Structural analyses in three‐dimensional atom probe: a Fourier transform approach

Abstract

SummaryThe three-dimensional atom probe (3DAP) technique gives the elemental identities and the position of atoms within the small volume analysed (on the order of 10 Â 10 Â 100 nm 3 ). The large number of atoms collected (up to two million) and the excellent spatial resolution of this instrument allows the observation of some crystallographic features of phases chemically identified. This paper shows that the application of a discrete Fourier transform algorithm to a 3DAP dataset provides information that is not easily accessible in real space. The derivation of the mean size of particles from Fourier intensities is an example. Using 3D`dark-field' imaging, single ordered grains were isolated from the disordered matrix of a ternary alloy. Moreover, the intrinsic spatial resolution of the instrument was evaluated by this method for pure metal; the resolution reaches 0.2 nm laterally and 0.06 nm in depth. This excellent resolution is shown to be sufficient to give access to the crystalline lattice. The use of image filtering in the reciprocal space enables for atomic columns to be imaged the first time from 3DAP data.

Influence of Tip Temperature on Field Evaporation in Atom Probe

“…6. The spatial resolution was in general calculated by the 3D Fourier transform method [18]. In this study, the spatial distributions in the depth direction along the (110) direction was simply calculated in only tomography in Fig.…”

A Brief Overview of Atom Probe Tomography Research

“…Finally, some methods have been developed to interrogate the structural integrity of the point cloud. Fourier transforms (Vurpillot et al, 2001(Vurpillot et al, , 2004 for instance, or real-space alternative such as the so-called 'atom vicinity' method (Boll et al, 2007) or spatial distribution maps (Geiser et al, 2007;Moody et al, 2009), which are a more or less a different representation of a split 3D radial distribution function, or the Hough transform and related techniques . Three main uses of these methods have so far been reported: help calibrate reconstructions (Gault et al, 2009b;Suram & Rajan, 2013), assess the true spatial resolution of the technique (Cadel et al, 2009;Gault et al, 2009aGault et al, , 2011a Kelly et al, 2009), and finally, offer a route to rectify the data to compensate for the limited spatial resolution and reposition the atoms onto a crystalline lattice Moody et al, 2011), thereby allowing for direct coupling with atomistic simulations .…”

Practical Determination of Spatial Resolution in Atom Probe Tomography

“…In their work, the spatial spread in the SDM about a real-space lattice point was used as a measure of spatial resolution. In fact, this latter approach is functionally equivalent to that of Vurpillot et al [1]. Kelly et al [3] used Fourier transforms of SDMs to describe spatial resolution in APT where the inverse of the longest statistically significant reciprocal lattice vector was called the spatial resolution but should be called the information limit in keeping with common practice in electron microscopy [4].…”

“…Vurpillot et al [1] defined spatial resolution in atom probe tomography (APT) as the inverse of the width of the damping function that is superimposed on the reciprocal space structure of an atom probe dataset. This parameter gives information about the uncertainty in interatomic distances as determined by APT.…”