Rapid Low-Dimensional Li⁺ Ion Hopping Processes in Synthetic Hectorite-Type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂

Abstract

Understanding the origins of fast ion transport in solids is important to develop new ionic conductors for batteries and sensors. Nature offers a rich assortment of rather inspiring structures to elucidate these origins. In particular, layer-structured materials are prone to show facile Li⁺ transport along their inner surfaces. Here, synthetic hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂, being a phyllosilicate, served as a model substance to investigate Li⁺ translational ion dynamics by both broadband conductivity spectroscopy and diffusion-induced ⁷Li nuclear magnetic resonance (NMR) spin–lattice relaxation experiments. It turned out that conductivity spectroscopy, electric modulus data, and NMR are indeed able to detect a rapid 2D Li⁺ exchange process governed by an activation energy as low as 0.35 eV. At room temperature, the bulk conductivity turned out to be in the order of 0.1 mS cm^–1. Thus, the silicate represents a promising starting point for further improvements by crystal chemical engineering. To the best of our knowledge, such a high Li⁺ ionic conductivity has not been observed for any silicate yet.

1. Introduction

The diffusion of small cations and anions plays an important role in many devices such as sensors¹⁻³ and batteries.⁴⁻¹¹ Although for some applications, e.g., in the semiconductor industry¹² or in the development of breeding materials¹³⁻¹⁵ for fusion reactor blankets, diffusion is unwanted, in other branches, materials with extremely high diffusion coefficients are desired.¹⁶⁻²¹ Finding the right material and tailoring its dynamic properties further requires an in-depth understanding of the origins that determine fast ion dynamics.²²⁻²⁶

In many cases, layer-structured materials²⁷⁻³⁰ are known to offer fast diffusion pathways along the buried interfaces or between larger gaps inside the crystal structure.³¹ Commonly, powder samples are synthesized and investigated; however, polycrystalline samples do not allow orientation-dependent measurements of ionic conductivity. Fortunately, anisotropic properties of ionic transport in polycrystalline samples can be probed by nuclear magnetic resonance (NMR) spin–lattice relaxation experiments.^5,30,32−35 The most prominent examples, whose Li⁺ diffusion properties were studied in this way,³⁶ include graphite^37,38 or transition metal chalcogenides such as TiS₂,³⁹⁻⁴³ NbS₂,^44,45 and SnS₂.⁴⁶ Recently, two-dimensional (2D) Li⁺ diffusion has also been determined in hexagonal LiBH₄.^29,47 Fast fluoride, F^–, diffusion is observed in MeSnF₄ (Me = Pb, Ba) and, as has been shown quite recently, also in layer-structured RbSn₂F₅.⁴⁸ In these materials, spatial constraints guide the ions over long distances. The principle of guided ions has also been found in Li₁₂Si₇.^49,50 In binary silicide, the Li⁺ ions are subjected to a fast one-dimensional diffusion process along the surface of a virtual pipe formed by the stacked Si₅ rings.⁴⁹ In channel-structured materials with the ions diffusing inside the channels, their diffusion pathways may, however, easily be blocked by foreign, immobile ions.⁵¹ The same effect might, of course, also influence 2D translational ion dynamics but to a lesser degree.

To understand Li⁺ diffusion in structures offering 2D diffusion pathways, we chose hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ as a model system, see Figure 1, and studied the Li⁺ self-diffusion properties and electrical ionic transport. While the latter is investigated by broadband conductivity spectroscopy,⁵² we took advantage of ⁷Li NMR spin–lattice relaxation measurements^32,53 to shed light on Li⁺ translational dynamics.

Figure 1.

(a) Idealized crystal structure of hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ (drawn according to the space group C2/m, the real structure is clearly turbostratic) with two distinct crystallographic sites occupied by the Li ions. Those between the Mg-rich layers (see (b)), which are here shown following a homogenous charge distribution, are expected to have access to fast 2D diffusion pathways.

Hectorite is, as montmorillonite, a clay mineral of the smectite group (gr. σμηκτις, soil with the ability to clean, to soak something up, e.g., swelling through water uptake). Such silicates belong to the family of phyllosilicates (gr. φυλλο, leaf). Fluorohectorite is a 2D host material with a rigid 2:1 sandwich-like structure;⁵⁴ each lamella is composed of two silicate and one Mg²⁺ rich layer where the earth alkaline cations are octahedrally coordinated by oxygen and fluorine anions. An idealized structure of synthetic (turbostratic) Li-bearing fluorohectorite [Li_0.5]^inter[Mg_2.5Li_0.5]^octa[Si₄]^tetraO₁₀F₂ is shown in Figure 1. Natural hectorite of the composition Na_0.3(Mg, Li)₃Si₄O₁₀(OH)₂, including also minor amounts of Ca²⁺, K⁺, and Al³⁺, was named for its occurrence 5 km south of Hector (San Bernardino County, California, USA).⁵⁵ It was first described in 1941 and found in a bentonite deposit, altered from clinoptilolite, a natural zeolite, derived from volcanic tuff and ash with a high glass content.⁵⁵ Cation exchange strategies allow one to effectively replace the Na ions in hectorite by Li ions; also larger inorganic or organic molecules (pillars) can be introduced, resulting in porous so-called pillared clays.⁵⁴ Exemplarily, the Khan group successfully used hectorite-based materials as passive and active filler materials to prepare nanocomposite polymer-based (gel) electrolytes as well as to develop composite LiCoO₂-based cathode materials.⁵⁶⁻⁵⁹ Here, our hypothesis is that the interlayer gap in such host structures, particularly that of hectorite, offers indeed fast diffusion pathways for small charge carriers such as Li⁺ and Na⁺ ions.

