  Advanced materials often consist of multiple elements which are arranged in a
complicated structure. Quantitative scanning transmission electron microscopy
is useful to determine the composition and thickness of nanostructures at the
atomic scale. However, significant difficulties remain to quantify mixed
columns by comparing the resulting atomic resolution images and spectroscopy
data with multislice simulations where dynamic scattering needs to be taken
into account. The combination of the computationally intensive nature of these
simulations and the enormous amount of possible mixed column configurations for
a given composition indeed severely hamper the quantification process. To
overcome these challenges, we here report the development of an incoherent
non-linear method for the fast prediction of ADF-EDX scattering cross-sections
of mixed columns under channelling conditions. We first explain the origin of
the ADF and EDX incoherence from scattering physics suggesting a linear
dependence between those two signals in the case of a high-angle ADF detector.
Taking EDX as a perfect incoherent reference mode, we quantitatively examine
the ADF longitudinal incoherence under different microscope conditions using
multislice simulations. Based on incoherent imaging, the atomic lensing model
previously developed for ADF is now expanded to EDX, which yields ADF-EDX
scattering cross-section predictions in good agreement with multislice
simulations for mixed columns in a core-shell nanoparticle and a high entropy
alloy. The fast and accurate prediction of ADF-EDX scattering cross-sections
opens up new opportunities to explore the wide range of ordering possibilities
of heterogeneous materials with multiple elements.
