Computer generation of Kikuchi projections and characterization of general bicrystals

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Virginia Polytechnic Institute and State University


Three parameters, i.e., misorientation angle, misorientation axis, and boundary normal, have been used to describe a general bicrystal, such as two adjacent grains, subgrains, twins, or two neighboring phases. A computer program has been developed to determine these three parameters. The angle and axis of misorientation are calculated from a misorientation matrix which is obtained by using two Kikuchi patterns, one taken from each of the two crystals. To obtain the boundary normal, a specimen tilt inside the microscope is required. A rotation matrix specifying the actual specimen tilt is formulated from two Kikuchi patterns taken from the same crystal before and after tilt. With this rotation matrix and the change of projected boundary images before and after tilt, the boundary normal can be calculated. It has been demonstrated that for high-angle bicrystal: the misorientation may be determined to within ±0.5°, and the misorientation axis to within ±0.2°. For low-angle bicrystals, the misfit angle can be obtained to within ±0.1°, and the axis of misfit to within ±4°. The boundary normals so determined are generally accurate to ±2° if suitable correction is made for magnification changes during crystal tilt.

Variations in magnification and camera length due to the shifting of specimen position along the electron-optical axis were investigated. It was found that a variation of 20% in both magnification and camera length may result when a tilting stage is used. A calibration curve was obtained which allows for correction of these errors in the Siemens Elmiskop lA.

The inherent accuracy of various beam axis solutions from a Kikuchi pattern, i.e., 3-pole, 3-normal, 2-pole/l-normal, 1-pole/2-normal, and 1-pole/matrix solutions, was also analyzed. The results indicated that the 3-normal solution is the most accurate one. The beam axis thus determined is accurate to ±0.05°, and is nearly independent of the effective camera length. For solutions in which at least one Kikuchi pole is used to formulate the equations, the beam axis may be obtained to ±0.1°, if the effective camera length is calculated from the Kikuchi pole separation. In order to eliminate the tedious calculations required to index Kikuchi patterns, computer programs were developed to provide for computer plotting of standard stereographic Kikuchi projections of any desired orientation and projection sphere radius for FCC, BCC, diamond cubic, and HCP crystals. The programs also provide for identification of Kikuchi poles as well as identification of individual Kikuchi lines. Indexing of observed patterns becomes a matter of comparison between the patterns and the projections. Coates projections for scanning electron microscopy and transmitted Kassel or pseudo-Kassel projections for x-ray diffraction studies can also be generated simply by changing the input wavelength.