Evidence against a universal electron-beam-induced virtual temperature in graphene

Abstract

The continuous electron bombardment of a sample during transmission electron microscopy (TEM) drives atomic-scale transformations. In earlier studies the transformations appeared to proceed as if the sample was held at an elevated temperature, and, indeed, the hypothesis of an electron-beam-induced virtual temperature has gained traction in the scientific community. However, the sample is not significantly heated by the electron beam, meaning the processes are not activated by thermal vibrations. Instead, individual collisions between the electrons and the target atoms, and/or excitations of the electronic system, lead to the observed transformations. It is not a priori clear what virtual temperature can be assigned to the conditions under the electron irradiation, or even if such a temperature can be defined at all. Here, we attempt to measure the virtual temperature, specific to this system, by comparing the relative population of the three different divacancy defect states in single-layer graphene to the Boltzmann distribution using calculated energy levels of the defect states. The experiment is conducted using aberration-corrected high-resolution TEM at an acceleration voltage of 80 kV. Atomistic simulations are used to learn about the energetics of the defects. We find that the measured populations cannot be fitted to the Boltzmann distribution, and consequently no universal virtual temperature can be assigned to the system.