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. 2022 Dec 16;35(1):27–40. doi: 10.1021/acs.chemmater.2c02101

Toward Understanding of the Li-Ion Migration Pathways in the Lithium Aluminum Sulfides Li3AlS3 and Li4.3AlS3.3Cl0.7 via 6,7Li Solid-State Nuclear Magnetic Resonance Spectroscopy

Benjamin B Duff †,‡, Stuart J Elliott †, Jacinthe Gamon †, Luke M Daniels †, Matthew J Rosseinsky †,§, Frédéric Blanc †,‡,§,*
PMCID: PMC9835825  PMID: 36644214

Abstract

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Li-containing materials providing fast ion transport pathways are fundamental in Li solid electrolytes and the future of all-solid-state batteries. Understanding these pathways, which usually benefit from structural disorder and cation/anion substitution, is paramount for further developments in next-generation Li solid electrolytes. Here, we exploit a range of variable temperature 6Li and 7Li nuclear magnetic resonance approaches to determine Li-ion mobility pathways, quantify Li-ion jump rates, and subsequently identify the limiting factors for Li-ion diffusion in Li3AlS3 and chlorine-doped analogue Li4.3AlS3.3Cl0.7. Static 7Li NMR line narrowing spectra of Li3AlS3 show the existence of both mobile and immobile Li ions, with the latter limiting long-range translational ion diffusion, while in Li4.3AlS3.3Cl0.7, a single type of fast-moving ion is present and responsible for the higher conductivity of this phase. 6Li–6Li exchange spectroscopy spectra of Li3AlS3 reveal that the slower moving ions hop between non-equivalent Li positions in different structural layers. The absence of the immobile ions in Li4.3AlS3.3Cl0.7, as revealed from 7Li line narrowing experiments, suggests an increased rate of ion exchange between the layers in this phase compared with Li3AlS3. Detailed analysis of spin–lattice relaxation data allows extraction of Li-ion jump rates that are significantly increased for the doped material and identify Li mobility pathways in both materials to be three-dimensional. The identification of factors limiting long-range translational Li diffusion and understanding the effects of structural modification (such as anion substitution) on Li-ion mobility provide a framework for the further development of more highly conductive Li solid electrolytes.

Introduction

In recent years, significant progress has been made in the advancement of next-generation energy storage materials, particularly the implementation of solid-state electrolytes (SSEs) for the production of all-solid-state batteries (ASSBs).1,2 Current generation lithium-ion batteries with liquid electrolytes composed of a Li salt in a solvent offer high performance arising from high ionic conductivity and excellent wetting of the electrode surfaces.3 Adversely, liquid electrolytes contain highly volatile and flammable organic solvents which present safety issues.4 By comparison, the application of an SSE mitigates this safety concern and is further coupled with an increased energy density.5 However, overcoming the intrinsically lower ionic conductivity of solids compared with liquids as well as meeting the requirement for electrochemical stability versus electrodes remains a substantial challenge in the deployment of ASSBs.6,7

A room-temperature lithium conductivity target of 10–3 S cm–1 has been set for SSEs6,8 based on the conductivities of current generation liquid electrolytes and has now been met in several different families of materials, including garnets (Li6.65Ga0.15La3Zr1.9Sc0.1O12),9 glass–ceramics (Li2S–P2S5),10 thio-LISICONs (Li9.54Si1.74P1.44S11.7Cl0.3),11 halide-based SSEs (Li3YBr6),12 and argyrodites (Li6.6Si0.6Sb0.4S5I).13 Nevertheless, these materials still suffer from limitations such as one or more of the following: air and moisture sensitivity, high production costs, and poor compatibility with electrode materials. New high-performance materials can be discovered by deploying design rules developed by understanding the mechanisms of lithium ionic conduction and the limiting factors to diffusion processes in solid-state electrolytes.14

Higher-symmetry structures with mixed site occupancy have been shown to lead to significant improvements in ionic conductivity, the reason for which remains somewhat uncertain.15,16 Anion substitution in order to produce mixed anion materials has been commonly utilized in solid-state chemistry to achieve improved electrolyte stability against electrodes. In particular, halides present the advantage of being highly stable against Li metal with increased conductivities compared to pure sulfide analogues and comparatively higher oxidation potentials leading to a lower likelihood of halide oxidation.2,11 Moreover, as halide anions have a lower charge compared to sulfide anions, halide–sulfide substitution enables cation off-stoichiometry, which is favorable for conductivity. In particular, the Cl– anion, which has a similar ionic radius to S2– (167 and 170 pm, respectively),20 favors mixed occupancy on the anionic sites and hence disorder, leading to increased performance as shown in disordered argyrodites17 and the previously mentioned Li9.54Si1.74P1.44S11.7Cl0.3.11

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an extremely powerful tool for the investigation of disordered materials as unlike diffraction-based methods, the technique does not depend on long-range structural order.18 NMR is widely used for structural determination purposes18 yet can also be very effectively employed for the assessment of ion dynamics and diffusion processes,19 complementing, for example, conductivity measurements from AC impedance spectroscopy (ACIS)20 or Muon spectroscopy.21 In particular, NMR spectroscopy offers a direct, non-destructive method to probe the mobility of Li+ specifically22−26 because of its unique inherent isotope specificity exploiting both NMR-active isotopes of lithium (6Li, 7.59% natural abundance, spin I = 1 and 7Li, 92.41%, I = 3/2) while also being suitable for powdered samples. The key to the study of dynamics by NMR lies in the wide range of timescales that can be accessed. These range from very fast motional processes in the order of 10–12 s–1 probed by measuring spin–lattice relaxation (SLR) time constants to much slower motion on the timescale of 10–3 s–1 from line shape analysis or s–1 in exchange spectroscopy (EXSY). NMR also allows for the extraction of site-selective dynamics information which is highly complementary to the mean structure with average occupancies of particular sites accessible by diffraction-based methods.

Static 7Li variable temperature (VT) NMR has been widely used to probe lithium-ion dynamics in ionic conductors, allowing for extraction of activation energies (Ea) and correlation rates (τc–1) of the Li-ion jump processes (τc–1 is essentially the jump rate τ–1).227Li VT NMR spectra can also provide qualitative insights into ion mobility in solids by identifying the sites contributing to long-range ion mobility and the pathways involved. For instance, a number of previous works27−29 have shown that static VT NMR spectra can support the presence of both mobile and immobile ions on the NMR timescale, which is evidenced by the superposition of resonances with different linewidths from ions moving at different rates. VT diffusion-induced 7Li NMR SLR rate constants in both the laboratory (T1–1) and rotating (T1ρ–1) frames allow access to quantitative information on the Li diffusion process. Additionally, the dimensionality of Li-ion mobility within the material can be extracted from the frequency dependence of the SLR rate constants as initially postulated based on theoretical calculations30 and recent experimental verification for Li12Si7.31 Two-dimensional (2D) EXSY NMR experiments are a powerful method for investigating chemical exchange in ionic conductors and allow for both qualitative observation of which inequivalent sites are involved in the ionic exchange and quantitative extraction of site-specific jump rates.32−35

Recently, we discovered two lithium aluminum sulfide phases, Li3AlS336 and Li4.3AlS3.3Cl0.7,37 through a computational approach involving the screening and identification of new materials in the Li–Al–S phase field. We utilized 6Li magic angle spinning (MAS) and 27Al (I = 5/2) multiple quantum MAS (MQMAS) NMR for structure determination. Here, we expand on this work by reporting a comprehensive understanding of the lithium-ion dynamics of these phases from 7Li line narrowing, relaxation, EXSY data, and site-specific 6Li exchange. The results identify the limiting factors for Li-ion mobility in Li3AlS3 and rationalize the increased ion mobility observed in the Li4.3AlS3.3Cl0.7 disordered mixed anion structure.

