Anisotropy of Vacancy Interactions in MXenes and their Effect on Mechanical Properties

The spatial distribution of defects on MXenes, and in general on two-dimensional (2D) materials, strongly influences their mechanical, electronic, catalytic, sensing, and transport properties. Using molecular statics calculations, we extract the interaction energy of vacancies for several MXene structured materials, uncovering spatial anisotropy. We find that the interactions of MXene surface vacancies originate from a combination of in-plane force tripoles and out-of-plane dipoles, with different power-law spatial dependence and no significant cross-talk. This differs from surface defects in 3D (semi-infinite bulk) whose interactions are longer ranged and vary as the inverse cube of their separation. The physical origin of the interactions suggested here is robust, as we find it on several MXenes, with different stacking, and different crystallographic directions. We corroborate it by creating symmetric defects with zero out of plane dipoles and verifying that the spatial dependence becomes a single power law, corresponding to the in-plane tripoles. While our results can be verified in future experiments, the attractive interaction revealed for nearest-neighbor Ti vacancies explains the reported clustering of vacancies. Hybrid Monte Carlo (MC) molecular dynamics (MD) calculations extend vacancy interactions to realistic configurations. These vacancy distributions are compared to experimental STEM images of Ti3C2 with machine learning (ML) and radial distribution functions (RDF).