shift of the Li1.08Mn1.92O4 film mainly arises from this macroscopic effect [1]. Finally, if the susceptibility of the magnetic ion is anisotropic, the inter-particle interactions produce an ABMS effect [19,20], which will cause broadening and shifting of the resonances. Again this can be ignored for Li1.08Mn1.92O4. 2.2. The orientation dependence of the BMS shift The dipolar field felt at the center of a particle can be calculated from the sum of all of the inter-particle (nuclear–electron) dipolar interactions and the dipolar interactions to all the other paramagnetic particles within the sample, in this case a film. We first consider the intra-particle interaction, with a Hamiltonian, Henðk2S0 Þ , by analogy with the dipolar coupling between a nuclear magnetic moment and a thermally averaged electron magnetic moment [21– 23], Henðk2SE Þ , that can be represented (in frequency units) by:

Henðk2S0 Þ ¼

X k2S0

l0 l ek  Den  ln ¼

X k2S0

cI l0 l ek  Den  I

ð1Þ

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L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

Fig. 1. Model of a polycrystalline sample in a container S, based on that described in Ref. [17]. (a) Crystallites, Si are assumed to be randomly packed into a cuboid shaped sample. (b) The crystallite containing the observed nucleus, S0(i = 0), has a volume magnetic susceptibility, vV i ¼ vmi =V i where vmi and Vi are the molar magnetic susceptibility and volume of the ith crystallite, respectively. (c) SE is a Lorentz sphere with a radius much smaller than the size of the crystallite, but large enough so that the dipolar average over the lattice points converges. p0 and pk indicate the observed nuclear and paramagnetic ions within the Lorentz sphere, respectively.

 ek denote the nuclear magnetic moment and the where ln and l thermally averaged electron magnetic moments within a paramagnetic ion, respectively. l0 is the vacuum permeability, k is a paramagnetic site within a particle S0 (Fig. 1), Den is the dipolar tensor defined in the crystal frame, cI is the nuclear gyromagnetic ratio and I is the nuclear spin angular momentum. (Note that this equation is identical to that appropriate for considering the sum within the Lorentz sphere, SE, Henði2SE Þ , the only difference being that the sum of the dipolar interactions between observed nuclear spin and paramagnetic ions, k is within SE instead of S0.) The ther e as defined is valid mally averaged electron magnetic moment, l when the thermal energy kBT is much larger than the splitting between the electronic Zeeman levels (the high temperature approximation), which is generally the case near room temperature. Thus,

l

l e ¼

þ 1ÞS g  g  B0 3kB T

l e lo B0

ð2Þ

ð3Þ

:

Note that vm is a scalar when the g tensor is isotropic. Eq. (1) can then be rewritten as

Henðk2S0 Þ ¼

X

X

k2S0

k2S0

cI vmk  B0  Den  I ¼

cI vV k V k  B0  Den  I ¼ cI B0  Di  I ð4Þ

X

X

k2S0

k2S0

vmk  Den ¼

vV k V k  Den

X

cI vmi  B0  Di  I

i2Wholesample

¼

X

cI vV k V k  B0  Di  I

i2Wholesample

¼ cI B0  D  I

ð5Þ

where Di now should be expressed in the sample frame and the inter-particle dipolar tensor, D, is defined by

X

vmi  Di ¼

i2Wholesample

X

vV i V i  Di :

ð4aÞ

where vmk is the molar susceptibility of the k paramagnetic ion. The P sum k2S0 vmk over all k spins within the particle represents the susceptibility of the whole paramagnetic particle i, vmi . This can also be

ð5aÞ

i2Wholesample

The observed 7Li static NMR shifts of a Li1.08Mn1.92O4 film mainly arise from two contributions, namely the Fermi-contact shift Hc and the inter-particle dipolar interaction Henði2WholesampleÞ (resulting in the BMS shift). All other smaller nuclear interactions such as the quadrupolar and chemical shift anisotropy of the Li nuclei similarly contribute to the broadening but do not give rise to a shift for a powder and are thus also ignored. The Hamiltonian describing the system is then given by:

~ I H ¼ Hc þ Henfi2Wholesampleg ¼ cI B0  C  I þ cI B0  D  I ¼ cI B0  r

ð6Þ

h  q s vm , 3S

where C ¼ and qs denotes the electron spin (i.e. unpaired elec~ is a tensor tron) density at the s orbital of the observed nucleus, r defined by:

r~ ¼ D þ C

with Di the intra-particle dipolar coupling tensor, defined in the crystal frame by [21]

Di ¼

Henði2WholeSample=SamplecontainerÞ ¼

D¼

2 B ðS

where lB is the Bohr magneton, S is the electronic spin angular momentum of the paramagnetic ion, kB is Boltzmann’s constant, g is the electron g tensor, and B0 is the magnetic induction experienced by the electron spin. The magnetic molar susceptibility, vm, of unpaired electrons in a paramagnetic ion can be defined as

vm ¼

written in terms of the volume magnetic susceptibility vV k of the k paramagnetic ion, by multiplying by the volume occupied by this ion Vk, since vV k ¼ vmk =V. An analogous expression can be readily derived for the inter-particle interaction, now summing over all i particles [21]:

ð6aÞ

Generally, only the secular part of these two Hamiltonians is considered, and the inter-particle dipolar Hamiltonian (similar to local dipolar interaction ðHen ðk2SE Þ Þ) can be described by a 2nd rank tensor, which for an isotropic susceptibility is given by [24]:

~ LF H ¼ cI B0  r zz  I z ¼ cI B0 CIz þ

X cI vm k

r 3k

k

ð3 cos2 bk  1ÞB0 Iz :

ð7Þ

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

~ LF The index LF indicates that r zz , is the zz element of the matrix of ~ the tensor r in its laboratory frame (LF) representation, b is the angle between the principal axis of the dipolar interaction and the Zeeman laboratory frame, and rk is the distance between the observed nucleus and a given paramagnetic center k. It is interesting to note the similarity between the total dipolar and Fermi-contact Hamiltonian and that of the chemical shielding ~ has an angular dependence interaction, cIB0  r  I. The tensor r with respect to the applied magnetic field, which comes from the dipolar tensor D, since the Fermi contact interaction is to a first ~ is symmetric and not traceapproximation scalar. Additionally, r ~ less, its trace being given by the Fermi contact shift. Therefore, r plays the role of an effective chemical shift shielding tensor [21] and for convenience is referred to as the pseudo chemical shielding tensor in the following discussion. 2.3. Simulation of BMS shift in a LiMn2O4 single crystal In order to model and explore the BMS shift induced in a nonspherical paramagnetic sample qualitatively, we first performed static NMR spectral simulations for a single crystal of LiMn2O4. In this case, the BMS is dominated by the intra-particle interactions, but the methodology is analogous to that described in Section 2.2. Since we are dealing with a single particle, rather than a collection of randomly oriented particles, the local intra-particle BMS effect is no longer zero and will be orientation dependent, with a dependence that is identical to that of the macroscopic sample as shown in Eqs. (4)–(5). The BMS shifts were calculated using a program written in C that computes the dipolar coupling between a given Li nucleus and each of the paramagnetic centers within the single crystal, then sums them up to give the total dipolar tensor for that Li site in the single crystal frame. Single crystal cells of varying dimensions, as specified below, were constructed by adding together unit cells of lithium manganese spinel of dimension 8.2  8.2  8.2 Å, each containing 8 Li, 16 Mn and 32 O. The Mn magnetic moment was calculated by assuming the spin-only formula with an average spin of S = 3.5 and it was scaled isotropically with temperature. All of the simulations were run at 300 K. Although a magnetic field strength of 4.7 T was used for the calculations, the results, quoted in units of ppm, are field independent. All other nuclear interactions, such as the Fermi contact interaction, homonuclear dipolar couplings, quadrupolar couplings and chemical shift are neglected in the simulation, since they are either orientation independent (the Fermi contact shift) or much smaller in magnitude than the BMS effect. It was undesirable to perform the calculation for each Li site in each cell, with the largest cells containing nearly 107 Li sites and twice as many Mn sites. Instead, the calculation was restricted to 50,000 Li sites in each cell, with the sites selected at random to ensure that the different types of environment (i.e. edge vs. bulk) were sampled according to the probability of their occurrence. The reliability of this approach was confirmed by comparing the results to those from calculations performed using all the Li sites (940,899 Li) for the 400  4000  40 Å cell, as will be described later. The computation results in a series of symmetric second rank tensors, Di, representing the intra-particle dipolar coupling interaction for each Li site used in the calculation. These tensors are defined in the crystal frame, which is coincident with the laboratory frame for the case where the sample is oriented with its short axis, C, parallel to z and its long axis, B, parallel to y, as depicted in Fig. 2. The BMS contributions to the overall shifts of each Li site were extracted for this specific crystal orientation using Eq. (4) directly. To simulate the rotation of the crystal with respect to the magnetic field, the application of Eq. (4) was repeated after rotation of the field direction and spin operator to the required