Experimental Section

Li3AlS336 and Li4.3AlS3.3Cl0.737 at natural abundance were synthesized according to reported solid-state synthesis procedures. 6Li-enriched Li3AlS3 and Li4.3AlS3.3Cl0.7 were prepared using the same procedure with 6Li-enriched Li2S (prepared from 95% 6Li-enriched Li2CO3,16 CortecNet, 99.7% purity) as the lithium precursor. Routine analysis of phase purity and lattice parameters was performed on a Bruker D8 Advance diffractometer with a monochromated Cu source (Kα1, λ = 1.54060 Å) in powder transmission Debye Scherrer geometry (capillary) with sample rotation. Powder X-ray diffraction patterns of the 6Li-enriched samples are shown in Figure S1 in the Supporting Information (SI) and are in agreement with the literature.36,37

Static 7Li VT NMR experiments were recorded on a 9.4 T Bruker Avance III HD spectrometer equipped with a 4 mm HX high-temperature MAS probe with the X channel tuned to 7Li at ω0/2π(7Li) = 156 MHz. All 7Li one-pulse NMR spectra were obtained with a hard 90° pulse at a radiofrequency (rf) field amplitude of ω1/2π(7Li) = 83 kHz. 7Li quantum-filtered NMR experiments were performed using the multiple-quantum filter pulse sequence π/2−τ1–π–τ1–θ–τ2–θ–acq with suitable phase cycling depending on whether double (θ = 54.7°) or triple (θ = 90°) quantum coherence was targeted for filtration.38−40 Delays τ1 and τ2 were optimized for maximum signal intensity. Hahn-echo experiments were performed using the sequence π/2−τ–π–τ–acq with hard pulses at rf field amplitudes of ω1/2π(7Li) = 83 kHz, with τ delays varied from 9 to 90 μs. All NMR spectra were obtained under quantitative recycle delays of more than 5 times the T1 time constants at each temperature. T1 time constants were measured using the saturation recovery pulse sequence (π/2)×100–τ–π/2–acq with increasing recovery delay values τ. For Li3AlS3, data were fitted with a bi-exponential recovery of the form 1 – a·exp[−(τ/T1,slow)] + b·exp[−(τ/T1,fast)] where T1,slow and T1,fast are the time constants and a and b are the proportional contributions associated with the slow and fast components of the buildup curves, respectively. For Li4.3AlS3.3Cl0.7, data were fitted with a stretch exponential function of the form 1 – exp[−(τ/T1)α] (with α ranging from 0.9 to 1). T1ρ time constants were recorded using a standard spin-lock pulse sequence π/2–spin lock–acq (where the duration of the spin-lock pulse is incremented) at frequencies of ω1/2π(7Li) = 10, 30, and 80 kHz, and the data were fitted to a stretch exponential function of the form exp[−(τ/T1ρ)β] (with β ranging from 0.5 to 1). The stretch exponential was used in order to account for a distribution of τc values, temperature gradients across the sample (see below), and the inherent multi-exponential behavior for relaxation of I = 3/2 nuclei.41−43 Static 7Li NMR line shapes obtained at various temperatures were simulated with the solid line shape analysis tool “Sola” in Topspin to determine the ratio of the two components contributing to the line shapes as well as the quadrupolar coupling constant CQ and the asymmetry parameter ηQ values. All samples for static experiments were flame-sealed in Pyrex inserts under an Ar atmosphere.

6Li MAS NMR experiments were performed on a 9.4 T Bruker DSX spectrometer using a 4 mm HXY MAS probe (in the double-resonance mode) with the X channel tuned to 6Li at ω0/2π(6Li) = 59 MHz. A 90° pulse of duration 3 μs at an rf amplitude of ω1/2π(6Li) = 83 kHz was used. The MAS frequency ωr/2π was set to 10 kHz. 6Li MAS NMR spectra were acquired under quantitative recycle delays of more than 5 times the 6Li T1, measured via the saturation recovery pulse sequence. Static 6Li T1 time constants were also recorded using the same pulse sequence. Additionally, 6Li MAS NMR spectra were also collected on a 20 T Bruker NEO spectrometer using a 3.2 mm HXY probe in double resonance mode, with the X channel tuned to 6Li at ω0/2π(6Li) = 126 MHz and at ωr/2π = 20 kHz with a 90° pulse duration 4.5 μs at an rf amplitude of ω1/2π(6Li) = 56 kHz for Li3AlS3 and a 90° pulse duration of 3 μs at an rf amplitude of ω1/2π(6Li) = 83 kHz for Li4.3AlS3.3Cl0.7.

6Li–6Li EXSY NMR experiments were performed on an 18.8 T Bruker NEO spectrometer equipped with a 1.3 mm HX MAS probe with the X channel tuned to 6Li at ω0/2π(6Li) = 118 MHz and a 90° pulse of duration of 3 μs at an rf amplitude of ω1/2π(6Li) = 83 kHz and under ωr/2π = 15 and 45 kHz. Diagonal and cross peak intensities Id and Ic, respectively, were extracted using TopSpin. The sample temperature increase due to frictional heating at faster MAS frequencies was calibrated via 79Br T1 measurements on the chemical shift thermometer KBr.44

Temperature calibrations of the 9.4 T NMR probes were performed with the chemical shift thermometers Pb(NO3)2 using 207Pb NMR45,46 and CuI and CuBr using 63Cu NMR.47,48 The errors associated with this method were calculated using the line broadening of the isotropic peak and are in the 5–20 K range. The 6Li and 7Li shifts were referenced to 10 M LiCl in D2O.

Results and Discussion

Structural Descriptions

The structure of Li3AlS336 consists of an hcp arrangement of sulfur atoms with an A B A* B* stacking of anion layers, giving rise to the four layer repeat (Figure 1ai) where B is the equivalent of A through the c glide plane and 2-fold axis symmetry operations. A* and B* are the equivalent of A and B through the C centering translation. The two different polyhedral layers are stacked alternately perpendicular to the bc plane (Figure 1a). In the tetrahedral layers (between A and B and between A* and B*), Li1 and Al atoms occupy 2/3 of the tetrahedral interstices between a pair of sulfur atom layers to form edge sharing tetrahedra. Between the second pairs of sulfur layers (between B and A* and between B* and A), Li2 and Li3 occupy octahedral interstices, whereas Li4 occupies a tetrahedral interstice, generating a mixed polyhedral (octahedral–tetrahedral) layer (Li-only layer). In the tetrahedral layer, Al, Li1, and vacancies are ordered in a 1:1:1 arrangement, and 2/3 of the octahedral interstices are occupied in the Li-only layer, resulting in edge sharing Li2 and Li3 octahedra, so that this structure presents a high proportion of ordered vacancies in both the tetrahedral and Li-only layers.

