THE LAGUERRE MODEL FOR GRAIN-GROWTH IN 3 DIMENSIONS

We propose a novel and poweful methodology for three-dimensional (3D) grain growth modelling in both the anisotropic and the locally inhomog eneous cases, thus significantly generalizing previous related two-dim ensional work. The fundamental modelling structures for the polycrysta ls and their behaviour are dynamically evolving Laguerre diagrams in t he flat 3D torus. The weighted generating sites of such diagrams obey motion equations ensuing from system interface energy minimization wit h consequent evolution of the associated structures and resulting in e lementary topological transformations thereof. We have implemented the models in state-of-the-art computer simulation codes and made large-s cale runs assuming either constant (isotropic) or variable (anisotropi c) interface specific energies. In both cases, the simulated evolution reproduced the main features of the normal grain growth process in po lycrystalline materials, that is the grain growth power law, typical d istributions of grain sizes and shapes, and the scaling behaviour in l ong-term regime. The simulated distribution of grain-to-grain misorien tation and its evolution in a simple hypothetical case have also been obtained for the first time.