Structural Disorder in Li6PS5I Speeds 7Li Nuclear Spin Recovery and Slows Down 31P Relaxation-Implications for Translational and Rotational Jumps as Seen by Nuclear Magnetic Resonance.

Lithium-thiophosphates have attracted great attention as they offer a rich playground to develop tailor-made solid electrolytes for clean energy storage systems. Here, we used poorly conducting Li6PS5I, which can be converted into a fast ion conductor by high-energy ball-milling to understand the fundamental guidelines that enable the Li+ ions to quickly diffuse through a polarizable but distorted matrix. In stark contrast to well-crystalline Li6PS5I (10-6 S cm-1), the ionic conductivity of its defect-rich nanostructured analog touches almost the mS cm-1 regime. Most likely, this immense enhancement originates from site disorder and polyhedral distortions introduced during mechanical treatment. We used the spin probes 7Li and 31P to monitor nuclear spin relaxation that is directly induced by Li+ translational and/or PS4 3- rotational motions. Compared to the ordered form, 7Li spin-lattice relaxation (SLR) in nano-Li6PS5I reveals an additional ultrafast process that is governed by activation energy as low as 160 meV. Presumably, this new relaxation peak, appearing at T max = 281 K, reflects extremely rapid Li hopping processes with a jump rate in the order of 109 s-1 at T max. Thus, the thiophosphate transforms from a poor electrolyte with island-like local diffusivity to a fast ion conductor with 3D cross-linked diffusion routes enabling long-range transport. On the other hand, the original 31P nuclear magnetic resonance (NMR) SLR rate peak, pointing to an effective 31P-31P spin relaxation source in ordered Li6PS5I, is either absent for the distorted form or shifts toward much higher temperatures. Assuming the 31P NMR peak as being a result of PS4 3- rotational jump processes, NMR unveils that disorder significantly slows down anion dynamics. The latter finding might also have broader implications and sheds light on the vital question how rotational dynamics are to be manipulated to effectively enhance Li+ cation transport.

Introduction

The enigmatic interplay between cation translational processes and rotational dynamics of complex anions[1−3] propelled the (re-)investigation of a range of Li-containing and Na-bearing thiophosphates.[4−7] The interest in fast ionic conductors[8] is spurred by the demand to develop high-performance energy storage systems relying on ceramic electrolytes.[9] Early examples for which the so-called “paddlewheel”[1−3] (or “cogwheel” or “revolving door”)[10] mechanism is used to describe the cation–anion coupled transport, include the rotator phases Li2SO4,[1−3,11−14] LiMSO4 (M = Na and Ag),[3,15,16] Na3PO4,[1,14] and several borohydrides[17−21] and a range of closo-boranes,[22−28] including the dynamics of cluster ions in Li3S(BF4)0.5Cl0.5 and Na3OBH4.[29−31] As is impressively seen for the low-T modification orthorhombic LiBH4, 7Li and 11B (and even 1H) nuclear magnetic resonance (NMR) is suited to directly probe local BH4– rotational motions in the borohydride.[32−35]

In its narrower sense, the paddlewheel mechanism[1,8,36] explains rapid cation translational dynamics by opening (or even closing) low-energy passageways through rotational (or librational) jumps of the polyanions that form the polarizable matrix of the electrolyte.[1] The cog-wheel mechanism requires significant dynamic coupling of neighboring anions, whereas the revolving door mechanism suggests that the anion reacts with an evasive motion to let the cation pass by.[1] Hence, it is still unclear which of the teammates act as the driving force.[7] Also, uncoupled fast rotational motions have been proposed to increase cation mobility through the generation of Coulombic fluctuations to affect the cation attempt frequencies.[1] The validity of such mechanisms has also been questioned in the past as the larger free transport volume for the rotational phases might play a role too;[3,10] conversely, an increase in lattice volume, e.g., also by the introduction of larger lattice units, will facilitate anion rotation.

