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Recent Developments in Material Microstructure: A Theory of Coarsening

: Barmak, Katayun; Eggeling, Eva; Emelianenko, Maria; Epshteyn, Yekaterina; Kinderlehrer, David; Sharp, Richard; Ta'asan, Shlomo


MRS online proceedings library. Online resource 1753 (2015), 11 pp.
ISSN: 1946-4274
Symposium NN "Mathematical and Computational Aspects of Materials Science" <2014, Boston/Mass.>
Journal Article, Conference Paper
Fraunhofer Austria ()
coarsening; texture; simulation and modeling; large scale simulation; large metastable network; Business Field: Virtual engineering; Research Area: Semantics in the modeling process

Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The recently discovered 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 normal. During the coarsening, or growth, process, an initially random grain boundary arrangement reaches a steady state that is strongly correlated to the interfacial energy density. In simulation, if the given energy density 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 simplicity emerge from such complexity? Here we describe an entropy based theory which suggests that the evolution of the GBCD satisfies a Fokker-Planck Equation, an equation whose stationary state is a Boltzmann distribution.