Verifying the hypothesis of 2D transport is, however, challenging if only powder samples are available at hand. Fortunately, ⁷Li NMR spin–lattice relaxation measurements,^49,53 also successfully used to characterize electrolytes for batteries,^60,61 represent a unique tool to study such anisotropic properties even for powdered samples, since the spectral density functions J governing the NMR spin–lattice relaxation rates 1/T₁ (∝ J) possess specific features for 1, 2, and 3D ion transport.^30,62 As intimated above, low-dimensional ionic transport has, so far, been probed only for a limited number of materials by NMR relaxation techniques.³⁶ The present study contributes to this research field and is aimed at answering the question whether 2D silicate structures offer an assortment of materials with enhanced ion diffusion properties.

2. Experimental Section

2.1. Preparation and Characterization of Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂

Lithium fluorohectorite with the nominal composition of Li_0.5[Mg_2.5Li_0.5]<Si₄ > O₁₀F₂ was prepared by a two-step ion exchange procedure starting from melt synthesized Na-fluorohectorite (Na_0.5[Mg_2.5Li_0.5]<Si₄ > O₁₀F₂). The Na-fluorohectorite was synthesized according to a preparation route published earlier.^54,63 To ensure the complete exchange of Na⁺ by Li⁺, Na-fluorohectorite was first treated with n-butylammonium chloride (C₄H₁₂ClN (C4), 2 M) using a 100-fold excess of its cation exchange capacity (CEC) to obtain the so-called C4-fluorohectorite. Typically, 500 mg of Na-fluorohectorite was exchanged overnight five times with 40 mL of C4 solution at 80 °C. The resulting product was washed five times with an ethanol–water mixture (1:1) and once more with pure ethanol. Atomic absorption spectroscopy (AAS), see below, was used to check the completeness of the ion exchange reaction. After this, the dried C4-fluorohectorite was treated with a 100-fold excess of the CEC of LiOH (2 M, 4 times 40 mL, 6 h, room temperature). While removing excessive LiOH by washing 6 times with 40 mL of deionized water, the ionic strength decreased to a value lower than 0.02 M; furthermore, complete delamination by repulsive osmotic swelling was observed.⁶³⁻⁶⁶ Finally, the gel of delaminated Li-fluorohectorite was freeze-dried followed by vacuum drying at 160 °C.

2.1.1. AAS

To verify complete Na⁺-exchange, AAS was used. For this purpose, approximately 20 mg of the samples were weighed into clean Teflon-flasks of 15 mL volume. After the addition of 1.5 mL of 30 wt % HCl (Merck), 0.5 mL of 85 wt % H₃PO₄ (Merck), 0.5 mL of 65% HNO₃ (Merck), and 1 mL of 48 %HBF₄ (Merck), the samples were digested in a 1200 Mega microwave digestion apparatus (MLS, Mikrowellen-Labor-Systeme) for 6.5 min and heated at 600 W. Afterward, the closed sample container was cooled to room temperature; the clear solution was diluted to 100 mL in a volumetric flask and analyzed with a Varian AA100-spectrometer. To determine the Na⁺-content by AAS, a five-point calibration curve (0.0 to 0.2 mg/100 mL) was measured by diluting a Na⁺ standard AAS-solution (1000 mg/mL) in nitric acid.

2.1.2. CHN-Analysis

A Elementar Unicode equipped with a combustion tube filled with tungsten(VI)-oxide-granules was used to analyze the elements C, H, and N at a combustion temperature of 1050 °C. Samples were dried at 120 °C prior to the measurement.

2.1.3. Physisorption Measurements

Argon adsorption measurements were performed using a Quantachrome Autosorb at 87.35 K using samples that were dried at 120 °C for 24 h in a high vacuum. The pore sizes and volumes were calculated using a nonlocal DFT model (software version 2.11, Ar on zeolite/silica, cylindrical pores, equilibrium model).

2.2. Conductivity Spectroscopy

To perform broadband conductivity measurements, the hectorite sample was first ground in a mortar before the sample was uniaxially pressed (0.5 tons) into a cylindrical pellet with a diameter of 5 mm and a thickness of approximately 1 mm; the exact thickness was determined with a vernier calliper. The pellet was equipped on both sides with Au electrodes that blocked Li⁺ ion transport. For this purpose, we used an EM SCD 050 sputter coater from LEICA. The thickness (100 nm) was controlled with a quartz thickness monitoring system. The pellet was then placed inside an active ZGS cell (Novocontrol), which was connected to a Novocontrol Concept 80 broadband dielectric spectrometer. We measured the complex impedance, conductivity, and permittivity as a function of temperature and in a frequency range of 0.01 Hz to 10 MHz. The ZGS sample holder was placed in a cryostat, allowing us to measure conductivity isotherms from 133 to 433 K in steps of 20 K. Temperature regulation and monitoring was carried out with a QUATRO controller (Novocontrol). In order to eliminate residual moisture, the pellet was pre-dried in the impedance cell at 433 K (160 °C) for 4 h. During the entire measurement, the impedance cell was permanently flushed with dry, freshly evaporated nitrogen gas.

2.3. Magic Angle Spinning (MAS) NMR

⁶Li (73.6 MHz, 120 W power amplifier, 1024 scans, recycle delay 5T₁ (see below), pulse length 3 μs) and ¹⁹F (470.6 MHz, 50 W, 32 scans, recycle delay 1 s, pulse length 2.1 μs) MAS one-pulse NMR spectra were recorded with a 500-MHz Avance spectrometer (Bruker). The measurements were carried out at a rotation speed of 25 kHz using 2.5 mm rotors. The spectra were recorded using one-pulse sequences with ambient bearing gas. Crystalline LiCH₃COO and liquid CFCl₃ served as reference materials to determine the isotropic chemical shifts δ_iso.

