In this paper, we apply phase field models to move beyond Fick's law in describing Li diffusion in secondary battery electrodes. Phase field models are potentially more accurate and allow simpler tracking of phase boundaries than Fick's equation. The phase field models are implemented using the highly accurate but fast Chebyshev-spectral method. Using the phase field we investigate to what extent non-Fickian behavior can affect results from experimental techniques for measuring diffusion coefficients, such as Galvanostatic Intermittent Titration Technique (GITT) and Potentiostatic Intermittent Titration Technique (PITT). We show that GITT and PITT can still accurately measure the diffusion coefficient in systems described by phase field models even when significant gradient energy terms are present. (C) 2004 Elsevier Ltd. All rights reserved.