Practical Electron Microscopy and Database

During the collision process between incident electrons and a nucleus, if the energy (E) received by an atomic nucleus exceeds the atomic surface-binding energy E_s, surface atoms can be removed in an average time, given by,
          <T> ~ e/(σ_sJ) ------------------- [4408a]
where,
          J -- The current density of the incident electron beam,
          σ_s -- The cross section of sputtering (or called knock-on).

The sputtering cross section can be given by, [1]

           ------------------- [4408b]
where,
          A -- The atomic mass number,
          Z -- The atomic number,
          E -- The energy received by an atomic nucleus due to the collision between the incident electrons and the nucleus,
          E₀ -- The energy of incident electrons.

Cross-sections (σ) of surface sputtering in conducting materials induced by electron irradiation is from 10^-22 to 10^-21 cm².

Conventional wisdom suggests that a low operating voltage (<100 kV) in TEMs is optimal for reducing radiation damage, but the calculated profiles as a function of incident electron energy E₀ in Figure 4408 demonstrate the minimum displacement cross-sections for lithium atoms in the elemental Li, lithiated graphite (LiC₆) and graphite are not at low operating voltages.

[1] Chadderton, L.T., 1965. Radiation Damage in Crystals, Methuen, London.
[2] FengWang, Jason Graetz, M. Sergio Moreno, Chao Ma, LijunWu, Vyacheslav Volkov, and Yimei Zhu, Chemical Distribution and Bonding of
Lithium in Intercalated Graphite: Identification with Optimized Electron Energy Loss Spectroscopy, ACS Nano, 5 (2), (2011) 1190.