From an experimental point of view, it is striking that the onset of rotational disorder seen in the high-temperature modifications of the sulfate or phosphate compounds[1] is accompanied by an increase in cation diffusivity and a decrease in activation energy.[1,10] Such a relationship, which may be regarded as a design tool to develop tailor-made, fast Li+ ion conductors, has also been proposed by Adams and Rao[37] to explain the overall dynamic situation in the famous ion conductor Li10GeP2S11.[38] Quite recently, Nazar and co-workers have used the paddlewheel concept to explain enhanced Na+-ion transport in Na11Sn2PS12 and provided supporting evidence for this cooperative interplay in β-Li3PS4 as well as its Si-substituted analog Li3.25Si0.25P0.75S4.[5,39] As the latter materials are expected to play decisive roles in all-solid-state batteries equipped with polycrystalline electrolytes or glassy compounds,[9,40,41] a deeper understanding of the dynamic processes from an atomic-scale point of view is desirable. Quite recently, Smith and Siegel have used ab initio molecular dynamics simulations to characterize translational-rotational coupling in glassy 25Li2S-75P2S5.[4] Their recent study[4] and the timeless report of Jansen[1] include precise and very helpful introductions into the topic, we recommend reading.

In our own group, we interpreted the low-temperature 31P NMR response in coarse-grained Li6PS5I as a signature of fast PS43– rotational jump processes.[7] In contrast to site-disordered Li6PS5Br and Li6PS5Cl, in the iodine compound with its expanded volume and ordered sublattices,[42−45] containing also polarizable I anions, the PS43– units seem to be able to freely perform rotational (and librational) dynamics. At least for Li6PS5I, this uncoupled rotational motion, even if generating periodically fluctuating electric potentials at the cation sites,[1] does not favor long-range Li+ transport.[46] Interestingly, site disorder and lattice contraction clearly disturb the effectiveness of the underlying 31P NMR spin–lattice relaxation processes and lead to a shift in the corresponding rate peaks toward higher temperatures when going from Li6PS5I to Li6PS5X (X = Br and Cl).[7] To underscore our hypothesis that structural disorder hampers rotational motions in Li6PS5X, we used Li6PS5I as a model substance[46] and introduced (site) disorder by soft high-energy ball-milling.[47] Soft milling takes advantage of a low sample-to-ball ratio in conjunction with low rotational speeds. This approach does not change the overall chemical composition of the nanocrystalline sample but leads to anion, and presumably, also to extensive cation disorder, polyhedral distortions, and strain. These structural changes were revealed by the broadening of the corresponding X-ray reflections and broadened 31P (magic angle spinning, MAS) NMR spectra.[47] The dynamic features of the coarse-grained Li6PS5I were investigated in detail in three earlier studies[7,46,47] by our group; the present study is based on these results.

Here, we used 31P NMR spin–lattice relaxation experiments to describe any possible influence of structural disorder on 31P nuclear spin recovery in nanostructured Li6PS5I. The results were compared with those obtained for the 7Li nucleus recently.[7,46,47] In general, the spin recovery is directly driven by the thermally activated jump processes taking place in the crystal structure of the thiophosphate. Most importantly, while Li+ self-diffusivity is enhanced in disordered Li6PS5I,[47] the effective source governing 31P nuclear spin relaxation in ordered Li6PS5I is indeed noticeably weakened in the ball-milled material. In nano-Li6PS5I, the distinct 31P NMR spin–lattice relaxation peak is no longer seen as a separate signal; its disappearance indicates that the disorder has a drastic influence on the temporal 31P-31P(7Li) magnetic interactions controlling nuclear spin recovery.

Materials and Methods

The preparation of Li6PS5I is described elsewhere;[46] for the present study, we used the material of the same synthesis batch that has been recently investigated by X-ray diffraction, 31P MAS NMR, and also by impedance measurements and NMR spectroscopy.[46] To prepare nanocrystalline Li6PS5I, 0.5 g of the starting powder was added to ZrO2 milling vials (45 mL) under an Ar atmosphere (H2O < 1 ppm, O2 < 1 ppm). The milling jars were filled with 60 milling balls (5 mm in diameter). Nano-Li6PS5I was treated in a Premium line 7 planetary mill (Fritsch) that was operated at a rotation speed of 400 rpm.[47] The milling time was set to 120 min. For NMR measurements, the powder was sealed in Duran ampoules.

