Atom counting in HAADF STEM using a statistical model-based approach: Methodology, possibilities, and inherent limitations

In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the p...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Ultramicroscopy 2013-11, Vol.134, p.23-33
Hauptverfasser: De Backer, A., Martinez, G.T., Rosenauer, A., Van Aert, S.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration. •We discuss a quantitative atom counting method for HAADF STEM in detail.•Statistical parameter estimation theory is used to determine scattered intensities of atom columns from HAADF STEM images.•Gaussian mixture models enable us to analyse distributions of scattered intensities of atom columns.•We discuss the conditions under which single atom sensitivity is feasible.
ISSN:0304-3991
1879-2723
DOI:10.1016/j.ultramic.2013.05.003