  Recent advances in scanning transmission electron microscopy (STEM) allow to
observe solid-state transformations and reactions in materials induced by
thermal stimulus or electron beam on the atomic level. However, despite the
rate at which large volumes of data can be generated (sometimes in the gigabyte
to terabyte range per single experiment), approaches for the extraction of
material-specific knowledge on the kinetics and thermodynamics of these
processes are still lacking. One of the critical issues lies in being able to
map the evolution of various atomic structures and determine the associated
transition probabilities directly from raw experimental data characterized by
high levels of noise and missing structural elements. Here, we demonstrate an
approach based on the combination of multiple machine learning techniques to
study the dynamic behavior of e-beam irradiated Si atoms in the bulk and at the
edges of single-layer graphene in STEM experiments. First, a deep learning
network is used to convert experimental STEM movies into coordinates of
individual Si and carbon atoms. Then, a Gaussian mixture model is further used
to establish the elementary atomic configurations of the Si atoms, defining the
bonding geometries and chemical species and accounting for the discrete
rotational symmetry of the host lattice. Finally, the frequencies and Markov
transition probabilities between these states are determined. This analysis
enables insight into the thermodynamics of defect populations and chemical
reaction networks from the atomically resolved STEM data. Here, we observe a
clear tendency for the formation of a 1D Si crystal along zigzag direction of
graphene edges and for the Si impurity coupling to topological defects in bulk
graphene.
