Dynamical Germ-Grain Models with Ellipsoidal Shape of the Grains for Some Particular Phase Transformations in Materials Science

A large number of engineering materials of interest are aggregate of many small crystals, called the grains of the polycrystal, which are often equiaxed. However, because of processing, the grain shape may become anisotropic; for instance, during recrystallization or phase transformations, the new grains may grow in the form of ellipsoids. Moreover, it is reasonable and it has also been found in experimental works, that the probability of a new nucleus forming very close to another one is likely to be low. From a mathematical point of view, such situation may be modelled by assuming hard-core nucleation processes. We collect here a series of recent results on mean volume and surface densities of suitable dynamical germ-grain models with ellipsoidal shape of the grains, with the aim to provide a unified approach in modelling phase transformations of this kind.