47

Fig. 2. The LiMn2O4 single crystal with lattice parameters A = 400, B = 4000 and C = 40 Å is represented by the yellow block with a cuboid shape. The single crystal’s frame axis system is defined such that the x axis coincides with the crystal’s short edge A, y with its long edge B and the z axis along the C direction. In the figure the magnetic field B0 is aligned along the single crystal’s z axis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

orientation. This approach offers computational advantages over rotating each of the dipolar tensors, of which there are many more compared to the number of orientations considered. Once the shifts for each site were calculated, they were combined in a histogram to approximate the NMR spectrum of the whole crystal at the given orientation. For rotation about the crystal x and y axes, the rotation angle is defined between the crystal z axis and magnetic field direction, B0, such that when ai = 0°, z and B0 are parallel. For rotation about the z axis, the B0 field is rotated in the xy plane of the crystal, and is parallel to the y axis when az = 0°. Reconstructed spectra of the single crystal with dimension 400  4000  40 Å at different ay for different sampling schemes (Li sites varying from 1000, 50,000 to 940,899) are shown in Fig. S1. The results show that the spectra for 50,000 Li sites agree very well with those using the full sampling scheme, reproducing every detail of the spectra, although with a higher noise level. Further analysis of the spectra (Fig. 3a) shows that there are always three peaks observed for each spectrum, i.e., an intense peak at 2670 ppm and two weaker peaks at 1190 and 3040 ppm were observed for the spectrum calculated for 50,000 Li sites at rotation angle ay = 0°. The main peak at 2670 ppm arises from the bulk Li (Li in the middle of the single crystal), while the two small peaks at 1190 and 3040 ppm are due to Li in the first AB (400  4000) surface layer (and edge) and second AB subsurface layer of the single crystal, respectively. This can be clearly seen by examining the contour plot of the BMS shifts vs. the position of Li within the single crystal (Fig. 3b). The shift corresponding to the most intense point in each spectrum (Fig. 3a) was taken as an approximation to the average shift; this is preferred to the average as it is less sensitive to edge effects caused by the finite cell size, and it matches the approach used to interpret the experimental results. This is the quantity plotted in the rotation plots of the single crystal with dimension 400  4000  40 Å in Fig. 4a. As the rotation angles ai (i = x, y, z) increase from 0° to 180° the BMS shift varies sinusoidally. For x and y rotation, the BMS shift increases from very negative, to positive values, and then decreases again. By contrast, the BMS shift upon rotation about z does not show a significant change. The variation in shifts upon z rotation is mainly due to the difference between the xx and yy elements of the Li dipolar coupling tensor (1200 and 1470 ppm, respectively (Fig. S2a)), which is accentuated in these calculations because we have chosen a large (A:B) aspect ratio for the single crystal of 1:10. This is confirmed by the results in Fig. 4b, for a crystal where the A (x dimension) has been increased

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L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

Fig. 3. The constructed (a) histogram/spectra for a single crystal with dimension 400  4000  40 Å oriented at different rotation angles ay with a bin width of 2 ppm and (b) a contour plot of BMS shift vs. Li position within the crystal at ay = 0°, for, top: Li sites at the surface and subsurface layers of the crystal and bottom, a plane of Li sites taken from a cross section through the middle of the crystal.

Fig. 4. The calculated 7Li BMS shift Ddi(i = x, y, z) (in ppm) of two LiMn2O4 crystals of dimensions A  4000  40 Å with A values of (a) 400 and (b) 3000 Å, rotating about their x, y, and z axes at an angle ai(i = x, y, z) with respect to B0 at 4.7 T.

from 400 to 3000 Å, which show that as the A:B aspect ratio approaches 1, the difference between the observed x and y rotation patterns, and therefore the xx and yy dipolar tensor elements (now 1570 and 1580 ppm, respectively (Fig. S2a)), becomes smaller. This aspect ratio (1:1.3) is close to that used in the experiments described later. As expected, if the thickness of the single crystal (C value in z dimension) is increased from 40 to 80, 200 and 400 Å there is an increased difference between the x and y rotation patterns, and thus the xx and yy tensor elements, which also results in larger BMS shift variations being observed in the z rotation (Fig. 5). Note that there is no BMS shift variation in the y rotation when A = C = 400 Å, because the xx and zz tensor elements become equal (Fig. 5d). As indicated above, we approximate the BMS shift properties of the system by using the most intense point of each spectrum/histogram, which arises from the Li in the bulk of the crystal (Fig. 3b). We can also compute the average Li BMS shift tensor of the whole crystal, obtained from a sum of all the individual Li intra-particle tensors in the same (single crystal) frame. Since the bulk Li provides the dominant contribution to the BMS shift and the contribution from the edge and surface Li is small, the average Li tensor is similar to the tensor obtained for the Li at the center of the single crystal as shown in Fig. S2 (the diagonal components of the tensor (xx  zz) differ by less than 20% for the single crystal dimensions explored). Since all of the simulated LiMn2O4 single crystals are cuboid, according to Neumann’s principal [25], the principal axis system (frame) of the BMS shift dipolar tensor must align along the x, y, z axes of the single crystal. This must also hold true for the average intra-particle Li dipolar BMS tensors, which are shown for different sizes and shapes of single crystal in Fig. S2b. The tensors are either close or exactly axially symmetric, for the crystals with dimension 3000  4000  40 and 400  4000  400 Å, since the C:(A, B), or B:(A, C), respectively, aspect ratios are large. As the tensors are all traceless, aligning any of the cells such that each of their principal axes lies at the magic angle with respect to B0 will ensure that on average there is no BMS contribution to the overall shift, although inhomogeneous broadening would still be apparent as Li in different parts of the cell experience slightly different BMS shifts. Critically, for the cells possessing closely axially symmetric BMS tensors, it is sufficient to align only the axis corresponding to the direction of the unique tensor element at the magic angle with respect to B0. For the 3000  4000  40 Å cell, the geometry of which corresponds most closely to the electrode films used in the experiments, the unique axis coincides with the z-axis of the cell and so there should be no BMS contribution to the shift when the z-axis of the cell is orientated at 54.7° with respect to B0. Consistent with this, BMS shifts are calculated to be about 5 and 5 ppm in this crystal at ax = ay = 54.7° respectively, which are very small in comparison to the values obtained for ax,y = 0° and 90° of 3140 and 1570 ppm respectively (Fig. 4b). The simulations show that films with C  A  B (or C  A  B) can be expected to have closely axially symmetric BMS tensors and thus have the favorable property that only a single axis need be oriented at the magic angle for the BMS shift to be neglected. Even when this relationship is not satisfied completely, as long as C  A and C  B (e.g., the 400  4000  40 Å crystal where A:B = 1:10 and A:C = 1:100), the residual BMS shift at either the y or x axis magic angles, is relatively small (Fig. 4a). In order to evaluate the dependence of the BMS effect (shift and broadening) on the packing density (i.e., heterogeneity in the distribution of the paramagnetic ions), LiMn2O4 unit cells (8.2  8.2  8.2 Å) were randomly taken out from the calculated single crystal (400  4000  40 Å) to form a series of single crystals with the same size but with different overall concentrations of paramagnetic ions varying from 100% to 10%. As before, an approximation of the average 7Li BMS shift was taken as the modal shift of

