  The atomic structure of nanomaterials is often studied using transmission
electron microscopy. In addition to image formation, the energetic electrons
may also cause damage while impinging on the sample. In a good conductor such
as graphene the damage is limited to the knock-on process caused by elastic
electron-nucleus collisions. This process is determined by the kinetic energy
an atom needs to be sputtered, ie, its displacement threshold energy. This is
typically assumed to have a fixed value for all electron impacts on equivalent
atoms within a crystal. Here we show using density functional tight-binding
simulations that the displacement threshold energy is affected by the thermal
perturbation of the atoms from their equilibrium positions. We show that this
can be accounted for in the estimation of the displacement cross section by
replacing the constant threshold value with a distribution. The improved model
better describes previous precision measurements of graphene knock-on damage,
and should be considered also for other low-dimensional materials.
