Revealing the Hidden Third Dimension of Point Defects in Two-Dimensional MXenes

Point defects govern many important functional properties of two - dimensional ( 2D) materials. However, resolving the three - dimensional (3D) arrangement of these defects in multi - layer 2D materials remains a fundamental challenge, hindering rational defect engineering . Our approach reconstructs the 3D coordinates of vacancies across hundreds of thousands of lattice sites, generating robust statistical insight into their dist ribution that can be correlated with specinullic synthesis pathways. This large - scale data enables us to classify a hierarchy of defect structures -- from isolated vacancies to nanopores -- revealing their preferred formation and interaction mechanisms, as corroborated by molecular dynamics simulations . This work provides a generalizable framework for understanding and ultimately controlling point defects across large volumes, paving the way for the rational design of defect - engineered functional 2D materials. Keywords: 2D materials, point defects, autonomous materials science, electron microscopy, machine learning 2 Two - dimensional (2D) materials have become a major nullield of modern research in materials science after the discovery of graphene in 2004 . The challenge of characterizing point defects is signinullicantly amplinullied in few - layered 2D materials. For instance, MXenes -- a class of 2D transition metal carbides, carbonitrides, and nitrides -- consist of nanosheets containing two to nullive layers of metal ato ms, which complicates defect analysis compared to single - layer materials .