Tessellation Models for Microstructure Evolution
Accurate morphological representation of polycrystalline microstructures is the key to structure-property linkage. Spatial tessellations exhibit great resemblance with the real microstructure evolution, which are driven by nucleation and growth. Voronoi, Avarami and Laguerre tessellations are the most popular models among the spatial tessellation models, but are only a small subset of the wide spectrum of the real microstructure evolution. Specifically, none of these models capture the anisotropy of grain shapes. The current research work proposes generalized ellipsoidal growth, in which grains grow as ellipsoids with specified 3D orientation and with velocities as a function of their size and initiate at different times from random nucleation sites represented by a spatial point process. This can be represented by a marked point process random field model. The mathematical representation of the grain cells, thus formed, is developed. This could be extended to the non-trivial inverse problem of locating a grain nucleation site from the grain centroid and volume data. This is demonstrated on data generated using diffraction Contrast Tomography (DCT).