New method for rapid determination of crystal orientation via Kikuchi patterns
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Kikuchi electron diffraction patterns are used extensively to determine crystal orientations via transmission electron microscopy (TEM) or in the electron backscattering pattern (EBSP) mode of scanning electron microscopy (SEM). A new method is presented that is capable of finding crystal orientations, the camera length, and the projection center from only one pattern per grain using a least-squares technique. This method eliminates the need to perform an alignment with a reference crystal in the backscattering mode. Application to a 1= 13a silicon bicrystal is presented for TEM patterns and EBSP's. A complete analysis of the propagation of random measurement errors into the disorientation axis/angle pair is carried out. The root mean square deviation from the nominal disorientation angle is found to be 0.3" in the case of TEM and 0.5" in the case of EBSP. The root mean square inclination between the nominal and measured disorientation axis is found to be 1" in the case of TEM and 0.5" in the case of EBSP.
1. INTRODUCTION
lattice microscopies that are able to extract bicrystal disorientations. High accuracy measurements (0.8") were Determination of crystal grain orientations with performed by means of field-ion microscopy in which respect to adjacent grains has numerous important two adjacent grains can be imaged simultaneously with applications such as texture determination,'-' rotating I' atomic resolution. crystallite experiment^,^,^ and studies of solute-atom Except for the triclinic system, the relative oriensegregation at individual grain boundaries ( G B ' s ) . ~ - ' ~ tation between two neighboring grains can be modeled General overviews of the possibilities can be found with a rotation. There are several ways to parameterize in reviews on this subject.Is Also, the five macroscopic this rotation. One approach defines a rotation axis and a degrees (DOF's) of an internal interface (grain boundary rotation angle. Since the rotation axis itself is not affected or heterophase interface) affect its interfacial Gibbs free by the rotation, its Miller indices have the same value in en erg^,^,'^,'^ and hence the measurement of an internal both grains. The symmetry of the crystal system results interface's DOF's is a basic quantity in understanding in a multitude of equivalent relative rotations (24 for the how the interfacial Gibbs free energy varies with cubic system). By convention, the one with the smallest misorientation in grain bomdary phase space. rotation angle, in the standard stereographic triangle, Electron diffraction has an advantage over x-ray is defined and referred to as the disorientation. Some techniques in the case of small crystal grain sizes, special disorientation in the cubic system are designated due to the availability of high-quality beam focusing of points in space that as 1-boundaries when the set optics in electron microscopes. Small crystal grains can belongs to both (infinite) crystal lattices form a new be selectively chosen and their orientation relationship lattice-the coincident
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