2.4. Time-Domain ⁷Li NMR Measurements

To prepare the sample for NMR measurements, the hectorite powder sample was ground using a mortar and pestle under an Ar atmosphere in a glove box. After this, it was dried in a vacuum at 160 °C before being fire-sealed in Duran ampoules under vacuum. We recorded both ⁷Li NMR spectra and ⁷Li NMR spin–lattice relaxation rates as a function of temperature (173 to 433 K). For this purpose, we used a Bruker 300-MHz spectrometer that was connected to a Bruker cryomagnet with a nominal magnetic field of 7 T. This field corresponds to a nominal ⁷Li Larmor frequency of ω₀/2π = 116 MHz. While laboratory frame spin–lattice relaxation rates (1/T₁) were recorded with the saturation recovery pulse sequence,⁶⁷ the spin-lock technique^67,68 was applied to measure transversal magnetization transients leading to the rate 1/T_1ρ, which characterizes spin–lattice relaxation in the so-called rotating frame of reference. The 90° pulse length (t_p) was 2 μs (200 W broadband amplifier) and showed only a slight dependence on temperature. To measure 1/T₁, we used a comb of 10 closely spaced (80 μs) radio frequency pulses to destroy any longitudinal magnetization M. The subsequent recovery of M as a function of the delay time t_d (4 scans) was followed with a 90° detection pulse; the delay between each scan, although not needed, was set to 1 s. In general, M(t_d) follows a stretched exponential behavior according to M(t_d) = M₀(1 – exp[−(t_d/T₁)^γ′]), 0<γ′≤1. M₀ denotes the equilibrium magnetization that is reached at t_d → ∞. Here, M(t_d) follows a bi-exponential behavior if the full area under the free induction decays (FIDs) is used to construct M(t_d), see the Supporting Information, Figure S2. In this case, we used a sum of stretched exponentials to parameterize the transient.^31,69,70 Alternatively, the two components of the FIDs were separately analyzed, as explained below. For the corresponding spin-lock M_ρ(t_d) transients (see also Figure S2), we used a single, stretched exponential function to analyze the decay functions: M_ρ(t_lock) ∝ exp[−(t_lock/T_1ρ)^γ]), t_lock denotes the duration of the locking pulse. We varied t_lock from 30 μs to 30 ms (8 scans per locking time) and used a power level that results in a locking frequency ω₁/2π of ca. 20 kHz. The recycle delay between each scan was at least 5T₁. This value is orders of magnitude lower than ω₀/2π used for the laboratory-frame measurements; hence, spin-lock NMR is sensitive to much slower Li ion dynamics compared to probing via T₁ measurements.

3. Results and Discussion

3.1. Synthesis of the Li-Fluorohectorites

Direct melt synthesis of Li-fluorohectorites is troublesome. In general, melt-synthesized Li-fluorohectorites may contain a range of impurities and could suffer from isomorphous substitution effects. Thus, the charge density of the silicate layers turned out to be heterogeneous as described earlier.⁷¹ In contrast to the Li-bearing compound, melt synthesis of Na-fluorohectorite followed by long-term annealing yields phase pure materials with a homogenous charge density and, thus, a uniform intracrystalline reactivity.^54,63 This uniform intracrystalline reactivity is especially important for a uniform cation distribution in the interlayer space, which in turn is expected to have a considerably high impact on cation transport properties. Therefore, the Li-fluorohectorite used for the present study was prepared by taking advantage of a complete ion exchange of Na-fluorohectorite. Unfortunately, the affinity of Li⁺ for the interlayer space of hectorites is lower than that of Na⁺.⁷² Consequently, complete ion exchange could not be accomplished directly, even at very high incoming Li⁺-concentrations. Therefore, Na⁺ was fully exchanged with C4 taking advantage of the much higher selectivity of organic cations for the interlayer space.⁷³ The completeness of ion exchange at this stage was verified by AAS.

In the next step, Li exchange to Li-fluorohectorite could be driven by deprotonation of the intercalated C4. Elemental analysis proved complete replacement of C4 within experimental errors. At low ionic strength, i.e., at values being smaller than 0.02 M as achieved during the washing procedure,⁶³ Li-hectorite delaminates spontaneously in aqueous suspension by repulsive osmotic swelling whereupon a liquid crystalline gel is obtained. Freeze drying of this gel leads to a voluminous, spongelike, and hierarchically porous material (Figure 2b).

Figure 2.

(a) Powder X-ray diffraction pattern of dry Li-fluorohectorite Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ with marked reflections of the 00 L series and the hk bands; the inset shows the representative bandlike structure of the hectorite. (b) Scanning electron micrograph of freeze-dried and partially restacked Li-fluorohectorite.

The powder X-ray diffraction pattern of dry Li-fluorohectorite is shown in Figure 2a and shows the characteristic reflections of the 00 L-series with a basal spacing of 10.2 Å. Missing hkl reflections and occurrence of the λ-shape of 02/11-, 13/20-, 04/22-, 15/24-, and 06-bands indicated a turbostratic type of stacking of adjacent silicate layers. Upon drying, partial restacking is forced with large overlapping areas between adjacent individual layers (20 μm diameter) and leads to bandlike aggregate structures (Figure 1b). Consequently, Li⁺ cations are residing at external basal planes and in the interlayer space. The ratio of the two Li sites can only be estimated. The thickness of the restacked tactoids cannot be determined by analyzing the full width at half maximum (fwhm) of basal reflections via the Scherrer equation because the broadening is largely determined by random interstratification of the slightly varying stacking vector. Because of turbostratic disorder, the PXRD pattern contains little structural information beyond basal spacing, which is obvious when comparing a simulated XRD pattern (see Figure S1) for a hypothetical, fully 3D ordered Li-hectorite structure (C2/m (no. 12), a = 5.25(2) Å, b = 9.08(3) Å, c = 10.37(4) Å, β = 96.51(8)°). Since the hk-bands are located approximately at the position of hk0 reflections, this unit cell could be refined by applying the experimental turbostratic pattern, although with some uncertainty in the ab-dimensions. As ion exchange is a topotactic reaction, the structure of the silicate layers is fully preserved as indicated by ab-dimensions being similar to dimensions found for a 3D ordered member of the hectorite family (a = 5.2434(10) Å; b = 9.0891(18) Å).⁷⁴ The latter, refined structure of the silicate layer could, therefore, be safely applied to obtain Figure 1 and to draw the scheme shown in the inset of Figure 2a.