Figure 1.

Figure 1

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Crystal structures of (a) Li3AlS3 and (b) Li4.3AlS3.3Cl0.7 showing the similar hcp arrangement of sulfur atoms and the alternating mixed cation polyhedral layer and Li-only layer stacked perpendicular to the (bc) and (ab) planes in Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively. (i) Layered view, (ii) Li only polyhedral layer, and (iii) mixed cation tetrahedral layer in the (bc) and (ab) planes for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively. In Li3AlS3, the A B A* B* stacking of anion layers leads to a four-layer repeat (A* and B* being the equivalent of A and B through the C centering translation). In Li4.3AlS3.3Cl0.7, only a two-layer repeat occurs with an A B stacking of the anion layers. Blue, orange, and red polyhedra correspond to Al tetrahedra, Li tetrahedra, and Li octahedra, respectively. Gray polyhedra correspond to Li tetrahedra from the mixed cation tetrahedral layer in Li3AlS3 and to mixed Al/Li occupied tetrahedra in Li4.3AlS3.3Cl0.7.

The substitution of Cl onto the hcp sulfur sites in Li3AlS3 gives the new Li4.3AlS3.3Cl0.737 phase (Figure 1b), which retains the hcp arrangement of Li3AlS3, as well as the alternating tetrahedral and Li-only layer, while leading to a strong cation site disorder within the polyhedral interstices, so that Li3AlS3 is a superstructure of Li4.3AlS3.3Cl0.7. In the latter, the anion stacking motif is A B with only a two-layer repeat. Within the tetrahedral layer, lithium (Li1, site occupancy factor: sofLi1 = 0.50(1)) and aluminum (sofAl = 0.25) are disordered among all the tetrahedral interstices. Within the Li-only layer, lithium and vacancies are disordered among all the octahedral (Li3, sofLi3 = 0.644(2)) and tetrahedral (Li2, sofLi2 = 0.260(2)) sites. Li1/Al and Li2 tetrahedra of the adjacent layer share a common base and form a polyhedral unit which can only host one cation. Indeed, the small hypothetical interatomic distances (dAl–Li2 = 1.543(13) Å and dLi1–Li2 = 1.274(14) Å) render the occupation of both the Li1/Al and Li2 sites of the same unit very unlikely. A summary of the various Li interatomic distances is available in Table S1.

Static 7Li VT Line Narrowing NMR

Static 7Li NMR spectra of Li3AlS3 and Li4.3AlS3.3Cl0.7 were collected in the 130–450 K temperature range (Figure 2) to provide information on the Li-ion dynamics on the kHz timescale. At low temperatures (<250 and <200 K for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively), the line shape of the 1/2 ↔ −1/2 central transition strongly suggests that the linewidth is dominated by the strong 7Li–7Li homonuclear dipolar broadening of the 7Li spins with a static 7Li NMR linewidth ω/2π at a half-height of ∼6.7 kHz for Li3AlS3 and ∼7.0 kHz for Li4.3AlS3.3Cl0.7. This broadening is significant given that it is proportional to the square of the gyromagnetic ratio γ of the nuclear spins, which is large for 7Li (γ (7Li) = 16.5 MHz T–1). At these low temperatures, the materials reside in the so-called rigid lattice regime and the corresponding Li+-ion τ–1 values are smaller than ω/2π. As the sample temperature is increased, the central transition linewidths of both phases significantly decrease at the onset temperatures Tonset of motional narrowing, which occur at around 270 and 220 K for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively (Figure 3). This narrowing effect arises from the continuous averaging of the 7Li–7Li homonuclear dipolar coupling due to the increasing motion of the Li+ ions at frequencies larger than ω/2π. Importantly, the significantly lower Tonset observed for Li4.3AlS3.3Cl0.7 versus Li3AlS3 indicates higher Li+-ion mobility in the former phase, supporting the previously reported results obtained via ACIS36,37 where room-temperature conductivity values in the order of 10–6 and 10–9 S cm–1 were extracted for the respective samples.

Figure 2.

Figure 2

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Static 7Li one-pulse NMR spectra of (a) Li3AlS3 and (b) Li4.3AlS3.3Cl0.7 as a function of temperature. The pink line displays a simulation of the static 7Li NMR spectrum of Li4.3AlS3.3Cl0.7 at 450 K using a single set of parameters describing the quadrupolar powder pattern for a spin 3/2 nucleus with a shift δ of 0 ppm, a quadrupolar coupling constant CQ of 30 kHz, and a quadrupolar asymmetry ηQ of 0.1.

Figure 3.

Figure 3

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Representative static 7Li one-pulse NMR spectra of (a) Li3AlS3 and (b) Li4.3AlS3.3Cl0.7 illustrating the broad and motionally narrowed components of the NMR line shape associated with Li-ion diffusion. The experimental spectra (solid lines), total fit (dashed lines), and spectral deconvolution (dotted lines) are shown. (c) Temperature dependence of 7Li NMR linewidth ω(Τ)/2π of Li3AlS3 (black) and Li4.3AlS3.3Cl0.7 (green). In Li3AlS3, the empty and filled squares represent the broad and narrow components of the line shape observed in (a), respectively, while circles for Li4.3AlS3.3Cl0.7 correspond to the total line shape in (b). The onset temperatures of line narrowing Tonset are given with double-length ticks on the upper vertical axis, with dashed lines showing the tangents of the curve used to extract Tonset. The solid black and green lines are fit to the data based on the sigmoidal regression given in eq 2 and are used to determine the inflection points of the respective curves.

Further sample heating above room temperature yields significantly narrower lines with ω/2π on the order of 750 Hz and a multicomponent line shape for Li3AlS3 (see below). This corresponds to τ–1 ≫ ω/2π in the static regime, with 7Li–7Li homonuclear dipolar coupling (fast motional regime) that is largely averaged out, and the residual linewidth is mainly governed by non-homonuclear dipolar interactions and inhomogeneities of the external magnetic field B0.49 The 7Li NMR spectrum of Li4.3AlS3.3Cl0.7 at 450 K displays the typical quadrupolar powder pattern of this spin I = 3/2 nucleus with a quadrupolar tensor in (or close to) axial symmetry, consisting of a central transition at 0 ppm and quadrupolar satellite transitions at approximately ±50 ppm corresponding to a quadrupolar coupling constant CQ of ∼30 kHz (Figure 2b). The axial symmetry suggests that Li+ ions exchange between axially symmetric sites of similar orientation or between sites with different orientations averaging out two of the three components of the quadrupolar tensors. Accessing these orientations is beyond the scope of the work as this would require significant computational work50 capturing the complex site disorder of Li4.3AlS3.3Cl0.7.

