Pulsed field gradient magnetic resonance measurements of lithium-ion diffusion

Abstract

The transport of lithium ions between the electrolyte-electrode interface and the electrode bulk is an essential and presently rate limiting process in the high-current operation of lithium-ion batteries. Despite their importance, few methods exist to experimentally investigate these macroscopic diffusion processes and, as a result, much remains unknown regarding their underlying mechanisms and the resulting macroscopic transport. Gradient nuclear magnetic resonance measurements are a mature and effective means of investigating macroscopic transport phenomena and posses several advantages over competing measures of transport in ionic solids. However, short coherence times, slow diffusion rates and a small gyromagnetic ratio have, to date, limited their usefulness for measurements of room-temperature transport in solid lithium-ion conductors. Recent developments in quantum control have demonstrated methods for extending the coherence times of dipolar-coupled nuclear spins by several orders of magnitude, into a regime enabling gradient measurements of slow lithium-ion diffusion. This thesis proposes and demonstrates, through the utilization of a dipolar refocusing sequence and a strong pulsed magnetic field gradient, a nuclear magnetic resonance method for the direct measurement of the lithium ion self-diffusion coefficient within room-temperature lithium-ion conductors. Magnetic resonance field gradient measurements derive ensemble transport statistics through observation of the residual phase mismatch following two position dependent phase rotations, implemented as DC pulses of a spatially varying gradient field, separated in time by a transport period. Generating sufficiently fine spatial encodings to be sensitive to slow diffusion has proven challenging in solids where strong relaxation due to the homonuclear dipole-dipole interaction drastically shortens coherence times and thus limits the duration of applied gradient pulses. This study utilizes a magic echo based refocusing sequence to nullify the dominant decoherence mechanism allowing effective gradient pulses on the order of one millisecond. Combined with a custom-built pulsed field gradient, spatial encodings on the order of 1 [mu]m are obtained. For a demonstrative sample, the lithium-ion conductor lithium sulfide is chosen both for its favorable NMR properties and for its role in the recent renewal of interest in nanostructured integration cathode materials. Initial sample characterization reveals two ⁷Li NMR lines distinguished by their static line widths and refocusing behavior. A modified version of the 1D EXSY selective inversion experiment is performed to characterize an exchange process between these two lines and extract their intrinsic spin-lattice relaxation rates. Two stimulated echo diffusion measurements are performed to identify the apparent diffusion coefficients of each line in the presence of exchange. The observed diffusion coefficient of the narrow line is determined to be 2.39 +/- 0.34 . 10-⁸ cm²/s. Diffusive attenuation is not observed for the broad line. These results are analyzed through a two bath exchange model parameterized by the results of the earlier exchange experiments. The influence of exchange on the observed diffusion coefficients is determined to be negligible as diffusion times are limited by the inverse of the exchange rates.