With a Little Help from ³¹P NMR: The Complete Picture on Localized and Long-Range Li⁺ Diffusion in Li₆PS₅I

Abstract

Li₆PS₅I acts as a perfect model substance to study length scale-dependent diffusion parameters in an ordered matrix. It provides Li-rich cages which offer rapid but localized Li⁺ translational jump processes. As jumps between these cages are assumed to be much less frequent, long-range ion transport is sluggish, resulting in ionic conductivities in the order of 10^-6 S cm^-1 at room temperature. In contrast, the site disordered analogues Li₆PS₅X (X = Br, Cl) are known as fast ion conductors because structural disorder facilities intercage dynamics. As yet, the two extremely distinct jump processes in Li₆PS₅I have not been visualized separately. Here, we used a combination of ³¹P and ⁷Li NMR relaxation measurements to probe this bimodal dynamic behavior, that is, ultrafast <i>intra</i>cage Li⁺ hopping and the much slower Li⁺ <i>inter</i>cage exchange process. While the first is to be characterized by an activation energy of ca. 0.2 eV as directly measured by ⁷Li NMR, the latter is best observed by ³¹P NMR and follows the Arrhenius law determined by 0.44 eV. This activation energy perfectly agrees with that seen by direct current conductivity spectroscopy being sensitive to long-range ion transport for which the intercage jumps are the rate limiting step. Moreover, quantitative agreement in terms of diffusion coefficients is also observed. The solid-state diffusion coefficient <i>D</i> _σ obtained from conductivity spectroscopy agrees very well with that from ³¹P NMR (<i>D</i> _NMR ≈ 4.6 × 10^-15 cm² s^-1). <i>D</i> _NMR was directly extracted from the pronounced diffusion-controlled ³¹P NMR spin-lock spin-lattice relaxation peak appearing at 366 K.