Diffusive relaxation of Li in particles of silicon oxycarbide measured by galvanostatic titrations

Experiments with silicon-oxycarbide, an anode material for Li-ion batteries, are compared with a rigorous solution for time-dependent diffusion profiles in spherical particles, which is supplemented by finite element analyses of cuboid shaped particles. In this way a value for the chemical diffusivity D = 1.8 × 10−18-4.2 × 10−18 m2 s−1 across the entire range of the state-of-charge is obtained. The method consists of galvanostatic titrations, where a constant current injection is followed by the measurement of the galvanic potential in open circuit relaxation, at various values of the state-of-charge. Comparison with theory shows that the relaxation time varies with the state-of-charge because the particles have variable size: small particles have short relaxations and dominate the low values of the state-of-charge. The theoretical results have additional notable features. We show that the solution for the spherical particles can be represented to a very good approximation by a single time constant of exponential relaxation. Its value is significantly slower than the results for one-dimensional solutions. The relaxation time is independent of the injection current and the state-of-charge, imparting significant generality to the results.