In the search of safe and long-lasting energy storage systems all-solid-state batteries entered the spotlight of research1. One of the major outstanding challenges is to develop stable electrolytes with extraordinarily high ion conductivities at ambient conditions2. Since no flammable liquids are used in such batteries they are regarded as inherently safe and might easily withstand high operation temperatures3. In recent years, we witnessed the discovery of a couple of very fast and promising Li+ ion conductors4,5,6,7,8,9,10. The market availability of Li might, however, narrow the widespread realization of large scale stationary applications. Sustainable batteries11,12 with Na+ as ionic charge carrier3,13,14,15 do not carry this risk as Na is abundantly available in the earth’s crust. The cost-effective realization of environmentally benign ceramic batteries, however, will need solid electrolytes with a very high ion mobility to compete with the much faster dynamic processes in the liquid state16,17.

Although moderate to very fast ion conducting Na compounds have so far been frequently presented;15,16,18,19,20,21; ion dynamics in non-sulfidic, i.e., air-insensitive, Na+ electrolytes with extremely high ion conductivities exceeding 1 mS/cm at room temperature have, apart from the well-known Na-β′′-alumina12, only very rarely been characterized in detail16,18,22. Here we present an in-depth study to explore the roots of extremely rapid 3D ion dynamics in Na3.4Sc0.4Zr1.6(SiO4)2PO4 (Sc-NZSP), which was prepared via a wet-chemical route18. The parent compound Na3Zr2(SiO4)2PO4 (NZSP), following the pioneering work of Hong and Goodenough23,24, served as benchmark. It has been shown recently that substitution of Zr by Sc in NZSP leads to an increase of ionic conductivity22. For the reason of charge compensation, the replacement of parts of Zr ions with an equimolar amount of Sc ions increases the number density of (mobile) Na ions. Sc-NZSP indeed exhibited Na ion bulk conductivities σ′ of 2 mS/cm at room temperature with activation energies ranging from 0.13 eV to 0.31 eV. Although in the Sc-free compound σ′ was somewhat lower (1 mS/cm) the grain-boundaries in NZSP turned out to be much less blocking for the Na+ ions. This feature ensured facile ion transport over distances in the µm range. Such long-range ion transport is above all the most important property for any battery application17.

It is beyond any doubt that reporting such high conductivities4,5,6,7,8,10,25,26,27,28, especially for sodium-based batteries19,20,21,29,30, is of enormous importance. Understanding their roots, preferably with the help of theory31,32, is also crucial and would enable us to safely control their dynamic properties. Yet, for many materials, however, there is still no complete picture available consistently describing the interrelation of the elementary steps of hopping with long-range ion transport. In many cases, it is not even clear which charge carrier and dynamic processes are responsible for the high conductivities reported. Such features cannot be probed by conductivity measurements alone. Instead, one should use complementary techniques that can observe dynamics over wide scales in time and length33,34,35. In this study, we combined time-domain nuclear magnetic resonance (NMR) spectroscopy with broadband conductivity spectroscopy to quantify short-range as well as long-range Na+ ion diffusivities. Using only NMR spin-lattice relaxometry working at atomic scale36,37 we managed to get a sneak peek at the very rapid exchange processes the Na ions are performing at temperatures very well below ambient. The data collected provide a first experimental rationale for the very high ionic conductivity observed in NZSP-type compounds.

Since our impedance measurements covered a dynamic range of more than ten decades they allowed us (i) to separate the bulk from grain boundary (g.b.) response at temperatures where batteries are usually operated and (ii) to directly compare electric relaxation with magnetic spin relaxation which was measured in the kHz and GHz range, respectively. Here, NMR relaxometry confirmed the extraordinarily high conductivity of Na3.4Sc0.4Zr1.6(SiO4)2PO4 and, furthermore, pointed to a distribution of activation energies including values as low as 0.13 eV and 0.16 eV. Hence, the ions are subjected not to a single but to various dynamic processes being stepwise activated with temperature or running in parallel. To our knowledge, this dynamic performance, although Na+ ions are of course larger and therefore perhaps more sluggish than Li+ ions, exceeds those of the best Li oxides currently discussed as ceramic electrolytes2,38. Considering the electrochemical stability of NZSP-type materials39 this behaviour clearly opens the field for the development of powerful Na ion solid-state batteries.

