Leigh T. Stephenson

New Techniques for the Analysis of Fine-Scaled Clustering Phenomena within Atom Probe Tomography (APT) Data

Nanoscale atomic clusters in atom probe tomographic data are not universally defined but instead are characterized by the clustering algorithm used and the parameter values controlling the algorithmic process. A new core-linkage clustering algorithm is developed, combining fundamental elements of the conventional maximum separation method with density-based analyses. A key improvement to the algorithm is the independence of algorithmic parameters inherently unified in previous techniques, enabling a more accurate analysis to be applied across a wider range of material systems. Further, an objective procedure for the selection of parameters based on approximating the data with a model of complete spatial randomness is developed and applied. The use of higher nearest neighbor distributions is highlighted to give insight into the nature of the clustering phenomena present in a system and to generalize the clustering algorithms used to analyze it. Maximum separation, density-based scanning, and the core linkage algorithm, developed within this study, were separately applied to the investigation of fine solute clustering of solute atoms in an Al-1.9Zn-1.7Mg (at.%) at two distinct states of early phase decomposition and the results of these analyses were evaluated.

Advances in the calibration of atom probe tomographic reconstruction

Modern wide field-of-view atom probes permit observation of a wide range of crystallographic features that can be used to calibrate the tomographic reconstruction of the analyzed volume. In this study, methodologies to determine values of the geometric parameters involved in the tomographic reconstruction of atom probe data sets are presented and discussed. The influence of the tip to electrode distance and specimen temperature on these parameters is explored. Significantly, their influence is demonstrated to be very limited, indicating a relatively wide regime of experimental parameters space for sound atom probe tomography (APT) experiments. These methods have been used on several specimens and material types, and the results indicate that the reconstruction parameters are specific to each specimen. Finally, it is shown how an accurate calibration of the reconstruction enables improvements to the quality and reliability of the microscopy and microanalysis capabilities of the atom probe.

Estimation of the Reconstruction Parameters for Atom Probe Tomography

The application of wide field-of-view detection systems to atom probe experiments emphasizes the importance of careful parameter selection in the tomographic reconstruction of the analyzed volume, as the sensitivity to errors rises steeply with increases in analysis dimensions. In this article, a self-consistent method is presented for the systematic determination of the main reconstruction parameters. In the proposed approach, the compression factor and the field factor are determined using geometrical projections from the desorption images. A three-dimensional Fourier transform is then applied to a series of reconstructions, and after comparing to the known material crystallography, the efficiency of the detector is estimated. The final results demonstrate a significant improvement in the accuracy of the reconstructed volumes.

Quantitative binomial distribution analyses of nanoscale like-solute atom clustering and segregation in atom probe tomography data

The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional χ2 statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, μ, is shown to normalize χ2 with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of μ over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results. Microsc. Res. Tech., 2008.

Spatial Resolution in Atom Probe Tomography

This article addresses gaps in definitions and a lack of standard measurement techniques to assess the spatial resolution in atom probe tomography. This resolution is known to be anisotropic, being better in-depth than laterally. Generally the presence of atomic planes in the tomographic reconstruction is considered as being a sufficient proof of the quality of the spatial resolution of the instrument. Based on advanced spatial distribution maps, an analysis methodology that interrogates the local neighborhood of the atoms within the tomographic reconstruction, it is shown how both the in-depth and the lateral resolution can be quantified. The influences of the crystallography and the temperature are investigated, and models are proposed to explain the observed results. We demonstrate that the absolute value of resolution is specimen specific.

Qualification of the tomographic reconstruction in atom probe by advanced spatial distribution map techniques.

