Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images

Understanding transformations under electron beam irradiation requires mapping the structural phases and their evolution in real time.To date,this has mostly been a manual endeavor comprising difficult frame-by-frame analysis that is simultaneously tedious and prone to error.Here,we turn toward the use of deep convolutional neural networks(DCNN)to automatically determine the Bravais lattice symmetry present in atomically resolved images.A DCNN is trained to identify the Bravais lattice class given a 2D fast Fourier transform of the input image.Monte-Carlo dropout is used for determining the prediction probability,and results are shown for both simulated and real atomically resolved images from scanning tunneling microscopy and scanning transmission electron microscopy.A reduced representation of the final layer output allows to visualize the separation of classes in the DCNN and agrees with physical intuition.We then apply the trained network to electron beam-induced transformations in WS2,which allows tracking and determination of growth rate of voids.We highlight two key aspects of these results:(1)it shows that DCNNs can be trained to recognize diffraction patterns,which is markedly different from the typical“real image”cases and(2)it provides a method with inbuilt uncertainty quantification,allowing the real-time analysis of phases present in atomically resolved images.

Reconstructing phase diagrams from local measurements via Gaussian processes:mapping the temperature-composition space toconfidence

We show the ability to map the phase diagram of a relaxor-ferroelectric system as a function of temperature and composition through local hysteresis curve acquisition,with the voltage spectroscopy data being used as a proxy for the(unknown)microscopic state or thermodynamic parameters of materials.Given the discrete nature of the measurement points,we use Gaussian processes to reconstruct hysteresis loops in temperature and voltage space,and compare the results with the raw data and bulk dielectric spectroscopy measurements.The results indicate that the surface transition temperature is similar for all but one composition with respect to the bulk.Through clustering algorithms,we recreate the main features of the bulk diagram,and provide statistical confidence estimates for the reconstructed phase transition temperatures.We validate the method by using Gaussian processes to predict hysteresis loops for a given temperature for a composition unseen by the algorithm,and compare with measurements.These techniques can be used to map phase diagrams from functional materials in an automated fashion,and provide a method for uncertainty quantification and model selection.

Author Correction:Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images

In the original version of this Article the term‘rhombohedral’was used incorrectly in place of‘oblique’,and the term‘rhombohedral’was used in Supplementary Figure 5 to describe the simulated lattice but we had instead simulated a rectangular centered lattice.All mentions of‘rhombohedral’have been corrected to‘oblique’in the manuscript,Fig.2 and Fig.4–6,and Supplementary Information.Similarly,‘centered rectangle’has been corrected to‘rectangular centered lattice’throughout the manuscript to avoid any confusion in terminology.