An Unexpected Pathway: 6Li-Exchange NMR Spectroscopy Points to

Article pubs.acs.org/JPCC

An Unexpected Pathway: 6Li-Exchange NMR Spectroscopy Points to Vacancy-Driven Out-of-Plane Li-Ion Hopping in Crystalline Li2SnO3 J. Langer,*,† D. L. Smiley,‡ A. D. Bain,‡ G. R. Goward,‡ and M. Wilkening*,† †

Institute for Chemistry and Technology of Materials (NAWI Graz) and DFG Research Unit 127, Graz University of Technology, 8010 Graz, Austria ‡ Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada ABSTRACT: The development and engineering of new materials for modern electrochemical energy-storage systems requires an in-depth understanding of Li-ion dynamics, not only on the macroscopic length scale but also from an atomic-scale point of view. Hence, the study of suitable model systems is indispensable to understand the complexity of nonmodel systems already applied, for example, as active materials in rechargeable batteries. Here, Li2SnO3 served as such a model system to enlighten the elementary steps of ion hopping between the three magnetically distinct Li sites. Through high-resolution 1D and 2D NMR spectroscopies, we probed the favored exchange pathway. Both 1D and 2D NMR spectroscopies point to nonuniform ion dynamics and two independent exchange processes perpendicular to the ab plane, namely, between the sites 4e [Li(3)] and 8f [Li(1)] and between 4e and 4d [Li(2)]. 6Li selectiveinversion NMR spectroscopy confirmed extremely slow Li exchange and yielded hopping rates on the order of 3 s−1 for 4e−8f and 0.7 s−1 for 4e−4d. Altogether, the findings provide evidence for a three-site, two-exchange model describing Li hopping along the c axis rather than in the Li-rich ab plane as one would expect at first glance. This unexpected result can, however, be understood when the site preference of Li vacancies is considered. Recent theoretical calculations predicted the preferred formation of Li vacancies at the Li(3) sites. This allows for localized Li-ion exchange involving Li(3), thus, perfectly corroborating the present findings obtained by 6Li MAS NMR spectroscopy.

1. INTRODUCTION

In particular, the study of diffusion mechanisms also includes the investigation of extremely slow ion dynamics by exchange spectroscopy and stimulated-echo NMR spectroscopy, for instance.10,12,22 Considering recent studies on this topic, Liion dynamics has already been studied for Li2TiO3 and Li2ZrO3 by both 6Li and 7Li NMR spectroscopies, as well as broadband conductivity spectroscopy (CS).23−27 These materials are structurally similar to Li2SnO3, as they all crystallize in the same monoclinic space group C2/c, i.e., that is, in a pseudoNaCl-type lattice (see Figure 1).28,29 In Li2ZrO3, there are two crystallographically inequivalent Li positions, whereas the βmodification of Li2TiO3 shows three distinct Li sites, as does Li2SnO3. So far, the corresponding three Li NMR lines have not been resolved by NMR spectroscopy. In a recent study by Salager et al. focusing on Li2Ru1−ySnyO3-type positive electrode materials, the 7Li magic-angle-spinning (MAS) NMR spectrum of the end member Li2SnO3, which was recorded at 17.6 T, showed two sharp signals with relative intensities of 28% and 72%; the latter was anticipated to be composed of two NMR lines with very similar chemical shifts.30 The Li jump rates measured for the analogous compounds Li2ZrO3 and the Li2TiO3 are very low; values are on the order

The study of Li-ion dynamics is of fundamental interest in the various subdisciplines of materials research. Aside from hydrogen, Li+ is the lightest and, thus, most mobile cation. Fast Li-ion conductors are of particular interest in Li-based energy-storage systems such as rechargeable Li-ion batteries, solid-state lithium batteries, and lithium−oxygen or lithium− sulfur batteries.1−6 On the other hand, slow ion conductors are needed, for example, in semiconductor or nuclear fusion research, where lithium metalates, such as Li2TiO3, Li2ZrO3, and Li2SnO3, serve as promising candidates to realize suitable blanket materials:7,8 Li is involved in the capture of neutrons and tritium breeding, as the tritium effusion rate is linked to Liion diffusion.9 From a fundamental point of view, it is necessary to gain a profound picture of the underlying Li-ion exchange mechanism to purposefully develop new Li-ion conductors.5,10−12 Understanding diffusion dynamics requires not only that macroscopic properties be studied but also that the mechanism behind longrange ion transport be revealed, that is, that the key elementary steps of Li+ hopping be identified.12−15 In ideal cases, these steps can be probed in great detail by nuclear magnetic resonance (NMR) spectroscopy, which offers a large portfolio of techniques that are able to measure (bulk) jump rates covering broad time and length scales.10,15−21 © 2015 American Chemical Society