The acquisition of 7Li (116 MHz Larmor frequency) and 31P (121 MHz) NMR spin–lattice relaxation rates (1/T1) was carried out using a Bruker 300-MHz NMR spectrometer; the procedures are identical to those described already elsewhere.[46] We used the well-known saturation recovery sequence to monitor the recovery of longitudinal magnetization after a comb of closely spaced 90° perturbation pulses. The curves were parametrized with appropriate exponential functions to extract the rate 1/T1 as a function of temperature, see the Supporting Information.

Results and Discussion

Li6PS5I crystallizes with cubic symmetry (space group F43m, see Figure a).[42] The Li ions occupy various lattice sites within the structure forming Li-rich cages. While fast Li+ exchange, with rates on the MHz rage, occurs within these cages for Li6PS5I, intercage jump processes are much less frequent, that is, reduced by 2–3 orders of magnitude.[48] As these processes are important to guarantee long-range ionic transport, highly crystalline Li6PS5I turned out to be a poor ionic conductor with an ionic conductivity in the order of 10–6 S cm–1 at room temperature.[46]

Figure 1

(a) Crystal structure of argyrodite-type Li6PS5I. While the I– anions occupy the 4a sites, the S2– anions reside on the 4d and 16e sites forming an ordered anion sublattice. PS43– tetrahedra are shown in blue. Li+ ions are arranged such that they build cages consisting of six 48 h-24 g-48h′ triplets. Intracage jumps include hopping processes between 48 h sites of two different triplets. Within the triplet 48 h-24 g-48h′, the Li ions perform highly restricted forward-backward hopping processes. (b) Long-range ion dynamics are possible either by direct jumps from cage to cage (48h1-48h2) or by using the interstitial sites that are illustrated by blue spheres (48 h and 16e).[43]

In contrast, the sibling compounds Li6PS5X (X = Br and Cl) benefit from both anion and cation site disorder resulting in ionic conductivities in the mS cm–1 range.[46,49] Hence, besides other effects such as the influence of anion polarizability, anion site disorder, i.e., the occupation of 4d sites within the Li-rich cages by X–, and, as has been shown quite recently,[43] the partial filling of the originally empty Li+ sites (see the 48 h and 16e voids shown in Figure b) guarantee rapid Li+ exchange. In addition to strain and polyhedra distortions generated, high-energy ball-milling is, thus, also expected to sensitively affect both the I–/S2– and Li+ site distribution in Li6PS5I. Indeed, as has been shown earlier, soft mechanical treatment can enhance ionic conductivity by several orders of magnitude.[47,50] The sample milled for 120 min in a planetary mill shows an ionic conductivity almost reaching the mS cm–1 regime at ambient conditions.[47]

To understand how mechanical treatment affects the various interactions of the 7Li (spin quantum number I = 3/2) and 31P (I = 1/2) spins, we recorded diffusion-induced 1/T1 NMR rates as a function of the inverse temperature. The change of variable-temperature 7Li NMR lines, clearly pointing to faster Li+ dynamics in nano-Li6PS5I, is discussed elsewhere.[47] In Figure , the 31P (and 7Li) NMR 1/T1 rates of unmilled Li6PS5I are shown using an Arrhenius representation.[7] In particular, the present paper focusses on the 31P NMR relaxation rates peaks (C) and (D) in Figure and the corresponding one in Figure . The values included correspond to the activation energies of either the low-T (Ea, high) and high-T flanks (Ea, high) of the peaks. The rates were extracted from the full magnetization transients shown in Figure S1. Here, we focus on data obtained for the cubic modification.[7] As indicated in Figure , below 160 K the iodide transforms into an orthorhombic phase.[46] Coming from low temperatures, the 7Li NMR rates pass into a well-defined relaxation rate peak, which was attributed to intracage Li+ jump processes.[46] We parameterized the peak with a modified Lorentzian-shaped spectral density function based on the relaxation model of Bloembergen, Purcell and Pound (BPP),[51,52] see the Supporting Information and Table S1 for further information. The peak turned out to be rather symmetric which is expected for 3D uncorrelated Li+ motions.[53]

