Non-equilibrium Interface and Surface Dynamics

Predictive theory for the grain boundary character distribution

David Kinderlehrer

Carnegie Mellon University

Mesoscale experiment and simulation permit harvesting information about both geometric features and texture in material microstructures. The grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and grain boundary normal. During the growth process, an initially random texture distribution reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, it is found that if the given energy depends only on lattice misorientation, then the steady state GBCD and the energy are related by a Boltzmann distribution. This is among the simplest non-random distributions, corresponding to independent trials with respect to the energy. Why does such a simple distribution arise from such a complex system? This is joint work with Katayun Barmak, Eva Eggeling, Yekaterina Epshteyn, Richard Sharp, and Shlomo Ta'asan and sponsored by the CMU Center for Excellence in Materials Research and Innovation.