Results and Discussion

Na3Zr2(SiO4)2(PO4) is reported to crystallize with monoclinic symmetry (space group C2/c, see the views along different crystallographic axes in Fig. 1a–c. In the monoclinic form of NZSP the Na+ ions occupy three crystallographically inequivalent sites 4d, 4e, and 8 f, which are partially occupied. The large fraction of vacant Na sites and the favourable connection of their polyhedra ensure rapid exchange of the Na+ ions as discussed in literature22,40. The preparation and characterisation of the samples studied here (NZSP and Sc-NZSP) has already been described elsewhere18,22. The characterization also includes analyses by X-ray powder diffraction and differential scanning measurements.

Figure 1
figure 1

Crystal structure and conductivity. (a–c) Crystal structure of monoclinic Na3Zr2(SiO4)2PO4. (d) Frequency dependence of the imaginary part of the complex impedance (−Z′′) and the complex modulus (M′′) of Sc-NZSP (−100 °C). For comparison, the variation of the real part ε′ of the complex permittivity is also shown. −Z′′ and M′′ each reveal two maxima which correspond to the grain boundary (g.b., ε′ = 3 × 103) and bulk response, respectively; the latter is seen in the high-frequency region, ε′ ranges from 10 to 20. (e) Complex plane plots of the impedance data (−100 °C). The depressed semicircle at high frequencies (left) represents the (overall) bulk response (Cbulk = 10 pF). The g.b. contribution is characterized by Cg.b. = 103 pF and a Debye-like non-depressed semicircle with its centre almost on the Z′ axis (Fig. S1); piling up of the ions near the blocking electrode, i.e., electrode polarization (EP), is seen as a spike at the lowest frequencies. (f ) Conductivity isotherms of Sc-NZSP. The frequency independent regions (A) and (B) represent either the g.b. or the bulk response. The direct current g.b. response directly merges into a linear conductivity-frequency regime, σ ν (slope = 1). The arrow points to σ′ in order of 10−4 S/cm at −40 °C. (g) Nyquist plots recorded at frequencies greater than 106 Hz. At elevated temperatures the bulk response seems to be composed of at least two semicircles (bulk 1, bulk 2).

Electrical conductivity: bulk vs. grain boundary responses

We used a sintered Sc-NZSP pellet (1.1 mm in thickness and 7 mm in diameter) equipped with sputtered ion-blocking electrodes of gold to ensure electrical contact for our conductivity and impedance measurements, see Fig. 1d–g. Conductivity isotherms showing the real part σ′ of the complex conductivity as a function of frequency ν are displayed in Fig. 1f, see also Figs S1 and S2 for the complete temperature range covered. We used two impedance analysers to construct the isotherms, a Novocontrol Alpha analyser and an Agilent impedance bridge (see also the grey area in Fig. 1d) to reach the GHz range. If we consider the conductivities over a frequency range from the µHz to the GHz regime at least two main contributions were revealed; they are labelled (A) and (B) in Fig. 1f. While they appear as plateaus in the σ′(ν) plot, they manifest as two independent semicircles in the complex plane plots, i.e., Nyquist illustrations, see Fig. 1e showing the responses recorded at −100 °C with the apex frequencies ωmax indicated; plots with equally scaled axes are shown in Figs S1 and S2. As the capacity C of plateau (A), if simply estimated via ωmaxRC = 1, is in the nF range, we attribute the semicircle in the low frequency range to the g.b. response. The spike seen at very low frequencies is attributed to ionic polarisation effects in front of the Na+ ion blocking electrodes. Plateau (B) is assigned to the bulk response as the corresponding capacity Cbulk is clearly in the pF range; such capacities are diagnostic for electrical relaxation processes taking place in the grain.