Close inspection of the 7Li NMR spectra for Li3AlS3 between 315 and 435 K (Figure 3a for representative spectra in the middle of this temperature range) clearly reveals two contributions to the line shape. This consists of a motionally narrowed line, corresponding to highly mobile Li+ ions (τ–1 < ω/2π), superimposed on a much broader line for slower-moving ions (τ–1 > ω/2π). The two components display significantly different CQ values of 58 and 15 kHz for the broad and narrow components, respectively (Figure S2). It is postulated that this two-component NMR line shape arises from ions moving along the faster diffusion pathways present in the layered structure (see below). At 315 K, approximately 12% of the Li ions present are mobile, with this percentage increasing as a function of temperature (Figure S3). This two-component line shape is not observed in the 7Li NMR spectra of Li4.3AlS3.3Cl0.7 (Figure 3b), which is ascribed to the improved mobility of the Li+ species facilitated by the presence of more favorable ion mobility pathways due to the introduction of disordered vacancies.

In order to confirm the presence of two superimposed quadrupolar line shapes in the 7Li NMR spectra of Li3AlS3, double- and triple-quantum filtration and Hahn-echo experiments were performed (Figure S4). In the double-quantum filtered spectrum, the central transition is suppressed, while the quadrupolar satellites associated with transitions between the ±3/2 <−> ±1/2 energy levels have opposite phases to one another. In Figure S4a, the presence of two sets of satellite peaks with an inverted phase can be seen. In the triple-quantum filtered spectrum, the central transition remains, while the quadrupolar satellites have an inverted phase. The triple-quantum filtered spectrum in Figure S4b displays two sets of satellite transitions with opposite phases to the central transition, with corresponding CQ values matching well the ones obtained from the static 7Li one-pulse spectra obtained at VT (Figure S2). Two static 7Li NMR Hahn-echo experiments with different echo delays (Figure S4c) reveal efficient T2 filtering to observe a line shape dominated by a broad component at a short dephasing time which is then largely removed at a longer dephasing time where the narrower component is isolated.

Using a simple expression introduced by Waugh and Fedin51 correlating Tonset to Ea of the diffusion process

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approximate Ea values of 0.5 and 0.4 eV were estimated for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively, suggesting more favorable local Li+-ion mobility in Li4.3AlS3.3Cl0.7 than in the non-doped parent material as previously indicated. Moreover, the inflection points of the line narrowing curves Tinflection (Figure 3c) define the Li+ τ–1, which is of the order of (ω/2π)rl (linewidth in the rigid lattice regime), and yield comparable values of ∼4.2(3) × 104 s–1 for Li3AlS3 and ∼4.4(4) × 104 s–1 for Li4.3AlS3.3Cl0.7. Tinflection values were determined from fitting the ω/2π data in Figure 3c to a Boltzmann sigmoid regression curve of the form

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where ω(Τ)/2π is the linewidth of the central transition at temperature T, (ω/2π)∞ is the residual linewidth at high temperature in the fast motional regime, and a is a fitting parameter that takes into a account the gradient of the slope. Importantly, the lower Tinflection value obtained for Li4.3AlS3.3Cl0.7 (276(6) K) than for Li3AlS3 (371(9) K) clearly indicates a faster Li+-ion diffusion process in the former phase.

6Li MAS NMR

Figure 4 compares the room-temperature 6Li MAS NMR spectra of Li3AlS336 and Li4.3AlS3.3Cl0.7.37 Li3AlS3 displays resonances at −0.2 ppm attributed to octahedrally coordinated Li2 and Li3 sites, 1.3 ppm for tetrahedral Li4, and 1.7 ppm corresponding to tetrahedral Li1,36 while Li4.3AlS3.3Cl0.7 shows an intense resonance at 1 ppm and a smaller peak at ∼−0.3 ppm assigned to the tetrahedral Li1/Li2 and octahedral Li3 sites, respectively37 (a smaller peak at −1.1 ppm is also visible and corresponds to residual solid LiCl).52 In Li4.3AlS3.3Cl0.7, the main signal at 1 ppm is narrow, with a peak width at a half-height of ω/2π = 50 Hz at room temperature, and suggests the presence of a motionally averaged NMR signal arising from fast Li+ hops between the two tetrahedral Li sites. This is not observed in the 6Li MAS spectrum of Li3AlS3 as Li-ion exchange between non-equivalent Li1–Li4 sites is comparatively slow on the NMR timescale. Reduced motional averaging from decreasing the Li+-ion mobility at 230 K revealed three different Li sites at 1.4, 0.9, and −0.55 ppm in Li4.3AlS3.3Cl0.7 (Figure 4c). These are assigned to tetrahedral Li2 in the Li-only layer (Figure 1b), tetrahedral Li1 in the Li/Al tetrahedral layer, and octahedral Li3 in the Li only polyhedral layer, respectively, based on the semi-empirical correlation between the lithium coordination environment and 6Li NMR shift.53 The higher resonance frequency of Li2 than Li1 arises from the large degree of bond length distortion present at Li1 (3 × 2.392(4), 2.615(6) and 3.625(6) Å), which can be considered pseudo trigonal–bipyramidal as the Li positions are strongly displaced toward one face of the tetrahedron37 and lead to a greater degree of chemical shielding for Li1. Note that the assignment of the tetrahedral sites in Li4.3AlS3.3Cl0.7 is the inverse of the spectral assignments in Li3AlS3 and this is due to the added polyhedral distortion of the Li1 position in the former, compared with the more tetrahedral Li1 in the latter. Note also that the signal intensity of the Li3 site seems to differ from the site occupancy refined against neutron powder diffraction data37 as, at 230 K the 6Li MAS NMR spectrum is in the intermediate motional regime where there is a strong interplay between signal intensity and broadening (see below).

Figure 4.

Figure 4

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6Li MAS one-pulse NMR spectra collected at 9.4 T and ωr/2π = 10 kHz of (a) Li3AlS3 at 294 K and Li4.3AlS3.3Cl0.7 at (b) 294 K and (c) 230 K. The experimental spectra (full lines), total fit (dashed lines), spectral deconvolution of each Li1/Li2/Li3/Li4 signals (dotted lines), impurities Li5AlS4 in Li3AlS3, and solid LiCl in Li4.3AlS3.3Cl0.7 as observed in the powder X-ray diffraction patterns (pink dotted line) and spectral assignments are shown. Room-temperature data at 20 T for both phases are shown in Figure S5 and have the same resolution.

The relative rates of site exchange occurring in Li4.3AlS3.3Cl0.7 can be qualitatively determined from the comparison of 6Li MAS spectra obtained at two different temperatures (Figure 4b,c). At 230 K, three resonances can be observed, and upon heating to room temperature, the Li1 and Li2 resonances have completely coalesced at a weighted shift average of 1 ppm. The following expression relating the frequency separation between resonances Δω/2π with the ion jump rate τ–1

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yields a Li+-ion exchange rate on the timescale of τ–1 > 66 s–1 (i.e., (1.4–0.9) ppm × 59·106 × π/Inline graphic) occurring between Li1 and Li2. Additionally, the intensity of the resonance associated with Li3 has decreased at room temperature and indicates that some exchange occurs between this octahedrally coordinated Li3 and the two tetrahedral Li1/Li2 sites at a rate of <203 s–1 (i.e., (1.0–(−0.55)) ppm × 59·106 × π/Inline graphic).

