Distribution of Grain Boundary Planes at Coincident Site Lattice Misorientations
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Distribution of Grain Boundary Planes at Coincident Site Lattice Misorientations Gregory S. Rohrer, Bassem S. El Dasher1, Herbert M. Miller, Anthony D. Rollett, David M. Saylor2 Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, U.S.A. 1 University of California, Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94511, U.S.A. 2 U.S.F.D.A., 12725 Twinbrook Parkway, Rockville, MD 20852, U.S.A. ABSTRACT The grain boundary plane distributions in MgO, SrTiO3, MgAl2O4, and Al are compared at lattice misorientations with a coincident site density of greater than or equal to 1/9. In most situations, the most frequently adopted grain boundary orientation is a habit plane of low index and low surface energy that depends on the particular material. Cases where the most common boundary orientation is a plane of high planar coincident site density instead of a characteristic habit plane are rare. In fact, in most cases, the distributions of grain boundary planes at misorientations with high lattice coincidence are not substantially different from the distributions at other, more general misorientations. The results indicate that a model for grain boundary energy and structure based on grain surface relationships is more appropriate than the widely accepted models based on lattice orientation relationships. INTRODUCTION To distinguish one grain boundary from another, five independent parameters must be specified. If the parameters are measured with a resolution of D°, then as D decreases and the resolution increases, the number of distinguishable grain boundaries increases in proportion to 1/D5. For example, in a cubic system, if the five angular parameters are measured with 10° of resolution, then there are approximately 6.5x103 distinct boundaries. By increasing the resolution to 5°, this number increases to 2x105. Historically, this complexity has been handled by assigning boundaries to broad categories, such as low misorientation angle grain boundaries, general boundaries, and coincident site lattice (CSL) boundaries. While reducing the number of grain boundary types to a manageable level, this approach obviously groups together many boundaries which are not identical in the crystallographic sense and may have very different properties. For example, when boundaries are classified by their coincident site lattice type, the two degrees of freedom that describe the interface plane remain unspecified. Because it has recently become possible to make comprehensive measurements of the grain boundary character distribution, it is now possible to classify boundaries by all five parameters. The purpose of this paper is to describe how the grain boundary planes are distributed at selected CSL misorientations in several polycrystalline materials. The CSL concept has been in use for more than 50 years [1]. The basic idea is that boundaries with misorientations that place a high fraction of lattice sites in coincidence are distinguished from more general boundar
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