Papers by Author: D. Kinderlehrer

Abstract: Relative grain boundary energy as a function of misorientation angle was measured in a cube-oriented, 120 µm-thick Al foil and in a <111> fiber-textured, 1.7 µm-thick Al film using a multiscale analysis of the grain boundary dihedral angles. For the Al foil, the energies of low-angle boundaries increased with misorientation angle, in good agreement with the Read-Shockley model. For the Al film, two energy minima were observed for high-angle boundaries. Grain growth was studied in 25 and 100 nm-thick films that were annealed at 400 °C for a series of times in the range of 0.5 to 10 h. For the 100 nm-thick film, grains approximately doubled their size (equivalent circular diameter) before grain growth stagnated. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo Potts and partial differential equation based simulations showed excellent agreement with each other, even when anisotropic boundary energies were used. However, the simulated distributions had fewer small grains than the experimental distributions.

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 state 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 grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Abstract: Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.