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

49

Fig. 5. The calculated 7Li BMS shift Ddi (i = x, y, z) (in ppm) of several LiMn2O4 single crystals (400  4000  C Å) with C values of (a) 40, (b) 80, (c) 200 to (d) 400 Å, rotating about their x, y, and z axes at an angle ai (i = x, y, z) with respect to B0 at 4.7 T.

a histogram built from the calculated shifts of 50,000, randomly selected Li sites. The results (Fig. 6a) show that as the packing density is reduced, the absolute BMS shifts decrease for both ay = 0° and ay = 90° although the decrease in BMS shift at ay = 90° is much smaller than that at ay = 0°. We have also calculated the standard deviation of the BMS shifts from the 50,000 calculated intra-particle Li dipolar tensors, which is a measure of inhomogeneous line broadening in the spectrum. The results (Fig. 6b) show that as the average packing density decreases, the line widths initially increase and reach a maximum at packing densities around 6050%. As the densities of the paramagnetic ions continuous to decrease, the expected line widths then decrease until reaching a plateau at a packing density of 20%. Independent of the packing density changes, the line widths observed at ay = 0° are generally larger than those at ay = 90°. The variation of the BMS shift and the line broadenings as a function of a few selected packing densities can also be seen clearly from the spectra (Fig. 6c and d) for the 400  4000  40 Å single crystal oriented at ay = 0° and ay = 90°.

3. Experimental section 3.1. Li1.08Mn1.92O4 electrode Lithium excess spinel, Li1.08Mn1.92O4, was synthesized via a solid-state method with Li2CO3 and Mn2O3 as starting materials. The appropriate amount of Li2CO3 (Fisher Scientific 99%) and Mn2O3 (Sigma Aldrich) with a Li/Mn ratio of 1.08/1.92 were mixed, pelletized, and then heated at 650 °C for 12 h and 850 °C for 24 h [13,26].

Both heating and cooling rates were 2 °C/ min. Li1.08Mn1.92O4 films of different dimension or thickness and concentration of active material were prepared either from a mixture of 70% Li1.08Mn1.92O4 and 30% polytetrafluoroethylene (PTFE, Sigma Aldrich) or a mixture of 70% Li1.08Mn1.92O4, 15% PTFE (Sigma Aldrich), and 15% Super P Li (Timcal). In addition, a Li1.08Mn1.92O4 film with a mixture of 85% Li1.08Mn1.92O4, 7.5% PTFE (Sigma Aldrich) and 7.5% Super P Li (Timcal) was prepared for the in situ plastic bag cell study. In all cases, the electrode mixture was ground and rolled until a smooth self-supporting film was obtained. The various Li1.08Mn1.92O4 electrode films used in this work are summarized in Table 1. The films are labeled as LMa_b_c, a, b and c referring to the weight% of Li1.08Mn1.92O4 in the film, the aspect ratio of the x (short):y (long axis) dimensions of the film, and whether carbon has been added to the film (c = C) or not (c = 0). 3.2. Plastic bag cells Bag cells were prepared by assembling all or part of the battery components, including the Li1.08Mn1.92O4 electrode film, glass fiber separator soaked with electrolyte solution (1 M LiPF6 in an ethylene carbonate/dimethyl carbonate (EC/DMC) 1:1 volume ratio (Merck)), a Li metal strip and current collectors (aluminum mesh (Dexmet corporation) on the Li1.08Mn1.92O4 side and copper mesh (Dexmet corporation) on the Li metal side), in a polyester bag as described previously [1]. The polyester bags (Kapak corporation, type 500-24) were hermetically sealed with a sealer (Pac Seal, impulse heat sealer) in an argon-filled glove box. The detailed information of the battery components contained in bag cells studied here is provided in third column of the Table S1.

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L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

Fig. 6. The plots of (a) the calculated absolute 7Li BMS shift |Ddy| (in ppm) and (b) standard deviation (SD) of the calculated BMS shift for each Li site vs. packing density of a series of LiMn2O4 single crystals with dimensions 400  4000  40 Å at ay ¼ 0 and ay ¼ 90 . The histogram (spectra) of this single crystal oriented at (c) ay ¼ 0 and (d) ay ¼ 90 as a function of packing density. The main (bulk Li) peak in the 100% dense single crystal spectra has been truncated so that the broader peaks in the lower density crystals are more clearly visible.

Table 1 The properties of the various Li1.08Mn1.92O4 electrode films used in this study. Label

Components

LM70_3:4_0 LM70_3:8_0 LM70_1:4_0 LM35_1:4_0 LM10_1:4_0 LM70_1:4_C LM85_4:13_C

Li1.08Mn1.92O4, Li1.08Mn1.92O4, Li1.08Mn1.92O4, Li1.08Mn1.92O4, Li1.08Mn1.92O4, Li1.08Mn1.92O4, Li1.08Mn1.92O4,

PTFE PTFE PTFE PTFE PTFE PTFE, Super P Li PTFE, Super P Li

Li1.08Mn1.92O4 (wt%)

Super P Li (wt%)

Li1.08Mn1.92O4 mass (mg)

Dimension (x  y  z mm)

70 70 70 35 10 70 85

0 0 0 0 0 15 7.5

——— ——— 47.3 56.4 63.5 ——— ———

3  4  0.5 3  8  0.5 3  12  0.5 3  12  0.5 3  12  0.5 3  12  0.5 4  13  0.2

The dashed lines ——— indicate that the mass of the Li1.08Mn1.92O4 was not determined.

3.3. Electrochemistry The in situ plastic bag cell containing LM85_4:13_C film (see Table 1) as a cathode was placed tightly inside the 6 mm coil of a conventional CMX static probe. A Biologic VSP (Ultimate Electrochemical Workstation) was used for cycling the cell in situ. Low pass filters (50 MHz) were used to filter the high frequency noise coming from the cycler to improve the signal-to-noise ratio of the NMR spectra. The in situ cell was cycled galvanostatically with C/50 rate between 3.0 and 4.5 V during the spectral acquisition. 3.4. NMR measurements of powder samples The 7Li static and MAS spectra of a Li1.08Mn1.92O4 powder were acquired at a Larmor frequency of 77.54 MHz on a Bruker Avance III 200 spectrometer (4.7 T) using a double resonance 1.8 mm MAS probe designed by Samoson and coworkers at a MAS

frequency of 0 kHz (static) and 40 kHz. The spectra were acquired with a Hahn echo sequence (90°-s-180°-s-acq) where the s value was set to 50 ls. The spectra are referenced to a standard 1 M 7LiCl solution set at 0 ppm. A p/2 pulse of 1.5 ls was used, with a relaxation delay of 0.05 s. 3.5. NMR measurements of films The LM70_3:4_0 film was sealed in a polyester bag. The sample was inserted into the slotted cube holder of a Doty single crystal probe. For convenience, an axes system fixed on the film was defined. Similar to the axes system of the single crystal (Fig. 2), the x axis coincides with the film’s short axis, the y axis with its long axis and the z axis is perpendicular to the film. In order to conveniently rotate the cell inside the coil, the rotation axis is fixed along the direction of the coil and the initial position of the cell was changed with its x, y, and z axes aligned along the rotation axis. The cell was rotated about the corresponding axis (x, y, and z),