Most importantly, at room temperature the bulk semicircle (see Fig. 1g), which was recorded in the GHz regime, corresponds to a specific conductivity in the mS range. At 20 °C the intercept of the −Z′′(Z′) curve with the real axis yields a conductivity of 8.3 mS (ca. 120 Ω) which results in a specific conductivity of 2.4 mS/cm. The g.b. response yields values which are two orders of magnitude lower (see also the difference of the plateaus σbulk(ν) and σg.b.(ν) in Fig. 1f). The two processes can also be clearly seen if the imaginary part Z″ of the complex impedance and that of the complex modulus (M″) are analysed. The corresponding curves −Z″(ν) and M″(ν) are shown in Fig. 1d and reveal two peaks that differ in amplitude according to the capacities associated with the two processes they represent. Here we have Cg.b./Cbulk ≈ 100 leading to the same ratio in peak amplitudes Mmax./bulk/Mmax./g.b.. Since M(max.) 1/C, bulk responses are more prominent in the modulus representation, as expected. Almost the same ratio is probed for the real part of the complex permittivity; values in the order of 103 or 104 are typically seen for g.b. contributions.

Measurements up to the GHz are indispensable to make the bulk response fully visible at temperatures above ambient, see the data points in the GHz range in Fig. 1d,f. The Nyquist curves in Fig. 1g show solely impedances measured at frequencies larger than 106 Hz. The curves in the complex plane plots reveal that several semicircles contribute to the overall bulk conductivity; this observation is especially indicated for the Nyquist curves recorded at 20 °C and 40 °C. The substructure of the curves of Sc-NZSP clearly points to multiple, simultaneously occurring electrical relaxation processes with very similar impedances.

Ionic vs. electronic conductivity

By reading off the conductivities of the plateaus in Fig. 1f, as indicated by the horizontally drawn arrow, we constructed an Arrhenius plot to analyse the temperature dependence of the two main electrical responses (see Fig. 2) Potentiostatic polarisation measurements, carried out prior to this analysis, ensured that the overall conductivity analysed is solely determined by ionic charge carriers. For this purpose, we used a symmetric Sc-NZSP pellet outfitted with ion blocking Au electrodes, applied a potential of 0.2 V and followed the current I over time t (Fig. 2a). After approximately 5 h a stationary state (It → ∞ = 63(5) pA) is reached in which the concentration gradients are fully developed and the only net charge transport across the material is due to electrons for which the Au contacts do not act as blockade. The final current of 63 pA (Fig. 2a) corresponds to an electronic conductivity of σeon, d.c. = 7.2(6) × 10−8 mS/cm. This value is lower by 7 to 8 orders of magnitude compared to the total conductivity σ ′ measured in the direct current (d.c.) limit ν → 0, i.e., for plateau (B), see Fig. 1f. Thus, Sc-NZSP must be regarded as a pure ionic conductor with the Na ion transference number tion close to 1.

Figure 2
figure 2

Electronic conductivity and temperature dependence of σ′ of Sc-NZSP, 23Na NMR spin-lattice relaxation. (a) Constant voltage (direct current) polarization curve of a sintered Sc-NZSP pellet. The high ionic conductivity translates into a rapid decay of the current at the beginning of the experiment. After a time lapse of sufficient length, the current approaches a value that is solely due to the transport of electrons. (b) Temperature dependence of the bulk and g.b. conductivity of Sc-NZSP (σbulk(298 K) = 2.0 mS cm−1). The results for NZSP free of Sc are also shown (σ′bulk(298 K) = 1.0 mS cm−1; σg.b.(298 K) = 0.7 mS cm−1). Filled symbols refer to bulk values, open ones represent the g.b. response. Crosses show conductivities taken from ref.22. (c) 23Na spin-lattice relaxation rates (R1, R) of Sc-NZSP recorded in both the laboratory frame of reference (79 MHz, R1) and the rotating-frame of reference (20 kHz, R). The sharp diffusion-induced peak of the latter and the shoulder of the R1(1/T) curve indicate extremely rapid Na ion diffusivity with rates in the order of ω0/2π ≈ 5 × 108 s−1 at T as low as 260 K. Error bars of the data points are smaller than the size of the symbols used. The solid line shows a fit with two BPP-terms to approximate the R1 rates; the dashed-dotted line highlights the asymmetric low-T peak with the activation energies 0.15 eV and 0.27 eV, respectively. The dashed-dotted line drawn through the R data points is to guide the eye. Unfilled symbols represent, for comparison, results from analogous measurements on a Li-analogue compound, Li1.5Al0.5Ti1.5(PO4)3 (LATP), see ref.49.

