Interactions of two-dimensional MXene sheets and electron beam of (scanning) transmission electron microscope are studied via first-principles calculations. We simulated the knock-on displacement threshold for Ti$_3$C$_2$ MXene sheet via ab initio molecular dynamics simulations and for five other MXenes (Ti$_2$C, Ti$_2$N, Nb$_2$C, Mo$_2$TiC$_2$, and Ti$_3$CN) approximately from defect formation energies. We evaluated sputtering cross section and sputtering rates, and based on those the evolution of the surface composition. We find that at the exit surface and for low TEM energies H and F sputter at equal rates, but at high TEM energies the F is sputtered most strongly. In the enter surface, H sputtering dominates. The results were found to be largely similar for all studied MXenes, and although the displacement thresholds varied between the different metal atoms the thresholds were always too high to lead to significant sputtering of the metal atoms. We simulated electron microscope images at the successive stages of sputtering, and found that while it is likely difficult to identify surface groups based on the spot intensities, the local contraction of lattice around O groups should be observable. We also studied MXenes encapsulated with graphene and found them to provide efficient protection from the knock-on damage for all surface group atoms except H.
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