EDP2PDF: a computer program for extracting a pair distribution function from an electron diffraction pattern for the structural analysis of materials.

Pair distribution function (PDF) analysis is a powerful technique to understand atomic scale structure in materials science. Unlike X-ray diffraction (XRD)-based PDF analysis, the PDF calculated from electron diffraction patterns (EDPs) using transmission electron microscopy can provide structural information from specific locations with high spatial resolution. The present work describes a new software tool for both periodic and amorphous structures that addresses several practical challenges in calculating the PDF from EDPs. The key features of this program include accurate background subtraction using a nonlinear iterative peak-clipping algorithm and automatic conversion of various types of diffraction intensity profiles into a PDF without requiring external software. The present study also evaluates the effect of background subtraction and the elliptical distortion of EDPs on PDF profiles. The EDP2PDF software is offered as a reliable tool to analyse the atomic structure of crystalline and non-crystalline materials.

Effects of thermal annealing on the distribution of boron and phosphorus in p-i-n structured silicon nanocrystals embedded in silicon dioxide.

Thermal annealing temperature and time dictate the microstructure of semiconductor materials such as silicon nanocrystals (Si NCs). Herein, atom probe tomography (APT) and density functional theory (DFT) calculations are used to understand the thermal annealing temperature effects on Si NCs grown in a SiO2matrix and the distribution behaviour of boron (B) and phosphorus (P) dopant atoms. The APT results demonstrate that raising the annealing temperature promotes growth and increased P concentration of the Si NCs. The data also shows that the thermal annealing does not promote the incorporation of B atoms into Si NCs. Instead, B atoms tend to locate at the interface between the Si NCs and SiO2matrix. The DFT calculations support the APT data and reveal that oxygen vacancies regulate Si NC growth and dopant distribution. This study provides the detailed microstructure of p-type, intrinsic, and n-type Si NCs with changing annealing temperature and highlights how B and P dopants preferentially locate with respect to the Si NCs embedded in the SiO2matrix with the aid of oxygen vacancies. These findings will be useful towards future optoelectronic applications.

Community-Driven Methods for Open and Reproducible Software Tools for Analyzing Datasets from Atom Probe Microscopy.

Atom probe tomography, and related methods, probe the composition and the three-dimensional architecture of materials. The software tools which microscopists use, and how these tools are connected into workflows, make a substantial contribution to the accuracy and precision of such material characterization experiments. Typically, we adapt methods from other communities like mathematics, data science, computational geometry, artificial intelligence, or scientific computing. We also realize that improving on research data management is a challenge when it comes to align with the FAIR data stewardship principles. Faced with this global challenge, we are convinced it is useful to join forces. Here, we report the results and challenges with an inter-laboratory call for developing test cases for several types of atom probe microscopy software tools. The results support why defining detailed recipes of software workflows and sharing these recipes is necessary and rewarding: Open source tools and (meta)data exchange can help to make our day-to-day data processing tasks become more efficient, the training of new users and knowledge transfer become easier, and assist us with automated quantification of uncertainties to gain access to substantiated results.

Integrative Atom Probe Tomography Using Scanning Transmission Electron Microscopy-Centric Atom Placement as a Step Toward Atomic-Scale Tomography.

Current reconstruction methodologies for atom probe tomography (APT) contain serious geometric artifacts that are difficult to address due to their reliance on empirical factors to generate a reconstructed volume. To overcome this limitation, a reconstruction technique is demonstrated where the analyzed volume is instead defined by the specimen geometry and crystal structure as determined by transmission electron microscopy (TEM) and diffraction acquired before and after APT analysis. APT data are reconstructed using a bottom-up approach, where the post-APT TEM image is used to define the substrate upon which APT detection events are placed. Transmission electron diffraction enables the quantification of the relationship between atomic positions and the evaporated specimen volume. Using an example dataset of ZnMgO:Ga grown epitaxially on c-plane sapphire, a volume is reconstructed that has the correct geometry and atomic spacings in 3D. APT data are thus reconstructed in 3D without using empirical parameters for the reverse projection reconstruction algorithm.

3D microstructure analysis of silicon-boron phosphide mixed nanocrystals.

The microstructure of boron (B) and phosphorus (P) codoped silicon (Si) nanocrystals (NCs), cubic boron phosphide (BP) NCs and their mixed NCs (BxSiyPz NCs) has been studied using atom probe tomography (APT), transmission electron microscopy (TEM), and Raman scattering spectroscopy. The BxSiyPz NCs inherit superior properties of B and P codoped Si NCs such as high dispersibility in aqueous media and near infrared (NIR) luminescence and those of cubic BP NCs such as high chemical stability. The microanalyses revealed that BxSiyPz NCs are composed of a crystalline core and an amorphous shell. The core possesses a lattice constant between that of Si (diamond-cubic) and BP (cubic). The amorphous shell is comprised of B, Si and P, though the composition is not uniform and there are local B-rich, Si-rich and P-rich domains connected contiguously. The amorphous shell is proposed to be responsible for their superior chemical properties such as high dispersibility in polar solvents and high resistance to acids, and the crystalline core is responsible for the stable NIR luminescence.

