Diffusion constants are typically considered to be independent of particle size with the benefit of nanosizing materials arising solely from shortened transport paths. We show that for materials with one-dimensional atomic migration channels, the diffusion constant depends on particle size with diffusion in bulk being much slower than in nanoparticles. This model accounts for conflicting data on LiFePO(4), an important material for rechargeable lithium batteries, specifically explaining why it functions exclusively on the nanoscale.
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