Full-Dynamics Field Evaporation Simulation: Overcoming Limitations of Transition State Theory for Atom Probe Tomography

In atom probe tomography (APT), individual atoms or molecules are field-evaporated by an intense electric field from the surface of a needle-shape specimen. Following a linear projection law, APT allows for the reconstruction of a three-dimensional distribution of atoms within the specimen using recorded impact positions and the chemical identity information obtained from a mass spectrometer. However, due to the destructive nature of the field evaporation process, the verification of reconstruction results and quantification of their uncertainty necessitate atomic-scale forward modeling, where each atom can be traced.<br/><br/>Previous atomic-scale models in APT have implicitly relied on harmonic transition state theory (TST) [1]. However, TST is limited to predicting the rate of transition between states and fails to describe the underlying dynamics. Consequently, these models introduce ad-hoc assumptions, typically assigning a zero-launch velocity to evaporating atoms, which introduces biases in the calculation of atom trajectories and impact positions on the detector. As a result, many distinct features observed in field evaporation maps and reconstruction, arising from the full dynamics of atoms, cannot be faithfully reproduced or explained.<br/><br/>To overcome the limitations of TST in describing field evaporation, we employ molecular dynamics (MD) simulations with appropriate acceleration algorithms as an alternative. Our "ab-initio" field evaporation simulation method "TAPSim-MD" [2] integrates evaporation events as part of the MD simulation. This approach combines the classical finite-element field evaporation modeling from the TAPSim code [3] with the MD code LAMMPS [4]. In the resulting full-dynamics approach, atoms in the specimen are evaporated in an “ab-initio” way during the competition between the interatomic forces and the electrostatic forces. This eliminates the need for ad-hoc assumptions regarding activation energy or launch velocity.<br/><br/>By employing full-dynamics simulations, we successfully reproduce and explain the emergence of enhanced zone lines in field evaporation maps, which are dynamic features beyond the capabilities of TST-based models [5]. In a recent study, we revisited field evaporation in an [001] oriented γ-TiAl intermetallic compound, where experimental observations often exhibit mixed-layer reconstruction results due to the alternating Ti/Al layers. While traditional simulation approaches explained this artifact by assuming a higher evaporation field for Al compared to Ti [6], they failed to account for the distinct field evaporation maps obtained for Ti and Al, which should be inherently related to the dynamics. Through our full-dynamics approach, we accurately predicted the correct evaporation sequence in an [001] oriented γ-TiAl virtual tip and reproduced the mixed-layer artifact in reconstruction without any ad-hoc assumptions regarding the evaporation field of Ti or Al. Furthermore, we identified two distinct paths of bond breaking during the evaporation process: Ti initially breaks 4 Ti-Al bonds before breaking 2 Ti-Ti bonds (a two-step process), while Al-Al simultaneously breaks 4 Ti-Al and 2 Al-Al bonds (a one-step process). These two distinct bond-breaking paths elucidate the distinct evaporation maps of Ti and Al, which also rationalizes the counter-intuitive higher evaporation field of Al, considering its generally weaker bonding ability.<br/><br/>References:<br/>[1] M Marcelin, Ann. Phys. 9 (3) (1915), p. 120–231.<br/>[2] J Qi et al., Phys. Rev. Mater. 6, 093602 (2022), p. 11.<br/>[3] C Oberdorfer et al., Mater. Charact. 146 (2018), p. 324.<br/>[4] S Plimpton, J. Comput. Phys. 117 (1995), p. 19.<br/>[5] J Qi et al., Scr. Mater. 230, 115406 (2023)<br/>[6] T Boll and T Al-Kassab, Ultramicroscopy 124 (2013), p. 1–5.<br/>[7] Funding for this work was provided by Dr. Ali Sayir's portfolio within the Air Force Office of Scientific Research under grant number FA9550-14-1-0249 and FA9550-19-1-0378.