Three-dimensional ab initio description of vibration-assisted electron knock-on displacements in graphene

Transmission electron microscopy characterization may damage materials, but an electron beam can also induce interesting dynamics. Elastic knock-on is the main electron irradiation damage mechanism in metals including graphene, and although atomic vibrations influence its cross section, only the out-of-plane direction has been considered so far. Here, we present a full three-dimensional first-principles theory of knock-on displacements including the effect of temperature on vibrations to describe dynamics into arbitrary directions. We validate the model with previously precisely measured knock-on damage of pristine graphene, where we show that the isotropic out-of-plane approximation correctly describes the cross section. We then apply our methodology to reversible jumps of pyridinic nitrogen atoms, whose probability under irradiation is measured at 55 and 60 keV. Direct displacement requiring a high emission angle and an alternative pathway via intermittent N adatom creation and recombination are computationally explored but are unable to explain the observed rates, implying stronger inelastic effects at the defect than in pristine graphene.