Received: October 9, 2015 Revised: December 7, 2015 Published: December 18, 2015 3130

DOI: 10.1021/acs.jpcc.5b09894 J. Phys. Chem. C 2016, 120, 3130−3138

Article

The Journal of Physical Chemistry C

Figure 1. (a) Crystal structure of monoclinic Li2SnO3 (C2/c). In panel b, the three distinct Li sites and the two magnetically inequivalent Sn sites are highlighted. Pure Li layers constituted by Li(1) on 8f and Li(2) on 4d sites alternate with LiSn2 layers, where Li(3), along with Sn(1) and Sn(2) ions are located on 4e sites. Li and Sn atoms are octahedrally coordinated by oxygen (cf. panels a and b). The LiO6 polyhedra share common edges and build a 3D network for Li+ self-diffusion. Li ions can hop between the regularly occupied positions through the empty tetrahedral sites T1, T2, and T3 (see panel b); see text for further discussion of the possible Li hopping pathways that differ in terms of the size of the tetrahedral sites and the repulsive interactions with neighboring SnO6 octahedra.

of 60 jumps per hour for the metazirconate27 (310 K) and approximately 60 jumps per second for the metatitanate24 (350 K). Li-ion exchange in Li2TiO3 is anticipated to occur in the ab plane and along the c axis, provided suitable nearby vacancies are available.23,24 Slow, long-range Li diffusion processes were investigated by Ruprecht et al. by CS and 7Li spin-alignment echo NMR spectroscopy; depending on the length scale used to acquire the data, activation energies of ca. 0.8 and 0.47 eV, respectively, were obtained.23 Despite the prior investigations on lithium metalates, there is, so far, no detailed picture of Li-ion motion or of the preferred Li+ diffusion pathways in Li2SnO3. Site-specific Li+ hopping can be made visible through 1D and 2D 6Li MAS NMR exchange spectroscopy (EXSY).31−35 To obtain quantitative results regarding exchange rates and local energy barriers, this often results in extremely time-consuming measurements lasting many days or even weeks. In particular, this is the case when diamagnetic materials with very long longitudinal NMR relaxation rates have to be studied.27 Therefore, as an alternative, 1D selective-inversion NMR spectroscopy provides a more time-saving means to collect information on Li-ion exchange processes.36−38 Here, in combination with 1D and 2D 6 Li NMR experiments, 1D selective-inversion NMR spectroscopy greatly helped in elucidating the ion dynamics in polycrystalline Li2SnO3. By using MAS NMR spectroscopy at high spinning speeds, we were able to resolve the three magnetically inequivalent sites in the oxide and, in the absence of Li motion, to accurately determine the individual site occupancies. Our 2D MAS NMR EXSY experiments shed light on the nature of the relevant (local) Li-ion exchange processes; the data obtained provided a valuable basis for the more complete analysis through 1D (shaped-pulse) selectiveinversion NMR spectroscopy, which is presented in the last section of this article.

2. EXPERIMENTAL SECTION Sample Preparation and Characterization. Li2SnO3 was prepared by the mechanochemical treatment of stoichiometric amounts of SnO2 and Li2CO3 through a conventional solidstate reaction route.39 In the first step, the powders were ground at 600 rpm for 15 h in a high-energy planetary ball mill (Fritsch Pulverisette 7, premium line). The mixture was then calcined at 1073 K for 6 h. Afterward, the powder was pressed into pellets and then sintered for 12 h at 1273 K in air, yielding transparent crystallites. Phase analysis of the powder by X-ray diffraction (XRD) was carried out on a Bruker D8 Advance diffractometer with the Bragg−Brentano geometry using Cu Kα radiation. 1D NMR/2D NMR EXSY. Variable-temperature 6Li 1D and 2D MAS NMR spectra were recorded on a 500-MHz Avance III solid-state NMR spectrometer connected to a cryomagnet with a nominal field of 11.7 T, which corresponds to a 6Li resonance frequency of ν0 = 74 MHz. A standard Bruker 2.5mm H/X probe was used; the rotation frequency was 30 kHz. Cooling of the sample was achieved through the evaporation of liquid nitrogen by means of a heat-exchange coil. The 1D NMR spectra were recorded in a single-pulse excitation experiment; they were referenced to solid lithium acetate (δ = −0.1 ppm) serving as a secondary reference. The primary reference was a 1 M aqueous solution of lithium chloride (δ = 0 ppm). Typically, a solid pulse of 3.2-μs length and recycle delays between 360 and 3600 s were used to ensure full longitudinal relaxation. In all experiments, temperatures were calibrated using the 79Br resonance in KBr as a chemical shift thermometer.40 119 Sn spectra were acquired at room temperature using a 900MHz high-performance Bruker Avance II spectrometer with a nominal field of 21.1 T (ν0 = 336 MHz). The 1D MAS spectra recorded at ultrahigh magnetic field were acquired in a onepulse experiment employing a pulse length of 3 μs and a recycle delay of 60 s. Experiments were carried out at various spinning rates, namely, 0, 3, 5, 10, 20, and 30 kHz; the corresponding 3131


