Fig. 2

NMR measuring the spontaneous lithium-ion transport between the Li₆PS₅Br solid electrolyte and the Li₂S cathode. a, e, i One-dimensional (1D) ⁷Li magic angle spinning (MAS) spectra corresponding to the Li₆PS₅Br–Li₂S cathode mixtures a mixture I, where Li₂S is micron-sized e mixture II, where Li₂S is nanosized i mixture III, where nanosized Li₂S is thoroughly mixed with Li₆PS₅Br. b-d, f-h, j-l Two-dimensional (2D) ⁷Li–⁷Li exchange spectra (2D-EXSY) recorded at a ⁷Li resonance frequency of 155.506 MHz and a spinning speed of 20 kHz at room temperature for short (100 µs) to long mixing times t _mix (100 ms) for b, c, d mixture I, f, g, h for mixture II, and j, k, l for mixture III. For both mixtures I and II, no obvious off-diagonal cross-peak intensity is observed, indicating that the exchange over the solid–solid Li₆PS₅Br–Li₂S is very small (based on whether an upper limit for the conductivity can be determined as shown in Fig. 4). For mixture III, the off-diagonal cross-peaks appear at t _mix = 10 ms, and are most pronounced at t _mix = 100 ms, and they correspond to lithium-ion exchange from Li₂S to Li₆PS₅Br and vice versa. Note that the star shape of the ⁷Li resonance in Li₆PS₅Br is the consequence of the 2D Fourier transform of its Lorentzian shape, a result of the high mobility of lithium ions within the Li₆PS₅Br phase