Determination of grain boundary geometry using TEM
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J. T. M. De Hosson Department of Applied Physics, University of Groningen, Nijenborgh 18, 9747 AG, Groningen, The Netherlands (Received 17 October 1991; accepted 19 March 1992)
An experimental method to obtain the grain boundary geometry using the transmission electron microscope is presented. The method allows S determination including grain boundary plane orientation. In order to determine the specialness of the grain boundary, three different criteria for maximum allowable deviations from exact CSL misorientations were examined. We tested these three criteria from a statistical distribution of grain boundary types in terms of E. We compared grain boundary distributions from other studies in Ni 3 Al and found discrepancies among them. It seems that the discrepancy came from the different criteria for special boundaries in S determination and different experimental procedures they used. The statistical distribution of grain boundary plane orientations showed that low S boundaries (S < 11) were oriented to the plane of high density of coincident sites.
I. INTRODUCTION It has long been known that the structure and energy of a grain boundary depend on the crystal misorientation between two adjacent grains and on the orientation of a particular interface plane adopted by the boundary. Several theoretical models have been proposed to describe the grain boundary structure. 110 Among the models, the coincident site lattice (CSL) representation of grain boundary structures has become dominant as a basis for grain boundary interpretation.11'12 The CSL model is based on the degree of coincidence between lattice points from both grains across a boundary. The presence of coincident orientations can lead to properties that are different from other boundaries.13 It is now generally accepted that grain boundaries can be "special" based on the degree of coincidence between two crystal points where the degree of coincidence can be calculated by the ratio between the volume of CSL lattice points and the volume of the basic lattice. The ratio has been symbolized by S. This approach mainly considered the macroscopic crystallography of the boundary without considering the detailed boundary structure after relaxation. Therefore, the variation of the grain boundary energy in this model is discontinuous with the misorientation of bicrystals. There exist two techniques to account for the discontinuity of the interfacial energy in the
"'Current address: Department of Materials Science and Engineering, Technological Institute, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3180. J. Mater. Res., Vol. 7, No. 7, Jul 1992 http://journals.cambridge.org
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CSL model. One is the atomistic computer simulation of grain boundary structures, which gives the relaxed atomic structure in the grain boundary.14'15 It is now well known that the detailed structure of grain boundaries has been studied successfully on various issues of grain boundary properties using atomistic computer simulations.16"19 Another
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