On the dynamical theory of electron transmission microscope images of dislocations and stacking faults

An examination is made of the properties of bright- and dark-field electron-microscope diffraction contrast images of dislocations with glide planes parallel to the crystal surface. In particular, the dependence of the image profiles on the crystal thickness and on the position of the dislocation in the foil is studied. The purely dynamic case, i.e. crystal exactly at the reflecting position, is considered. The foil is composed of three partial parallel foils; a central portion, containing the dislocation, sandwiched between two outer portions which have a high degree of perfection. The transmission and diffraction of electrons by each portion is described by a scattering matrix, the matrix for the complete foil being the product of these three matrices. The matrices are obtained by using the system of differential equations derived by Howie and Whelax for the dynamic case of transmission and diffraction of electrons (with absorption), using the column and two-beam approximations. It is shown that several properties of the contrast images can be derived without detailed solution of the equations only their structure and the properties of the displacement functions of the dislocation being considered. These properties are found to be in full agreement with both the profiles obtained by Howie and Whelan by numerical integration of their equations for a large number of cases, and their discussion. The amplitudes of the waves transmitted and diffracted by a foil containing a sequence of stacking faults, parallel to the surface of the foil, are also calculated.