Toward understanding the anomalous Li diffusion in inorganic solid electrolytes by studying a single-crystal garnet of LLZO–Ta by pulsed-gradient spin-echo nuclear magnetic resonance spectroscopy

Analysis of the Diffusion in a Multilayer Structure under a Constant Heating Rate: The Calculation of Activation Energy from the In Situ Neutron Reflectometry Measurement

Understanding mass transport in micro- and nanostructures is of paramount importance in improving the performance and reliability of the micro- and nanostructures. In this work, we solve the diffusion problem in a multilayer structure with periodic conditions under a constant heating rate via a Fourier series. Analytical relation is established between the coefficients of eigenfunctions and the intensity of X-ray or neutron Bragg peak. The logarithm of temporal variation of the intensity of X-ray or neutron Bragg peak is a linear function of the nominal diffusion time, with the nominal diffusion time being dependent on the heating rate. This linear relation is validated by experimental data. The Taylor series expansion of the linear relation to the first order of the diffusion time yields an approximately linear relation between the logarithm of temporal variation of the intensity of X-ray or neutron peak and the diffusion time for small diffusion times, which can be likely used to calculate the activation energy for the diffusion in a multilayer structure. The validation of such an approach is subjected to the fact that the characteristic time for heat conduction is much less than the characteristic time for the ramp heating as well as the characteristic time for diffusion.

Study of diffusion and conduction in lithium garnet oxides LixLa3Zrx-5Ta7-xO12 by machine learning interatomic potentials

Lithium garnet oxides are an attractive family of solid-state electrolytes due to their high Li-ion conductivity and good chemical stability against Li metal. Experimental study of these materials is often troubled by chemical contamination (e.g. Al) or lithium loss, while computational study, theoretically with controlled composition, is often limited either by accuracy (e.g. conventional interatomic potential) or efficiency (e.g. density-function theory or DFT). In this work, we report the study of diffusion and conduction of lithium garnets by a machine learning interatomic potential (MLIP) that is approaching DFT accuracy but orders of magnitude faster. We found that this MLIP is more accurate than other commonly applied models to study lithium garnets and is able to predict diffusion and conduction properties that are consistent with experiments. Computational studies enabled by this MLIP, combined with experimental data, suggest that ionic conduction is non-Arrhenius and maximum conductivity occurs around x = 6.6 to 6.8 in Li_xLa₃Zr_x-5Ta_7-xO₁₂.

Mechanical behaviour of inorganic solid-state batteries: can we model the ionic mobility in the electrolyte with Nernst-Einstein's relation?

Inorganic solid-state lithium-metal batteries could be the next-generation batteries owing to their non-flammability and higher specific energy density. Many research efforts have been devoted to improving the ionic conductivity of inorganic solid electrolytes. For a wide range of electrolytes including liquid and solid polymer electrolytes, an independent measurement or calculation of both electrolyte conductivity and diffusion coefficient is often time-consuming and challenging. As a result, Nernst-Einstein's relation has been used to relate the ionic conductivity to ionic diffusivity after the determination of either parameter. Although Nernst-Einstein's relation has been used for different electrolytes, we demonstrate in this perspective that this relation is not directly transferable to describe the ionic mobility for many inorganic solid electrolytes. The fundamental physics of Nernst-Einstein's relation shows that the relationship between the diffusion coefficient and electrolyte conductivity is derived for ionic mobility in a viscous or a gaseous medium. This postulation contradicts state-of-the-art experimental studies measuring the mechanical behaviour of inorganic solid electrolytes, which show that inorganic solid electrolytes are usually brittle rather than viscoelastic at ambient room temperature. The measurement of loss tangent is required to justify the use of Nernst-Einstein's relation. The outcome of such measurement has two implications. First, if the loss tangent of inorganic solid electrolytes is less than unity in the range of batteries operating temperatures, the impacts of using Nernst-Einstein's relation in modelling the ionic mobility should be quantified. Secondly, if the measured loss tangent is comparable to that of solid polymers and lithium metal, inorganic solid electrolytes may behave in a viscoelastic manner as opposed to the brittle behaviour usually suggested.

High-Temperature Pulsed-Field-Gradient 7Li-NMR Measurements of Li2CO3 over 700 K

Understanding the transport property of Li ions is crucial for improving the performance of Li-ion batteries. To investigate the ion diffusion at high temperatures, we constructed a high-temperature pulsed-field-gradient (PFG) nuclear magnetic resonance (NMR) probe capable of measurements at temperatures >700 K. The accuracy of the sample temperature was confirmed via ⁷⁹Br NMR measurements of KBr. ⁷Li PFG-NMR measurements of Li₂CO₃ were performed at temperatures up to 724 K using the probe. The apparent diffusion coefficient of Li ions in Li₂CO₃ was obtained experimentally.

NMR Investigations of Crystalline and Glassy Solid Electrolytes for Lithium Batteries: A Brief Review

The widespread use of energy storage for commercial products and services have led to great advancements in the field of lithium-based battery research. In particular, solid state lithium batteries show great promise for future commercial use, as solid electrolytes safely allow for the use of lithium-metal anodes, which can significantly increase the total energy density. Of the solid electrolytes, inorganic glass-ceramics and Li-based garnet electrolytes have received much attention in the past few years due to the high ionic conductivity achieved compared to polymer-based electrolytes. This review covers recent work on novel glassy and crystalline electrolyte materials, with a particular focus on the use of solid-state nuclear magnetic resonance spectroscopy for structural characterization and transport measurements.

Relationship between Li+ diffusion and ion conduction for single-crystal and powder garnet-type electrolytes studied by 7Li PGSE NMR spectroscopy

Ion-conducting garnets are important candidates for use in all-solid Li batteries and numerous materials have been synthesized with high ionic conductivities. For understanding ion conduction mechanisms, knowledge on Li⁺ diffusion behaviour is essential. The proposed nano-scale lithium pathways are composed of tortuous and narrow Li⁺ channels. The pulsed gradient spin-echo (PGSE) NMR method provides time-dependent ⁷Li diffusion on the micrometre space. For powder samples, collision-diffraction echo-attenuation plots were observed in a short observation time, which had not been fully explained. The diffraction patterns were reduced or disappeared for single-crystal garnet samples of Li_6.5La₃Zr_1.5Ta_0.5O₁₂ (LLZO-Ta) and Li_6.5La₃Zr_1.5Nb_0.5O₁₂ (LLZO-Nb). The inner morphology and grain boundaries affect importantly the collision-diffraction behaviours which is inherent to powder samples. The ⁷Li diffusion observed by PGSE-NMR depends on the observation time (Δ) and the pulsed field gradient (PFG) strength (g) in both powder and single-crystal samples, and the anomalous effects were reduced in the single-crystal samples. The scattered Li diffusion constants converged to a unique value (D_Li) with a long Δ and a large g, which is eventually the smallest value. The D_Li activation energy was close to that of the ionic conductivity (σ). The D_Li values are plotted versus the σ values measured for four powder and two single-crystal garnet samples. Assuming the Nernst-Einstein (NE) relation which was derived for isolated ions in solution, the carrier numbers (N_NE) were estimated from the experimental values of D_Li and σ. The N_NE values of metal-containing garnets were large (<10²³ cm^-3) and insensitive to temperature. They were larger than Li atomic numbers in cm³ calculated from the density, molecular formula and Avogadro number for LLZOs except for cubic LLZO (Li₇La₃Zr₂O₁₂, N_NE∼ 10²⁰ cm^-3).