Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution



David Kinderlehrer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
davidk@andrew.cmu.edu

Irene Livshits
Department of Mathematics
UCA Box 4912
201 Donaghey Avenue
University of Central Arkansas
Conway, AR 72032

Gregory S. Rohrer
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh, PA 15213

Shlomo Ta'asan
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
shlomo@andrew.cmu.edu

and

Peng Yu
Department of Mathematics
Pennsylvania State University
University Park, PA 16802



Abstract: A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady stat that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grainb oundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

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