The room-temperature 6Li MAS spectra of the parent material reveal that the exchange between tetrahedral Li4 and octahedral Li2/3 in the mixed polyhedral layer is <197 s–1 (i.e., (1.3–(−0.2)) ppm × 59·106 × π/Inline graphic), while the exchange between tetrahedral Li1 and Li4 is <52 s–1 (i.e., (1.7–1.3) ppm × 59·106 × π/Inline graphic). The upper bound of this exchange rate is lower compared to the ones in the halide-substituted analogue at low temperatures and highlights increased mobility of ions exchanging between the two distinct layers in Li4.3AlS3.3Cl0.7. Figure 5 provides a summary of the various τ–1 extracted and visualizes the interlayer Li-ion migration pathway superposed on to schematics of the crystal structures.

Figure 5.

Figure 5

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Visualization of the interlayer Li-ion migration pathway for (a) Li3AlS3 and (b) Li4.3AlS3.3Cl0.7 showing a schematic of the polyhedral arrangement of both phases as well as the τ–1 values associated with the corresponding Li-ion jumps. These values are obtained from the magnetization buildup of the 2D 6Li–6Li EXSY spectra (Figure 6) and line shape analysis of the VT one pulse 6Li NMR spectra (Figure 4) for Li3AlS3 and Li4.3AlS3.3Cl0.7. Colored spheres correspond to tetrahedral Li in the tetrahedral layer (gray), octahedral Li (red), and tetrahedral Li in the mixed polyhedral layer (orange). τ–1 values underneath the schematics are derived from the linear fits to the data points in Figure 8 and correspond to average jump rate values across the entire sample. Activation energies quoted are taken from the linear fit of the high-temperature data in Figure 7.

6Li–6Li EXSY NMR

Further insights into this pathway in Li3AlS3 were obtained from homonuclear 6Li–6Li 2D EXSY spectra on a 6Li-enriched sample of Li3AlS3, as a function of mixing time τm (Figure 6a–c), which exploit the high spectral resolution of the one-dimensional 6Li MAS spectrum of this phase. Exchange is observed experimentally in the form of off-diagonal cross peaks in the 2D EXSY spectra at the corresponding shifts and starts to emerge at around τm = 30 ms (Figure 6b) between all the sites of 6Li-enriched Li3AlS3. These cross peaks arise from either chemical exchange or spin diffusion from 6Li–6Li homonuclear coupling (as the sample is 95% 6Li-enriched) at a rate that is governed by the rate of exchange occurring during τm (Figure S6). Site-specific Li-ion correlation rates τc–1 (and jump rates τ–1) can be extracted by fitting the relative intensities of diagonal (Id) and cross peaks (Ic) as a function of τm to the following expression32

graphic file with name cm2c02101_m008.jpg 4

as shown in Figure 6d–f with the extracted Li+ τ–1 values summarized in Table 1. Chemical exchange and spin diffusion processes can be differentiated by performing EXSY experiments at different MAS rates since faster MAS averages dipole–dipole interactions more efficiently and hence reduces spin diffusion. Faster cross peak buildup rates are observed for Li2/3–Li4 and Li4–Li1 when increasing the MAS rate from 15 to 45 kHz (Figures 6 and S6 and Table 1), which rules out spin diffusion in favor of supporting chemical exchange and jumps between the magnetically inequivalent sites (note that the increased rates of cross peak buildup are likely due to the temperature increase from MAS frictional heating). However, the opposite trend is observed for the Li1–Li2/3 cross peaks (i.e., a slower rate at a faster MAS frequency) and is evidence for spin diffusion between these two sites. This is unsurprising as in order for Li ions to exchange between these two sites, a three-step jump process is required along the Li1–tetrahedral vacancy–Li4–Li2/3 pathway, which would be less favored than dipolar coupling-driven spin diffusion between Li1 and Li2/3 (Figure 5).

Figure 6.

Figure 6

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2D 6Li–6Li EXSY NMR spectra of 6Li-enriched Li3AlS3 recorded at ωr/2π = 45 kHz and mixing times τm of (a) 0, (b) 0.03, and (c) 4 s with diagonal and cross peaks shown in black and blue, respectively. The solid black lines outline the position of the diagonal. 2D 6Li–6Li EXSY NMR spectra of 6Li-enriched Li4.3AlS3.3Cl0.7 are available in Figure S8d–f plots of the cross peak buildup curves at ωr/2π = 45 kHz. The solid lines show the accompanying fits to eq 4, where Ic and Id are the intensities of the observed cross and diagonal peaks, respectively.

Table 1. Site-Specific Li-Ion Jump Rates τ–1 for Li3AlS3 Extracted from 6Li–6Li EXSY Data at Two Different MAS Frequencies.

    τ–1/s–1
ωr/2π/kHz T/K Li1–Li2/3 Li2/3–Li4 Li4–Li1
15 309(5) 4.4(4) 5.2(6) 3.0(2)
45 333(7) 2.6(4) 7(1) 4.0(7)
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The extracted τ–1 values clearly show the highest ion migration rates for inequivalent site exchange between Li2/3 and Li4 (dLi2–Li4 = 4.49(8) Å, dLi3–Li4 = 2.83(3) Å), which correspond to Li+ mobility between the tetrahedral and octahedral sites in the mixed polyhedral layer occurring through a shared face. Note that due to the lack of resolution between Li2 and Li3, it is not possible to quantify the ion migration between these two octahedral sites in the mixed polyhedral layer that form chains running along the c-axis. Exchange also exists between the tetrahedral Li4 and Li1 (dLi1–Li4 = 3.322(13) Å) in mixed polyhedral and tetrahedral layers, respectively, and occurs via a mutually shared face of a vacant tetrahedral site.

The lack of resolution observed in the room-temperature 6Li MAS spectrum of Li4.3AlS3.3Cl0.7 between Li1 and Li2 sites due to motional averaging, coupled with the low intensity of the Li3 resonance discussed above, prevents access to τ–1 values from the 2D EXSY spectra. Nevertheless, these data provide supporting evidence for the assignment of the one-dimensional 6Li MAS spectrum as cross peaks can be observed between the motionally averaged Li1/L2 site at ∼1 ppm and the octahedral Li3 site at ∼−0.3 ppm (Figure S8).

