Image deformation in field ion microscopy of faceted crystals

Abstract

We perform detailed numerical simulations of field ion microscopy images of faceted crystals and compare them with experimental observations. In contrast to the case of crystals with a smooth surface, for a faceted topography we find extreme deformations of the ion image. Local magnification is highly inhomogeneous and may vary by an order of magnitude: from 0.64 to 6.7. Moreover, the anisotropy of the magnification at a point located on the facet edge may reach a factor of 10.

Level Set Methods for Modelling Field Evaporation in Atom Probe

“…Another limitation is that of the continuum assumptions that underpin the method; solutions to atomic projection functions have been shown to be dependent upon local atomic ordering (Niewieczerzal et al, 2010), which is not fully represented in this model. Finally, a fundamental limitation of the level set method is that integration can only be performed in the forward time direction, due to the information transfer being irreversible during evolution (Osher & Fedkiw, 2003; Sethian, 2003).…”

Atom probe trajectory mapping using experimental tip shape measurements

“…Regardless, the precise measurement of atomic terracing is currently beyond the resolution of electron tomography. Starting from explicit atom models, simulation studies have shown that the electrostatic effects of terraces can accurately reproduce prominent local features in atom probe datasets such as zone lines (Vurpilot et al , 2001; Niewieczerzal et al , 2010). To incorporate such detail into the tip shape modelling described here, additional computational methods and theoretical models would be required, which are outside the scope of this work.…”

“…Somewhat critically, the algorithm is limited by the scale of the data maintained in the transmission electron microscope tomography -slightly higher than the atomic scale required to visualize the surface modification that are construed by the atomic surface. It is well known that local atomic arrangements in FIM can radically affect the local distortions in the resultant image (Larson & Stiller, 2007;Niewieczerzal et al, 2010), and this also extends to atom probe, with local density distortion an artefact which has previously been the subject of numerical research (Vurpillot et al, 2001). There is an implicit smoothing during the acquisition of the TEM image owing to the function of the instrument; and is one limit to the local roughness that can be estimated from the tip during STOMO reconstructionassuming a clean in-vacuum movement of the tip from imaging to atom probe analysis.…”

“…Numerical methods have previously shown that the stereographic or modified stereographic projection laws for ion trajectories may be insufficient to represent the complex geometries involved in the field evaporation process (Smith et al , 1978; Vurpillot et al , 2001; Niewieczerzal et al , 2010; Oberdorfer & Schmitz, 2011). In principle, if the precise specimen shape could be known throughout an evaporation sequence, the lens action of the tip could be computed and used for reverse projection of the ion trajectories.…”

Oxygen-covered tungsten crystal shape: Time effects, equilibrium, surface energy and the edge-rounding temperature

“…In the next step, we analyse the FIM image of the crystal annealed at temperature T and determine |BD|, the distance between the edge end points. This would be easy if the microscope maginfication was uniform -but it is not 30 , and for faceted crystals local magnification may vary by as much as an order magnitude 37 . We use the results of very complex and time consuming ion trajectory calculations to calculate the local enhancement of the microscope magnification near the crystal vertex 37 .…”