Activation energies and solid-state diffusion coefficients

The total conductivities plotted in Fig. 2b reveal that the overall electric transport in Sc-NZSP is determined by activation energies ranging from 0.29 eV to 0.31 eV (−100 °C to 130 °C). The Arrhenius line of the bulk process shows slight deviations from a perfectly linear behaviour. Such a deviation is even more pronounced for the g.b. response for which we identified several regions with activation energies ranging from 0.32 eV to values as high as 0.47 eV. While for temperatures lower than −20 °C bulk and g.b. conductivities differ by two orders of magnitude, above −20 °C σg.b. increased stronger than expected and was thermally activated with 0.47 eV. At temperatures higher than 120 °C the difference between σbulk and σg.b. turned out to be is less than 1 order of magnitude. A ratio σbulk/σg.b. close to 1 is, however, observed for NZSP. At 20 °C the bulk conductivity of Na3Zr2(SiO4)2PO4 is 1.0 mS/cm, for σg.b. we found 0.7 mS/cm (Fig. 2b, see also Fig. S2 for the corresponding Nyquist plots). A conductivity of 2.0 mS/cm for Sc-NZSP results in a room-temperature solid-state diffusion coefficient D of 2 × 10−12 m2/s if we use the Nernst-Einstein equation to estimate D via D = σbulkkBT/(Nq2) where kB denotes Boltzmann’s constant, T the absolute temperature in K, and q the elementary charge of the Na ions. N refers to the number density of charge carriers. Values for D in the order of 10−12 m2/s are comparable with the diffusion coefficients of the best ceramic Li ion conductors known today.

23Na NMR spin-lattice relaxation: Na+ motions on the angstrom scale

To check whether the high Na+ ion mobility seen in electrical measurements for Sc-NZSP is also reflected in NMR relaxation, we carried out variable-temperature 23Na spin-lattice relaxation (SLR) measurements in both the laboratory (R1) and rotating frame of reference (R), see Fig. 2c. The corresponding magnetization transients are shown in Fig. S3. While the first are sensitive to diffusive spin fluctuations in the MHz to GHz range, the spin-lock technique allows for the detection of slower motions in the kHz range. As we used a 23Na NMR Larmor frequency of ω0/(2π) = 79 MHz to record the 23NMR SLR rates, we expect the diffusion-induced rate R1 to pass through a maximum at temperatures near or slightly above 20 °C. The jump rate 1/τNMR at such a maximum is directly determined by the relation ω0τNMR ≈ 1 yielding DNMR = a2/(6τ) = 9 × 10−12 m2/s; for 1/τNMR we obtain 5 × 108 s−1. This estimation uses the Einstein-Smoluchowski equation for uncorrelated 3D diffusion and an average jump distance of 3.3 Å for the various possible exchange processes between the Na sites. In fact, we observe a complex relaxation behaviour with two R1 rate peaks as shown in Fig. 2c. One of these peaks appears as a shoulder of the main one. It is located at approximately −10 °C if we parameterize the overall relaxation response with a sum of two spectral density functions (for 3D diffusion) according to a modified version of the model of Bloembergen, Purcell and Pound41,42, see Supporting Information and Table S1. Interestingly, the low-T peak indicates even faster Na ion exchange processes than seen by conductivity spectroscopy. The question of whether it is triggered by a possible phase transformation occurring below room temperature and slightly changing the Na+ distribution in Sc-NZSP needs to be checked in further studies.