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

where the rotation angle ai(i = x, y, z) is defined as the angle between the magnetic field and the film frame axes (z, z, and x). The angles were varied between 0° and 180° with values used as follows: 0°, 15°, 35.3°, 45°, 54.7°, 60°, 75°, 90°, 105°, 120°, 125.3°, 135°, 144.7°, 165°, and 180°. The 7Li NMR spectra of the LM70_3_4_0 film at various orientations were acquired at a Larmor frequency of 77.54 MHz on a Bruker Avance III 200 spectrometer (4.7 T) using a Doty Singlecrystal probe (Doty Scientific, DS1-133). The p/2 pulse length was 2.75 ls. The spectra were acquired using a Hahn-echo pulse sequence with a recycle delay of 0.05 s. 7 Li NMR spectra of Li1.08Mn1.92O4 electrodes with different shapes (LM70_3:4_0, LM70_3:8_0, LM70_1:4_0) and different concentrations of active material (LM70_1:4_0, LM35_1:4_0, LM10_1:4_0,) and LM70_3:4_0 type of films with different thicknesses (0.5, 0.3, 0.2 and 0.1 mm), placed in the coil with rotation angles ay = 0° and 90°, were acquired at a Larmor frequency of 116.6 MHz on a 7 T magnet using a pulse length of 3.5 ls with a Tecmag LapNMR spectrometer for samples with different shapes and different thicknesses and a pulse length of 3 ls with a CMX spectrometer for samples with different concentrations. The spectra were acquired using a Hahn-echo pulse sequence with a relaxation delay of 0.05 s. Bag cells, which contain all or part of the components of the complete LM70_1:4_C vs. Li metal cell, were placed in the coil at rotation angles of either ay = 0°, 54.7° or 90° with respect to B0. 7Li NMR spectra were acquired at a Larmor frequency of 116.6 MHz on a 7 T OXFORD instruments magnet using a p/2 pulse length of 3.5 ls with a Tecmag LapNMR spectrometer. The spectra were acquired using a Hahn-echo pulse sequence with a recycle delay of 0.05 s. Echo delays of 20 ls and 500 ls were used for acquiring the 7Li spectra of Li1.08Mn1.92O4 electrode and electrolyte, respectively.

51

Fig. 7. The 7Li (a) MAS and (b) static NMR spectra of Li1.08Mn1.92O4 powder sample. The spectra were acquired at 4.7 T using a 1.8 mm MAS probe with a MAS frequency of 40 kHz (a) and 0 kHz (b), respectively. Isotropic resonances are labeled and

indicates the spinning sidebands.

temperature of the two samples, the MAS spectrum being acquired at slightly higher temperature, due to the frictional heating associated with MAS. 4.2. The BMS shift of Li1.08Mn1.92O4 film and its orientation dependence

4.1. BMS effects in Li1.08Mn1.92O4 powders

The 7Li BMS shift tensor components (and thus the pseudo chemical shielding tensor) of film comprising only Li1.08Mn1.92O4 and the PTFE binder (LM70_3:4_0) with dimensions 3  4  0.5 mm was measured by employing a method which is analogous to that used to measure the chemical shift anisotropy (CSA) of a single crystal, wherein the spectra are acquired at different orientations of the single crystal with respect to B0 (Fig. 8) [27,28]. The analogy between these two properties, the CSA components of a single crystal and the BMS or pseudo chemical shielding components of a film, (Section 2.2) provides the physical basis for performing this measurement. Instead of rotating the Li1.08Mn1.92O4 film about three orthogonal x, y and z axes of the sample frame, we fix the rotation axis along the direction of the coil, and change the initial position of the film inside the coil with the x, y, and z axes of the film aligned along the rotation axis, then rotate the film correspondingly (Fig. 8). 15 spectra were acquired for each rotation angle. As in the static powder spectrum (Fig. 7b), only one broad peak, assigned to the lithium in the tetrahedral sites of Li1.08Mn1.92O4, was observed in each 7Li NMR

A typical 7Li MAS NMR spectrum of Li1.08Mn1.92O4 is shown in Fig. 7a. Several resonances between 505 and 719 ppm are observed and are assigned to the Li in the tetrahedral sites. The shifts are dominated by the Fermi contact interaction. The strong dipolar interaction between 7Li nuclei and the Mn unpaired electrons is partially removed by the fast MAS (spinning at 40 kHz). However, when the NMR spectrum is acquired for a static sample, these strong dipolar interactions broaden the 7Li resonances (Fig. 7b), and only a broad peak with a peak maximum at 579 ppm is observed. Note that this static spectrum was acquired with a MAS probe, and the long axis of the cylindrical rotor is aligned at 54.7°. Thus, there will be no overall shift due to the BMS, since (as discussed in Section 2.2), the inter-particle dipolar interactions over all the particles in the cylinder, are averaged to zero at magic angle. This mechanism will, however, give rise to peak broadening. The small shift of the peak’s center of gravity from 562 ppm (Fig. 7a) to 579 ppm (Fig. 7b) is ascribed to the difference in

Fig. 8. Side view illustrating the rotation of the Li1.08Mn1.92O4 film (LM70_3:4_0) about a rotation axis that is always along the direction of the coil (indicated by a circle). The initial position of the film inside the coil is changed with the (a) x (b) y and (c) z axes of the sample frame aligned along the rotation axis. For rotation about the (a) x and (b) y axes of the sample frame, the rotation angle ai (i = x, y) is defined between the film z axis and the magnetic field direction, B0 such that when ai = 0°, z and B0 are parallel. For rotation about the z axis, the rotation angle az is defined as lying between the film x axis and the B0 field such that when ai = 0°, x and B0 are parallel.

3.6. In situ NMR measurement of a Li1.08Mn1.92O4 vs. Li bag cell In situ 7Li NMR spectra of a full Li1.08Mn1.92O4 vs. Li bag cell oriented at an angle ay = 54.7° with respect to B0 were acquired at a Larmor frequency of 116.6 MHz on a 7 T OXFORD instruments magnet using a p/2 pulse length of 2.125 ls with a Tecmag LapNMR spectrometer. The spectra were acquired using a Hahn-echo pulse sequence with echo delay and recycle delay of 10 ls and 0.05 s respectively. All the spectra were referenced to 1 M 7LiCl aqueous solution set at 0 ppm. 4. Results and discussion

52

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

spectrum. The peak positions (i.e., the peak maxima) of Li1.08Mn1.92O4 were fitted with a sinusoidal function as shown in Eq. (8) (see Supporting information (SI)) to obtain the components of the pseudo chemical shift tensor [27,28] (Fig. 9).

di ðaÞ ¼ Ai þ Bi cosð2aÞ þ ðC i Þ sinð2aÞ

ð8Þ

For each rotation around the axes (x, y, z), a set of coefficients, A, B, C was generated, yielding a total of 9 coefficients Ai, Bi, Ci with i = x, y, z as listed in Table 2. By substituting the set of coefficients from the curve fitting into Eqs. (S8)–(S12) (see SI), we can calculate the principal components of the pseudo chemical shielding tensor r~ and the direction cosines relating the principal axis system (PAS) ~ to the sample frame (see Table 3). A value for the span of the of r ~ pseudo chemical shielding tensor, Dr given by ~ ¼r ~ zz  ðr ~ xx þ r ~ yy Þ=2 of 860 ppm and the isotropic shift, Dr ~ xx þ r ~ yy þ r ~ zz Þ are then extracted from this 571 ppm equal to 1=3ðr measurement. This isotropic shift matches very well with the static 7 Li NMR shift of Li1.08Mn1.92O4 at 579 ppm (Fig. 7b). ~ c ~ ; b; ~Þ specifying the transformation between The Euler angles ða ~ can be calculated from the sample frame and the PAS frame of r the direction cosines given in Table 2 (Eq. (S13)), yielding Euler an~ ¼ 0 ; c ~ ¼ 43:3 ; b ~ ¼ 90 . Thus a conversion from the sample gles a frame to the PAS frame can be achieved by rotating the former ~þc ~ ¼ 133:3 (using a right-hand rule) about the z axis. frame by a It is worth noting that this rotation angle is extremely sensitive to the values of the off-diagonal elements of the calculated pseudo ~ xy ; r ~ xz ; r ~ yz ) which chemical shielding tensor in the crystal frame (r are derived directly from the Ci parameters defined by Eq. (8) and (S10)–(S12). As the Ci values are small and have large percentage errors, the calculated rotation angle is expected to have a large error. Indeed, according to Neuman’s principal [24] and all of the simulation results presented here, the PAS tensor is expected to align with the axes system of the sample. By subtracting the value of the extracted isotropic shift, 571 ppm, the principal components of the dipolar tensor D can be obtained and are listed in Table 4. Notably, the measured Dxx is almost equal to Dyy and (Dxx + Dyy + Dzz)/3= 0 within error, which indicates that the calculated dipolar tensor is approximately axially symmetric and traceless, even though the film is not exactly tetragonal. Furthermore, the unique axis or z axis of the Table 2 Li pseudo chemical shift parameters (ppm) obtained from a leastsquares fit of the experimental peak positions obtained for the Li1.08Mn1.92O4 film as a function of orientation with respect to B0 direction. Standard deviation is given in parentheses.

