Weak-beam and high-resolution bright-field contrast from misfitting spherical inclusions

Criteria have been derived for the position of the intensity maxima of weak-beam images of spherical inclusions with a misfit. These approximate expressions are compared to many-beam calculations performed at 1 MV for different sizes of inclusions, misfit ratios, and excitation errors. The intensity minima of bright-field images and the intensity maxima of dark-field images are found to fall on the projection of the interface of the inclusion when an excitation error |sg| ≈ |gϵ/2| is used. In the case of bright-field images g refers to the most strongly excited reflection. If a well collimated beam is used to image small inclusions the weak-beam peak intensities oscillate substantially with foil thickness or position of the inclusion in the foil which can cause difficulties in the image interpretation. Explicit calculations show, however, that these difficulties can be overcome by using a convergent electron beam. The possibilities to analyse the shape and size of small inclusions is limited by the visibility above the background intensity. Starting from the theoretical results a method is proposed to determine the shape and size of spherical inclusions. The method is applied to TiC inclusions in an austenitic stainless steel.