Generation and absorption of characteristic X-rays under dynamical electron diffraction conditions

The theory for formation of incoherent channelling patterns (ICPs), produced by variations in characteristic X-ray emission in response to a systematic scan in the direction of the incident electron beam for orientations near a zone axis, is extended to account for absorption of X-rays within the specimen. This is achieved by calculating the probability of X-ray generation as a function of depth within a crystal prior to the inclusion of an absorptive term which is dependent on the geometry of the X-ray detector relative to the crystal as well as the absorption characteristics of the specimen for the particular X-ray energy. ICPs from three major zones of the L1(0) phase in Ti-Al and Ti-Ga alloys are compared and effects of different absorption due to variation of goniometer tilt with respect to the X-ray detector are calculated. Although fast electron quantum states that are peaked on Ti atomic sites have similar eigenvalues (binding energies) in both alloys, it is shown that differences in complex eigenvalues (including absorption) occur between states that are localized on Al or Ga, and that this results in substantially different contrast between the two alloys in ICPs from Al and Ga characteristic X-rays. (C) 1997 Elsevier Science Ltd.