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Figure 2. (a) Powder XRD pattern of Li2SnO3 after annealing at 1273 K (shown in black). Reflections marked with dots can be assigned to a small amount of (Li-free) SnO2. The Li2SnO3 reference (ICSD-35235) is shown in red. (b) Corresponding 6Li MAS NMR spectrum (B0 = 11.7 T). To avoid the effect of Li exchange on the three lines observed, the spectrum was recorded at sufficiently low T (i.e., at 285 K).

Figure 3. 119Sn NMR spectra (ν0 = 336 MHz) of HT-Li2SnO3 recorded at different MAS frequencies (3−30 kHz) and an ultrahigh magnetic field B0 of 21.1 T. Asterisks denote spinning sidebands. For comparison, the static NMR spectrum is also shown.

much larger than the time period determined by tm, that is, T1 ≫ τ, a saturation comb, consisting of up to 16 closely spaced 90° pulses, was used, allowing relaxation delays shorter than 5T1. 1D Selective-Inversion NMR Spectroscopy. One-dimensional selective-inversion experiments under MAS conditions were also performed on a Bruker Avance III spectrometer operating at a 6Li Larmor frequency of 74 MHz; the rotational speed was 30 kHz. A Bruker 2.5-mm triple-resonance probe was used in all experiments. Cooling of the sample was achieved by fresh evaporation of liquid nitrogen using a heatexchange coil. The 1D NMR spectra were obtained using a one-pulse experiment with a (90°) solid pulse of 5 μs and recycle delays ranging from 160 to 300 s; the spectra were referenced to a solution of 1 M 6Li-enriched LiCl (δ = 0 ppm).

spectra were referenced to solid SrSnO3, which resonates at −640 ppm.41 The spinning sideband manifolds were analyzed with the DMFit software42 to determine chemical shift anisotropy (CSA) parameters. A nuclear Overhauser enhancement spectroscopy (NOESY) pulse sequence was employed to record the 6Li 2D NMR spectra at mixing times (tm) of 0.1 and 1 s. The sample was spun at an MAS speed of 30 kHz using ambient bearing gas. For the spectrum with tm = 1 s, we employed time domains (TDs) of 128 data points (dp’s) in the F1 direction and 1024 points in the F2 direction. The 2D NMR spectrum at tm = 0.1 s was recorded with TD(F1) = 32 dp and TD(F2) = 512 dp. Acquisition of the spectra was performed in both experiments using dwell times of 250 μs, a recycle delay of 120 s, and 32 scans. Because the NMR spin−lattice relaxation time T1 is 3132


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Variable-Temperature 1D 6Li MAS NMR Spectroscopy. The structure of Li2SnO3 provides three crystallographically and, thus, magnetically inequivalent Li sites that are each characterized by site-specific NMR chemical shift values. The random distribution of Li and Sn cations might lead to a distribution of chemical shifts according to the small variations of local structures. All three Li sites have octahedral coordination where Li(1)O6 and Li(2)O6, connected by sharing common edges (see Figure 1), have very similar nearest-neighbor distances. Therefore, they are expected to exhibit very similar 6Li NMR chemical shifts. Indeed, the 1D 6Li MAS NMR spectrum recorded at 11.7 T and sufficiently low T (see Figures 2 and 4) is composed