Figure 2

(a) Change of the diffusion-induced 7Li (116 MHz) and 31P (121 MHz) NMR spin–lattice relaxation rates 1/T1 of microcrystalline, that is, unmilled Li6PS5I. Solid lines show fits with appropriate Lorentzian-shaped BPP functions. The values indicate the activation energies of the high-temperature and low-temperature flanks, respectively. Dashed lines show individual 31P NMR peaks 1/T1(1/T) whose sum yield the overall 31P NMR response comprising two peaks at T > 400 K. (b) Same data as in (a) but including the 7Li and 31P NMR responses of the nanocrystalline Li6PS5I. The 7Li NMR 1/T1(1/T) peak shifts toward a higher T and exhibits a shoulder located at 281 K representing extremely fast spin fluctuations sensed by the 7Li nuclei. For comparison, the 31P NMR rates pass through a broadened peak likely being the superposition of several relaxation processes. Most importantly, the prominent low-temperature peak seen in (a) that appeared at 220 K (peak (D)) is either absent for nanocrystalline Li6PS5I or has shifted toward higher T as indicated by the curved arrow. The increase in 31P NMR rates at the highest temperatures, the arrow in (a), points to a third relaxation process with even longer motional residence times.

The same relaxation source, that is, the 31P NMR relaxation due to the translational motion of the Li+ ions is indirectly sensed by the 31P nuclei; see peak (C) in Figure . In addition, the 31P NMR data unveil a second, more prominent peak at T = 220 K (D), which we assume is mainly driven by the homonuclear 31P-31P dipole–dipole interactions. Presumably, this peak mirrors the fast PS43– rotational motions.[7] Interestingly, both NMR peaks are governed by almost the same activation energy of Ea, high = 0.20 eV (Figure a). The fact that the 31P NMR peak (D) is not visible in 7Li NMR could have various reasons. Heteronuclear 31P-7Li coupling, which is generally weaker than the homonuclear interactions, might be too low or the peak might be hidden in the low-temperature region shown as a dashed area in Figure a. In this region, the 7Li NMR rates are increasingly dominated by the nondiffusive relaxation processes such as the coupling of the Li spins to lattice vibrations or paramagnetic impurities.

7Li and 31P NMR experiments on nano-Li6PS5I reveal two important differences compared to the unmilled sample. First, the prominent 31P NMR rate peak seen at 220 K is absent for the nanocrystalline sample. Hence, the relaxation source is either switched off or the original peak (D) is shifted toward higher temperatures as indicated by the curved arrow in Figure b. This shift means that the PS43– rotational motion is slowing down in nano-Li6PS5I. It also helps interpret the width of the 31P NMR peak of nano-Li6PS5I, which now turned out to be a superposition of several rate peaks. The 31P spins are sensing, including peaks (A) and (B) seen by 7Li NMR, see below. The activation energies calculated from the flanks of the 31P 1/T1(1/T) peak are regarded as apparent values that do not represent a single, distinct motional process.

Second, the original 7Li NMR response of coarse-grained, i.e., structurally ordered Li6PS5I, is split into two rate peaks labeled (A) and (B); these peaks appear at Tmax = 373 K and 281 K, respectively. The shift is mainly due to a reduction in the activation energy from Ea, high = 0.23 eV to Ea, high = 0.16 eV. The corresponding prefactors τ0–1 of the underlying Arrhenius relations, τ–1 = τ0–1 exp. (−Ea, high/kBT), where kB denotes Boltzmann’s constant, turned out to be in the same order of magnitude (1012 s–1, see Table S1); they simply differ by a factor of two. It is a fundamental question whether this “attempt frequency” τ0–1 is related to a vibrational frequency experienced by the mobile ion residing in a potential well between the hops, as suggested by the simple, classical diffusion theory. Phonon frequencies usually take values from 1012 to 1014 s–1; thus, the τ0–1 values extracted from the NMR data lie at the lower limit of this range.

