Lithium ion dynamics in Li2S+GeS2+GeO2 glasses studied using 7Li NMR field-cycling relaxometry and line-shape analysis

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Abstract

We use 7Li NMR to study the ionic jump motion in ternary 0.5Li2S+0.5[(1–x)GeS2+xGeO2] glassy lithium ion conductors. Exploring the “mixed glass former effect” in this system led to the assumption of a homogeneous and random variation of diffusion barriers in this system. We exploit that combining traditional line-shape analysis with novel field-cycling relaxometry, it is possible to measure the spectral density of the ionic jump motion in broad frequency and temperature ranges and, thus, to determine the distribution of activation energies. Two models are employed to parameterize the 7Li NMR data, namely, the multi-exponential autocorrelation function model and the power-law waiting times model. Careful evaluation of both of these models indicates a broadly inhomogeneous energy landscape for both the single (x=0.0) and the mixed (x=0.1) network former glasses. The multi-exponential autocorrelation function model can be well described by a Gaussian distribution of activation barriers. Applicability of the methods used and their sensitivity to microscopic details of ionic motion are discussed.

Introduction

The ionic conductivity of lithium sulfide containing glasses can reach values as high as and even higher than 10−3  cm)−1 at room temperature [1], which makes them attractive as electrolytes for new all solid state Li-ion batteries. Seeking to combine the high conductivity with improved chemical stability under application conditions, Kim et al. [2] have explored the ternary glass system 0.5Li2S+0.5[(1–x)GeS2+xGeO2], with a variable GeO2 fraction x. Mixing two types of network formers, herein GeS2 and GeO2, has been known to have a positive effect on the ionic conductivity. Specifically, the addition of 10 mol% of GeO2 was found to increase the conductivity by the factor of four compared to a pure sulfide glass, while for higher fractions of GeO2 the Li-ion conductivity eventually decreases below the original value of the pure 0.5Li2S+0.5GeS2 glass [2]. A like dependence of the ionic conductivity on glass composition was observed in various other mixed oxy-sulfide ternary systems (see Refs. in [3], [4], [5]). This increase of the conductivity above the base value at a certain fraction of mixing of the glass formers is referred to as the “mixed glass former effect”.

Understanding this effect is hindered by a diversity of factors contributing to the ionic conductivity in those systems. Kim et al. emphasized that in the case of the Li2S+GeS2+GeO2 system, one could take advantage of a simple substitution of oxygen for sulfur and analyze the effect “on the basis of purely structural (mobility) changes” [2]. An accurate model was developed [2] that relates the increase of the conductivity in this system to a reduction of the mechanical strain energy required for Li+ diffusion caused by the addition of the smaller oxygen anion. Further, Schuch et al. [4] developed an appropriate model, called “mixed barrier model”, which described the mixed glass former effect in terms of reduced energy barriers for the mobile ions conducting in a mixed-former environment (i.e., sites containing both network former units).

An ansatz in the mixed barrier model was to suppose a random variation of barrier heights. The concept of the activation barrier distribution has been long employed in NMR and dielectric/impedance spectroscopy of ion-conducting glasses to describe the non-exponential relaxation as well as unique temperature and frequency dependences of the relaxation rates. Svare et al. [6] analyzed nuclear spin–lattice relaxation (NSLR) in lithium sulfide glasses in terms of a Gaussian barrier distribution and used the NMR determined distribution of activation energies (DAE) to fully calculate the corresponding ionic conductivity in these same glasses. A similar Gaussian DAE but with a low-barrier tail was employed in Ref. [7] to derive information on the microscopic lithium ion dynamics as a function of glass composition.

A DAE is naturally related to dynamic heterogeneity, i.e. dynamically distinguishable sub-ensembles of ions, which can be probed, among other methods, by measuring time correlation functions of fluctuating local fields. However, to ascertain whether the existence of dynamic heterogeneity is a real effect or merely a theoretical concept, it is insufficient to observe two-time correlation functions, which are accessible from the majority of experimental methods, but it is necessary to analyze higher-order correlation functions. Thus, NMR measurements of three- and four-time correlation functions indicated that dynamic heterogeneity is a key feature of the ionic hopping motion in various solid electrolytes [8], [9], [10], [11], [12], [13].

Essentially, the NSLR measurements of a DAE rely on the modeling of the correlation function, or equivalently, the spectral density function, J(ω), of fluctuations responsible for relaxation. One or more of the model’s parameters are then considered temperature dependent and subject to fitting for variable-temperature data. In the above examples [6], [7], such a parameter was a correlation time, τc(T), defined in the framework of the Bloembergen–Purcell–Pound (BPP) model. A direct measurement of the frequency dependence of J(ω) is not as practical as the fixed frequency variable-temperature measurements for the technical difficulty of varying the frequency using standard NMR equipment where typically a different magnet is used for each frequency. Indeed, the extensive T1 measurements for many lithium ion conducting glasses by Martin et al. were only performed at four frequencies spanning the modest frequency range of 4 MHz to 40 MHz. Recently, we demonstrated that 7Li field-cycling (FC) approaches allow us to continuously vary the resonance frequency, providing direct access to the spectral density of ionic dynamics in a broad range of 105–109 s−1 [14].

