Microsc. Microanal. 23, 238–246, 2017 doi:10.1017/S1431927616012721
© MICROSCOPY SOCIETY OF AMERICA 2017
Reflections on the Projection of Ions in Atom Probe Tomography
Frédéric De Geuser,1,2 and Baptiste Gault3,*
1Université Grenoble Alpes, SIMAP, F-38000 Grenoble, France 2CNRS, SIMAP, F-38000 Grenoble, France 3Max-Planck Institut für Eisenforschung, Max-Planck-Straße 1, D-40237 Dsseldorf, Germany
Abstract: There are two main projections used to transform, and reconstruct, field ion micrographs or atom probe tomography data into atomic coordinates at the specimen surface and, subsequently, in three dimensions. In this article, we present a perspective on the strength of the azimuthal equidistant projection in comparison with the more widely used and well-established point projection (or pseudo-stereographic projection), which underpins data reconstruction in most software packages currently in use across the community. After an overview of the reconstruction methodology, we demonstrate that the azimuthal equidistant is more robust with regards to errors on the parameters used to perform the reconstruction and is therefore more likely to yield more accurate tomographic reconstructions.
Key words: atom probe tomography, field ion microscopy, tomographic reconstruction, projection
INTRODUCTION Since the introduction of the field emission electron microscope and subsequently of the field ion microscope (FIM), it has been recognized that they are projection microscopes that provide a highly magnified image of the surface of the specimen. This projection also underpins atom probe tomography (APT) and enables the technique to analyze individual features at the sub-nanometer scale. The high spatial resolution of the FIM and its capacity to
resolve individual atomic terraces has made it a tool of choice for investigating the true nature of the projection. A field ion micrograph is indeed a projected image of the specimen surface, revealing details of its structure down to the atomic level. In the 1960s and 1970s, Brandon (1964) and Newman et al. (1967), among others, reported on the study of the properties of the projection in FIM. They compared micro- graphs with known point projections, such as gnomonic or stereographic, only to show that none of those projections often used in other microscopy techniques could be used as such. Based on the arguments of Newman, Wilkes et al. (1974) proposed that the projection led to features separated by an angle θ at the specimen surface would be separated by a distance ρ=kθ×θ at the detector. This was subsequently referred to as a linear projection. From the 1980s, the community’s focus progressively
shifted to atom probe microanalysis and then to APT. The progressive adoption of the reconstruction protocol, proposed by Blavette et al. (1982) and Bas et al. (1995), and subsequently modified to remove small-angle approxima- tions (Geiser et al., 2009; Gault et al., 2011), across the entire atom probe user base has led to a premature end of the
*Corresponding author.
b.gault@
mpie.de Received June 24, 2016; accepted December 12, 2016
discussions on this topic. However, as the performance of APT are routinely challenged, particularly in the analysis of complex materials, it is important to revisit the properties of the ion projection, and its intimate link to the specimen geometry. In 1999, Cerezo et al. (1999) revisited the linear
projection must be defined and that the azimuths are maintained through the projection: the ions fly within a plane that contains the main specimen axis and its original position at the specimen surface. If we assume azimuths are conserved, thenwe are dealingwith an azimuthal equidistant projection, which is a well-known and well-described pro- jection used, e.g., by geographers (Snyder, 2007), and is the projection model of the Earth represented on the United Nations emblem. More recently, Miller & Forbes (2014) also discussed the Hawkes–Kasper approach, which is an equivalent to this projection model. In this article, we provide a critical viewpoint of the
projection, and highlighted once again that it was a better representation of the actual ion projection in FIM than a pseudo-stereographic projection, but also tested its limits. Two interesting points arose from this study: the linear projection holds through a tilt series, or if the specimen is rotated about its main axis; however, the proportionality factor between the angle at the specimen surface and the distance on the detector cannot be assumed constant across all possible combinations of poles. Cerezo’s work pointed to the idea that a center of the
main projection models, showcase how a precise determi- nation of the orientation of the specimen can be achieved via the identification of the crystallographic features present in the detector hit map, and finally introduce a framework that could be generalized and form the base for a new reconstruction paradigm, which is described and discussed.
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