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              <p>Recent work [Biesuz et al., J. Appl. Phys. 120, 145107 (2016)] showed analogies between the flash sintering and dielectric breakdown in α-aluminas pre-sintered to different densities. Here, we show that flash sintering of dielectric nanoparticles can be described as a universal behavior by the percolation model. The electrical system is composed of particles and their contact point resistances, the latter softened first due to preferred local Joule heating and thermal runaway during the flash. Local softening has a hierarchical and invasive nature and propagates between the electrodes. The flash event signals the percolation threshold by invasive nature of the softened layer at the particle surfaces. Rapid densification is associated with local particle rearrangements due to attractive capillary forces induced by the softened film at the particle contacts. Flash sintering is a critical phenomenon with a self-organizing character. The experimental electric conductivity results from flash sintering are in full agreement with those calculated from the percolation model.</p>
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