6

Li NMR selective-inversion recovery spectra were acquired using a 180°−τmix−90° sequence, where the long, soft 180° Gaussian-shaped pulse43 was 25 ms in length with a soft pulse power of 0.0154 W. The mixing time, τmix, was varied across a series of experiments; it was chosen to range from 0.05 μs to 100 s. A hard 5-μs pulse was used to acquire the final signal. Temperatures were calibrated with Sm2Sn2O7 as described elsewhere.44 Deconvolution and integration of the pseudo-2D data sets was done with a Mathematica notebook developed by D. Brouwer (Redeemer University, Ancaster, Ontario, Canada). Each integral was normalized to the integration value of the slice collected at the longest mixing time for the inverted site. The data were analyzed using the CIFIT program developed by Bain and Cramer.45 The program uses the observed areas for all sites in the NMR spectrum as a function of mixing time to determine a set of parameters: lithium-ion jump rates (k), spin−lattice relaxation times (T1) in the absence of chemical exchange, and the difference in magnetization between initial [Mi(0)] and equilibrium [Mi(∞)] conditions. CIFIT utilizes a rate matrix that describes the relaxation of spins under the influence of chemical exchange, as described in greater detail elsewhere.45,46 The program adjusts the free parameters using a Levenberg−Marquardt algorithm until the sum of the squares of the differences between the experimental and calculated data is minimized.

3. RESULTS AND DISCUSSION Structural Characterization by XRD and 6Li NMR Spectroscopy. According to the structure refinement of Hodeau et al.,29 Li2SnO3 crystallizes with a distorted NaCl-type structure having monoclinic symmetry (C2/c). Oxygen forms a distorted cubic close-packed network where fully occupied Li layers with Li(1) and Li(2) in 8f and 4d position alternate with LiSn2 layers. In these layers, the Li ions Li(3) and the two crystallograhically inequivalent Sn ions, Sn(1) and Sn(2), share the octahedral 4e position (see Figure 1). It is known that the layers can show complex stacking disorder along the c axis.28,29,47 At temperatures equal to or higher than 1273 K, a high-T (HT) phase of Li2SnO3 forms. The corresponding powder XRD pattern is used as a reference, which is compared with our sample in Figure 2. Because we observed additional line broadening of the XRD reflections, we cannot rule out some stacking faults along the c axis.47 According to the crystal structure of Li2SnO3, there should be two slightly different crystallographic positions for Sn (cf. Figure 1); the two Sn ions share the 4e position but differ in lattice parameters y/b and z/c. Even by the use of high-field 119 Sn MAS NMR spectroscopy at 21.1 T, however, we were not able to resolve the two lines. Instead, a single resonance, as can be seen in Figure 3, was observed even when we increased the spinning frequency to 30 kHz. Nevertheless, by recording 119Sn NMR spectra at various spinning speeds, we were able to gain information on the (average) local tin environment, which is reflected by simulating the isotropic chemical shift δiso, the anisotropy ηCS, and the axiality Δ (i.e., the “reduced anisotropy”) of the chemical shift anisotropy (CSA) tensor. The latter is defined by the relation Δ = δzz − δiso. The anisotropy parameter indicates by how much the line shape deviates from that of an axially symmetric tensor. In Figure 3, our static 119Sn NMR spectrum is characterized by ηCS = 0.36; Δ lies between 44.7 and 47.5 ppm. The 119Sn NMR spectra recorded at high spinning speeds point to δiso = −445 ppm.

Figure 4. Evolution of the 6Li MAS NMR spectrum (ν0 = 74 MHz) of Li2SnO3 with increasing temperature. Areas of the Li(3)A, Li(2)B, and Li(1)C NMR lines corresponding to the spectrum recorded at 285 K are illustrated at the bottom. The triangles indicate the effect of coalescence due to Li(3)−Li(1) exchange. See text for further discussion.

of three well-resolved lines labeled as Li(3)A, Li(2)B, and Li(1)C. In earlier studies, it was not possible to resolve three NMR lines corresponding to the different Li environments.30 In accordance with a CASTEP simulation of chemical shift parameters, signal Li(3)A (0.51 ppm, 285 K) is assigned to Li(3), whereas the crystallograhically more similar sites Li(2) and Li(1) appear at chemical shift values of −0.48 and −0.63 ppm (285 K). In Li2SnO3 with ideal stoichiometry, Li(1) constitutes 50% of the total number of Li ions present, and 25% are distributed each among the Li(2) and Li(3) sites. In fact, at 3133


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Figure 5. 2D 6Li NMR exchange spectra (ν0 = 74 MHz, T = 323 K) recorded at two different mixing times tm: (a) 0.1 and (b) 1 s. Off-diagonal cross-signals (in red) indicate Li-ion hopping perpendicular to the ab plane in Li2SnO3. In-plane exchange through Li(1) and Li(2) is hardly seen because of the small spectral distance of the corresponding NMR lines, which is only 0.15 ppm (11 Hz) at 285 K (see Figure 2).