Conductivity measurements are sensitive to successful Na ion displacements in the so-called d.c. limit characterized by the respective σbulk plateau (Fig. 1f); here the corresponding activation energy is given by Ea,d.c. = 0.29(1) eV. The very low activation energy Ea,NMR of 0.15 eV (see also ref.43 for comparison) extracted from the diffusion-induced NMR rate peak R1(1/T) seen at lower T (Fig. 2c) indicates that 23Na NMR SLR senses the elementary diffusion processes to which local, correlated motions do also contribute. In general, the low-T flank of a given NMR rate peak is influenced by correlation effects such as Coulomb interactions and structural disorder. The latter is present also in the form of stress the jumping ions experience while moving in a heterogeneous, irregularly shaped potential landscape38. This landscape contains stable as well as transitions states with shorter residence times for the Na+ ions. We anticipate that forward-backward jumps involving interjacent bottleneck sites22,40,44 result in highly correlated jump processes that manifests as dispersive regions in the conductivity isotherms. These dispersive regions are seen in Fig. 1f in the high frequency region (>1 MHz) of the bulk isotherms. The activation energy of the high-T flank of the R1(1/T) peak should be comparable to Ea,d.c..

NMR and conductivity spectroscopy: a comparison

To compare activation energies from conductivity measurements directly with those from NMR relaxometry we need to analyse alternating current (a.c.) conductivities not in the limit ν → 0 but in the MHz regime, i.e., on the same time scale where NMR operates. We therefore determined σbulk(ν) at ν = 10 MHz. At this frequency, the dispersive parts are seen fully in the temperature range from −100 °C to −50 °C, which coincides with that of the low-T flank of the first R1(1/T) peak. A plot of log(σa.c.,bulk(10 MHz)T) vs. 1/T (see the inset of Fig. 2c) revealed an activation energy Ea,a.c. of 0.147(5) eV which is close to that seen by 23Na NMR SLR in the same temperature range, Ea,a.c. = Ea, NMR. The ratio Ea,d.c./Ea,a.c. = 1/βn turns out to be approximately 1.97. On the other hand, βn = 1/1.97 ≈ 0.5 is related to the Jonscher power law exponent45 describing the dispersive regime of σbulk(ν) via the relation βn = 1 – n, see ref.46. If NMR and a.c. conductivity spectroscopy are governed by very similar motional correlation functions in the temperature range given above, n ≈ 0.5 should be found. In general, βn can be used as a measure to describe the deviation from ideal Debye relaxation that relies on a pure exponential decay function. In the present case, parameterizing the corresponding a.c. isotherms with σbulk νn indeed yields n = 0.54 indicating similarly shaped correlation functions. This similarity does not contradict the finding that DNMR is larger than D from conductivity measurements. A relatively small correlation factor f ′ (≤0.1) linking the two coefficients via D = f′ · DNMR, see47,48 would explain the difference pointing to highly correlated motions in Sc-NZSP. f′ is given by the Haven ratio Hr and f. The two factors connect the tracer diffusion coefficient with either the Nernst-Einstein coefficient D or the self-diffusion coefficient D(NMR), see38. Most likely, here DNMR is indeed influenced by a huge number of unsuccessful, localized jump processes which are not contained in D that is sensitive to successful ionic displacements only. These localized motions may, however, stimulate long-range ion transport leading to ionic conductivities exceeding that of the Sc-free parent compound with a lower number density of Na+ ions.