7Li Relaxometry

SLR rate constants in the laboratory frame T1–1 and the rotating frame T1ρ–1 were also obtained to provide further information on Li+ dynamics on the MHz and kHz frequency scales, respectively. Relaxation is dependent on the random fluctuation of local magnetic fields caused by the motion of atoms or functional groups. These microscopic fluctuating fields are captured by the time-dependent correlation function G(t) that contains quantitative information on the diffusion process. τc describes the timescale of these fluctuations, and in the Bloembergen–Purcell–Pound (BPP) theory, the correlation function decays exponentially and follows the equation

graphic file with name cm2c02101_m009.jpg 5

where G(0) is the value of the correlation function at time t = 0 and is equal to the mean square of the local magnetic fields. Fourier transformation of G(t) gives the spectral density function J(ω0) which quantifies the motion at the Larmor frequency ω054,55

graphic file with name cm2c02101_m010.jpg 6

where in this work, changes in τc are solely induced by the diffusion and motion of the spins as the increased mobility of 7Li nuclei with increasing temperature is the primary factor affecting the reorientation of the local magnetic fields. τc−1 is thus temperature dependent and follows an Arrhenius relation of the type

graphic file with name cm2c02101_m011.jpg 7

where τc,0–1 is the Arrhenius pre-exponential factor, T is the temperature, and kB is the Boltzmann constant. The temperature dependence of the 7Li SLR rate constants under static conditions were collected and exploited to access the activation energy, conductivity, and dimensionality of the Li diffusion processes.

In the case of Li3AlS3, the SLR T1–1 buildup rates were best fitted to a bi-exponential function (Figure S9) with slow and fast relaxing components T1,slow and T1,fast, respectively. There are two possible explanations for this behavior. First, quadrupolar nuclei with spin 3/2 such as 7Li will inherently relax bi-exponentially with a theoretical percentage contribution of 80 and 20% for the fast (satellite transition) and slow (central transition) relaxing contributions,41−43 respectively. Therefore, it is possible that the superimposed line shapes observed in the static 7Li VT NMR (Figure 3a) may be due to quadrupolar satellite transitions. However, if this was the case, the percentage contributions of T1,slow and T1,fast would be expected to remain fairly constant with temperature. In the case of Li3AlS3, the percentage contribution is 40 and 60% for T1,slow and T1,fast, respectively, with the percentage contribution of T1,slow increasing to 50% as the temperature increases. The second possibility is the presence of two batches of Li ions with differing τc values, giving rise to two differing values of T1. This explanation is supported by the two superimposed 7Li line shapes discussed previously as the double- and triple-quantum filtration and Hahn-echo experiments (Figure S4) display two sets of quadrupolar satellite transitions, arising from the two differing batches of Li ions. Therefore, we attribute the bi-exponentiality in Li3AlS3 to the presence of at least two batches of differing Li ions, which are governed by the same relaxation process but with differing values of τc. In the case of Li4.3AlS3.3Cl0.7, the T1 buildup rates were mono-exponential as evidenced by the high stretch exponential factors α of around 0.9.

Upon heating from room temperature to 490 K, the SLR T1–1 rate constants for Li3AlS3 increase from 0.22(3) to 9.4(6) s–1 and from 1.0(3) to 28(3) s–1 for the slow and fast relaxing components, respectively, while heating Li4.3AlS3.3Cl0.7 from 250 to 505 K results in a T1–1 increase from 0.46(1) to 13.6(5) s–1 (Figure 7). Both materials largely follow an Arrhenius behavior from which Ea barriers of 0.22(6) and 0.25(6) eV for the fast and slow components of T1–1 in Li3AlS3 and 0.15(5) eV for Li4.3AlS3.3Cl0.7 could be obtained and illustrate a significant difference between both phases. The increase in SLR T1–1 rate constants with higher T imply data in the low-temperature flank of the SLR rate constants, which are indicative of short-range motional processes, and demonstrate more energetically favorable short-range Li-ion diffusion in the more disordered Cl-doped phase.

Figure 7.

Figure 7

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Arrhenius plots of 7Li NMR SLR rate constants in the laboratory frame (T1–1) at ω0/2π = 156 MHz and rotating frame (T1ρ–1) at ω1/2π = 10, 30, and 80 kHz for (a) Li3AlS3, where the filled blue triangles and empty blue triangles are the T1–1 SLR rate constants associated with the slow and fast components of the buildup curves, respectively, and (b) Li4.3AlS3.3Cl0.7. The colored ticks on the temperature scale represent the position of T1ρ–1 maxima. 7Li T1ρ–1 vs τc for (c) Li3AlS3 and (d) Li4.3AlS3.3Cl0.7. Data were collected at spin-lock frequencies of ω1/2π of 10 kHz (red and orange), 30 kHz (purple and pink), and 80 kHz (green and olive), and the solid lines are those obtained from eq 10 using the experimentally determined local magnetic field fluctuation terms of 1.1(6) × 109 and 6.3(8) × 108 Hz2 for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively. Averaged values over the three ω1/2π were used, resulting in the slight offsets observed at high τc. 7Li T1ρ–1 vs τc data for both phases for each ω1/2π are given in Figure S11 for clarity.

The SLR T1ρ–1 data recorded at three different spin-lock frequencies ω1/2π are given in Figure 7. The rates initially increase with temperatures above room temperature (i.e., low-temperature flank), and activation barriers indicative of more accessible local Li+ jump processes for Li4.3AlS3.3Cl0.7 (Ea = 0.19(4) eV) than for Li3AlS3 (Ea = 0.42(8) eV) are extracted. Upon heating further, the SLR T1ρ–1 rate constants pass through maxima (in the 325–495 K temperature range) before decreasing (i.e., high-temperature flank) with activation barrier values for translational diffusion of 0.52(8) and 0.33(5) eV for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively, indicating that long-range Li+ diffusion is also more favorable in Li4.3AlS3.3Cl0.7.

SLR T1ρ–1 rate constants at different frequencies also provides information on the dimensionality of the Li+ diffusion process, and for diffusion-induced rates in solids, the high-temperature limits of the spectral density function J(ω1) have the following frequency dependence to (τc/ω1)0.5, τc ln(1/ω1τc), and τc for one-, two-, and three-dimensional diffusion processes, respectively.30,31 Both Li3AlS3 and Li4.3AlS3.3Cl0.7 materials show T1ρ–1 rate constants that are independent of the probe frequencies ω1/2π (Figure 7), which is strong evidence for the presence of three-dimensional Li+ mobility within both materials. This is an experimental validation of the computational prediction from ab initio molecular dynamics simulations and further evidence of the diffusion pathway revealed by the scattering density of the diffraction data,37 although via the direct detection of the Li+ ions as they proceed along the determined pathway. It is therefore postulated that Li-ion mobility occurs both between the layers and within the layers, which is in agreement with the observation of cross peaks for all Li sites in the 6Li–6Li EXSY spectra of Li3AlS3.

At the temperatures of the T1ρ–1 maxima, the Li+ τ–1 values are on the order of the spin-lock probe frequency ω1 and satisfy the following relationship49

graphic file with name cm2c02101_m012.jpg 8

Li+ τ–1 values in the order of 1.3 × 105–1.0 × 106 s–1 are therefore obtained in the 420–495 and 325–380 K temperature ranges for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively, and the lower temperatures in the latter again demonstrate increased Li+ mobility.

The SLR values can be further parameterized using the following expression to extract τc from T1–1 rates

graphic file with name cm2c02101_m013.jpg 9

and from T1ρ–1

graphic file with name cm2c02101_m014.jpg 10

where K is the local fluctuating magnetic field term in these expressions and depends on the relaxation mechanism.