Sn layer. Before we discuss the relevant hopping pathways that connect the three Li sites through the various tetrahedral voids in Li2SnO3 (see Figure 1), we should take a closer look at the evolution of the 1D spectra with temperature, that is, the coalescence of the NMR lines. The position of the line affected by coalescence is directly linked to the occupancies of the sites involved. As the population of Li(1) is double that of Li(2) and Li(3), it is shifted toward signal Li(1)C, that is, negative part-per-million values. The shift of the resulting line assuming full coalescence can be calculated according to the expression δcoal = f1δ1 + f 2δ2 + f 3δ3, where f1−f 3 represent the individual (normalized) populations ( f1 + f 2 + f 3 = 1) and δ1−δ3 are the corresponding site-specific chemical shifts unaffected by any exchange processes. Fast exchange among all three sites would result in δcoal = −0.31 ppm. From our 1D spectrum, we find δcoal,exp = −0.19 ppm (348 K). This value would be in good agreement with a calculated value of δcoal = −0.15 ppm obtained if one assumes that Li-ion exchange is mainly between Li(1) and Li(3). Interestingly, the resonance lines do not fully coalesce even if the temperature is raised to 348 K. The fact that coalescence of the NMR lines covers a broad temperature range might be interpreted as heterogeneous Li-ion dynamics in Li2SnO3, controlled by the low number density of vacant Li sites present. For some of the Li ions, a spatially heterogeneous distribution of Li vacancies might result in a limited capability to jump between next neighboring sites; efficient exchange is possible only in those regions with a sufficiently large number of vacancies accumulated. Because we deal with a sample consisting of micrometer-sized crystallites, we can rule out the possibility that surface or grain-boundary sites, which lack suitable neighbors for direct exchange, are responsible for this

285 K, the ratio of the corresponding areas is 0.93:0.96:2, which is in very good agreement with the distribution expected. As can be easily shown by static, variable-temperature 7Li NMR line-shape studies, at 285 K, which characterizes the rigid-lattice regime, Li-ion diffusivity is extremely slow.48 At such low temperatures, the average Li+ jump rate is much lower than the spectral separation of NMR lines Li(3)A and Li(1)C. For that reason, the 6Li MAS NMR spectrum is unaffected by any Li-ion exchange processes, meaning that the areas under the lines are expected to approximately reflect the populations of the three distinct Li sites. At T = 312 K, a “shoulder” emerges in the 1D 6Li NMR spectrum that is located at ca. −0.2 ppm; it significantly gains in intensity when temperature is increased to 348 K. Simultaneously, the intensities of lines Li(3)A and Li(1)C decrease considerably. Importantly, signal Li(2)B remains almost unaffected by any coalescence as compared to the lines assigned to Li(1) and Li(3). This points toward enhanced Liion exchange between the Li(1) and Li(3) sites. Li(1)−Li(3) exchange means that local Li-ion hopping perpendicular to the ab plane is more frequent as compared to jumping between sites Li(1) and Li(2) (see Figure 1). Because the spectral separation of the Li(1) and Li(3) lines is ca. 84 Hz, we estimate that the corresponding hopping rate of Li(1)−Li(3) exchange is of the same order of magnitude. On the other hand, the Li(2) ions seem to be less involved in Li+ self-diffusivity, at least if one considers the regime of slow ion dynamics. At this stage, any exchange processes between Li(1) and Li(2), or between Li(2) and Li(3), cannot be excluded. The 1D NMR data, however, provide evidence that ion hopping between Li(1) and Li(3) is energetically favored. This is an unexpected result because Li(1) is located in the Li-rich layer and Li(3) is the site that is 6-fold-coordinated by Sn in the Li− 3134


