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

TL;DR

Atom probe tomography simulations suffer trajectory artefacts from surface diffusion and roll-up. The authors introduce two physically motivated stochastic perturbations—lateral velocity perturbations $E_\perp$ and a roll-up mechanism—into the Robin--Rolland model, and validate against Al and Ni experiments using SSIM to compare detector maps. The energy distributions that maximize structure similarity differ by material, with Al favoring a high-mean, moderately dispersed $E_\perp$ and Ni favoring a lower-mean, highly dispersed distribution, yielding substantially improved agreement over previous models. This work provides a physics-based, scalable perturbation framework that enhances reconstruction fidelity and motivates future MD-informed refinements and expansion to additional field-evaporation effects.

Abstract

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.

Figures (7)

• Figure 1: (a) A schematic drawing of the lateral velocity perturbation for the field evaporation of a fcc hemisphere. The normal vector $\hat{\bm{n}}$ at the evaporation site (orange atom) is obtained by first computing the barycentric vector $\bm{b}$, which runs from the geometric center of the base of the hemispherical cap of the specimen to the center-of-mass (red) of the local neighborhood (green) surrounding the evaporating atom. The surface normal is then defined as the direction from this center-of-mass to the evaporating atom itself. The lateral velocity component $\bm{v}\perp$ is chosen perpendicular to this normal and assigned a random azimuthal direction. (b) A schematic drawing of roll-up distortion implementation where the evaporating atom (orange) is first displaced (rolled-up) on top of the second highest field neighboring atom (red atom and green arrow), and then an additional lateral velocity component $\bm{v}_\perp$ oriented in the roll-up direction and perpendicular to the local surface normal, is then applied.
• Figure 2: (a) Some representative atoms on the sample surface, shown by dashed circles and differentiated by different colors. (b) The effect of lateral velocity perturbation on the detector coordinates $(X, Y)$ for selected evaporated atoms (the ones shown in panel a). The colored points correspond to the detector hit points without any perturbation energy (colors as in panel a) and the colormap shows the perturbation energy corresponding to the other detector hits. All perturbation directions are considered. The inset shows a zoomed-in view for one of these atoms. (c) Same as panel b, but for the roll-up perturbation with different energies shown in the colormap. The inset shows the track for a single case.
• Figure 3: Matrices of the structural similarity index measures (SSIMs) between the experimental detector images and simulated detector images for the lateral velocity perturbation corresponding to Al experiments (left) and the roll-up perturbation corresponding to Ni experiments (right). The axes correspond to the values of the mean perturbation energy $\langle E_\perp \rangle$ and the standard deviation $\sigma_{E_\perp}$ normalized by the mean. A clear maximum of the SSIM is seen in both cases, corresponding to an optimal distribution of stochastic perturbation energies.
• Figure 4: Matrices of the SSIMs between the experimental detector images and simulated detector images for Ni, when both lateral velocity perturbation and roll-up are considered. The different matrices correspond to different fractions $f_{\rm r}$ of the total perturbation energy $E_\perp$ (mean $\langle E_\perp \rangle$, standard deviation $\sigma_{E_\perp}$) used for the roll-up perturbation.
• Figure 5: Comparison of experimental and simulated detector maps for the Al[012] system, illustrating the effect of lateral velocity perturbations on detector pattern formation. (a) The detector maps for experimental Al[012] showing characteristic artefacts including enhanced and depleted zone lines, as well as depleted poles. (b) The simulated detector map without the added lateral velocity perturbation ($E_\perp = 0$), showing clearly different characteristic features. (c) Simulated detector map with optimal perturbation energy distribution ($E_\perp > 0$), producing patterns that qualitatively resemble the experimental map in panel a. To illustrate the similarity, we concentrate on a specific area (red circle in panels a and c) and show the magnified views for (d) experimental data and (e) simulation data with perturbations.