As the interlayer surface area in the collapsed dry state is not accessible to probe gas molecules, the degree of restacking can, however, be deduced from the specific surface area determined by physisorption. Given the large diameter, the contribution of edges to the total surface area can be safely neglected. The specific surface area per gram for an individual delaminated silicate layer was calculated from the known ab dimension and the formula weight. The ratio of this calculated surface area (759.368 m²/g) and the surface area measured by Brunauer–Emmett–Teller analysis (5.174 m²/g) yields the average number n_l of layers in the stack, n_l = 147. This estimation indicates that most of the Li⁺ ions are indeed located in the interlayer space.

3.2. Ionic Transport and Li⁺ Diffusivity

In Figure 3a, the broadband conductivity isotherms of layer-structured Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ are shown. The isotherms, which show the real part of the complex conductivity σ’ as a function of frequency ν, were recorded over a dynamic range of 9 decades.

Figure 3.

(a) Conductivity isotherms of layer-structured, hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ recorded from T = 133 K to T = 433 K; the measurements span a frequency range of 9 decades. In regime I, the isotherms are governed by the grain boundary (g.b.) response, while in regime II, bulk properties dominate the shape of the curves. See text for further details. (b) Arrhenius plot showing both log₁₀(σ’_DCT/(S cm^–1 K)) and log₁₀(1/τ_M / s^–1) vs. the inverse temperature 1000/T. The left axis refers to σ’_DC showing either the temperature behavior of the bulk ion conductivity or that governed by the highly resistive g.b. regions. The latter denotes the total conductivity seen in regime I of the isotherms shown in (a). 1/τ_Mi refers to the two maxima (i = 1, 2) seen in the electric modulus curves M”(ν), see Figure 4b, whereas 1/τ_M1 refers to the g. b. response and 1/τ_M1 denotes the characteristic electrical relaxation rates of the M”(ν)-peak representing the bulk response. Lines, either dashed or dotted, show Arrhenius fits with the activation energies indicated. At room temperature, σ’_DC, bulk ≈ 0.14 mS cm^–1 is expected through extrapolation of the Arrhenius line shown. For comparison, the rates 1/τ_ρ from electrical resistivity measurements carried out at a fixed frequency (1.2 MHz, 10 MHz, see Figure 5b) are included as well.

The conductivity curves can be subdivided into several parts, labelled A, B, and C (Figure 3a). To explain these features, we first consider the isotherm recorded at the highest temperature, that is, at T = 433 K (regime I). At low frequencies ν, electrode polarization appears, which manifests itself as a drop in conductivity (A). With increasing frequency, σ’ enters the so-called direct current (DC) plateau that corresponds to long-range ion transport in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ (B). The associated capacitance C of this distinct plateau is in the order of 300 pF (= C_gb). Without any doubt, such a high value corresponds to an electrical process that is dominated by g.b. regions.⁷⁵ Increasing the frequency further leads to the associated dispersive part (C) of the DC plateau, which follows a σ’ ∝ ν^p = 1 behavior as indicated by the dashed line in Figure 3a.

With decreasing temperature, σ’_DC, gb decreases and the curves are shifted toward lower frequencies. At sufficiently low T, a second DC plateau could be revealed (see regime II). This plateau does only appear as a curvature of the isotherms shown in regime II of Figure 3a. Its dispersive regime is only hardly visible; at very low temperatures and high frequency, the exponent p in the Jonscher-type relation σ’ ∝ ν^p approaches 1, indicating the beginning of a nearly constant loss behavior.⁷⁶⁻⁸¹ Most importantly, while total conductivities, dominated by the g.b. response, can easily be read off from the distinct plateaus in regime I (see Figure 3a), σ’_DC, b values characterizing bulk ion transport are only accessible by careful evaluation of the curvature seen in regime II. Filled symbols in Figure 3a mark estimations of these values.

The temperature dependence of both values, σ’_DC, b and σ’_DC, gb, is analyzed using the Arrhenius plot shown in Figure 3b. Conductivities dominated by ion-blocking grain boundaries obey the Arrhenius law with an activation energy E_a gb of 0.58 eV. Lines in Figure 3b refer to σ’_DCT = σ₀ exp. (−E_a/(k_BT)) with σ₀ being the pre-exponential factor and k_B denoting Boltzmann’s constant. Compared to σ’_DC, gb the bulk conductivity values σ’_DC, b turned out to be higher by 6 orders of magnitude, and bulk ion transport has to be characterized by an activation energy of E_a, b = 0.36 eV. Extrapolating the estimated values σ’_DC, b toward room temperature yields 0.14 mS cm^–1 at 293 K. This value is comparable to those reported for garnet-type oxides such as cubic-Li₇La₃Zr₂O₁₂ being considered as powerful electrolytes for ceramic electrochemical energy storage systems.¹⁰

To support our claim that the curvatures in regime II of Figure 3a are suitable to estimate bulk ion conductivities of hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂, we analyzed electric modulus curves, M’’(ν), which we recorded at a fixed temperature and variable frequencies.⁴⁸ The corresponding curves are shown in Figure 4a by using a half-logarithmic plot and in Figure 4b by taking advantage of the double-logarithmic scaling to illustrate the change of M’’ with frequency.

Figure 4.

(a) Electrical modulus curves M”(ν) of hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂, which were recorded at the temperatures indicated. (b) Same curves as in (a) but using a double logarithmic plot to visualize also those peaks that are governed by a higher permittivity (and capacitance), see arrow pointing at the peak that appears at 0.03 Hz (233 K). The latter reflects g.b. responses, while the main modulus peaks are produced by bulk electrical relaxation processes characterized by a much lower permittivity, see the arrow pointing at the peak at ν = 8 × 10⁵ Hz. The dashed lines show the response of a measurement on a second pellet prepared, indicating the good reproducibility of the analysis.

