Lithium iron phosphate is one of the most promising positive-electrode materials for the next generation of lithium-ion batteries that will be used in electric and plug-in hybrid vehicles. Lithium deintercalation (intercalation) proceeds through a two-phase reaction between compositions very close to LiFePO(4) and FePO(4). As both endmember phases are very poor ionic and electronic conductors, it is difficult to understand the intercalation mechanism at the microscopic scale. Here, we report a characterization of electrochemically deintercalated nanomaterials by X-ray diffraction and electron microscopy that shows the coexistence of fully intercalated and fully deintercalated individual particles. This result indicates that the growth reaction is considerably faster than its nucleation. The reaction mechanism is described by a 'domino-cascade model' and is explained by the existence of structural constraints occurring just at the reaction interface: the minimization of the elastic energy enhances the deintercalation (intercalation) process that occurs as a wave moving through the entire crystal. This model opens new perspectives in the search for new electrode materials even with poor ionic and electronic conductivities.