Hidden Markov model for atom-counting from sequential ADF STEM images: Methodology, possibilities and limitations

We present a quantitative method which allows us to reliably measure dynamic changes in the atomic structure of monatomic crystalline nanomaterials from a time series of atomic resolution annular dark field scanning transmission electron microscopy images. The approach is based on the so-called hidden Markov model and estimates the number of atoms in each atomic column of the nanomaterial in each frame of the time series. We discuss the origin of the improved performance for time series atom-counting as compared to the current state-of-the-art atom-counting procedures, and show that the so-called transition probabilities that describe the probability for an atomic column to lose or gain one or more atoms from frame to frame are particularly important. Using these transition probabilities, we show that the method can also be used to estimate the probability and cross section related to structural changes. Furthermore, we explore the possibilities for applying the method to time series recorded under variable environmental conditions. The method is shown to be promising for a reliable quantitative analysis of dynamic processes such as surface diffusion, adatom dynamics, beam effects, or in situ experiments.