Hyperbolic grain boundaries

In the amorphous-to-crystalline phase transformation of thin film Co${\mathrm{Si}}_2$, all grain boundaries in the crystalline microstructure viewed in projection have the shape of a hyperbola. This is due to the continuous nucleation and constant growth rate which gives circular Co${\mathrm{Si}}_2$ grains before impingement. Such a mode of transformation results in a macroscopic nonequilibrium state at the triple points where a grain boundary meets two amorphous-to-crystalline interfaces.