Beam induced heating in electron microscopy modeled with machine learning interatomic potentials.

We develop a combined theoretical and experimental method for estimating the amount of heating that occurs in metallic nanoparticles that are being imaged in an electron microscope. We model the thermal transport between the nanoparticle and the supporting material using molecular dynamics and equivariant neural network potentials. The potentials are trained to Density Functional Theory (DFT) calculations, and we show that an ensemble of potentials can be used as an estimate of the errors the neural network make in predicting energies and forces. This can be used both to improve the networks during the training phase, and to validate the performance when simulating systems too big to be described by DFT. The energy deposited into the nanoparticle by the electron beam is estimated by measuring the mean free path of the electrons and the average energy loss, both are done with Electron Energy Loss Spectroscopy (EELS) within the microscope. In combination, this allows us to predict the heating incurred by a nanoparticle as a function of its size, its shape, the support material, and the electron beam energy and intensity.