Estimating the physical cluster‐size distribution within materials using atom‐probe

Abstract

A limiting characteristic of the atom-probe technique is the nondetection of ions and this embodies a significant "missing information" problem in investigations of atomic clustering phenomena causing difficulty in the interpretation of any atom-probe experiment. It is shown that the measurable cluster-size distribution can be modeled by a mixed binomial distribution. A deconvolution method based upon expectation-maximization (EM) algorithm is presented to obtain the original physical distribution from an efficiency-degraded distribution, thereby providing means to calculate accurate cluster number densities from atom probe results. The accuracy of this restoration was predominantly dependent upon the detector efficiency and was proved to be highly accurate in the case of conventional atom-probe detector efficiencies (ε = 57%). Such considerations and measures are absolutely necessary when the number density of clusters and small precipitates is in any way regarded as important. We conclude that limitations in detector efficiency are more limiting for cluster-finding analyses via atom-probe techniques than spatial resolution issues, and therefore the current endeavors for improving detector technologies are well found.

Nano- and micro-geochronology in Hadean and Archean zircons by atom-probe tomography and SIMS: New tools for old minerals

“…Methods for identifying clusters (nanometer-scale concentrations of one or more element) in atom-probe data have been the subject of various approaches (Blavette et al 1988;Vurpillot et al 2004;Miller and Kenik 2004;Miller et al 2007;De Geuser et al 2006;Cerezo and Davin 2007;Marquis and Hyde 2010;Stephenson et al 2011;Serizawa and Miller 2013). The full details of these approaches are beyond the scope of this paper.…”

Lattice Rectification in Atom Probe Tomography: Toward True Three-Dimensional Atomic Microscopy

“…However, in the case of alloys, accurate restoration of the missing atoms, at least in a broader statistical sense, is an exciting yet now achievable goal. Limited detection efficiency can introduce serious ambiguity into the interpretation of the results (Moody et al, 2008; Stephenson et al, 2010), and the capacity to restore this missing data will enable a far more complete and quantitative characterization of material nanostructure. If the missing data can be replaced with a high degree of confidence, one is now dealing with a complete 3D atomistic rendering of a material, allowing for highly accurate quantitative analysis.…”

Clustering in Age‐Hardenable Aluminum Alloys

“…With high enough detection efficiency cluster size distributions can be estimated to real clusters size distributions. [103] Another limitation is the loss of crystallographic information, strongly dependent on the alloy, and À experimental parameters; in some regions of the reconstruction can lattice planes of certain directions be resolved (pole regions À poles). Although, in special cases, APT can be used to clarify occupancy of elements on sublattices [104,105] or it has been shown that crystallographic arrangement of atoms may be regained altogether.…”