Correction terms and approximations for atom location by channelling enhanced microanalysis

A theory for X-ray emission from crystals, when subjected to electron beam irradiation under dynamical electron diffraction conditions, is used to der ive correction terms which account for differences in measured responses fr om atoms due to variations in delocalization and X-ray absorption. The (e,2 e) interaction kernel, involving ionization of target atoms within the latt ice, is modelled using Hartree-Fock atomic bound-state wavefunctions. Incoh erent channelling patterns are calculated for Al K-shell as well as Co K- a nd L-shell emissions from beta phase AlCo for a 250 keV electron beam and c ompared with experiment. This theory enables a correction factor G(s) to be defined for each orientation s, facilitating an exact implementation of st atistical ALCHEMI (atom location by channelling enhanced microanalysis), re ferred to as Model A. Various levels of approximation are then applied to t his exact model and compared with previous implementations of ALCHEMI analy sis. In a first approximation (Model B), an averaged correction factor G is used to calculate an offset constant C for the overall fit between dopant and host atom responses, and G is used to extract relative partitioning fro m the fitted parameters. The next approximation, Model C, allows the offset constant to be determined from the fitting procedure itself. The last Mode l D has no correction terms in the fitting procedures. Experimental data we re found to have sufficient systematic error that it was not useful to asse ss accurately the differences between these models. Thus pseudodata were us ed to investigate both precision and goodness of fit parameter for these mo dels for ALCHEMI. The effect of increasing X-ray detection times land hence decreasing relative levels of statistical noise) was considered. The theor y also yields a measure of ionization delocalization from first principles, and we find the mean impact parameter for Co L-shell ionization to be abou t twice that derived from the previous semiclassical estimates. (C) 1999 El sevier Science B.V. All rights reserved.