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

We define a measure for the accuracy of tomographic reconstruction in atom probe tomography, named here the spatial error index. We demonstrate that this index can be used to compare rigorously the spatial accuracy of various different approaches to the calculation of tomographic reconstruction. This is useful, for example, to evaluate the performance of alternate tomographic reconstruction approaches, and ensures that the comparisons are independent of individual data quality or other instrumental parameters. We then introduce a new "adaptive reconstruction" formalism that uses a progression of reconstruction parameters based on a per-atom correction from the cube root of the inverse of the voltage, along with linear correction factors linked to the evaporation sequence. We apply the measure for spatial accuracy to this new reconstruction protocol.

Introducing a Crystallography-Mediated Reconstruction (CMR) Approach to Atom Probe Tomography.

Current approaches to reconstruction in atom probe tomography produce results that exhibit substantial distortions throughout the analysis depth. This is largely because of the need to apply a multitude of assumptions when estimating the evolution of the tip shape, and other pseudo-empirical reconstruction factors, which vary both across the face of the tip and throughout the analysis depth. We introduce a new crystallography-mediated reconstruction to improve the spatial accuracy and dramatically reduce these in-depth variations. To achieve this, we developed a barycentric transform to directly relate atomic positions in detector space to real space. This is mediated by novel crystallographic analysis techniques, including: (1) calculating the orientation of a crystal directly from the field evaporation map, (2) tracking pole locations throughout the evaporation sequence, and (3) accounting for the evolving tip radius in a manner that removes the dependence on the geometric field factor. By improving the in-depth spatial accuracy of the atom probe reconstruction, a greater accuracy of the atomic neighborhood relationships is available. This is critical in modern materials science and engineering, where an understanding of the solid solution architecture, precipitate dispersions, and descriptions of the interfaces between phases or grains are key inputs to microstructure-property relationships.

On the retrieval of crystallographic information from atom probe microscopy data via signal mapping from the detector coordinate space.

Atom probe tomography is a powerful microscopy technique capable of reconstructing the 3D position and chemical identity of millions of atoms within engineering materials, at the atomic level. Crystallographic information contained within the data is particularly valuable for the purposes of reconstruction calibration and grain boundary analysis. Typically, analysing this data is a manual, time-consuming and error prone process. In many cases, the crystallographic signal is so weak that it is difficult to detect at all. In this study, a new automated signal processing methodology is demonstrated. We use the affine properties of the detector coordinate space, or the 'detector stack', as the basis for our calculations. The methodological framework and the visualisation tools are shown to be superior to the standard method of crystallographic pole visualisation directly from field evaporation images and there is no requirement for iterations between a full real-space initial tomographic reconstruction and the detector stack. The mapping approaches are demonstrated for aluminium, tungsten, magnesium and molybdenum. Implications for reconstruction calibration, accuracy of crystallographic measurements, reliability and repeatability are discussed.

A New Approach to Understand the Adsorption of Thiophene on Different Surfaces: An Atom Probe Investigation of Self-Assembled Monolayers.

Atom probe tomography was used to analyze self-assembled monolayers of thiophene on different surfaces, including tungsten, platinum, and aluminum, where the tungsten was examined in both pristine and oxidized forms. A glovebag with controlled atmospheres was used to alter the level of oxidation for tungsten. It was shown that different substrates lead to substantial changes in the way thiophene adsorbs on the surface. Furthermore, the oxidation of the surface strongly influenced the adsorption behavior of the thiophene molecules, leading to clear differences in the amounts and compositions of field evaporated ions and molecular ions.

Restoring the lattice of Si-based atom probe reconstructions for enhanced information on dopant positioning.

The following manuscript presents a novel approach for creating lattice based models of Sb-doped Si directly from atom probe reconstructions for the purposes of improving information on dopant positioning and directly informing quantum mechanics based materials modeling approaches. Sophisticated crystallographic analysis techniques are used to detect latent crystal structure within the atom probe reconstructions with unprecedented accuracy. A distortion correction algorithm is then developed to precisely calibrate the detected crystal structure to the theoretically known diamond cubic lattice. The reconstructed atoms are then positioned on their most likely lattice positions. Simulations are then used to determine the accuracy of such an approach and show that improvements to short-range order measurements are possible for noise levels and detector efficiencies comparable with experimentally collected atom probe data.

Interpreting atom probe data from chromium oxide scales.

Picosecond-pulsed ultraviolet-laser (UV-355 nm) assisted atom probe tomography (APT) was used to analyze protective, thermally grown chromium oxides formed on stainless steel. The influence of analysis parameters on the thermal tail observed in the mass spectra and the chemical composition is investigated. A new parameter termed "laser sensitivity factor" is introduced in order to quantify the effect of laser energy on the extent of the thermal tail. This parameter is used to compare the effect of increasing laser energy on thermal tails in chromia and chromite samples. Also explored is the effect of increasing laser energy on the measured oxygen content and the effect of specimen base temperature and laser pulse frequency on the mass spectrum. Finally, we report a preliminary analysis of molecular ion dissociations in chromia.