In the following, we discuss a possible scenario that explains the splitting of the 7Li NMR peak, thereby also pointing out the differences between results from NMR relaxation and conductivity spectroscopy. In line with earlier studies,[46] we suppose that the original, almost symmetric BPP-type peak of microcrystalline Li6PS5I is mainly mirroring fast intracage jump processes involving the sites 24 g and 48 h. Because of its relatively larger peak amplitude compared to that of peak (B) that is determined by the underlying coupling constant, we suppose that peak (A) is also governed by stronger Li–Li interactions of the Li-rich cages. From the maximum condition, ω0τ = 1,[54,55] with τ being the residence time and ω0/2π = 116 MHz representing the Larmor frequency, we estimate that at Tmax = 329 K, the average jump rate should be in the order of τ–1 = 7.3 × 108 s–1. This value roughly translates into a self-diffusion coefficient of D329 K = 4.86 × 10–12 m2s–1, if we use the Einstein–Smoluchowski equation to relate τ with D according to D = a2/(6τ).[56,57] Here, we used a jump distance of a = 2 Å as a good approximation of the average Li–Li distance. According to the Nernst–Einstein equation,[58]D329 K corresponds to conductivity σ in the order of 1.6 mS cm–1 at 329 K. This value is much too high to explain the experimental value of 10–6 S cm–1 observed at ambient conditions. Even if we take into account any deviations of the Haven ratio Hr and the correlation factor f from 1, as might be expected for correlated diffusion,[58] the difference between the solid-state diffusion coefficient Dσ, as extractable from conductivity measurements, and the self-diffusion coefficient D = (Hr/f)Dσ, as probed by NMR, is several orders of magnitude. Hence, we are confident that the symmetric rate peak seen at 329 K mirrors the rapid but spatially constrained ion dynamics that do not contribute to long-range ion transport that is probed by σ. This interpretation has also been underscored by 7Li NMR line width measurements performed recently.[47] They reveal only a partial averaging of the Li–Li dipolar interactions[46] as the important intercage jump processes needed to fully average homonuclear broadening take place much less frequently. However, full averaging is seen at higher temperatures.[46,47]

For the ball-milled sample, this BPP-type peak that does not change much in shape (Ea,high = 0.2 eV, see Figure ) shifts by approximately 50 K toward higher temperatures, see peak (A). Obviously, the disorder perturbs the Li+ dynamics associated with the Li-rich cages, as pointed out recently.[47] The Arrhenius laws belonging to the original and final peak differ in activation energy; however, the prefactors remain almost unaffected (Table S1). Hence, in contrast to macroscopic bulk electrical relaxation for which a significant change in prefactor was observed,[47]7Li NMR does not reveal a strong influence of the prefactor on this spatially restricted type of Li+ motion.

Most importantly, a careful evaluation of the rates below 330 K reveals a second 1/T1(1/T) peak, labeled (B) in Figure b, that is located at Tmax = 281 K. For comparison, the corresponding and prominent 7Li NMR rate peaks of the fast Li+ ion conductor Li6PS5Br appear at almost the same temperature, Tmax = 286 K. Hence, nanocrystalline Li6PS5I increasingly start to resemble the nuclear spin behavior of the site-disordered bromide analog. As mentioned above, neutron diffraction revealed that the Li+ ions in Li6PS5Br do also populate the so far unexplored intercage voids (48 h sites)[43] that are empty in structurally ordered Li6PS5I. The interplay between the anion disorder and Li+ charge distribution seems to play the decisive role in explaining the facile Li+ transport observed. This finding can also be used to explain the highly asymmetric shape[46,59] of the 1/T1 peak of Li6PS5Br being produced by a superposition of elementary jump processes including localized ones and those enabling long-range ion transport. Frustration effects introduced by the anion disorder and concerted motions have been considered to explain the overall dynamic situation in Li6PS5X (X = Br and Cl), which also seems to be triggered by the Li-Li Coulombic interactions.[60]

Assuming that mechanical treatment forces the Li ions in Li6PS5I also to considerably occupy the additional sites outside the cages, we could interpret peak (B) as being controlled by fast intercage jump processes. Indeed, 7Li NMR linewidth measurements unveiled that almost fully hopping-controlled dipole–dipole averaging takes place in nano-Li6PS5I.[47] In addition, to underpin this scenario from a quantitative point of view, we calculated the ionic conductivity expected for the Tmax of peak (B). Anticipating that 10% of the total number of ions have access to the fast intercage jump processes yields σcalc 0.19 mS cm–1. This value is in good agreement with the experimental one (σexp = 0.14 mS cm–1). Increasing the effective number density N1 to 20% of the total number of available Li+ ions per unit cell[43] increases σcalc to 0.37 mS cm–1. Again, the deviations of Hr and especially f from 1 will further influence σcalc. In the latter case, a correlation factor of f ≈ 0.4 will immediately result in σcalc = σexp at 281 K. Altogether, we found evidence that the boost in ionic conductivity seen for Li6PS5I is represented by the 7Li NMR relaxation peak appearing at 281 K. Its presence helps explain the colossal increase in Li+ ion dynamics when going from microcrystalline to nanocrystalline Li6PS5I. In addition, further dynamic processes were also probed by spin-lock 7Li NMR, recently.[47] As an example, at locking frequencies in the kHz range, a spin-lock relaxation peak at a temperature as low as 190 K shows up for nano-Li6PS5I.[47]

