Fractal dimension of the grain boundaries in ceramics with nanodispersed additions

The fractal dimension of the grain boundaries in Al$_2$O$_3$–MgO–SiO$_2$ corundum ceramic is measured. It is shown for the first time that a similarity exists between the aggregation of solid disperse particles and the grain formation in the ceramic and that this similarity can be used to reveal grain formation mechanisms. The fractal dimension of the grain boundaries is found to be 1.68 and 1.42 at sintering temperatures of 1200 and 1600$^\circ$C, respectively. These values correspond to primary recrystallization and normal grain growth in the ceramic. A relationship between the fractal dimension of the grain boundaries and the sintering temperature of the corundum ceramic is obtained.