Statistical Analysis and Classification of Atomic Structural Dynamics in Nanoparticles

Transmission electron microscopy data corresponding to CeO2 nanoparticle images acquired at 400 frames per second. On the top box, a 1000 single frames lead to a summed image with a good signal to noise ratio. The good quality of the 1000-frame summed image enables to determine accurately the atomic position and the intensities on the columns of the nanoparticle. The middle box represents an example of a single frame (2.5 ms) of the movie, where the evident poor signal to noise ratio makes a hard task to track the position of the atomic columns and their intensities (red circle over the single frame shows how the tracking is failing at certain points, specially on the surface, where more structural dynamics are taking place). In the bottom box, the left figure represents the spatio-temporal visualization after the Gaussian filtering from two movie sequences of 8913 frames in 22.3 sec., where the color indicates the flag status after filtering; the right figure displays the time series of separations between atomic columns 23 and 27.

3-State hidden Markov model for separation between atomic columns 23 and 27 in previous figure. The left figure shows the estimated densities and mean values for each state. The central portion displays the estimated initial state probabilities, transition matrix, and mean and standard deviation of the emission distribution. The right figure shows the separation (blue lines), Viterbi path (red lines), and states (colored regions).

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