Numerical model for particle size effects on flash sintering temperature of ionic nanoparticles

A numerical model is presented to predict the particle size effect on the flash onset temperature, using a granular network consisting of ceramic nanoparticles and their contacts as resistors. The theoretical calculations are compared to the experimental data of 3 mol% yttria-stabilized zirconia as ionic ceramic from the literature. The electric resistances at the particle contacts and the granular compact volume primarily depend on the contact to particle radius ratio. This ratio increases with the increase in the cold compaction pressure and during the heating to the flash temperature. This ratio also dictates the electric resistance via conventional or quantum mode, depending on the bulk resistivity character. Smaller particles lead to higher neck to particle radius ratio during the heating, hence to lower flash sintering temperatures. Apparently, the need for a critical current through the necks is crucial in determining the flash temperature, in agreement with Joule heating.