An activation energy comparable to Ea,d.c. = 0.29 eV is seen in NMR relaxation spectroscopy only if the high-T flank of the diffusion-induced peak R1(1/T) can be reached33. In our case the high-T flank of the spin-lock R(1/T) peak recorded at a locking frequency ω1/2π = 20 kHz points to such a value, see Fig. 2c. However, the peak itself shows anomalous behaviour as the low-T side is characterized by a larger activation energy (0.41 eV) than that on the high-T flank. While such features might be ascribed to low-dimensional diffusion pathways, here the anomaly is supposedly caused by various superimposing jump processes. A point worth mentioning is that the conductivity spectroscopy in the d.c. limit yields an average activation energy of successful net charge transport over a long length scale. The corresponding activation energies extractable from NMR, particularly those in the low-T region of the R1(ρ)(1/T) peaks, specify distinct motional processes with activation energies Ea low-T being smaller or even higher than Ea, d.c.. The modified BPP fits shown in Fig. 2c for the R1(1/T) behaviour consistently yield a high-T activation energy Ea high-T of 0.27 eV being very similar to Ea, d.c., see Table S1 for the NMR results. The resulting asymmetry of the peak (see Supporting Information) has frequently been assigned to correlated motion governed by a distribution of (non-)exponential motional correlation functions. The two activation energies of the peak (Ea low-T = 0.15 eV and Ea high-T = 0.27 eV) are linked to each other via Ea low-T = (αNMR − 1)Ea high-T yielding αNMR = 1.55. αNMR = 2 would correspond to a quadratic frequency dependence, R1 ω02, on the low-T side and would indicate uncorrelated, isotropic motion. Furthermore, Ea high-T (and Ea, d.c.) is in line with the activation energy if we analyse the characteristic electric relaxation frequencies ωmax = νmax × 2π (see Fig. 1d) of the Modulus curves in the MHz to GHz regime. 1/τNMR = 5 × 108 s−1 agrees perfectly with ωmax(1/T) read off from the M′′ peaks, see Fig. S4. Hence, modulus spectroscopy and NMR probe the same time scale and sense the same Na+ motional correlation function and thus the same ionic exchange process.

For comparison, in Fig. 2c also 7Li NMR rates of Nasicon-type Li1.5Al0.5Ti1.5(PO4)3 (LATP) are shown49. LATP crystallizes with rhombohedral structure and belongs to one the fastest Li-containing phosphates50. Although the peak positions of the Na compound studied here are shifted toward somewhat higher temperatures, Sc-NZSP can compete with the high Li+ diffusivity in LATP. As for Sc-NZSP the 7Li NMR relaxation response of LATP was analysed with a superposition of at least two diffusion-induced relaxation rate peaks49. Since the quadrupolar interactions experienced by 7Li spins are much lower than those in the case of 23Na, the 23Na rates are shifted toward larger rates. Stretching factors of the underlying 23Na R1 magnetization transients, see Fig. S3, point to (localized) diffusion-induced quadrupolar field fluctuations that cause the recovery of the longitudinal magnetization for Sc-NZSP.


In summary, Na ion dynamics in sol-gel prepared Na3.4Sc0.4Zr1.6(SiO4)2PO4 turned out to be extremely rapid at temperatures around ambient. 23Na NMR spin-lattice relaxation is governed by complex Na+ dynamics as the relaxation rates reveal several diffusion-induced peaks. While short-range Na motion has to be characterized by activation energies ranging from 0.13 to 0.15 eV, long-range ion transport, on the other hand, follows Arrhenius behaviour with 0.29 to 0.31 eV. Facile Na ion exchange results in room-temperature ion conductivities of 2.0 mS/cm for Na3.4Sc0.4Zr1.6(SiO4)2PO4 and 1.0 mS/cm for the parent compound Na3Zr2(SiO4)2PO4, respectively. Such high bulk conductivities correspond to solid-state diffusion coefficients in the order of 2 × 10−12 m2/s. Indeed, for Sc-NZSP 23Na spin-lattice relaxation NMR points to a self-diffusion coefficient of 9 × 10−12 m2/s at 21 °C. Evidently, extremely rapid ion jump processes between regular and intermediate positions contribute to this high value. Such rapid movements obviously trigger the successful jump processes among the different crystallographic sites in the 3D framework of the phosphosilicate and facilitate net charge transport over macroscopic distances in Sc-NZSP.

