Na+ self-diffusion and ionic transport in sodium β″-alumina

Fast ion transport is crucial for solid materials to serve as electrolytes, with only a few classes achieving the high ionic conductivity needed for practical use. The discovery of fast ion transport in Na β″-alumina not only introduced a groundbreaking class of materials but also marked the advent of the research field now known as solid-state ionics. Since the early 1980s, Na β″-alumina has been widely recognized as a solid electrolyte for high-temperature sodium-based batteries, such as Na‑sulfur batteries. Despite numerous studies on the diffusion and transport properties of layer-structured Na β″-alumina, a comprehensive investigation combining conductivity and nuclear magnetic resonance (NMR) to study both short-range and long-range ion dynamics has been lacking. In this work, we used a commercially available, highly sintered Na β″-alumina sample to explore Na⁺ dynamics in detail through GHz conductivity spectroscopy and ²³Na nuclear spin relaxation. The two methods provide a rather consistent picture of ion transport. While long-range Na⁺ transport, reaching a conductivity of 4 mS cm⁻¹ at ambient temperature, is governed by an activation energy of 0.3 eV, short-range motions sense a barrier of 0.13 eV. The Arrhenius pre-factor obtained from characteristic electric relaxation frequencies is consist with that determined from diffusion-induced longitudinal NMR spin-lattice relaxation rates if analyzed with a modified BPP (Bloembergen, Purcell, Pound) spectral density function.