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tetrahedra, which differ in size and the number of Sn atoms in their direct neighborhood, connect the LiO6 octahedra by face sharing. Whereas Li(1)−Li(2) exchange is possible through T3, Li(1) [and Li(2)] ions can reach the Li(3) position through T1 and T2. To understand the Li(1)−Li(3) exchange probed in the present study, either Li(1) or Li(3) should offer an increased probability to accommodate Li vacancies. Indeed, recent calculations by Brant et al. showed that it is energetically favorable to create vacancies at the 4e [Li(3)] sites compared with the 8f [Li(1)] and 4d [Li(2)] sites by 0.1 eV.53 These findings perfectly agree with the Li deficiency, 0.93 instead of 1, found for the Li(3) and Li(2) sites as reflected by the ratio of the corresponding areas in the 1D NMR spectrum recorded at 285 K (vide supra). Thus, if we assume a vacant Li(3) site in the honeycomb [SnO3]2− layer, we have to look for a possible Li jump pathway connecting the sites Li(3) and Li(1). Li(1) can leave its position through T2, then entering the Li(3)O6 octahedron perpendicular to the plane defined by the Sn6 hexagon while passing the F2 face with an area of 4.05 Å2 (see Figure 6 and the red arrow shown in Figure 1).

observation; their number density is expected to be too low to explain the observed effect. As discussed below, recent calculations showed that Li vacancies in the bulk form preferably on Li(3) sites. This preference is expected to make out the main hopping exchange process (vide infra). In the extreme, a heterogeneous ion dynamics might be due to a clustering effect of vacancies. Such a behavior could stem from the mechanochemical synthesis procedure where the high mechanical impact forces lead to defect-rich structures.49−52 Even if annealed at high temperatures, at which defects are usually cured, such regions might leave its fingerprints although much less pronouncedin the final crystalline product. Slight deviations from the ideal stoichiometry could greatly influence the dynamic parameters. Partial and very slow Li diffusion was also deduced from results of a combined 6Li and 7Li NMR study on isostructural Li2TiO3.24 Heterogeneous ion dynamics was attributed to a slight deviation in Li stoichiometry sensitively influencing the vacancy concentration. It is worth mentioning that molecular dynamics (MD) simulations have shown that diffusion pathways both in the ab plane and along the c axis are equally probable in Li2TiO3; the exact diffusion properties, however, depend on the location of any Li vacancies formed.24 For the sake of completeness, we could definitely rule out the possibility of structural rearrangements, such as polyhedral distortion or formation of new, even amorphous, phases during our NMR measurements, which were restricted to temperatures well below 400 K. In situ XRD data show no evidence of any reversible or irreversible structural transformation occurring in this temperature range.48 2D 6Li NMR EXSY. To refine the picture seen by 1D MAS NMR spectroscopy, we used 2D NMR EXSY to visualize Li exchange in contour plots. 2D NMR EXSY is perfectly suited to directly study exchange processes through the analysis of crosssignal (off-diagonal) intensities. Off-diagonal intensities in the corresponding contour plots result when jumps between magnetically inequivalent sites occur during the mixing time tm chosen. In perfect agreement with our 6Li 1D NMR spectra, Li exchange between Li(3)A and Li(1)C is clearly seen already at a short mixing time of only 100 μs (see Figure 5). In addition to 6Li NMR spectroscopy, we were able to reveal further crosspeak intensities indicating a second site-exchange process between Li(3)A and Li(2)B. The corresponding signal was even more pronounced when a mixing time of 1 s was applied. This definitely confirms that the exchange rate associated is much lower. Because the Li(2)B and Li(1)C signals are close to each other on the part-per-million scale (δ2 = −0.48 ppm, δ1 = −0.63 ppm,), signal overlapping masks Li-ion exchange between the neighboring Li(2) and Li(1) sites in the Li-rich layer. The fact that no coalescence of the Li(2)B and Li(1)C lines is seen points to a very slow diffusion process as compared to Li(3)−Li(1) and Li(3)−Li(2). In summary, 2D EXSY nicely corroborates the findings from 1D NMR spectroscopy; furthermore, it definitely refines the picture derived from the line-shape analyses by revealing that overall coalescence is due to two individual two-site hopping processes whereby the Li(3)−Li(1) exchange is faster than that describing hopping between Li(3) and Li(2). The site preferences of local Li-ion hopping, as derived from 2D NMR EXSY, can be understood by considering the crystal structure and local environment of the three Li sites: Exchange between filled and vacant sites is possible through several tetrahedral sites, labeled T1, T2, and T3 in Figure 1. The

Figure 6. Li-ion jump pathways connecting the Li(3) site with sites Li(1) and Li(2) through empty tetrahedral voids in Li2SnO3. Values given denote oxygen−oxygen distances in angstroms. Li(1) and Li(2) can reach the vacant Li(3) site through T2 and T1. The T2 tetrahedron is larger than T1. At the same time, it is less influenced by repulsive interactions with neighboring SnO6 octahedra, which share common faces with T1.