For homonuclear dipolar relaxation involving spin 3/2 nuclei such as 7Li, K is proportional to the square of the dipolar coupling constant and is given by56

graphic file with name cm2c02101_m015.jpg 11

where μ0 is the permeability of free space, ℏ is the reduced Planck constant, γ is the gyromagnetic ratio of the nuclear spins, and r is the distance between the two nuclear spins, while for quadrupolar relaxation, K is proportional to the quadrupolar tensor parameters and expressed as

graphic file with name cm2c02101_m016.jpg 12

where ηQ is the asymmetry parameter. Accessing τc from T1–1 and T1ρ–1 data first requires a dominant relaxation mechanism to be postulated, which for 6,7Li NMR is best obtained from comparing 6Li and 7Li T1 time constants under static conditions.57

Given the power law of 4 and quadratic dependencies of T1–1 rate constants on γ and the quadrupolar moment Q in the dipolar and quadrupolar relaxation mechanisms, respectively, a ratio of

graphic file with name cm2c02101_m017.jpg 13

is expected in the case of dipolar relaxation, while a ratio of

graphic file with name cm2c02101_m018.jpg 14

is anticipated for a quadrupolar relaxation mechanism. Experimental T1(7Li)/T1(6Li) ratios of 0.10(3) for Li3AlS3 and 0.48(8) for Li4.3AlS3.3Cl0.7 were obtained at room temperature, which suggests that either cross relaxation mechanisms or a mixture of the two mechanisms contributes to the overall SLR for Li3AlS3, while dipolar relaxation mechanism dominates for Li4.3AlS3.3Cl0.7. The origin of this difference and of the cross relaxation may be due to a rather complex situation where the dominant relaxation mechanism changes between low and high temperatures or that the SLR rate constant measured corresponds to an average across the whole sample. Therefore, it is possible that the slow and fast moving ions observed in Figure 3 for Li3AlS3 may have these different relaxation mechanisms, as previously observed in other systems.58,59 Additionally, the presence of 27Al (a 100% abundant spin 5/2 nucleus) in close proximity with lithium ions may introduce additional heteronuclear dipolar coupling and dipolar–quadrupolar cross relaxation terms.

At the 7Li T1ρ–1 maxima, substituting eq 8 into eq 10 enables experimental determination of the local fluctuating magnetic field term K. A value of 1.1(6) × 109 Hz2 (averaged over the three consistent values of K for the three different ω1/2π frequencies used) was extracted for Li3AlS3 and lies between the calculated K terms for the dipolar (2 × 107 Hz2 using eq 11 and the closest Li–Li jump distance of 3.3 Å at room temperature for Li3AlS3 based on the crystal structure) and quadrupolar (4 × 109 Hz2, eq 12) relaxation mechanisms as one would expect for cross relaxation. In Li4.3AlS3.3Cl0.7, the experimental (averaged) K value of 6.3(8) × 108 Hz2 compares favorably with the dipolar dominated relaxation value of 5 × 107 Hz2 (using a static 2.4 Å Li–Li jump distance for Li4.3AlS3.3Cl0.7). These experimentally determined K values are then used to convert experimental T1ρ–1 values to τc values at each temperature using eq 10 (Figure 7) and allows access to τc and NMR-derived jump rates τ–1 at all temperatures (Figure 8).

Figure 8.

Figure 8

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Arrhenius plot of Li-ion jump rates τ–1 extracted from 7Li linewidth, 2D 6Li–6Li EXSY experiments, and 7Li SLR T1ρ–1 rate constants. Purple and pink open circles are data points from 7Li SLR T1ρ–1 rate constants at ω1/2π = 30 kHz for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively. Red/orange (for Li3AlS3) and green/olive (for Li4.3AlS3.3Cl0.7) are τ–1 extracted from 7Li SLR T1ρ–1 maxima at ω1/2π = 10 and 80 kHz, respectively. The complete data sets at these frequencies have been omitted for clarity and can be found in Figures S12 and S13. Solid lines correspond to the fits to eq 7 for the experimentally determined SLR T1ρ–1 maxima and the value of τ–1 extracted from 7Li linewidth experiments for Li3AlS3 (black) and Li4.3AlS3.3Cl0.7 (green). The inset demonstrates a magnified view of the region at which τ–1 values extracted from 2D 6Li–6Li EXSY experiments of Li3AlS3 reside.

NMR-Derived Li+-Ion τ–1 Values

NMR-derived jump rates τ–1 obtained from NMR line narrowing experiments (Figure 3), EXSYs (Figure 6), and relaxometry experiments (Figure 7) are plotted against reciprocal temperature in Figure 8 for ω1/2π = 30 kHz (data for ω1/2π = 10 and 80 kHz are given in Figures S12 and S13, respectively). Overall, Li-ion jump rates τ–1 are significantly lower for Li3AlS3 than for Li4.3AlS3.3Cl0.7 and reinforce the increased Li-ion mobility in the latter phase as revealed from the known ACIS impedance data.36,37 For both phases, there is an excellent agreement between τ–1 obtained from 7Li line narrowing spectra and relaxometry data, and fitting those to an Arrhenius equation yields activation barriers of 0.29 (0.21–0.41) and 0.29 (0.25–0.37) eV for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively. The values of the activation energies here are lower than the previously reported values from bulk conductivity observed by ACIS (0.48(1) and 0.33(1) eV), which is a common experimental observation60−63 due to the largely different approaches used where NMR spectroscopy determines the activation barrier for Li-ion mobility to neighboring sites over a much shorter length scale, whereas impedance measurements probe longer-range translational Li diffusion. Additionally, NMR also accesses unsuccessful Li-ion hops, which is likely prevalent in Li3AlS3 and Li4.3AlS3.3Cl0.7 as the Li+ sites are partially occupied. While the same activation energy is extracted from Figure 8 for both phases, the errors are particularly large due to the combination of various methods used. Hence, the energy barriers obtained from 7Li line narrowing and SLR experiments are likely to be more informative. A summary of the activation energies obtained via the various spectroscopic methods is available in Table S2.