In contrast to conductivity spectroscopy being sensitive to long-range ion transport, the flanks of 7Li NMR relaxation rate peaks, unlike stimulated echo techniques,[61,62] capture the barriers of the elementary steps of ion hopping. In addition, in the low-T regime, the slopes of these flanks are influenced by correlation effects. Thus, the activation energies calculated from NMR, here ranging from 0.23 to 0.16 eV (Figure , do not agree with the macroscopic activation energy seen by conductivity spectroscopy (0.36 eV) and electric modulus measurements (0.33 eV).[47] Such discrepancies are well known in the literature[63] and leave room for ideas that, for example, Li+ ions have to surmount even larger barriers of a macroscopic length scale or the underlying motional correlation functions, probed by the different methods, simply differ.

Coming back to 31P NMR relaxometry, we recognize that the Tmax of the 7Li 1/T1(1/T) rate peak (B) agrees very well with the position of the 31P NMR peak of nano-Li6PS5I (Figure . If we assume that PS43– rotational jumps contribute to the overall 31P response, these processes take place on the same time scale as Li+ hopping does, that is, on the ns scale (300 K). Thus, they are in resonance with Li+ translational dynamics. This situation is in stark contrast to that discussed recently for ordered Li6PS5I.[7] In the structurally ordered counterpart, the translational and any rotational jump processes seem to be, at least, temporarily decoupled;[7] in unmilled Li6PS5I, the rotational motions are much faster than the long-range Li+ ion dynamics. On the other hand, in disordered Li6PS5I, the matching characteristic motional correlation rates τ–1 point to dynamic cation–anion coupling that affects the overall Li+ ion translational dynamics, possibly due to the paddle-wheel mechanism. This view is in line with that of Smith and Siegel who presented evidence that this mechanism is relevant for ion dynamics in glassy electrolytes such as 75Li2S-25P2S5.[4] Certainly, further spectroscopic studies in combination with calculations are needed to support our findings and to unravel the true nature of anion–cation coupling in thiophosphates. We are still at the beginning to understand this important interaction. Such a beginning resembles a dialog of Rowling: “Is this real? Or has this been happening in my head?” “Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real.” (J. K. Rowling, Harry Potter and the Deathly Hallows, 2007.)

Conclusions

Li6PS5I serves as a highly suitable model system to study the influence of the structural disorder on dynamic properties. Here, the disorder was introduced by a soft mechanical treatment. We assume that the distortions and (anion and cation) site disorders are responsible for the immense increase in the ionic conductivity of the nanocrystalline, ball-milled Li6PS5I. Such disorder is absent for the unmilled samples. Variable-temperature 31P NMR reveals that an important source for spin–lattice relaxation is significantly changed after ball-milling. For ordered Li6PS5I, the prominent 31P NMR relaxation peak attributed to the ultrarapid PS4–3 rotational jumps either shifts toward higher T or is missing. We conclude that structural disorder in Li6PS5I sensitively affect such motions. Moreover, it does not only alter the 31P NMR relaxation response but also reveals the subtle, but important, differences in 7Li NMR relaxation. While structural disorder slow down the fast intracage Li+ dynamics, a new rate peak emerges at 281 K pointing to the highly effective source inducing 7Li NMR spin–lattice relaxation. We propose that this peak is responsible for the fast jump processes that enable the ions to diffuse over long distances. The mean activation energy for these elementary jump processes turned out to range between 150 and 160 meV. The associated translational jump rate is in the GHz range (τ–1(281 K) = 7.3 × 108 s–1) and would be in resonance with the mean rotational jump rate of the PS4–3 polyanions.