principal-axis system of the averaged long distance dipolar interaction (BMS shift) of the Li1.08Mn1.92O4 film (LM70_3:4_0) lies perpendicular to the film and not along its long axis. Similar to the simulation results obtained for the LiMn2O4 single crystal (see Section 2.3), we expect that the average inter-particle dipolar interaction (BMS shift) with its geometric dependence, 3cos2 b – 1, will average to 0 when b = a = 54.7° or 125.3°. Consistent with this, the shifts obtained at angles ai = 54.7° or 125.3° (i = x, y) in the 7 Li NMR spectra are very close to the static 7Li NMR shift of Li1.08Mn1.92O4 powder at 579 ppm (Fig. 7b) as seen in Table 5. The slight discrepancy between these values (Fig. 7b) and (Table 5), is ascribed to the error in determining the rotation angle of the film. The experimentally determined orientation dependence of the BMS shifts and the observation that the unique axis of the PAS of the dipolar tensor lies along the z axis of the Li1.08Mn1.92O4 (LM70_3:4_0) film with dimensions 3  4  0.5 mm is qualitatively supported by the BMS shift simulations of, for example, the LiMn2O4 single crystals with dimensions (3000  4000  40 Å) and 400  4000  40 Å (compare Figs. 4 and 9). 4.3. Factors affecting the BMS effects in Li1.08Mn1.92O4 electrode films 4.3.1. Dependence of the BMS effects on the aspect ratio of the film The effect of the aspect ratio on the BMS shift was examined in three Li1.08Mn1.92O4/PTFE films, denoted as LM70_1:4_0 (3  12  0.5 mm (A  B  C)), LM70_3:8_0 (3  8  0.5 mm) and LM70_3:4_0 (3  4  0.5 mm) in Table 1. The static 7Li NMR spectra of these films are shown in Fig. 10a. As long as the film

Table 4 Li dipolar tensor principal components (in ppm) for the Li1.08Mn1.92O4 electrode film. 7

Dxx

Dyy

Dzz

279(10)

295(14)

575(18)

Table 5 Observed 7Li NMR shift di (i = x, y) of the Li1.08Mn1.92O4 film (in ppm) with rotation angles ai = 54.7° and 125.3° (i = x, y). Rotation angle

dx

dy

ai = 54.7° ai = 125.3°

569 (75) 589 (73)

559 (70) 561 (70)

7

Parameter Ax Bx Cx Ay By Cy Az Bz Cz

438 (6) 450 (8) 15 (8) 428 (9) 422 (13) 14 (12) 847 (2) 20 (3) 8 (3)

Table 3 Principal components of the 7Li pseudo chemical shielding tensor in ppm (top row) and the direction cosine relative to the orthogonalized sample frame (bottom three rows) of the Li1.08Mn1.92O4 film.

r~ xx

r~ yy

r~ zz

850(10) 0.6861 0.7275 0.0015

866 (14) 0.7273 0.6859 0.0235

4 (18) 0.0161 0.0173 0.9997

Fig. 9. The 7Li peak positions (di) for the Li1.08Mn1.92O4 film as a function of the rotation angle ai. The three rotation curves were fitted with Eq. (8) (d = A + Bcos(2a) + C sin(2a)) and the extracted values for A, B and C are given in Table 2. The experimental error bars reflect the estimated error in determining the rotation angle of Day ¼ 5 .

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

thickness is significantly smaller than the film size (5C 6 A, 5C 6 B and B:A 6 5), on the basis of the simulations, the BMS shift tensor is close to being axially symmetric and the A:B aspect ratio should have little effect on the BMS shift. Consistent with this, as the aspect ratio of the film along the x and y directions increases from 1:4, 1:2.6 to 1:1.3 in these films, the corresponding changes in the resonance position are small (75, 60, 40 ppm at an angle ay ¼ 0 and 806, 810 and 830 ppm at ay ¼ 90 ). The small variations in the 7Li shift at ay ¼ 0 and 90° are in part due to the difficulty in controlling the film’s thickness. This effect is demonstrated in Fig. 11, where the dependence of the observed shifts on the thickness (i.e., an increase in the length along z) is plotted for a 3  4  0.5 mm film. Shifts of the order of 50 and 25 ppm are expected for variations of 0.1 mm in the film’s thickness for angles of ay ¼ 0 and ay ¼ 90 respectively, which is much larger than the variation observed in Fig. 10a. Error in setting the rotation angles ay ¼ 0 and 90° are expected to cause only a small shifts of ±2.5 ppm for Day ¼ 5 .

Fig. 10. Static 7Li NMR spectra of Li1.08Mn1.92O4/PTFE electrode films with (a) different x:y aspect ratio, LM70_1:4_0 (3  12  0.5 mm), LM70_3:8_0 (3  8  0.5 mm), LM70_3:4_0 (3  4  0.5 mm), (b) with and without carbon, Li1.08Mn1.92O4/PTFE (LM70_1:4_0) and Li1.08Mn1.92O4/PTFE/Carbon (LM70_1:4_C) films but with the same dimension (3  12  0.5 mm), and (c) different spinel contents, LM10_1:4_0, LM35_1:4_0 and LM70_1:4_0, varying from 10%, 35% to 70%. Films were placed in the coil with rotation angles of ay = 0° and ay = 90°.

53

4.3.2. Dependence of the BMS effects on the heterogeneity of Li1.08Mn1.92O4 In order to investigate the effect of the heterogeneous properties of the electrode film on the BMS shift of Li1.08Mn1.92O4, Li1.08Mn1.92O4/PTFE (LM70_1:4_0) and Li1.08Mn1.92O4/PTFE/Carbon (LM70_1:4_C) electrode films with dimensions 3  12  0.5 mm were studied (see Table 1). Note that, in this case, we have prepared films with dimensions closer to those used as electrodes in working bag cells, rather than the 3  4  0.5 mm dimensions used in previous sections (the smaller aspect ratio being needed so as to allow for the full rotation of the film in the coil). The 7Li NMR shifts measured for the LM70_1:4_0 and LM70_1:4_C films were 74 and 17 ppm for ay ¼ 0 and 816 and 808 ppm for ay ¼ 90 , respectively (Fig. 10b). Independent of the film’s orientation, the absolute BMS shift (635 ppm at ay ¼ 0 and 255 ppm at ay ¼ 90 ) of the LM70_1:4_0 film is larger than that of LM70_1:4_C films (544 ppm at ay ¼ 0 and 247 ppm at ay ¼ 90 ), which indicates that the addition of carbon diluting the spinel component slightly, resulting in smaller BMS shifts (Table 6). The FWHM (full line width at half maximum) of LM70_1:4_C (715 ppm at ay ¼ 0 and 615 ppm at ay ¼ 90 ) by contrast was larger than that of the LM70_1:4_0 film (559 ppm at ay ¼ 0 and 560 ppm at ay ¼ 90 (Table 6)) regardless of the film’s orientation, with the lineshape being less symmetrical. This effect indicates that the addition of carbon to film LM70_1:4_C, which increases its heterogeneity but dilutes the paramagnetic component, leads to a stronger variation in magnetic susceptibility within the film and thus a smaller BMS shift and increased broadening. The observed asymmetry of the lineshape is in part ascribed to non-uniformity in the distribution of the different components in the film. 4.3.3. Dependence of the BMS effects on the packing density of the Li1.08Mn1.92O4 film Three Li1.08Mn1.92O4/PTFE electrode films with dimensions 3  12  0.5 mm, denoted as LM10_1:4_0, LM35_1:4_0 and LM70_1:4_0 (Table 1), which contained 10%, 35% and 75% (wt%) Li1.08Mn1.92O4, were then studied. The packing density of Li1.08Mn1.92O4, m(Li1.08Mn1.92O4)/V(film) = m(Li1.08Mn1.92O4)/ (3  12  0.5 mm3) where m(Li1.08Mn1.92O4) is the weight of active material and V (film) is the volume the Li1.08Mn1.92O4 film, was calculated, and the values, the observed 7Li NMR shifts (Fig. 10c), the absolute BMS shifts and the line widths of the different films are summarized in Table 6. As the weight ratio of active material Li1.08Mn1.92O4 in these films increases from 10% to 70%, the packing density increases from 0.26 to 2.47, which is associated with an increase in the magnitude of BMS shift from 325 to 712 ppm for ay ¼ 0 The same trend is observed for ay ¼ 90 but the effect is smaller. Independent of the film’s orientation, the largest FWHM is found for the film with 35% weight ratio of active (paramagnetic) material (LM35_1:4_0). Moreover the FWHM for all three films at ay ¼ 0 is about 100 ppm larger than those observed at ay ¼ 90 (Table 6). This is qualitatively consistent with the results of BMS shift simulation of LiMn2O4 single crystals (400  4000  40 Å) with various packing densities (Fig. 5a) which showed the absolute BMS shift at ay ¼ 0 is larger than that at ay ¼ 90 . The same trends were also observed for line widths (evaluated from standard deviation of BMS shifts) of the calculated 7Li BMS shift spectra of the single crystal (400  4000  40 Å) (see Section 2.3) wherein the maximum line width is observed in the middle range of the packing density (Fig. 5b) for both ay ¼ 0 and ay ¼ 90 . 4.4. The BMS effect of Li1.08Mn1.92O4 on the other battery components

