Tracking Ions the Direct Way: Long-Range Li+ Dynamics in the Thio-LISICON Family Li4MCh4 (M = Sn, Ge; Ch = S, Se) as Probed by 7Li NMR Relaxometry and 7Li Spin-Alignment Echo NMR

Solid electrolytes are key elements for next-generation energy storage systems. To design powerful electrolytes with high ionic conductivity, we need to improve our understanding of the mechanisms that are at the heart of the rapid ion exchange processes in solids. Such an understanding also requires evaluation and testing of methods not routinely used to characterize ion conductors. Here, the ternary Li4MCh4 system (M = Ge, Sn; Ch = Se, S) provides model compounds to study the applicability of 7Li nuclear magnetic resonance (NMR) spin-alignment echo (SAE) spectroscopy to probe slow Li+ exchange processes. Whereas the exact interpretation of conventional spin–lattice relaxation data depends on models, SAE NMR offers a model-independent, direct access to motional correlation rates. Indeed, the jump rates and activation energies deduced from time-domain relaxometry data perfectly agree with results from 7Li SAE NMR. In particular, long-range Li+ diffusion in polycrystalline Li4SnS4 as seen by NMR in a dynamic range covering 6 orders of magnitude is determined by an activation energy of Ea = 0.55 eV and a pre-exponential factor of 3 × 1013 s–1. The variation in Ea and 1/τ0 is related to the LiCh4 volume that changes within the four Li4MCh4 compounds studied. The corresponding volume of Li4SnS4 seems to be close to optimum for Li+ diffusivity.


7
Li NMR line widths analysis. We applied two different approaches to analyze the motionally narrowing curve to derive activation energies for the Li hopping process. Hendrickson is the temperature dependent line width, 0 v ∆ is the temperature-independent line width at very low temperatures, v ∞ accounts for the small contribution by temperature-independent broadening effects, kB is the Boltzmann constant in eV/K, T the temperature and Ea, HB the respective activation energy. The constant B describes to which extent the averaging by ionic motion of locally varying magnetic fields can be correlated to the range of ionic motion. Accordingly, B is also an indicator for the number of thermally activated ions. 1 Another relation between the line width evolution with temperature actually origins from BPP 2 and was reformulated to the well-known and used expression by Gutowsky et al. 3 Abragam formulates the equation as follows. 4 This equation resembles the expression by Hendrickson and Bray in many variables.
2 0 v ∆ is the second moment of the final rigid lattice line width, the factor α is a fitting coefficient and τ0 the pre-factor in the Arrhenius relation of the temperature-dependent correlation time.
SAE NMR. Figure S1 shows 7 Li NMR lines of the four compounds investigated; the bottom of the spectra is magnified to illustrate the evolution of the quadrupole powder patterns with increasing temperature. Figure S1. Magnification of the 7 Li NMR spectra of Li4SnS4, Li4GeS4, Li4GeSe4 and Li4SnSe4 measured at (a) 253 K, (b) 313 K, (c) 353 K and (d) 433 K to illustrate the quadrupole satellites resulting from the interaction of the 7 Li quadrupole moment with non-vanishing electric field gradients at the nuclear site. Arrows point to singularities from which the quadrupole coupling constants were estimated assuming axially symmetric, motionally averaged electric field gradients. 6 Li MAS NMR. We fitted the 6 Li MAS NMR signal of Li4SnS4 by two Gaussian functions to derive the area ratio of the two contributions to the spectrum. The corresponding fit is shown in Figure S2. We derived an area ratio of 17.3 : 82.7 for the small signal compared to the larger one. Kaib et al. 5 observed an area ratio of 27 : 73 and assigned the smaller signal to the octahedral Li-sites in Li4SnS4. Recently published data from neutron diffraction shows that 31% of the Li-ions occupy octahedral-sites. 5 Correlating this to our results, the area fraction of the smaller signal in MAS NMR is too small to account for all these octahedral sites. Considering, however, only the Li4 octahedral site with 11.5% to 12.5% of the total Li-content, a far better agreement is found. Another fact that is in favour of this argument is the sole appearance of the small 6 Li MAS NMR signal in the spectrum of Li4SnS4. For the other compounds we observed no such signal in MAS NMR even though all four structures include octahedral sites. The unique feature in Li4SnS4 is the Li4 position, which might give a hint for the explanation of the two contributions to the 6 Li MAS NMR spectrum.

S3
In Figure S3a and Figure S3b the different origins leading to the damping of the 7 Li SAE NMR two-time correlation functions S2 of Li4SnS4 are shown. In Figure S3a we see the evolution of S2 with temperature, in Figure  4Sb the influence of varying tp is illustrated for two different evolution times. Note that for different temperatures the decay rate 1/τSAE changes whereas the final amplitudes S∞ remain rather constant. In contrast, with increasing tp the amplitude S∞ decreases while the decay rate 1/τSAE is largely unaffected by tp if varied from 15 µs to 30 µs. The same 1/τSAE rates are also obtained for longer tp reaching 100 µs.
In Figure S3c we present the decay of the echo amplitude S2 recorded at 253 K and compare it with the magnetization transient obtained from an independent T1 experiment carried out at the same temperature. For S2 the two decay steps are characterized by the time constants τSAE, directly probing slow Li + jumps, and T1, SAE, which is influenced by quadrupole longitudinal relaxation. With regard to the scaling on the x-axis we see that T1, SAE proceeds on the same time scale as T1.