A theory of Bragg diffraction phase contrast due to defects in crystals observed by transmission electron microscopy

Abstract

The contrast on transmission micrographs of crystals is mainly due to local differences in the intensities of the Bragg diffracted beams. Since the wavelength of the electrons in electron microscopes operating usually at 50–100 kV is very short (about 0.05 A), and since the Bragg angles are only of the order of a few degrees, there is a high probability that for an arbitrary orientation of the crystal the incident beam will have a direction not very far away from that corresponding to the Bragg angle of a set of reflecting planes. Thus, in general, some electrons are diffracted by crystals in arbitrary orientation, although of course the electron beam is particularly strongly diffracted when the crystal is in such an orientation that a set of reflecting planes is exactly at the Bragg angle relative to the incident beam. In the latter case the electron beam can be reflected completely if the thickness of the specimen, in the case of a metal, is only of the order of a few 100 A. Since usually the Bragg diffracted electrons are prevented from reaching the image by placing a suitable aperture in the microscope, large contrast effects can result from local differences in orientation. Thus different grains in a polycrystalline material, or subgrains in a crystal, can be distinguished clearly on transmission micrographs (1, 2, 3). If the crystals are bent, the loci of points on the specimen where the reflecting planes are at a reflecting position are called extinction contours due to bending (or bend contours) (1). Fig. 1 shows an example of a transmission micrograph from a polycrystalline specimen of annealed stainless steel; the different grains and extinction contours are clearly visible.