T2 is rather symmetric, with relatively long O−O distances ranging from 3.06 to 3.34 Å. Each empty Li(3) position can be reached through two T2 tetrahedra. Alternatively, Li(1) can use the T1 tetrahedron as another pathway to reach Li(3) through the F1 face (Figure 6). T1 and F1 (3.51 Å2) are smaller, however; the O−O distances of T1 range from 2.73 to 3.06 Å. Additionally, T1 shares two faces with SnO6 octahedra (Figure 6). Thus, repulsive Li−Sn interactions make this an energetically unfavorable pathway. For Li(2), the same T2 pathway exists; thus, from simple geometric considerations, Li(1)−Li(3) and Li(2)−Li(3) exchanges through T2 seem to represent the most probable local exchange pathways. Li-ion exchange is, however, driven by the existence of Li(3) vacancies in the Snrich layer, assuming that Li(3) vacancies are in line with the NMR results from our 1D and 2D experiments. As pointed out 3135


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visualize the data, we have plotted the time axis of Figure 7 on a logarithmic scale. The magnetization buildup curve of signal Li(3)A clearly shows that the return to equilibrium is governed by longitudinal relaxation. For transient Li(1)C, we found a pronounced attenuation of the magnetization due to ion hopping between sites Li(3)A and Li(1)C. Interestingly, for Li(2)B, we observed only a small change in the magnetization transient, indicating slower cation exchange between the Li(3)A and Li(2)B sites. Note that, at 285 K, no coalescence of the three NMR lines was observed (vide supra), and the inversion of signal Li(3)A was experimentally reasonable. With increasing T, however, coalescence effects make it difficult to precisely monitor the areas under the resonances as a function of mixing time tm. Hence, we were limited to a quite narrow temperature range that did not allow for reliable T-dependent measurements to extract an activation energy. These are much more accessible by time-domain NMR methods.48 At 285 K, however, we could extract some quantitative information on the jump processes. The corresponding exchange rates were found to be k3−1 = 3 s−1 (4e−8f) and k3−2 = 0.7 s−1 (4e−4d). As expected, the exchange rates at 285 K are much lower than 84 Hz as estimated from our 1D 6Li NMR spectra discussed above. In good agreement with 2D NMR EXSY, the Li(3)−Li(1) exchange process is the dominant one, whereas hopping between Li(3) and Li(2) is indeed characterized by a lower rate. As with 2D NMR EXSY, ion hopping in the 2D plane between neighboring Li(2) and Li(1) sites cannot be ruled out, although it could not be resolved in the selective-inversion experiments carried out. The absence of significant coalescence in 1D 6Li NMR spectroscopy, however, indicates that in-plane Li exchange is less frequent than out-of-plane hopping. Obviously, the latter is driven by vacant Li(3) sites in Li2SnO3, making the hopping pathway including the T2 tetrahedra the preferred pathway, as is illustrated in Figure 6.

by Brant et al., the preference to form vacancies at the 4e sites changes when going from the oxide to the sulfide, Li2SnS3. In Li2SnS3, vacancies at 8f and 4d are more stable by −0.3 eV.53 Obviously, in Li2SnO3, the Li(3) position is prone to accommodate Li vacancies, resulting in Li exchange perpendicular to the ab plane whereas in-plane Li(1)−Li(2) exchange is much less frequent. This observation is at least valid for the regime of ultraslow Li hopping, i.e., temperatures below 330 K. 1D Selective-Inversion 6Li MAS NMR Spectroscopy. Slow chemical exchange processes, relative to (longitudinal) spin−lattice relaxation, can also be studied with the help of 1D selective-inversion MAS NMR spectroscopy.36−38,54 Through selective-inversion measurements, we tried to quantify the Li(1)−Li(3) and Li(2)−Li(3) exchanges made visible by 2D NMR EXSY. Following the selective inversion of the magnetization of the Li spins at a particular site, the return to the condition of thermal equilibrium is monitored as a function of a variable delay time. Signal recovery is governed by (i) the ion exchange rate with the noninverted spins and (ii) the inherent spin−lattice relaxation governed by the rate 1/T1. The magnetization buildup changes as a function of temperature and, thus, provides a mean to determine ion hopping rates and activation energies. Additionally, 1/T1 rates are measured independently and are included in the fitting procedure. In the present study, we looked at two individual Li jump processes between three sites using the CIFIT program45,46 to analyze the experimental 6Li NMR data. Whereas the Li(3)A signal can be selectively inverted with a long, soft Gaussianshaped pulse, the Li(2)B and Li(1)C lines cannot be inverted individually. The two lines are separated by only 0.15 ppm, which leads to significant overlapping of the resonances. Upon inversion of site Li(3)A, the transient magnetizations of sites Li(2)B and Li(1)C are plotted in Figure 7. The curves were used to extract the Li(3)A−Li(2)B and Li(3)A−Li(1)C rate constants. Importantly, the depth of the transient well increases when exchange with the inverted site becomes more rapid before any 6 Li NMR spin−lattice relaxation processes take over. To better