The Li3AlS3 τ–1 values obtained from the EXSYs are notably lower than those extracted from the other approaches used. This is attributed to site-specific diffusion processes captured by the EXSY experiments compared to the information averaged across all Li sites only accessible from 7Li line narrowing and SLR measurements. The two components of the static 7Li NMR line shape observed in line narrowing experiments of Li3AlS3 can therefore be attributed to slow-moving ions (τ–1 ≪ ω/2π, broad component in 7Li static NMR spectra) associated with non-equivalent site exchange occurring between the layers (dLi1–Li2 = 4.07(13) Å, dLi1–Li3 = 3.12(3) Å, dLi1–Li4 = 3.322(13) Å) and between tetrahedral Li4 and octahedral Li2/3 sites in the mixed polyhedral layer (dLi2–Li4 = 4.49(8) Å, dLi3–Li4 = 2.83(3) Å), while the fast-moving ions (τ–1 ≫ ω/2π, narrow component) can be assigned to exchange occurring within the layers themselves along the c-axis between equivalent sites. Since the ion mobility mechanism is three-dimensional, migration between the layers is crucial for long-range translational diffusion since it connects the different diffusion channels along the c-axis so as to avoid any blockages that may occur in the diffusion pathways. We note that the calculated τ–1 values for Li3AlS3 derived from BPP theory deviate slightly from the expected trend observed from the experimentally determined τ–1 (through 7Li line narrowing and T1ρ–1 maxima) at low temperatures. A possible explanation for this observation is that since the Li-ion τ–1 for the various different sites in Li3AlS3 are expected to differ, it seems that the dependence of τ–1 on the temperature should also differ for the different sites. Additionally, it is possible that there is a significant number of unsuccessful Li-ion jumps given that ion mobility between non-equivalent sites is limited. The large distribution of Li-ion τ–1 values, originating from both fast and slow Li-ion mobility, likely results in a complex relaxation profile that deviates from the single τ–1 approach in the BPP model used, and the potential use of other models such as the Cole–Cole,42 Cole–Davidson,43 or a related model64 could potentially further rationalize this behavior. However, these models are used in order to account for a distribution of τc values across various sites and pathways, while in the case of Li3AlS3, we are probing one Li-ion pathway with two largely different τc values. Moreover, in this work, we are interested in comparing the diffusion pathways in Li3AlS3 and Li4.3AlS3.3Cl0.7, two closely related phases with connected chemistries, and we have chosen to exploit the BPP model as the relaxation behavior of Li4.3AlS3.3Cl0.7 is close to being mono-exponential.

τ–1 can then be used to derive conductivities σNMR from NMR data using the combined Nernst–Einstein and Einstein–Smoluchowski equations

graphic file with name cm2c02101_m019.jpg 15

where f and HR are the correlation factor and Haven ratio, respectively (f/HR is assumed to be smaller than 1 for correlated motion as per our previous ab initio calculations on Li4.3AlS3.3Cl0.737), NCC is the number of charge carriers per unit cell volume (based on unit cell volumes obtained from diffraction of 1014 Å3 for Li3AlS336 and 83.5 Å3 for Li4.3AlS3.3Cl0.737), q is the ionic charge of Li, r is the closest Li–Li jump distance as given above, and NNN is the number of neighboring Li sites (6 for the three-dimensional diffusion here). Obtaining f and HR is beyond the scope of this work as exemplified for the extremely well-studied Li garnet,65 and we have therefore chosen to provide the upper boundary of the extrapolated conductivity values. At 303 K, these are 4(3) × 10–8 and 3(2) × 10–6 S cm–1 for Li3AlS3 and Li4.3AlS3.3Cl0.7, respectively, which are in cautious agreement with the values determined by ACIS (10–9 and 10–6 S cm–1 for Li3AlS336 and Li4.3AlS3.3Cl0.7,37 respectively).

Conclusions

We employed a range of complementary NMR approaches focusing on both 6Li and 7Li nuclear spins to capture the Li+ dynamics of two newly discovered Li-containing materials, Li3AlS3 and Li4.3AlS3.3Cl0.7. In the parent Li3AlS3 phase, the two-component line shapes of the 7Li static NMR spectra demonstrate the existence of fast- and slow-moving Li+. The slow-moving ions were identified to diffuse between non-equivalent sites and are located between the two distinct tetrahedral and mixed polyhedral layers of the material, as captured by 2D 6Li–6Li EXSY spectra on 6Li-enriched Li3AlS3. In Li4.3AlS3.3Cl0.7, the single component observed in the static 7Li NMR spectra and the absence of the broad component contribution to the 7Li line shape indicate that the exchange of Li ions between the layers facilitates an overall increase in conductivity, as confirmed by the NMR-derived conductivities, and is associated with accelerated Li+ diffusion of the immobile ions of the parent Li3AlS3 material. This arises from the introduction of disordered octahedral lithium vacancies in the mixed polyhedral layer of Li4.3AlS3.3Cl0.7 that opens up Li-ion diffusion pathways not available by the presence of ordered vacancies in the tetrahedral layer of Li3AlS3. The frequency dependence of the SLR rate constants provides direct experimental evidence of the three-dimensional Li+ diffusion previously proposed. This dimensionality is, therefore, an important factor to increase ion mobility by accelerating ion exchange between layers to avoid any bottlenecks that occur via faster diffusion pathways along the c-axis for Li3AlS3 and the ab plane for Li4.3AlS3.3Cl0.7. Overall, this work illustrates the importance of 6Li and 7Li NMR data in accessing dynamics to understand Li-ion mobility pathways in structures that are structurally related by order/disorder.

Acknowledgments

The authors acknowledge the Industrial Strategy Challenge Fund (ISCF) Faraday challenge project: “SOLBAT – The Solid-State (Li or Na) Metal-Anode Battery” for funding including partial support of a studentship to B.B.D., also supported by the University of Liverpool. F.B. and S.J.E. would like to thank the Leverhulme Trust for funding a Research Grant under RPG-20202-066. The authors thank the Engineering and Physical Sciences Research Council (EPSRC) for funding a Programme Grant to M.J.R. under EP/N004884/1 and the 800 MHz NMR spectrometer to F.B. under EP/S013393/1. The UK High-Field Solid-State NMR Facility at 850 MHz used in this research was funded by EPSRC and BBSRC (EP/T015063/1) as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF). Collaborative assistance from the Technical Director of the UK High-Field Solid-State NMR Facility (Dr. Dinu Iuga, University of Warwick) is acknowledged. M.J.R. would like to thank the Royal Society for a Research Professorship.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.2c02101.

  • Powder XRD patterns of 6Li-enriched Li3AlS3 and Li4.3AlS3.3Cl0.7, static 7Li VT NMR of Li3AlS3 displaying full spectral region, percentage of mobile ions in Li3AlS3 as a function of temperature, multiple-quantum and Hahn echo 7Li NMR spectra of Li3AlS3, 6Li MAS NMR of Li3AlS3 and Li4.3AlS3.3Cl0.7, 6Li–6Li EXSY buildups and fits of Li3AlS3, 2D EXSY of Li4.3AlS3.3Cl0.7, comparison of fits for T1 magnetization buildups of Li3AlS3 and Li4.3AlS3.3Cl0.7, 7Li relaxometry BPP curves, and 7Li jump rate plots displaying calculated values at spin lock ω1/2π = 10 and 80 kHz (PDF)

Author Present Address

∥ Molecular Sciences Research Hub, Imperial College London, London W12 0BZ, United Kingdom

Author Present Address

⊥ CNRS, Université Bordeaux, Bordeaux INP, ICMCB UPR 9048, Pessac 33600, France.

The authors declare no competing financial interest.

Notes

Data availability: The research data supporting this publication including XRD patterns, static 7Li VT, 6Li MAS, 6Li–6Li EXSY, and 7Li relaxometry experiments as well as jump rate plots are accessible from the University of Liverpool Data catalogue: https://doi.org/10.17638/datacat.liverpool.ac.uk/1977.

Supplementary Material

cm2c02101_si_001.pdf (1.1MB, pdf)

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