In general, the complex modulus M* is given by the inverse complex permittivity, M* = 1/ε*. The real part of ε*, denoted as ε’, is shown in Figure 5a. As seen for σ’, also ε’(ν) passes through the same electrical regimes viz. electrode polarization, g.b., and bulk response. The latter is only slightly seen for the isotherms recorded at very low temperatures. The permittivity value ε’_b(ν → 0) = 10 (see Figure 5a) corresponds to C_b< 10 pF if we use the relation for a plate capacitor, C = ε₀ε’_bA/d, to estimate the associated bulk capacitance. Here, ε₀ is the vacuum permittivity, A denotes the area of the pellet and d its thickness. Importantly, the imaginary part of M*, M’’, is dominated by bulk effects as the amplitude of M’’ is proportional to the inverse of C_b, (gb), M’’ ∝ 1/C. Hence, we expect a clearly visible bulk M’’(ν) peak accompanied by a second one, the g.b. response, being drastically reduced in magnitude. As compared to the main peak, the g.b. peak (denoted as peak 1 in the following, see Figure 4b) is expected to be shifted toward lower frequencies by at least 6 orders of magnitude, as σ’_DC, gb/σ’_DC, b ≈ 10.⁶ While in the semilog plot, see Figure 4a, only the main peak (peak 2) is seen, in the double-logarithmic representation of the data, two modulus peaks are indeed recognizable, see the arrows in Figure 4b that exemplarily point to these two peaks that belong to the curve measured at 233 K. The ratio of the peak amplitudes is given by M’’_max(peak 2)/M’’_max(peak 1), which, in the present case, amounts to 30–40. Of course, this value reflects the ratio ε’_gb/ε’_b (see Figure 5a) and the ratio C_gb/C_b as well. Note that these values are rough estimations, as they assume Debye-like responses. In general, deviations from Debye-like behavior are seen if correlated motion or, as argued in the following, low-dimensional transport governs the electrical relaxation processes.^82,83

Figure 5.

(a) Change of the electrical permittivity of layer-structured Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ as a function of frequency and temperature. While the bulk region (ε’_b(0) = 10) is hardly seen in this representation, the g.b. response (ε’_gb(0) = 360) and electrode polarization (ε’_p(0)>10⁶) dominate the isotherms, which were recorded from 133 to 433 K in steps of 20 K. (b) Temperature behavior of the electric resistivity is expressed as M”/ω and measured at two different frequencies ω/2π = 1.2 and 10.0 MHz. The fact that the flanks at high temperatures do not coincide is an indication of low-dimensional ion transport; 3D ion dynamics would yield the behavior indicated by the dashed-dotted lines. From the peak maxima, two electrical relaxation rates can be deduced that are also included in Figure 3b. See text for further explanations.

Here, the most important parameter, which we deduce from the two peaks of the modulus curves shown in Figure 4b, is the characteristic relaxation rate τ_M^–1. It corresponds to the frequency at which the peak appears, i.e., at M’’ = M’’_max. In Figure 3b, log₁₀(τ_M1^–1) and log₁₀(τ_M2^–1) of the two peaks 1 and 2 are plotted vs 1000/T. τ_M2^–1(1/T) reveals almost the same activation energy (0.35 eV) as σ’_DC, b, thus supporting our interpretation of σ’_DC, b to represent a parameter characterizing a bulk response. The difference in activation energies is less than 0.015 eV, which is within the error range of the values. The same holds for the activation energies obtained for τ_M1^–1 and σ’_DC, gb (0.60 eV vs 0.58 eV). Note that the rates τ_M^–1 shown in Figure 3b refer to technical frequencies ν_max; using angular frequencies instead (ω_max = 2π ν_max) would simply shift the Arrhenius line by an additive constant (log₁₀(2π) ≈ 0.8) upward on the log₁₀ scale.

In addition to the possibility to extract characteristic relaxation rates from M’’(ν) peaks, we measured the quantity M’’/ω as a function of the inverse temperature at a fixed frequency.^52,84,85M’’/ω corresponds to the resistivity ρ’ and is expected to pass through an electrical relaxation peak that should be parameterizable with a Lorentzian shaped function: ρ’ = M’’/ω = τ_ρ/(1 + (τ_ρω)^β) with 1<β≤2. Here, τ_ρ denotes the electrical relaxation time, and β is a parameter that expresses the deviation of the peak, log₁₀(ρ’) vs 1/T, from symmetric behavior. Symmetric rate peaks are obtained for β = 2; β<2, however, indicates correlated motion affecting the electrical process probed. In the case of 3D motions, the latter case would result in asymmetric peaks with the so-called low-temperature flank, showing a lower slope than the high-temperature flank. If measured at different frequencies, the rates in the latter regime are expected to coincide. This feature is indicated in Figure 5b by the dashed-dotted lines. The activation energy of the high-T flanks should correspond to E_a sensed by σ_DC b and τ_M2^–1, which are characterized by 0.36 eV. Astonishingly, in the present case, E_a in the high-T limit ranges from only 0.06 to 0.08 eV. Moreover, the high-temperature flanks of the two peaks clearly do not coincide. As an example, at 330 K, the corresponding values M’’/ω differ by more than one order of magnitude revealing a dispersive behavior of the underlying electrical relaxation function. We attribute this deviation seen by the resistivity measurements to the low-dimension, i.e., 2D ionic transport in the Li-bearing phyllosilicate Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂. This assignment is considered to be in analogy to the interpretation of diffusion-induced NMR spin–lattice relaxation rate (1/T₁) peaks as a function of the inverse temperature at various frequencies. In the case of, e.g., the 2D Li-ion conductor Li_xTiS₂, the dispersive behavior of the NMR correlation function in the high-T, that is, the low-frequency, limit was in quantitative agreement with the NMR theory.⁴⁰ Although, in principle, NMR and conductivity relaxation are governed by different correlation functions,^83,86 the conclusion that the high-T flank is sensitive to the dimensionality of diffusion holds qualitatively also for the resistivity.

