Estimating the physical cluster-size distribution within materials using atom-probe.

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.