Fig. 11. The 7Li peak positions (di) observed for a Li1.08Mn1.92O4 film (in ppm) as a function of thickness of the film at rotation angles ay = 0° and ay = 90°.

In a whole bag cell, the BMS effects of other components such as the Li metal and electrolyte should also be considered. Typically, the susceptibility effect of the diamagnetic electrolyte and

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L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

Table 6 Spectral properties of Li1.08Mn1.92O4/PTFE (LM70_1:4_0) and Li1.08Mn1.92O4/PTFE/Carbon (LM70_1:4_C) films and three Li1.08Mn1.92O4/PTFE electrode films (LM10_1:4_0, LM35_1:4_0, LM70_1:4_0), with different packing densities at rotation angles ay = 0° and ay = 90°. Sample

LM70_1:4_0 LM70_1:4_C LM10_1:4_0 LM35_1:4_0 LM70_1:4_0

Packing density

ay = 0° Observed shift (ppm)

Absolute BMS shifta (ppm)

FWHM (ppm)

Observed shift (ppm)

ay = 90° Absolute BMS shifta (ppm)

FWHM (ppm)

——— ——— 0.260 1.097 2.469

74 17 254 109 133

635 544 325 470 712

559 715 764 786 718

816 808 712 758 813

255 247 133 179 234

560 615 630 652 607

a The absolute value of the BMS shift is calculated by subtracting the static 7Li NMR shift of Li1.08Mn1.92O4 powder (Fig. 7b) at 579 ppm from the observed 7Li shift. The symbol ——— indicates that the packing density of the Li1.08Mn1.92O4 is not determined.

separator is small, with only a small shift of ±1.6 ppm of the electrolyte peak being observed when a bag containing an electrolytesoaked borosilicate separator is rotated in the coil (Fig. 12a). When Li metal is added to the cell, the BMS effect increases significantly, due to the (temperature independent) paramagnetism associated with the metal’s delocalized electrons, as is evident from the much larger shifts of both the electrolyte and metal signals (Fig. 12b) [1]. Thus in a real bag cell we can expect a complex and additive effect from all of the different components on the resonance position and width, and it may be difficult to determine which component is leading to the shift of another [29]. However, since the BMS shift arising from paramagnetic Li1.08Mn1.92O4 is much larger than that arising from both the Li metal and electrolyte, it is likely that the BMS induced by this component will be the dominant contribution. To demonstrate the effect we acquired the 7Li NMR spectra of two bag cells, the first containing Li1.08Mn1.92O4/PTFE/Carbon film (LM70_1:4_C) and a glass fiber separator soaked with electrolyte, and the second the same components but with a strip of Li metal (dimensions 2  9  0.38 mm) added (Fig. 13). For the first bag cell, the broad Li1.08Mn1.92O4, peak shifts from 58 ppm to 824 ppm as

Fig. 12. 7Li static spectra acquired for two bag cells containing (a) a borosilicate glass separator soaked with electrolyte only and (b) the borosilicate glass separator, electrolyte and a Li metal, oriented at ay = 0° and ay = 90°.

the angle rotates from ay ¼ 0 to ay ¼ 90 (Fig. 13a). The sharp peaks in Fig. 13a are due to the electrolyte, their signal being weak, because a short relaxation delay of 0.05 s was used so as to optimize the signal for detection of the fast relaxing Li1.08Mn1.92O4 component. However, by varying the echo delay, s, of the spinecho (used to acquire these spectra) from 20 ls (Fig. 13a) to 500 ls (Fig. 13b) we can suppress the Li1.08Mn1.92O4 signal and only observe the electrolyte signal. At least three resonances are now clearly observed in the spectrum (Fig. 13b) of the cell at ay ¼ 0 and ay ¼ 90 which are assigned to electrolyte in different regions of the cell, the local field clearly varying throughout the whole bag-cell. For a cell oriented at ay ¼ 0 both negative (peaks at 27 and 67 ppm) and positive shifts (100 ppm) were observed. On the basis of the orientation dependences observed above, we assign the positive peak at 100 ppm (ay = 0°) and the 43 and 91 ppm (ay = 90°) to the same part of the electrolyte. (Similarly, the peaks at 27 and 67 ppm (ay = 0°) correspond to the peak at 75 ppm (ay = 90°).) This assignment is consistent with the intensity ratios of the two different components. We tentatively ascribe the negative peaks (43 and 91 ppm) and positive peak

Fig. 13. 7Li static spectra of two bag cells containing LM70_1:4_C film and a borosilicate glass separator soaked with electrolyte (a and b), for two different spinecho delays (20 and 500 ls respectively) and a LM70_1:4_C film, a borosilicate separator and a Li metal strip (2  9  0.38 mm) (c), at rotation angles ay = 0° and ay = 90°. The inset in (c) shows an enlarged region containing the Li metal signal. The recycle and spin-echo delay were 0.05 s and 20 ls in (a and c), and 0.05 s and 500 ls in (b), respectively.

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57

55

component. In order to understand why more than one Li metal resonance is observed, another bag cell was prepared now with a Cu metal foil added on top of the Li foil (see Supplemental information) to make a Li1.08Mn1.92O4 film (LM70_1:4_0), electrolyte soaked separator, Li metal, Cu foil stack. Due to the radio frequency (RF) skin depth effect, the Li metal signal only arises from the first few microns of the strip [4,30]. Thus, the addition of a strip of copper metal to one side of the Li strip should at least partially block the Li signal from the side of the Li strip next to the Cu foil. Spectra of these new bag cells are shown in the SI and confirm that the two sides of the Li metal are associated with different BMS shifts. 4.5. Analysis of the 7Li NMR spectra of a full Li1.08Mn1.92O4 vs. a Li bag cell placed at various orientations

Fig. 14. 7Li static spectra acquired for a bag cell containing Li1.08Mn1.92O4/PTFE/ Carbon (LM70_1:4_C) film, Li metal (dimensions 2  9  0.38 mm) and borosilicate glass separator soaked with electrolyte, oriented at rotation angles ay = 0°, 54.7°, 90°. The recycle and echo delay were 0.05 s and 20 ls in (a) and 0.05 s and 500 ls in (b).

