Quantitative alchemi with error analysis

The ALCHEMI (atomic localization by channeling enhanced microanalysis) technique for determining the site distribution f_ip of impurity elements p (= 1...P) on host element lattice sites i ( = 1...I). Changes in x-ray emission from host atoms and impurities with crystal orientation are monitored under strong planar or axial diffraction conditions, and f_ip is derived via a ratio method. However, ratio analysis involves count ratios (and ratios of ratios), leading to severe error amplification. Neglect of delocalization leads to further error. To overcome these inherent errors in the standard ALCHEMI method, the authors make the single assumption that the impurity count for each of the spectra s = 1...m may be written as a linear combination of the host atom counts. Results for Cr₂MnO₄ are presented and analyzed.