At the peak maximum, i.e., at T = T_max, the condition τ_ρω ≈ 1 is valid. With ν = ω/2π for each frequency (ν = 1.2 MHz and ν = 10.0 MHz), a rate τ_ρ^–1(1/T_max) can be estimated, which we included in Figure 3b as well. τ_ρ^–1 agrees with τ_M2^–1deduced from the M’’(ν) peaks if we extrapolate the corresponding Arrhenius line toward higher temperatures. Hence, long-range ion transport in the bulk of Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ is given by an activation energy of 0.35 eV. This value is comparable to those energies ordinarily seen for Li⁺ ionic transport in, e.g., garnet-type oxides.^10,87,88 Identifying E_a = 0.35 eV with the activation energy, which should actually be seen in the high-T regime of the ρ’(1/T) peak, the parameter β would take a value of approximately 1.29, as β is given by 0.10 eV/0.35 eV = β – 1, if we adopt the analogy between conductivity and NMR relaxation more quantitatively.^5,30 In this relation, the value of 0.10 eV represents the activation energy in the low-T regime of the ρ’(1/T) peak, see Figure 5b. β = 1.29 indicates rather strong ion–ion correlation effects. While such effects reduce the slope of the low-T flank, dimensionality effects will only influence the rates in the high-T regime. Semi-empirical models for 2D diffusion predict that the slope of the high-T flank should take a value that is approximately 75% of the slope in the low-T limit.⁶² Here, the combination of ion–ion correlation and 2D diffusion results in apparently symmetric peak shapes even for low-dimensional dynamics. A very similar behavior has been observed earlier by Li⁺ nuclear spin-relaxation in Li_xTiS₂.⁴⁰

In conclusion, we found evidence that a 2D ionic transport is present in the phyllosilicate under study, which is governed by a rather low activation energy of only 0.35 eV. From Figure 3b, we see that the ratios τ_M2^–1/τ_M1^–1 (= τ_M1/τ_M2) and σ’_DC, b/σ’_DC, gb differ by at least one order of magnitude. This observation is independent of T, as the differences in E_a for the two processes show only little change with temperature. Hence, we might have underestimated rather than overestimated the bulk ion conductivity, which we read off from the σ’(ν) curvatures seen in regime I (Figure 3a) by one order of magnitude. Such a rapid ionic transport process is expected to be measurable also in ⁷Li nuclear spin relaxation. Indeed, both NMR line-shape measurements and spin-lock NMR spin–lattice relaxation rates point to temporary spin fluctuations being extremely rapid on the NMR time scale.

In Figure 6, ⁷Li NMR line shapes are shown, which we recorded at temperatures ranging from 173 to 433 K. As can be seen in Figure 6b, the line consists of two components. A broader line with a width of ca. 12 kHz is superimposed by a narrower one whose width narrows with temperature because of increasing dipole–dipole averaging. Such averaging originates from motional processes rendering the homonuclear Li–Li dipolar interactions time dependent. The broad line can either be interpreted as a result of electric quadrupole interactions of the Li spins with nonvanishing electric field gradients or as a signal representing a group of Li ions with much lower diffusivity. As we do not recognize the emergence of a sharp quadrupole powder pattern at high temperatures, which would be in line with the universal temperature behavior of ⁷Li NMR line shapes affected by averaging processes,^89,90 we assume that the broad line originates from a slow Li⁺ subensemble. Most likely, this ensemble represents those ions sharing the same crystallographic position as Mg²⁺. We assume that the Li ions located at 2a, i.e., between the layers, give rise to the narrow line observed.

Figure 6.

(a) ⁷Li NMR line shapes recorded at the temperatures indicated. At 173 K, the fwhm of the superimposed complete line is given by 2.08 kHz. It reduces to 516 Hz at 413 K. This overall line is composed of two contributions; a deconvolution is seen in (b). In (b), the change of fwhm, either determined by using the full line shape or by analyzing the narrow component only, is shown as a function of temperature. Inset: deconvoluted ⁷Li NMR spectra with the area of the Lorentzian (narrowed line) taking 28%, i.e., ca. 30%, of the full area under the line. See text for further explanation.

To analyze the change in line width, we read off the fwhm of the total line; the line width as a function of temperature is shown in Figure 6. Starting from ca. 2 kHz, it reduces to values of ca. 500 Hz at 413 K, which is the so-called regime of extreme narrowing. We observe that the line width sharply increases at low temperature reaching 0.75 kHz at 250 K, at even higher temperatures, a shallower decrease is seen, which is still not fully completed at T = 450 K. To find out whether this is an exclusive feature of the overall line, we deconvoluted the lines with the help of a sum of a Lorentzian and a Gaussian function. Here, the narrow, Lorentzian-shaped line reveals the same temperature dependence as the overall line. The mainly homonuclear interactions of this line are averaged when T = 250 K is reached. Further averaging of residual couplings, likely between Li(2a) and Li(4 h), is seen at higher temperatures. Importantly, even at T = 173 K, the line has not reached its temperature-independent rigid-lattice value, i.e., rather rapid Li⁺ exchange processes are present in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂. We estimate that at 225 K, the associated average jump rate 1/τ should be in the order of 10 kHz or higher, as full averaging will be achieved if 1/τ greatly exceeds the spectral width of the NMR signal in the rigid lattice regime.

