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Electrochemical Strain Microscopy (ESM) can provide useful information on ionic diffusion in solids at the local scale. In this work, a finite element model of ESM measurements was developed and applied to commercial lithium manganese (III,IV) oxide (LiMn 2 O 4 ) particles. ESM time spectroscopy was used, where a direct current (DC) voltage pulse locally disturbs the spatial distribution of mobile ions. After the pulse is off, the ions return to equilibrium at a rate which depends on the Li diffusivity in the material. At each stage, Li diffusivity is monitored by measuring the ESM response to a small alternative current (AC) voltage simultaneously applied to the tip. The model separates two different mechanisms, one linked to the response to DC bias and another one related to the AC excitation. It is argued that the second one is not diffusiondriven but is rather a contribution of the sum of several mechanisms with at least one depending on the lithium ion concentration explaining the relaxation process. With proper fitting of this decay, diffusion coefficients of lithium hosts could be extracted. Additionally, the effect of phase transition in LiMn 2 O 4 is taken into account, explaining some experimental observations. V C 2015 AIP Publishing LLC. [http://dx

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