Structural and energetic properties of vacancy defects in MXene surfaces

Density functional theory calculations were employed to investigate the structure and energetics of vacancy defects on 84 MXene surfaces, composed of different M (Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, or W), X (carbon or nitrogen), T (oxygen of fluorine), and atomic layer stacking (ABC or ABA) combinations. Structurally, we found that, in most cases, the effect of the presence of the vacancy on the surrounding atoms is to push them away from the vacant site due to the missing screening charge and the reinforcement of the remaining interatomic bonds. The reconstruction energy associated to this surface relaxation was found to range from a few tenths of eV to a few eV. On the bare ABC-stacked carbide MXenes, we found M and X vacancy formation energies between 2 and 3 eV. On nitrides, M vacancy formation energies are decreased, while X ones seem to increase. By terminating the MXenes with an O layer, M formation energies are significantly increased, reaching over 9 eV in some cases, in agreement with theoretical and experimental results of the literature, whereas X vacancy formation energies become smaller. The F termination was found to have the same effect as O on X vacancy formation energies with respect to clean MXenes, but to decrease M vacancy formation energies. The F termination allows more easily created M and N vacancies than the O termination. The creation of vacancies on some ABC-stacked ${\mathrm{M}}_{2}{\mathrm{XF}}_{2}$ MXenes led to extreme lattice deformation which suggests that the experimental synthesis of ${\mathrm{M}}_{2}{\mathrm{NF}}_{2}$ with metals from groups 5 and 6 of the Periodic Table, and ${\mathrm{M}}_{2}{\mathrm{CF}}_{2}$ with metals from group 6, through etching using a hydrogen fluoride aqueous solution [HF (aq)] will lead to ABA-stacked MXenes. The formation energies of the MT double vacancies were found to correlate approximately linearly with the sum of the corresponding M and T single-atom vacancy formation energies. All MXenes studied in this work fit in the same correlation line, implying that one can predict the formation energy of double vacancies on MXenes, made of any M, X, and T elements, and with atomic layers stacked in an ABC or ABA fashion, if the formation energies of the corresponding single vacancies are known. The method used by theoretical works, such as this one, to calculate formation energies has two crucial limitations: the values thus obtained depend on the chosen single-atom energy references, and kinetic effects such as energy barriers are not included. Here, we cautiously discuss these limitations, compare formation energies calculated using different energy references, and propose mechanisms for the formation of vacancies that include atomic migration barriers.