The deconvolution of the ⁷Li NMR spectra tells us that approximately 30% (see the deconvoluted spectra shown in the inset of Figure 6b) of the total number of Li ions in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ have access to fast diffusion pathways, see the inset of Figure 6b. This value might be even higher, as we cannot exclude that the broad component includes some quadrupole satellite intensities associated with the narrow line. In such a case, the value might reach 50%, which would be in line with what the chemical formula Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ suggests. To shed light on this assumption, we recorded high-resolution ⁶Li MAS NMR spectra, see Figure 7, for which first-order quadrupolar interactions and dipole–dipole broadening, both interactions being smaller for ⁶Li anyway, are artificially averaged out through fast sample rotation. In agreement with the static line shapes, the ⁶Li MAS line can be best approximated with a superposition of two distinct lines whereby the area under the narrow one again amounts to approximately 30%. A certain extent of Li–Mg exchange could serve as an explanation to understand the reduced spin density between the layers in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂. For the sake of completeness, in Figure 7, the corresponding ¹⁹F MAS NMR spectrum is shown, which reveals the two magnetically inequivalent F sites in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂.

Figure 7.

(a) ⁶Li and ¹⁹F MAS NMR spectra of Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ recorded under ambient bearing gas conditions (300 K). The ⁶Li MAS NMR spectrum can be best approximated with a combination of two spectral components as indicated. A deconvolution was possible with a sum of a Lorentzian line (narrow line) and a Gaussian one (broad line). Values denote line widths. Isotropic shifts were allowed to float. Approximately 32% of the Li ions, see also Figure 6b, are responsible for the narrow line. (b) In ¹⁹F MAS NMR, two lines with equal intensities are seen reflecting the two magnetically inequivalent F sites in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂. Asterisks mark spinning sidebands appearing at an interval of 25 kHz for each F signal.

The two-component features seen in both ⁷Li and ⁶Li NMR also affect the evolution of the magnetization transients, recorded in the former case, to extract diffusion-induced ⁷Li NMR spin–lattice relaxation rates. As mentioned above, M(t_d) can only be parameterized satisfactorily with a single, stretched exponential at sufficiently low temperatures (T<225 K). Above this threshold, which coincides with the beginning of the shallowly decaying part of the NMR line width (see Figure 6b), the transients start to follow a two-exponential time behavior, see also Figure S2. Therefore, we used a sum of two stretched exponentials, see the Supporting Information, to parameterize the overall transients; the same procedure, using the same terminology, is described in detail elsewhere.^31,70 The two rates 1/T_1,slow and 1/T_1,fast are shown in the Arrhenius plot of Figure 8a. The corresponding stretching exponents are displayed in the upper part of Figure 8. While 1/T_1,slow does not depend on temperature within the error limit of the analysis, 1/T_1,fast reveals a shallow diffusion-induced peak at T_max = 385 K. The low-T flank points to a very low activation energy of only 0.06 eV, which is likely to be dominated by strictly localized, i.e., short-range, Li⁺ hopping processes and/or correlation effects.^30,32 Almost the same value was probed by the resistivity measurements, see Figure 5b.

Figure 8.

(a) ⁷Li NMR spin–lattice relaxation rates of Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ recorded in the laboratory frame of reference at a Larmor frequency of 116 MHz. The lower part shows an Arrhenius plot. The two-component ⁷Li NMR line shape produces bi-exponential magnetization transients M(t_d) leading to two rates 1/T_1fast and 1/T_1slow that reflect the fast and slow ions in Li-bearing fluorohectorite, also seen in ⁷Li NMR lines. Alternatively, the stepwise analysis of the underlying FIDs also yields two relaxation rates. Stretching exponents γ are shown in the upper part of the figure. (b) Comparison of the spin-lock ⁷Li NMR spin–lattice relaxation rates (1/T_1ρ, 20 kHz) with those measured in the laboratory frame of reference. The rate 1/T_1ρ passes through a diffusion-induced maximum at approximately 205 K. At this temperature, the corresponding γ passes through a minimum. Lines (dashed and solid) are to guide the eyes. Linear parts were analyzed with the Arrhenius law to extract the activation energies (in eV) as indicated.

Alternatively, we separated the two spectral contributions directly in the time domain of the underlying FIDs by individual analysis of the corresponding components that reveal quite different effective spin–spin relaxation rates. This procedure is described in detail elsewhere.^31,69,70,91 The FIDs are composed of a sharply (FID_fast) and a slowly decaying part (FID_slow), leading to two distinct rates, see Figure 7a. While the first decay reflects the broad spectral component, the latter decay, FID_slow, arises from the motionally narrowed component that represents fast Li⁺ ions. At least for high temperatures, the rates associated with FID_slow agree with those obtained when analyzing the full M(t_d) curves. Again, a relatively low activation energy of 0.12 eV can be estimated from the corresponding low-T flank. This value resembles that also seen in the resistivity peaks ρ’(1/T) shown in Figure 5b, cf. the data recorded at 1.2 MHz. For the separated rates of the slow subensemble, a temperature independent behavior is seen for T>330 K.

To further characterize Li⁺ ion hopping with methods that are also able to probe long-range ion dynamics, we performed variable-temperature spin-lock NMR measurements.⁹² The corresponding 1/T_1ρ rates are shown in Figure 8b. The magnetization transients (Figure S2) do not allow for a separate investigation as it has been carried out for the 1/T₁ measurements. Hence, they are to be regarded as averaged values. Likely, the fast Li⁺ ions will dominate the overall nuclear spin response. Coming from low temperatures, the rates experience a sharp increase with temperature and pass through a maximum at T = 210 K; the maximum in1/T_1ρ corresponds to a minimum in the stretching factor, see arrow in the upper graph of Figure 8b. The slope of the low-T flank of this prominent peak yields an activation energy of 0.39 eV, which is very similar to that seen by both conductivity spectroscopy and the modulus analysis, cf. the temperature dependence of σ’_DC, bT, and τ_M2^–1 (Figure 3b). Thus, we found a strong indication that the peak probed by 1/T_1ρ, which appeared at 205 K, reflects the same temporary fluctuations as detected by electrical relaxation. Interestingly, the activation energy of its high-T flank is comparable with those also characterizing the modulus peaks in Figure 5b. A value of 0.08 eV is also very similar to the estimated ones from 1/T₁ NMR measurements (0.06 and 0.12 eV, see Figure 8a). Assuming a symmetric 1/T₁(1/T) peak, the activation energies in the high-T limit would be characterized by the same activation. In general, this similarity would be expected if the two methods probe the same (low-dimensional) diffusion process.⁵³ Importantly, dimensionality effects affect the slope of the NMR rate peaks in the high-T regime and yield apparent, reduced values.^32,43

