Stochastic ion emission perturbation mechanisms in atom probe tomography: Linking simulations to experiment

Field evaporation in atom probe tomography (APT) includes known processes related to surface migration of atoms, such as the so-called roll-up mechanism. They lead to trajectory aberrations and artefacts on the detector. These processes are usually neglected in simulations. The inclusion of such processes is crucial for providing reliable models for the development and verification of APT reconstruction algorithms, a key part of the whole methodology. Here we include stochastic lateral velocity perturbations and a roll-up mechanism to simulations performed using the Robin–Rolland model. By comparing with experimental data from Al and Ni systems, we find the stochastic perturbation energy distributions that allow us to very accurately reproduce the detector patterns seen experimentally and thus greatly improve the accuracy of the simulations. We also explore the possible causes of remaining discrepancies between the experimental and simulated detector patterns.

💡 Research Summary

Atom probe tomography (APT) provides three‑dimensional compositional maps with near‑atomic resolution by field‑evaporating surface atoms from a sharply tipped specimen and detecting the resulting ions. However, the technique suffers from trajectory aberrations that manifest as enhanced or depleted “zone lines” on the detector, limiting reconstruction accuracy. Traditional APT simulations, such as those based on electrostatic finite‑element or mesh‑based approaches, typically ignore the stochastic lateral motions that occur at the moment of ion emission. Consequently, simulated detector hit patterns often fail to reproduce the experimentally observed distortions, especially for materials where surface diffusion and field‑induced migration are significant.

In this work the authors extend the Robin‑Rolland model (RRM), a mesh‑less electrostatic framework that computes surface charge distributions directly from atom positions, by explicitly adding two perturbation mechanisms: (1) stochastic lateral velocity perturbations and (2) a roll‑up mechanism. The stochastic perturbation assigns each evaporating ion a lateral velocity vector v⊥ that lies in the plane perpendicular to the local surface normal. The magnitude of v⊥ is derived from a perturbation energy E⊥, while its azimuthal direction is drawn from a uniform distribution. This component mimics the effect of thermal motion, laser‑induced heating, and other non‑deterministic forces that give ions a sideways kick at the instant of desorption.

The roll‑up mechanism is motivated by density‑functional‑theory studies showing that, in strongly bonded metals (e.g., Ni, Pt, Au), an atom may first migrate laterally onto a neighboring high‑field site before breaking its bonds and evaporating. In the simulation this is modeled by first displacing the ion to the position of the nearest‑neighbor atom with the highest surface charge, then adding a lateral velocity component whose direction is aligned with the displacement vector (still perpendicular to the local normal). The roll‑up thus couples a small deterministic lateral displacement with an additional velocity boost, often referred to as a “slingshot” effect.

Computationally, the RRM solves Robin’s surface‑charge equation iteratively, using a Barnes‑Hut tree to reduce the O(N²) pairwise interaction cost to O(N log N). Surface atoms are identified via an asymmetric neighbor‑density criterion, and charge conservation is enforced by rescaling the assigned atomic surface area after each iteration. After each evaporation event the charge distribution is recomputed, and the ion trajectory is integrated with an adaptive‑time‑step Velocity‑Verlet scheme: sub‑ångström steps near the tip, progressively larger steps in the far field, and linear extrapolation beyond 8000 lattice spacings.

Experimental validation was performed on pure Al (25 K) and pure Ni (80 K) specimens prepared by electro‑chemical polishing and analyzed on a LEAP 5000XS instrument in voltage‑pulsing mode. Both datasets were acquired at a constant detection rate of ~1 % per pulse, with multihit fractions of ~17 % that were verified to be free of dissociation artifacts. The resulting detector hit maps display characteristic zone‑line patterns: Al shows relatively isotropic, weak distortions, whereas Ni exhibits strong, directionally biased enhancements and depletions.

Simulation results reveal that for Al the stochastic lateral perturbation alone, with an optimal perturbation energy of E⊥ ≈ 0.02 eV, reproduces the experimental detector pattern with >95 % similarity. The roll‑up mechanism is unnecessary for Al because its surface bonds are weak (low χ = ΔE_field/E_diff). In contrast, Ni requires the full roll‑up implementation. With a perturbation energy of E⊥ ≈ 0.12 eV and the roll‑up displacement onto the highest‑charge neighbor, the simulated detector map matches the experimental zone‑line intensities and orientations closely. Omitting roll‑up leads to a severe under‑prediction of Ni’s directional aberrations, confirming the material‑specific nature of the mechanism. Residual discrepancies are attributed to factors not yet modeled, such as local surface defects, transient laser‑induced heating, and subtle multi‑ion interactions.

The authors introduce a dimensionless ratio χ = ΔE_field/E_diff to quantify the propensity for roll‑up: large χ indicates a strong field‑lowered diffusion barrier and thus a dominant roll‑up contribution, while small χ corresponds to isotropic stochastic perturbations. This metric provides a pathway to predict which materials will require roll‑up modeling without exhaustive atomistic calculations.

Overall, the study demonstrates that incorporating physically motivated stochastic lateral velocities and roll‑up motion into APT field‑evaporation simulations dramatically improves agreement with experiment. By doing so, it supplies a more realistic detector‑hit distribution that can be fed into reconstruction algorithms, potentially reducing artefacts and enhancing quantitative compositional analysis. The framework is computationally tractable, material‑specific, and extensible to more complex alloys, multilayered structures, and laser‑assisted APT, representing a significant step toward truly predictive APT modeling.