Mesoscale experiment and simulation permit harvesting information about both geometric features and texture in polycrystals. The grain boundary character distribution was an empirical distribution of the relative length (two dimensions) or area (three dimensions) of an interface with a given lattice misorientation and normal. During the growth process, an initially random distribution of boundary types reaches a steady state that was strongly correlated to the interfacial energy density. In simulation, it was found that if the given energy density depended only upon lattice misorientation, then the steady-state grain boundary character distribution and the energy were related by a Boltzmann distribution. This was among the simplest non-random distributions, corresponding to independent trials with respect to the energy. An entropy-based theory was derived here which suggested that the evolution of the grain boundary character distribution satisfied a Fokker-Planck equation: whose stationary state was a Boltzmann distribution. Cellular structures coarsened according to a local evolution law, curvature-driven growth, and were limited by space-filling constraints. The interaction between the evolution law and the constraints was governed primarily by the force balance at triple junctions, the natural boundary condition associated with curvature-driven growth, and determines a dissipation relation. A simplified coarsening model was introduced that was driven by the boundary conditions and reflects the network level dissipation relation of the grain growth system. It resembles an ensemble of inertia-free spring-mass dashpots. Application was made of the recent characterization of Fokker-Planck kinetics as a gradient flow for a free energy in deriving the theory. The theory predicts the results of large-scale two-dimensional simulations and was consistent with experiment.

Critical Events, Entropy, and the Grain Boundary Character Distribution. K.Barmak, E.Eggeling, M.Emelianenko, Y.Epshteyn, D.Kinderlehrer, R.Sharp, S.Taasan: Physical Review B, 2011, 83[13], 134117