Measuring the spectral density as a function of frequency has certain advantage compared to the fixed frequency variable temperature measurements. The shape of J(ω) for ion conductors relies strongly on the mechanism for the ionic motion (see e.g. [15]). Given J(ω), one can therefore infer essential features of ionic dynamics directly from the experiment. For comparison, the NSLR times obtained from conventional measurements as a function of temperature, T1(T), depend on the temperature evolution of both the correlation time and the shape of the spectral density, which are difficult to disentangle.

To take this advantage, we use 7Li FC NMR to measure J(ω) in the glass system 0.5Li2S+0.5[(1–x)GeS2+xGeO2]. These experiments are accompanied by regular high-field 7Li NMR line-shape and spin-lattice relaxation measurements at variable temperature. To investigate the mixed glass former effect, we compare results for the mixed GeS2–GeO2 glass with the highest conductivity of the series (x=0.1) [16] with that for the pure GeS2 glass (x=0.0). Unlike dc conductivity, the 7Li NMR data are dominated by local jumps of single lithium ions, thus providing, in principle, access to the energy landscape on length scales that are smaller than the expected percolation threshold of the dc ionic conductivity. In our analysis, we pay special attention to the general aspects of modeling the non-exponential ionic correlation functions, a common problem for studies of ion transport in glasses, including conductivity, dielectric and mechanical approaches, and to the accompanying difficulties in relating the model’s parameters to the energy landscape.

Section snippets

Effects of lithium ionic motion on 7Li line–shape and spin–lattice relaxation results

The quadrupole coupling constant amounts to ca. 50 kHz in lithium compounds [17], which makes the quadrupole interaction dominant in a typical 7Li NMR spectrum. It is indeed the case for the studied glasses whose static spectral pattern is mainly determined by the quadrupole interaction, giving rise to a characteristic central peak and a satellite contribution (see below). The effect of the magnetic dipole–dipole coupling is only to broaden those spectral components.

Similarly, 7Li NSLR is

Sample preparation

Vitreous GeS2 was prepared by mixing and reacting stoichiometric amounts of germanium (Cerac, 99.999%) and sulfur (Cerac, 99.999%) in an evacuated silica tube. The silica tube was rotated at ∼5 r.p.m. at an angle of ∼10° in a tube furnace and heated at 1 °C/min to 900 °C, held for ∼8 h and then quenched in air.

Ternary Li2S+GeS2+GeO2 glasses were prepared by melting stoichiometric amounts of Li2S (Cerac, 99.999%), GeS2, and GeO2 (Cerac, 99.999%) starting materials. They were mixed and then placed in

NMR experiments

7Li FC measurements were carried out on a home-built FC relaxometer [24] with the magnetic field varied between 60 μT and 1.5 T, corresponding to the 7Li Larmor frequency range 100 kHz to 12 MHz. We should mention that measurements at lower fields are possible, but then the Zeeman interaction becomes comparable to or even smaller than the fluctuating quadrupolar coupling (ωQ∼50 kHz, see the 7Li line shape), thereby making the usual perturbation-theory treatment inapplicable to NSLR analysis. The

Spin–lattice relaxation

The saturation-recovery curves recorded on the high-field spectrometers are well fit to a mono-exponential function over the entire temperature interval. The resulting NSLR rates are plotted for the studied 0.5Li2S+0.5[(1–x)GeS2+xGeO2] glasses in Fig. 2. For both x=0.0 and x=0.1, the monotonic decrease of R1 with 1/T indicates that the Li-ion dynamics are slow on the time scale of the inverse Larmor frequency at the studied temperatures, which corresponds to the low-temperature regime in the

The multi-exponential ACF model

The broadening of χNMR(ω0) compared to the case of a single-exponential ACF can always be reproduced by summation of individual Lorentzian spectra, provided that an appropriate τc distribution is used [35]. A key issue is whether such a distribution arises from a heterogeneous dynamics, e.g., when different values τc can be ascribed to sub-ensembles of sites explored by a tagged ion, or it is merely a multi-exponential representation of an intrinsically non-exponential dynamic process in a

Discussion and conclusion

The 7Li FC NMR measurements show, in the most direct manner, that NSLR in the studied 0.5Li2S+0.5[(1–x)GeS2+xGeO2] glasses is not consistent with the BPP model for exponential correlation functions of ionic dynamics. We take this fact as a signature of a random activation barrier variation over the glass structure. Therefore, the relaxation rate dispersion R1(ω0) provides access to the barrier distribution. We parameterized R1(ω0) using a weighted superposition of Lorentzian spectral densities

Acknowledgments

Funding of the Deutsche Forschungsgemeinschaft (DFG) through grant VO 905/12-1 is gratefully acknowledged. Funding for the part of the work conducted at Iowa State was provided in part by the NASA Jet Propulsion Laboratory under Grant no. 1250174 and by the National Science Foundation under Grant nos. DMR 0710564 and 1304977.

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