In summary, electrical modulus measurements and spin-lock ⁷Li NMR support the finding that long-range ion transport in hectorite-type Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ is characterized by an activation energy of approximately 0.35 eV (see Figure 3b). In contrast to long-range transport, barriers with values of approximately 0.1 eV govern the local hopping processes. However, the values from high-T flanks, either seen in 1/T_1ρ or in M’’(ν), are affected by dimensionality effects. As also recognized for the M’’(ν) peaks, we observe that the rates 1/T_1ρ of the high-T flank do not coincide (see arrow in Figure 8b), with those expected from 1/T₁ as is indicated by the dashed line in Figure 8b. This line extrapolates the high-T flank to even higher temperatures. The same feature is seen in Figure 5b. This dispersive behavior strongly supports our idea about 2D diffusion in the synthetic hectorite studied. Finally, 1/T_1ρ(1/T) revealed a second peak appearing at T_max = 350 K (marked by a star in Figure 8b), which, most likely, is to be assigned to the low translational ion mobility of the Li⁺ ions sharing sites with Mg²⁺ in the layers of the phyllosilicate.

To directly compare the different responses seen by NMR and electrical relaxation, we finally estimated Li⁺ jump rates from the maxima seen in 1/T₁ and 1/T_1ρ at T_max = 385 K and T_max = 205 K, respectively, by using the maximum condition τ_NMRω₀₍₁₎ ≈ 1. The rates obtained are included in Figure 9. In the present case, they agree very well with those from electrical measurements. At 293 K, the Arrhenius line yields a mean jump rate 1/τ of approximately 3 × 10⁷ s^–1, which translates into a 2D diffusion coefficient D_2D = a²/(4τ) of 4.7 × 10^–13 m² s^–1 if we use a ≈ 2.5 Å. The crystallographic Li–Li distance is ca. 5 Å, which we think is too large for a single Li⁺ jump. Assuming temporarily occupied interstitial positions connecting two or more regular sites in a distance of 2.5 Å seems to be more reasonable. D = 4.7 × 10^–13 m² s^–1 would indeed correspond to an estimated ionic conductivity σ_est., almost reaching the order of 0.1 mS cm^–1 if we use the (idealized) cell volume of 490 ų to estimate a charge carrier concentration of ca. N¹ = 2 × 10²⁷ m^–3. σ_est. is related to D_NE via the Nernst-Einstein relation, which reads in general D_NE = σk_BT/(N¹q), with q being the charge of the Li⁺ ions. We assumed that D_2D and D_NE are connected by D_2D = (H_R/f)D_NE with H_R being the Haven ratio and f denoting the correlation factor. Our estimation anticipated H_R/f being of the order of unity. Taking into account that only 30% of the ions participate in Li⁺ long-range ion transport, D_2D = (H_R/f)D_NE is fulfilled if we chose H_R/f ≈ 0.3. The relatively high value of D_2D obtained clearly renders hectorite as a fast ion conductor.

Figure 9.

Arrhenius plot of the Li⁺ hopping rates 1/τ deduced from both nuclear spin relaxation and electrical relaxation taking advantage of the modulus representation and resistivity measurements, see Figure 3. Data from NMR, if restricted to the maxima of the spin–lattice relaxation rate peaks, agree well with the results from broadband electrical characterization. The dashed line represents a linear fit yielding 0.35(1) eV. For comparison, jump rates measured for Li_xTiS₂ (x = 0.7, 0.41 eV)⁴³ and Li_xC₆ (x = 1, 0.55 eV)³⁸ are also shown, see dotted lines.

Rapid ion exchange in Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ benefits from a wide interlayer gap giving the ions the necessary space to freely diffuse in the phyllosilicate. To the best of our knowledge, this is the first time that such high cation diffusivities were probed in a synthetic clay mineral. For comparison, in Figure 9, we included jump rates of two other 2D materials, Li_xTiS₂ (0.41 eV)⁴³ and LiC₆ (0.55 eV),³⁸ studied by NMR (and other methods) earlier. Inspired by the present results, one might think about crystal-chemical modifications that could lead to even higher diffusivities. Nature may offer a range of further silicate structures, including also layered ones, from which the necessary inspiration can be drawn to develop both powerful electrolytes and active materials for, e.g., lithium-ion batteries. Exemplarily, the Khan group studied hectorite-containing composite materials for this purpose.⁵⁶⁻⁵⁹

4. Conclusions

Li⁺ ion diffusion and electrical transport in the hectorite-type phyllosilicate Li_0.5[Mg_2.5Li_0.5]Si₄O₁₀F₂ was studied by broadband conductivity spectroscopy, modulus analysis, and ⁷Li NMR spin–lattice relaxation measurements. Electrical and nuclear spin relaxation confirmed our hypothesis of rapid interlayer (2D) Li⁺ exchange processes in the silicate. This process is characterized by an overall activation energy of approximately 0.35 eV. Under ambient conditions, conductivity spectroscopy points to an ionic conductivity as high as 0.14 mS cm^–1, representing a favorable starting point for further improvements by crystal-chemical engineering. In addition, we derived a consistent picture of Li⁺ ion dynamics and showed that the electric and magnetic fluctuations probed originate from the same translational process. Our study supports the general idea that spatial confinement, able to guide the charge carriers over long distances, is helpful in enabling fast ion transport.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.0c02460.

• Simulated X-ray powder diffraction; ⁷Li NMR magnetization transients from which the spin–lattice relaxation rates were extracted (PDF).

Author Contributions

^# C.H. and M.B. contributed equally to this work.

The authors declare no competing financial interest.