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Predictive Theory for the Grain Boundary Character Distribution

Mesoscale experiment and simulation permit harvesting information about both geometric featuresand texture in material microstructures. The grain boundary character distribution (GBCD) is an em-pirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misori-entation and grain boundary normal. During the growth process, an initially random texture distribu-tion reaches a steady state that is strongly correlated to the interfacial energy density [9]. In simulation,it is found that if the given energy depends only on lattice misorientation, then the steady state GBCDand the energy are related by a Boltzmann distribution. This is among the simplest non-random dis-tributions, corresponding to independent trials with respect to the energy. Why does such a simpledistribution arise from such a complex system.