Machine-learned Interatomic Potential for Ti$_{n+1}$C$_n$ MXenes: Application to Ion Irradiation Simulations

Abstract

A computationally efficient and accurate machine-learned (ML) interatomic potential is developed for Ti$_{n+1}$C$_n$ MXenes. With a diverse set of structures computed with density functional theory, the trained ML potential demonstrates good accuracy and robustness to a wide range of bond distances and environments, making it a useful tool for molecular dynamics simulations of MXenes subjected to mechanical load or irradiation. The ML potential is applied to simulations of light and heavy ion irradiation, gathering insight into the statistics and probabilities of sputtering, reflection, defect creation, and implantation into Ti$_{n+1}$C$_n$ MXene sheets. The results provide guidelines for defect engineering of MXenes through ion irradiation and implantation. Additionally, the ML potential development provides a landmark recipe for enabling machine-learning-driven atomistic simulations of other MXenes.

Figures (7)

• Figure 1: Illustration of the structures constructed and included in the training database for the ML potential, grouped into three classes: MXenes, non-MXenes, and "iterative learning" (see text for details). The percentages are computed by counting atoms in all structures of each class (in total 24150 atoms). MXenes include both ABC and AB stacking and from single-layer up to Ti$_5$C$_4$. Non-MXenes include a small set of bulk Ti, C, and TiC structures as well as graphene to ensure correct thermodynamic stability of the MXenes. The right panel shows train errors in parity plots of the ML potential energy and force compared to the DFT reference values.
• Figure 2: Energy as functions of the in-plane lattice constant $a$ for Ti$_{n+1}$C$_n$ MXene sheets with increasing $n$, compared between tabGAP, the Tersoff potential plummer_bondorder_2022, and DFT. The atom positions are fully relaxed at every lattice constant in all cases. Results are shown for both ABC and AB stackings, illustrated at the right. For visibility and direct comparison, the Tersoff data are shifted in energy to match the DFT energy minima for ABC stacking.
• Figure 3: Theoretical shear strength of an ABC-stacked Ti$_2$C MXene sheet for collective shearing of an entire Ti monolayer (top) or C monolayer (bottom) along the two different illustrated directions ('armchair' and 'zigzag'). Atoms are relaxed along the surface normal direction only. Results are compared between tabGAP, the Tersoff potential, and DFT. The key saddle points and maxima are indicated and illustrated at the right, where for example the ideal AB stacking is reached when shearing a Ti layer in the zigzag direction 1/3 of a zigzag period.
• Figure 4: Phonon dispersion of Ti2C and Ti3C2 MXenes compared between tabGAP, Tersoff, and DFT.
• Figure 5: Potential energy landscape of a Ti atom (left) and C (right) atom dragged up along the surface normal in a rigid Ti$_2$C sheet, compared between DFT, tabGAP, and the Tersoff potential. The DFT calculations are done without spin polarization, which leads to incorrect energy as the dragged atom becomes isolated. The difference is marked by a line and the energy corrected by the difference between the nonmagnetic and spin-polarized isolated atom is shown with a star. The tabGAP is trained with the correct spin-polarized energy of the isolated atom and hence reproduces the correct limits indicated by the stars.