Methods and Experimental Design

Conductivity analysis

Sintered pellets with sputtered or evaporated Au electrodes were used to measure complex conductivities at various temperatures and from 0.1 Hz up to the GHz range with a Novocontrol Concept 80 setup. The setup consists of a broadband analyser (Alpha-AN, Novocontrol), which is connected to a BDS 1200 cell in combination with an active ZGS cell interface (Novocontrol) allowing 2-electrode dielectric measurements. The temperature is automatically controlled by means of a QUATRO cryo-system (Novocontrol) making use of a heating element which builds up a specified pressure in a liquid nitrogen Dewar vessel to create a highly constant N2 gas flow. After being heated by a gas jet, the evaporated N2 flows directly through the sample cell that is mounted in a cryostat. With this setup, temperatures can be set with an accuracy of ±0.01 °C. To reach up to 3 GHz we used an Agilent E4991 A high-frequency analyser connected to a high frequency cell designed by Novocontrol.

Polarisation measurements

For the d.c. polarisation measurement a sintered pellet (0.89 mm thick, 7 mm in diameter) was metallised with Au on both sides by evaporation. The pellet was then mounted in an air-tight 2-electrode Swagelok-type cell and connected to the Parstat MC potentiostat equipped with a low-current option. All the preparation steps, including the metallisation, were carried out in Ar or N2 filled gloveboxes filled with an oxygen and water content of less than 1 ppm. The polarisation experiments were performed in a Faraday cage at 23(1) °C.

23Na NMR measurements

All static 23Na NMR measurements were carried out using a Bruker Avance III spectrometer equipped with a shimmed cryo-magnet with a nominal magnetic field B0 of approximately 7.04 T. This field strength corresponds to a 23Na resonance frequency of ω0/2π = 79.35 MHz. For the NMR measurements, we used sintered pellets which were fire-sealed under vacuum in quartz glass ampoules to permanently protect them from moisture and/or air. We used a Bruker broadband probe (80 mm in diameter) designed for static variable-temperature measurements. The temperature in the sample chamber made of Teflon® was adjusted with a stream of freshly evaporated nitrogen gas. The heating coil was controlled by a Eurotherm unit connected to copper-constantan type T thermocouple placed in the immediate vicinity of the sample. To study Na ion dynamics, 23Na NMR spin-lattice relaxation experiments in both in the laboratory and in the rotating frame were carried out with pulse sequences using suitable phase cycling to suppress unwanted coherences. R1 rates were recorded with the saturation recovery pulse sequence consisting of a train of 90° pulses to destroy any longitudinal magnetization M. The subsequent recovery of M was recorded after variable delay times td with a 90° reading pulse. The π/2 pulse lengths ranged from 2 to 4 μs at 200 W, depending on temperature. Up to 64 scans were accumulated to obtain M(td) for each waiting time. The area under the free induction decays was used as a measure for M(td). The magnetization transients M(td) were analysed with stretched exponential functions to extract the rates R1; stretching exponents varied from 0.8 to 1. The spin-lock measurements were recorded with a locking frequency of 20 kHz. At the beginning of the pulse sequence a 90° pulse prepares the spin system. Immediately after this, the locking pulse with variable duration tlock (46 μs to 46 ms) was used to observe transversal relaxation of the flipped magnetization Mρ. The decay of Mρ in the (xy)ρ-plane of the rotating frame of reference is detected with a 90° reading pulse. The number of scans for each data point of the magnetization curve was 64. A recycle delay of at least 5 × 1/R1 ensured full longitudinal relaxation. Mρ(tlock) could be fitted with stretched exponentials; the stretching factors ranged from 0.8 to 0.4 depending on temperature.