4. SUMMARY AND CONCLUSIONS Lithium stannate, Li2SnO3, serves as a useful model compound for studying slow Li+ exchange processes in a complex oxide with three magnetically distinct Li sites. Whereas recent 7Li MAS studies on this material revealed a spectrum composed of only two contributions,30 in our study, the three sites could be clearly resolved by the use of 1D/2D 6Li MAS NMR spectroscopy, although the corresponding chemical shift values span only a very narrow range of less than 1.5 ppm; signals Li(2) and Li(3) are separated by only 0.15 ppm, that is, 11 Hz on the frequency scale. Slow Li-ion exchange in Li2SnO3 occurs between the pure Li layer and the LiSn2 layer, ultimately culminating in a coalescence of the 6Li NMR resonance signals involved. The variable-temperature 6Li NMR spectra recorded point to heterogeneous ion dynamics. This might be related to the small number fraction of Li ions present that could strongly affect ultraslow Li+ exchange processes governing translational ion dynamics at low temperatures. Although the sample was annealed at high temperatures, one might think of an inhomogeneous distribution of vacancies that partly remained even after the final calcination step. Note that the present sample was prepared by mechanical pretreatment in a highenergy planetary mill combined with subsequent annealing at 1073 and 1273 K. The history of the sample, which directly affects the defect chemistry stored, might crucially determine both short-range and long-range Li-ion dynamics. In the

Figure 7. Results from 1D selective-inversion 6Li MAS NMR analysis (ν0 = 74 MHz): Transient curves of the inverted [Li(3)A] and noninverted [Li(2)B and Li(1)C] sites following a selective inversion of resonance Li(3)A at 285 K. For reasons of better visibility, the x coordinate is plotted on a logarithmic scale. The solid lines show the results of the fitting procedure using the CIFIT program. 3136


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The Journal of Physical Chemistry C present case, 1D 6Li MAS NMR spectroscopy provides evidence for a Li deficiency in the Li(3) sites, as is also predicted by theory.48 In detail, combined time-dependent 2D 6Li NMR EXSY and 1D 6Li NMR selective-inversion experiments point toward a three-site, two-fold exchange mechanism [Li(1)−Li(3), Li(2)− Li(3)] that governs Li+ exchange at low temperatures. So far, we have not been able to identify the third exchange process between neighboring sites Li(2) and Li(1) within the ab plane. Off-diagonal intensities in the 2D spectra clearly show that Li+ hopping between sites Li(3) and Li(1) is faster than cation exchange between positions Li(3) and Li(2). Our selectiveinversion recovery experiments recorded at 285 K clearly support this view and yield ion hopping rates on the order of k3−1 = 3 s−1 for Li(3)−Li(1) and k3−2 = 0.7 s−1 for Li(3)−Li(2). This points to slow Li-ion diffusion perpendicular to the ab plane, which is in agreement with recent calculations predicting Li vacancies to be formed preferably on the Li(3) sites in the [SnO3]2− honeycomb-like layers. Preliminary conductivity measurements on Li2SnO3 corroborate the extremely slow Liion dynamics as seen by high-resolution 6Li NMR spectroscopy.48

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.L. is grateful to V. Terskikh for numerous helpful discussions. J.L. and M.W. thank the DFG Research Unit 1277 (Grant WI3600 4-2) for financial support. Access to the 21.1 T NMR spectrometer was provided by the National Ultrahigh-Field NMR Facility for Solids (Ottawa, Canada), a national research facility funded by a consortium of Canadian universities, supported by the National Research Council Canada and Bruker BioSpin, and managed by the University of Ottawa (http://nmr900.ca).

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