A new systematic framework for crystallographic analysis of atom probe data.

In this article, after a brief introduction to the principles behind atom probe crystallography, we introduce methods for unambiguously determining the presence of crystal planes within atom probe datasets, as well as their characteristics: location; orientation and interplanar spacing. These methods, which we refer to as plane orientation extraction (POE) and local crystallography mapping (LCM) make use of real-space data and allow for systematic analyses. We present here application of POE and LCM to datasets of pure Al, industrial aluminium alloys and doped-silicon. Data was collected both in DC voltage mode and laser-assisted mode (in the latter of which extracting crystallographic information is known to be more difficult due to distortions). The nature of the atomic planes in both datasets was extracted and analysed.

Atomically resolved tomography to directly inform simulations for structure-property relationships.

Microscopy encompasses a wide variety of forms and scales. So too does the array of simulation techniques developed that correlate to and build upon microstructural information. Nevertheless, a true nexus between microscopy and atomistic simulations is lacking. Atom probe has emerged as a potential means of achieving this goal. Atom probe generates three-dimensional atomistic images in a format almost identical to many atomistic simulations. However, this data is imperfect, preventing input into computational algorithms to predict material properties. Here we describe a methodology to overcome these limitations, based on a hybrid data format, blending atom probe and predictive Monte Carlo simulations. We create atomically complete and lattice-bound models of material specimens. This hybrid data can then be used as direct input into density functional theory simulations to calculate local energetics and elastic properties. This research demonstrates the role that atom probe combined with theoretical approaches can play in modern materials engineering.

Point-by-point compositional analysis for atom probe tomography.

This new alternate approach to data processing for analyses that traditionally employed grid-based counting methods is necessary because it removes a user-imposed coordinate system that not only limits an analysis but also may introduce errors. We have modified the widely used "binomial" analysis for APT data by replacing grid-based counting with coordinate-independent nearest neighbour identification, improving the measurements and the statistics obtained, allowing quantitative analysis of smaller datasets, and datasets from non-dilute solid solutions. It also allows better visualisation of compositional fluctuations in the data. Our modifications include:.•using spherical k-atom blocks identified by each detected atom's first k nearest neighbours.•3D data visualisation of block composition and nearest neighbour anisotropy.•using z-statistics to directly compare experimental and expected composition curves. Similar modifications may be made to other grid-based counting analyses (contingency table, Langer-Bar-on-Miller, sinusoidal model) and could be instrumental in developing novel data visualisation options.

Quantitative dopant distributions in GaAs nanowires using atom probe tomography.

Controllable doping of semiconductor nanowires is critical to realize their proposed applications, however precise and reliable characterization of dopant distributions remains challenging. In this article, we demonstrate an atomic-resolution three-dimensional elemental mapping of pristine semiconductor nanowires on growth substrates by using atom probe tomography to tackle this major challenge. This highly transferrable method is able to analyze the full diameter of a nanowire, with a depth resolution better than 0.17 nm thanks to an advanced reconstruction method exploiting the specimen's crystallography, and an enhanced chemical sensitivity of better than 8-fold increase in the signal-to-noise ratio.

Spatial decomposition of molecular ions within 3D atom probe reconstructions.

Two methods for separating the constituent atoms of molecular ions within atom probe tomography reconstructions are presented. The Gaussian Separation Method efficiently deconvolutes molecular ions containing two constituent atoms and is tested on simulated data before being applied to an experimental HSLA steel dataset containing NbN. The Delaunay Separation Method extends separation to larger complex ions and is also tested on simulated data before being applied to an experimental GaAs dataset containing many large (>3 atoms) complex ions. First nearest neighbour (1NN) distributions and images of the reconstruction before and after the separations are used to show the effect of the algorithms and their validity and practicality are also discussed.

Short-range order in multicomponent materials.

The generalized multicomponent short-range order (GM-SRO) parameter has been adapted for the characterization of short-range order within the highly chemically and spatially resolved three-dimensional atomistic images provided by the microscopy technique of atom-probe tomography (APT). It is demonstrated that, despite the experimental limitations of APT, in many cases the GM-SRO results derived from APT data can provide a highly representative description of the atomic scale chemical arrangement in the original specimen. Further, based upon a target set of the GM-SRO parameters, measured from APT experiments, a Monte Carlo algorithm was utilized to simulate statistically equivalent atomistic systems which, unlike APT data, are complete and lattice based. The simulations replicate solute structures that are statistically consistent with other correlation measures such as solute cluster distributions, enable more quantitative characterization of nanostructural phenomena in the original specimen and, significantly, can be incorporated directly into other models and simulations.

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.

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 chi(2) 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, mu, is shown to normalize chi(2) 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 mu 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.