= Solution
<NMR> probes the chosen <isotope>'s local environments and motion in the bulk without electrical contacts. Line narrowing, relaxation and exchange measurements can expose hopping across a broad range of timescales, separate sites with resolved shifts, and provide microscopic <activation energies>. Pulsed-field-gradient measurements can sometimes measure longer-range displacement directly; local relaxation measurements usually infer it through a model.
Limitations include low sensitivity for dilute or low-abundance nuclei, overlap of inequivalent sites, quadrupolar broadening for <spins> above one-half, and contributions from paramagnetic impurities or other relaxation mechanisms. Heating can change defect populations or phase composition. Most importantly, \b[local hopping need not produce long-range <ionic conductivity>]: back-and-forth motion, correlated jumps and trapped <ions> can relax <spins> without carrying charge over macroscopic distances. Connecting $T_1$ to a <diffusion coefficient> requires an explicit jump model and comparison with a bulk transport measurement.
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