(100 ppm) to Li+ within the separator and the Li+ electrolyte at the edge of the bag, respectively, the two regions experiencing very different dipolar fields resulting from the Li1.08Mn1.92O4 film. Analysis of the spectra of the second bag cell (Fig. 13c) placed at ay ¼ 0 and ay ¼ 90 shows that the broad resonance, associated with Li1.08Mn1.92O4, shifts from 32 ppm to 774 ppm. The shifts are different slightly from those observed for the bag cell without Li metal indicating that the BMS effect on the 7Li NMR shift of Li1.08Mn1.92O4 is modified somewhat by the Li metal. The resonance due to the Li metal itself has shifted noticeably and broadened asymmetrically with two peaks being observed at 332 and 300 ppm for ay ¼ 0 and 210 and 181 ppm for ay ¼ 90 . These splitting and shifts are again ascribed to the BMS effect of the Li1.08Mn1.92O4

Having analyzed the spectra of several bag cells containing only a few individual components, the spectra of a full bag cell orientated at angles ay ¼ 0 , 54.7°, 90° were acquired (Fig. 14a). Qualitatively similar resonances are observed in comparison to the spectra shown in Fig. 13 and again the broad peaks in the spectra are ascribed to Li1.08Mn1.92O4. The resonances in the 187–316 ppm range arise from Li metal, and the peaks in the 89 to 80 ppm range can be assigned to the electrolyte. In order to enhance the Li metal and electrolyte signal, the echo delay s was changed to 500 ls to suppress the signal from Li1.08Mn1.92O4. As seen more clearly in Fig. 14b, as the cell’s rotational angle increases, the resonance of Li metal and electrolyte both shift from higher frequency to lower frequency, following the trend described in Section 4.4. When the cell is placed in the coil at ay ¼ 54:7 the observed Li1.08Mn1.92O4 resonance is 577 ppm, which is close to the isotropic shift at 579 ppm for Li1.08Mn1.92O4 powder acquired in MAS probe under static conditions (Fig. 7b). This result is consistent with our analysis of the single crystals in Section 2.3, i.e., that the average long distance dipolar interaction will be averaged to 0 at ay ¼ 54:7 for a two-dimensional thin film. Additionally, at this angle (ay ¼ 54:7 ), the BMS effect from Li1.08Mn1.92O4 on the 7Li NMR shift of the Li metal is also reduced: A broad Li metal resonance with discontinuities at 276, 247 and 187 ppm (Fig. 14b) was observed; the first two are in the expected frequency range of Li metal, and the third one may arise from the part of Li surface which has a slightly different rotation angles due to bending of the Li strip or residual BMS effects from the Li1.08Mn1.92O4. For the electrolyte, different local fields are still experienced by the electrolyte in

Fig. 15. In situ 7Li static NMR spectra for the first cycle of an Li1.08Mn1.92O4 vs. Li/Li+ bag cell. (a) Voltage profile (black line) and Li1.08Mn1.92O4 isotropic shifts (blue square) vs. capacity plots. (b) Stacked plot of the 7Li spectra. The in situ cell was cycled galvanostatically with a C/50 rate between 3.0 and 4.5 V during the spectral acquisition. A Hahnecho pulse sequence with echo delay 10 ls was used to collect a total of 72,000 scans for each spectrum. A recycle delay of 0.05 s was used.

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different regions of the cell, i.e., the effect of the BMS cannot be simply modeled by our planar electrode model, which is not too surprising given that the electrolyte is located between the Li metal slab and the Li1.08Mn1.92O4 film and also at the edge of the bag. 4.6. In situ NMR of a bag cell with Li1.08Mn1.92O4 as cathode Having investigated the BMS effects in the previous sections, we now describe the in situ NMR spectra of a Li1.08Mn1.92O4 vs. Li/Li+ bag cell acquired under conditions so as to minimize the BMS shift, i.e., with the bag cell oriented at an angle ay ¼ 54:7 (Note that the size of the Li1.08Mn1.92O4 film is 4  13  0.2 mm (A  B  C) and thus 10C 6 A, 10C 6 B and B:A 6 5). The electrochemical profile for the first charge of the battery shows two processes (at approximately 4.05 V and 4.15 V) as lithium is extracted from the tetrahedral sites and Mn3+ is oxidized to Mn4+ until the voltage reaches 4.5 V [13] (Fig. 15a). The two processes originate from the ordering of the lithium ion on one half of the tetrahedral 8a sites at approximately 4.10 V, when approximately 50% of the tetrahedral lithium ions are removed [31]. During charge/discharge process, the corresponding capacities are 128mAh/g and 122mAh/g, respectively (the deviation from the theoretical capacity of 115 mAh/g are probably due to variation in the Li content in the pristine material). In the initial spectrum (indicated by a black arrow in Fig. 15b), acquired at the beginning of the electrochemical cycle, we assign the broad peak observed at 570 ppm to Li1.08Mn1.92O4 electrode and the three peaks at around 240 ppm to the Li metal and the small peaks around 0 ppm to the Li ions in the electrolyte solution as well as to the lithium in the solid electrolyte interface (SEI) on both positive and negative electrodes. Upon charging, the broad peak shifts to higher frequency as the Mn3+ ions are oxidized to Mn4+ and then shifts back to lower frequency during the discharge process (Fig. 15a). Interestingly, we observed the significant decrease in the intensity of Li1.08Mn1.92O4 at the beginning of the electrochemical process as Li is removed, and an increase in the intensity in the intermediate region when 0.5 Li is removed, and then further decrease in the intensity until the end of the charge. The trend is reversed during the discharge process. The changes in intensity are ascribed to the removal of Li and the effect of transverse relaxation (T2). Adjusting the intensity by taking account into the T2 effect, the intensity drop becomes more gradual as Li is removed. A detailed analysis of in situ T2 and the line width and shift changes of Li1.08Mn1.92O4 is outside the scope of this paper and will be published in a subsequent paper [32].

dependence of BMS shift performed on LiMn2O4 single crystals (with sizes of for example, 3000  4000  40, 400  4000  400 and 400  4000  40 Å) show similar trends for the BMS shifts. We have explored experimentally (and via simulations on single crystals) the effect that the shape of the electrode film, the heterogeneous properties of the electrode film and concentration of Li1.08Mn1.92O4 particles within the electrode film has on the BMS broadening and BMS shifts. As the aspect ratio of the films (A  B  C mm) matches the condition that 5C 6 A, 5C 6 B and B:A 6 5, the A:B aspect ratio has little effect on the BMS shifts. The addition of carbon into Li1.08Mn1.92O4 film increases the heterogeneity of the film and results in a smaller BMS shift but larger BMS broadening. As the concentration of Li1.08Mn1.92O4 particles increases, the absolute BMS shifts increase and the BMS broadening decreases. Furthermore, the strong BMS effect due to the Li1.08Mn1.92O4 film can cause shift and broadening of signals of other components in the battery such as those originating from the Li metal and electrolyte. Although the BMS effect complicates the spectra, its effects on the resonance lines position can be minimized by orientating the bag cell at ay ¼ 54:7 Finally, we would like to stress that small variations to the angle around the condition ay ¼ 54:7 may be required due to the shape of the film used and the BMS effect coming from the Li metal. However, as these variations are expected to be minimal, in practice, when setting up the in situ NMR experiment, the rotation angle can be set to 54.7° in order to minimize the BMS shift as long as the size of films (A  B  C mm) matches the condition that 5C 6 A, 5C 6 B and B:A 6 5.

Acknowledgments This work was supported by the Northeastern Center for Chemical Energy Storage, and Energy Frontier Research Center funded by the U.S. DOE, BES under Award No. DE-SC0001294 (method development, supporting A.J.I. and N.M.T.). Application of this methodology to the spinel (and support of L.Z.) was provided by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. DOE, under Contract DE-AC02-05CH11231, as part of the BATT Program; Subcontract 6517749. M.L. is an awardee of the Weizmann institute of Science – national postdoctoral award program for advancing women in science and a Marie Curie FP7 fellow. We thank Rangeet Bhattacharyya for developing the matlab program for in situ data processing and Ben YunXu Zhu for writing much of the dipolar coupling code.