New and improved spatial distribution map (SDM) methods are developed to identify and extract crystallographic information within atom probe tomography three-dimensional (3D) reconstructions. Detailed structural information is retrieved by combining z-SDM offset distribution analyses computed in multiple crystallographic directions, accurately determining inter-planar spacings and crystallographic angles. The advantages of this technique in comparison to applying the complete z-SDM and complementary xy-SDM analysis to a single crystallographic direction are investigated. Further, in determining these multidirectional z-SDM and xy-SDM profiles, background noise reduction and automatic peak identification algorithms are adapted to attain increased accuracy and is shown to be particularly effective in cases where crystal structure is present but poorly resolved. These techniques may be used to calibrate the reconstruction parameters and investigate their dependence on the design of individual atom probe experiments.

Origin of the spatial resolution in atom probe microscopy

Atom-probe microscopy offers unprecedented insights on the subnanometer structure and chemistry of materials in three dimensions. The actual spatial resolution achievable is however still an uncertain parameter, as no comprehensive study has been undertaken to unveil the physics underpinning how key parameters impact the performance. Here, we present a comprehensive investigation of the in-depth and lateral resolution of the technique. We discuss methods to estimate the resolution and show a resolution better than 20 pm in-depth. Models to support our results were developed and are discussed in the present letter.

Dynamic reconstruction for atom probe tomography

Progress in the reconstruction for atom probe tomography has been limited since the first implementation of the protocol proposed by Bas et al. in 1995. This approach and those subsequently developed assume that the geometric parameters used to build the three-dimensional atom map are constant over the course of an analysis. Here, we test this assumption within the analyses of low-alloyed materials. By building upon methods recently proposed to measure the tomographic reconstruction parameters, we demonstrate that this assumption can introduce significant limitations in the accuracy of the analysis. Moreover, we propose a strategy to alleviate this problem through the implementation of a new reconstruction algorithm that dynamically accommodates variations in the tomographic reconstruction parameters.

Lattice rectification in atom probe tomography: toward true three-dimensional atomic microscopy

Atom probe tomography (APT) represents a significant step toward atomic resolution microscopy, analytically imaging individual atoms with highly accurate, though imperfect, chemical identity and three-dimensional (3D) positional information. Here, a technique to retrieve crystallographic information from raw APT data and restore the lattice-specific atomic configuration of the original specimen is presented. This lattice rectification technique has been applied to a pure metal, W, and then to the analysis of a multicomponent Al alloy. Significantly, the atoms are located to their true lattice sites not by an averaging, but by triangulation of each particular atom detected in the 3D atom-by-atom reconstruction. Lattice rectification of raw APT reconstruction provides unprecedented detail as to the fundamental solute hierarchy of the solid solution. Atomic clustering has been recognized as important in affecting alloy behavior, such as for the Al-1.1 Cu-1.7 Mg (at. %) investigated here, which exhibits a remarkable rapid hardening reaction during the early stages of aging, linked to clustering of solutes. The technique has enabled lattice-site and species-specific radial distribution functions, nearest-neighbor analyses, and short-range order parameters, and we demonstrate a characterization of solute-clustering with unmatched sensitivity and precision.

A three-dimensional Markov field approach for the analysis of atomic clustering in atom probe data

Solute clustering is increasingly recognised as a significant characteristic within certain material systems that can be tailored to the optimization of bulk properties and performance. Atom probe tomography (APT) is emerging as a powerful tool for the detection of these nanoscale features; however, complementary to experiment, precise and efficient characterization algorithms are required to identify and characterise these nanoclusters within the potentially massive three-dimensional atomistic APT datasets. In this study, a new three-dimensional Markov field (3DMF) cluster identification algorithm is proposed. The algorithm is based upon an analysis of the direct atomic neighbourhood surrounding each atom, and the only input parameter required utilises known crystallographic properties of the system. Further, an array of statistical approaches has been developed and applied with respect to the results generated by the 3DMF algorithm including: an S N statistic, a two-tailed z-test, a difference measure, the χ2 test, and a direct evaluation of the Warren–Cowley parameter for short-range ordering. Finally, the methodologies have been applied to the characterization of the nanostructural evolution of an Al-1.1Cu-0.5Mg (at.%) alloy subjected to a variety of heat treatments.