Machine learning assisted crystallographic reconstruction from atom probe tomographic images.

Atom probe tomography (APT) is a powerful technique for three-dimensional atomic-scale imaging, enabling the accurate analysis on the compositional distribution at the nanoscale. How to accurately reconstruct crystallographic information from APT data, however, is still a great challenge due to the intrinsic nature of the APT technique. In this paper, we propose a novel approach that consists of the modified forward simulation process and the backward machine learning process to recover the tested crystal from APT data. The high-throughput forward simulations on Al single crystals of different orientations generate 10,000 original 3D images and data augmentation is implemented on the original images, resulting in 100,000 3D images. The big data allows the development of deep learning models and three deep learning algorithms of Convolutional Neural Network (CNN), Vision Transformer (ViT), and Variational Autoencoder (VAE) are used in the backward process. After training, the ViT model performs superior than the CNN and VAE models, which can recover the crystalline orientation outstandingly, as evaluated by the coefficient of determination R^2 and the Mean Percent Error (MPE), viz., R^2=0.93 and MPE=0.43%, R^2=0.97 and MPE=0.35%, and R^2=0.93 and MPE=0.77% for the rotation angles ϕ, ψ and θ, respectively, on the test dataset. The present work clearly demonstrates the capability of deep learning models in the recovery of the tested crystals from APT data, thereby paving the way for the further development of large artificial intelligent models of APT.