5. Conclusions The in situ NMR studies of lithium ion batteries with paramagnetic cathode materials such as Li1.08Mn1.92O4 are strongly affected by bulk magnetic susceptibility effects. The orientation dependence of the BMS shift was modeled in this work by calculating the long range inter-particle dipolar couplings between nuclear and electron spins. Based on the analogy between the dipolar interaction and the chemical shift interaction, we have used the CSA single-crystal technique to extract the size and orientation of the BMS (inter-particle dipolar interaction) tensor within the Li1.08Mn1.92O4 paramagnetic electrode film. The principal values were determined by rotating the film in the coil about its three orthogonal axes and the isotropic shift calculated from these values is consistent with the value obtained under MAS. Interestingly, as long as the size of the film (A  B  C mm) matches the condition that 5C 6 A, 5C 6 B and B:A 6 5, the inter-particle dipolar tensor (BMS shift tensor) is close to being axial with the (unique) principal axis lying normal to the film (along the short axis) rather than along the film’s long axis. Simulations of the orientation

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmr.2013.05.011.

References [1] N.M. Trease, L.N. Zhou, H.J. Chang, B.Y.X. Zhu, C.P. Grey, In situ NMR of lithium ion batteries: bulk susceptibility effects and practical considerations, Solid State Nucl. Magn. Reson. 42 (2012) 62–70. [2] C.P. Grey, N. Dupre, NMR studies of cathode materials for lithium-ion rechargeable batteries, Chem. Rev. 104 (2004) 4493–4512. [3] B. Key, R. Bhattacharyya, M. Morcrette, V. Seznec, J.M. Tarascon, C.P. Grey, Realtime NMR investigations of structural changes in silicon electrodes for lithiumion batteries, J. Am. Chem. Soc. 131 (2009) 9239–9249. [4] R. Bhattacharyya, B. Key, H.L. Chen, A.S. Best, A.F. Hollenkamp, C.P. Grey, In situ NMR observation of the formation of metallic lithium microstructures in lithium batteries, Nat. Mater. 9 (2010) 504–510. [5] M. Letellier, F. Chevallier, F. Beguin, In situ 7Li NMR during lithium electrochemical insertion into graphite and a carbon/carbon composite, J. Phys. Chem. Solids 67 (2006) 1228–1232.

L. Zhou et al. / Journal of Magnetic Resonance 234 (2013) 44–57 [6] M. Letellier, F. Chevallier, M. Morcrette, In situ 7Li nuclear magnetic resonance observation of the electrochemical intercalation of lithium in graphite; 1st cycle, Carbon 45 (2007) 1025–1034. [7] F. Chevallier, M. Letellier, M. Morcrette, J.M. Tarascon, E. Frackowiak, J.N. Rouzaud, F. Beguin, In situ 7Li nuclear magnetic resonance observation of reversible lithium insertion into disordered carbons, Electrochem. Solid State Lett. 6 (2003) A225–A228. [8] H.M. McConnell, R.E. Robertson, Isotropic nuclear resonance shifts, J. Chem. Phys. 29 (1958) 1361–1365. [9] W.C. Dickinson, The time average magnetic field at the nucleus in nuclear magnetic resonance experiments, Phys. Rev. 81 (1951) 717–731. [10] N. Bloembergen, W.C. Dickinson, On the shift of the nuclear magnetic resonance in paramagnetic solutions, Phys. Rev. 79 (1950) 179–180. [11] S.C.K. Chu, Y. Xu, J.A. Balschi, C.S. Springer, Bulk magnetic susceptibility shifts in NMR studies of compartmentalized samples – use of the paramagnetic reagents, Magn. Reson. Med. 13 (1990) 239–262. [12] H.W. Chan, J.G. Duh, S.R. Sheen, LiMn2O4 cathode doped with excess lithium and synthesized by co-precipitation for Li-ion batteries, J. Power Sources 115 (2003) 110–118. [13] Y.J. Lee, C.P. Grey, 6Li magic angle spinning nuclear magnetic resonance study of the cathode materials Li1+aMn2aO4d – the effect of local structure on the electrochemical properties, J. Electrochem. Soc. 149 (2002) A103–A114. [14] V.W.J. Verhoeven, I.M. de Schepper, G. Nachtegaal, A.P.M. Kentgens, E.M. Kelder, J. Schoonman, F.M. Mulder, Lithium dynamics in LiMn2O4 probed directly by two-dimensional 7Li NMR, Phys. Rev. Lett. 86 (2001) 4314–4317. [15] Y.J. Lee, C.P. Grey, Determining the lithium local environments in the lithium manganates LiZn0.5Mn1.5O4 and Li2MnO3 by analysis of the 6Li MAS NMR spinning sideband manifolds, J. Phys. Chem. B 106 (2002) 3576–3582. [16] L.E. Drain, Broadening of magnetic resonance lines due to field inhomogeneities in powdered samples, Proc. Phys. Soc. 80 (1962) 1380–1382. [17] A. Kubo, T.P. Spaniol, T. Terao, THe effect of bulk magnetic susceptibility on solid state NMR spectra of paramagnetic compounds, J. Magn. Reson. 133 (1998) 330–340. [18] U. Schwerk, D. Michel, M. Pruski, Local magnetic field distribution in a polycrystalline sample exposed to a strong magnetic field, J. Magn. Reson., Ser. A 119 (1996) 157–164.

57

[19] D.L. Vanderhart, W.L. Earl, A.N. Garroway, Resolution in 13C NMR of organicsolids using high-power proton decoupling and magic-angle sample spinning, J. Magn. Reson. 44 (1981) 361–401. [20] M. Alla, E. Lippmaa, Resolution limits in magic angle rotation NMR spectra of polycrystalline solids, Chem. Phys. Lett. 87 (1982) 30–33. [21] A. Nayeem, J.P. Yesinowski, Calculation of magic-angle spinning nuclear magnetic resonance spectra of paramagnetic solids, J. Chem. Phys. 89 (1988) 4600–4608. [22] I. Bertini, C. Luchinat, G. Parigi, Magnetic susceptibility in paramagnetic NMR, Prog. Nucl. Magn. Reson. Spectrosc. 40 (2002) 249–273. [23] G.K.G. Pintacuda, Paramagnetic solid-state magic-angle spinning NMR spectroscopy, Top. Curr. Chem. (2012). [24] M. Mehring, Principles of High Resolution NMR in Solids, Springer-verlag, New York, 1983. [25] E. Hartman, An Introduction to Crystal Physics, J.W. Arrowsmith Ltd., Bristol, 1984. [26] Y.J. Lee, F. Wang, C.P. Grey, 6Li and 7Li MAS NMR studies of lithium manganate cathode materials, J. Am. Chem. Soc. 120 (1998) 12601–12613. [27] M.A. Kennedy, P.D. Ellis, The single-crystal NMR experiment: an experimentalist’s guide Part II: data analysis and assignment of symmetryrelated tensors, Concepts Magn. Reson. 1 (1989) 109–209. [28] M.A. Kennedy, P.D. Ellis, The single-crystal NMR experiment: an experimentalist’s guide Part I: experimental aspects and symmetry considerations, Concepts Magn. Reson. 1 (1989) 35–47. [29] R. Ulrich, R.W. Glaser, A.S. Ulrich, Susceptibility corrections in solid state NMR experiments with oriented membrane samples. Part II: Theory, J. Magn. Reson. 164 (2003) 115–127. [30] S. Chandrashekar, N.M. Trease, H.J. Chang, L.S. Du, C.P. Grey, A. Jerschow, 7Li MRI of Li batteries reveals location of microstructural lithium, Nat. Mater. 11 (2012) 311–315. [31] M.M. Thackeray, Manganese oxides for lithium batteries, Prog. Solid State Chem. 25 (1997) 1–71. [32] L. Zhou, M. Leskes, C.P. Grey, in preparation.