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 derive correction terms which account for differences in measured responses from atoms due to variations in delocalization and X-ray absorption. The (e,2e) interaction kernel, involving ionization of target atoms within the lattice, is modelled using Hartree–Fock atomic bound-state wavefunctions. Incoherent channelling patterns are calculated for Al K-shell as well as Co K- and L-shell emissions from beta phase AlCo for a 250 keV electron beam and compared with experiment. This theory enables a correction factor Gs to be defined for each orientation s, facilitating an exact implementation of statistical ALCHEMI (atom location by channelling enhanced microanalysis), referred to as Model A. Various levels of approximation are then applied to this exact model and compared with previous implementations of ALCHEMI analysis. 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 from the fitted parameters. The next approximation, Model C, allows the offset constant to be determined from the fitting procedure itself. The last Model D has no correction terms in the fitting procedures. Experimental data were found to have sufficient systematic error that it was not useful to assess accurately the differences between these models. Thus pseudodata were used to investigate both precision and goodness of fit parameter for these models for ALCHEMI. The effect of increasing X-ray detection times (and hence decreasing relative levels of statistical noise) was considered. The theory also yields a measure of ionization delocalization from first principles, and we find the mean impact parameter for Co L-shell ionization to be about twice that derived from the previous semiclassical estimates.