The dynamic responses of a rhodium catalyst and a graphene sheet are investigated upon random excitation with 80 kV electrons. An extraordinary electron microscope stability and resolution allow studying temporary atom displacements from their equilibrium lattice sites into metastable sites across projected distances as short as 60 pm. In the rhodium catalyst, directed and reversible atom displacements emerge from excitations into metastable interstitial sites and surface states that can be explained by single atom trajectories. Calculated energy barriers of 0.13 eV and 1.05 eV allow capturing single atom trapping events at video rates that are stabilized by the Rh [110] surface corrugation. Molecular dynamics simulations reveal that randomly delivered electrons can also reversibly enhance the and the characters of the -bonded carbon atoms in graphene. The underlying collective atom motion can dynamically stabilize characteristic atom displacements that are unpredictable by single atom trajectories. We detect three specific displacements and use two of them to propose a path for the irreversible phase transformation of a graphene nanoribbon into carbene. Collectively stabilized atom displacements greatly exceed the thermal vibration amplitudes described by Debye-Waller factors and their measured dose rate dependence is attributed to tunable phonon contributions to the internal energy of the systems. Our experiments suggest operating electron microscopes with beam currents as small as zepto-amperes/nm in a weak-excitation approach to improve on sample integrity and allow for time-resolved studies of conformational object changes that probe for functional behavior of catalytic surfaces or molecules.