Definition of Spatial Resolution in Atom Probe Tomography

Abstract

It is common that atomic planes are visible in atom probe tomographs of crystalline materials when the atomic plane normals are close to the direction of analysis, Fig. 1a, and the visibility of these atomic planes is the principal evidence for high spatial resolution in APT. However, the spatial resolution may actually be better than the value inferred from the spacing of the visible planes. Fourier analysis of APT images has been used to show that multiple atomic planes may be present though not observed in an atom map [1-3]. Recent work with spatial distribution maps has shown that the real space lattice may be resolved with many higher-index atomic planes in APT images [4]. Furthermore, the spatial information in the analysis direction derives from a fundamentally different mechanism than that in the transverse direction and it is desirable to quantify spatial resolution separately in each direction. A common method for determining spatial resolution in opticallyformed images uses Fourier analysis of the (two-dimensional) image to assess and quantify the spatial frequencies that are present in an image. Though Fourier techniques have been used similarly in (three-dimensional) APT, they are limited by their low signal and by the high demands for computational resources for three-dimensional transforms [2,3]. Vurpillot et al. defined spatial resolution in APT as the reciprocal of the width of the Fourier-space damping function that is convoluted with the reciprocal space spectrum [3]. However, this parameter is a measure of the uncertainty of atom position determinations and does not directly address the physical spatial scales resolved.

Spatial Resolution in Atom Probe Tomography

“…Recently, sub-0.5 Å information limit was achieved on the Transmission Electron Aberrationcorrected Microscope (TEAM) based on an assessment of Au [110] surfaces as a benchmark for the measurement (Kisielowski, et al, 2008). This approach to estimate the resolution in atom probe tomography had previously been proposed by Kelly et al(Kelly, et al, 2007), however, it would only enable assessment of the information limit, not the actual spatial resolution.…”

“…More recently, Kelly et al proposed a definition based on the image analysis of a thin slice of a spatial distribution map. The spatial frequencies within the image were revealed using Fourier transform, and they defined the spatial resolution as the longest vector of the reciprocal space (Kelly, et al, 2007). This definition is somehow erroneous, this approach reveals down to what interspacing the instrument can image atomic planes, which is the definition of the limit of information and not the resolution in itself.…”

“…The validity of this approach seems thus questionable. More recently, Kelly et al (2007) proposed a definition based on the image analysis of a thin slice of a spatial distribution map. The spatial frequencies within the image were revealed using Fourier transform, and they defined the spatial resolution as the longest vector of the reciprocal space.…”

Assessing the Spatial Accuracy of the Reconstruction in Atom Probe Tomography and a New Calibratable Adaptive Reconstruction

“…The proposed measures of resolution in APT (Vurpillot et al, 2001; Kelly et al, 2007) are not suitable to evaluate the accuracy of one reconstruction against another, as they convolve information about the suitability of the instrumental settings such as pulse fraction, laser energy, temperature, and material-specific evaporation characteristics that may show influence in an individual experiment. General metrics of the reconstruction quality through measurements of angular distortions and distance accuracy have been previously defined (Bas et al, 1995; De Geuser & Gault, 2017) and crystallographic signals have been used to assess reconstruction methodologies (Gault et al, 2011 a ).…”

Atom probe microscopy of three-dimensional distribution of silicon isotopes in Si28∕Si30 isotope superlattices with sub-nanometer spatial resolution

“…During the analysis, the base temperature of samples was cooled down to ϳ50 K. The estimated depth and lateral resolutions were 0.2 and 0.4 nm, respectively, 30 whereas ideal resolutions have been reported recently. 5,8,31,32 The detection efficiency was approximately 50 at. %, which is consistent with the value of 57% on the same LEAP system.…”