Atomically resolved tomography to directly inform simulations for structure–property relationships

Quantifying short-range order using atom probe tomography

Medium- and high-entropy alloys are an emerging class of materials that can exhibit outstanding combinations of strength and ductility for engineering applications. Computational simulations have suggested the presence of short-range order (SRO) in these alloys, and recent experimental evidence is also beginning to emerge. Unfortunately, the difficulty in quantifying the SRO under different heat treatment conditions has generated much debate on the atomic preferencing and implications of SRO on mechanical properties. Here we develop an approach to measure SRO using atom probe tomography. This method balances the limitations of atom probe tomography with the threshold values of SRO to map the regimes where the required atomistic neighbourhood information is preserved and where it is not. We demonstrate the method with a case study of the CoCrNi alloy and use this to monitor SRO changes induced by heat treatments. These species-specific SRO measurements enable the generation of computational simulations of atomic neighbourhood models that are equivalent to the experiment and can contribute to the further understanding and design of medium- and high-entropy alloys and other materials systems where SRO may occur.

Quantitative three-dimensional imaging of chemical short-range order via machine learning enhanced atom probe tomography

Chemical short-range order (CSRO) refers to atoms of specific elements self-organising within a disordered crystalline matrix to form particular atomic neighbourhoods. CSRO is typically characterized indirectly, using volume-averaged or through projection microscopy techniques that fail to capture the three-dimensional atomistic architectures. Here, we present a machine-learning enhanced approach to break the inherent resolution limits of atom probe tomography enabling three-dimensional imaging of multiple CSROs. We showcase our approach by addressing a long-standing question encountered in body-centred-cubic Fe-Al alloys that see anomalous property changes upon heat treatment. We use it to evidence non-statistical B2-CSRO instead of the generally-expected D03-CSRO. We introduce quantitative correlations among annealing temperature, CSRO, and nano-hardness and electrical resistivity. Our approach is further validated on modified D03-CSRO detected in Fe-Ga. The proposed strategy can be generally employed to investigate short/medium/long-range ordering phenomena in different materials and help design future high-performance materials.

Freezing solute atoms in nanograined aluminum alloys via high-density vacancies

Low-temperature decomposition of supersaturated solid solution into unfavorable intergranular precipitates is a long-standing bottleneck limiting the practical applications of nanograined aluminum alloys that are prepared by severe plastic deformation. Minimizing the vacancy concentration is generally regarded as an effective approach in suppressing the decomposition process. Here we report a counterintuitive strategy to stabilize supersaturated solid solution in nanograined Al-Cu alloys via high-density vacancies in combination with Sc microalloying. By generating a two orders of magnitude higher concentration of vacancies bonded in strong (Cu, Sc, vacancy)-rich atomic complexes, a high thermal stability is achieved in an Al-Cu-Sc alloy that precipitation is nearly suppressed up to ~230 °C. The solute-vacancy complexes also enable the nanograined Al-Cu alloys with higher strength, greater strain hardening capability and ductility. These findings provide perspectives towards the great potentials of solute-vacancy interaction and the development of nanograined alloys with high stability and well-performed mechanical properties.

Low-temperature decomposition and insufficient plastic deformability are bottlenecks that limit the practical applications of nanograined Al alloys. Here the authors utilize a high density vacancies in combination with Sc microalloying to stabilize nanograined Al-Cu alloys.

Liquid-Phase Transmission Electron Microscopy for Reliable In Situ Imaging of Nanomaterials

Liquid-phase transmission electron microscopy (LPTEM) is a powerful in situ visualization technique for directly characterizing nanomaterials in the liquid state. Despite its successful application in many fields, several challenges remain in achieving more accurate and reliable observations. We present LPTEM in chemical and biological applications, including studies for the morphological transformation and dynamics of nanoparticles, battery systems, catalysis, biomolecules, and organic systems. We describe the possible interactions and effects of the electron beam on specimens during observation and present sample-specific approaches to mitigate and control these electron-beam effects. We provide recent advances in achieving atomic-level resolution for liquid-phase investigation of structures anddynamics. Moreover, we discuss the development of liquid cell platforms and the introduction of machine-learning data processing for quantitative and objective LPTEM analysis.

3D Nanoscale Mapping of Short-Range Order in GeSn Alloys

GeSn on Si has attracted much research interest due to its tunable direct bandgap for mid-infrared applications. Recently, short-range order (SRO) in GeSn alloys has been theoretically predicted, which profoundly impacts the band structure. However, characterizing SRO in GeSn is challenging. Guided by physics-informed Poisson statistical analyses of k-nearest neighbors (KNN) in atom probe tomography (APT), a new approach is demonstrated here for 3D nanoscale SRO mapping and semi-quantitative strain mapping in GeSn. For GeSn with ≈14 at. % Sn, the SRO parameters of Sn-Sn 1NN in 10 × 10 × 10 nm³ nanocubes can deviate from that of the random alloys by ±15 %. The relatively large fluctuation of the SRO parameters contributes to band-edge softening observed optically. Sn-Sn 1NN also tends to be more favored toward the surface, less favored under strain relaxation or tensile strain, while almost independent of local Sn composition. An algorithm based on least square fit of atomic positions further verifies this Poisson-KNN statistical method. Compared to existing macroscopic spectroscopy or electron microscopy techniques, this new APT statistical analysis uniquely offers 3D SRO mapping at nanoscale resolution in a relatively large volume with millions of atoms. It can also be extended to investigate SRO in other alloy systems.

Reflections on the Spatial Performance of Atom Probe Tomography in the Analysis of Atomic Neighborhoods

Atom probe tomography (APT) is often introduced as providing “atomic-scale” mapping of the composition of materials and as such is often exploited to analyze atomic neighborhoods within a material. Yet quantifying the actual spatial performance of the technique in a general case remains challenging, as it depends on the material system being investigated as well as on the specimen's geometry. Here, by using comparisons with field-ion microscopy experiments, field-ion imaging and field evaporation simulations, we provide the basis for a critical reflection on the spatial performance of APT in the analysis of pure metals, low alloyed systems and concentrated solid solutions (i.e., akin to high-entropy alloys). The spatial resolution imposes strong limitations on the possible interpretation of measured atomic neighborhoods, and directional neighborhood analyses restricted to the depth are expected to be more robust. We hope this work gets the community to reflect on its practices, in the same way, it got us to reflect on our work.

Open and strong-scaling tools for atom-probe crystallography: high-throughput methods for indexing crystal structure and orientation

Volumetric crystal structure indexing and orientation mapping are key data processing steps for virtually any quantitative study of spatial correlations between the local chemical composition features and the microstructure of a material. For electron and X-ray diffraction methods it is possible to develop indexing tools which compare measured and analytically computed patterns to decode the structure and relative orientation within local regions of interest. Consequently, a number of numerically efficient and automated software tools exist to solve the above characterization tasks. For atom-probe tomography (APT) experiments, however, the strategy of making comparisons between measured and analytically computed patterns is less robust because many APT data sets contain substantial noise. Given that sufficiently general predictive models for such noise remain elusive, crystallography tools for APT face several limitations: their robustness to noise is limited, and therefore so too is their capability to identify and distinguish different crystal structures and orientations. In addition, the tools are sequential and demand substantial manual interaction. In combination, this makes robust uncertainty quantification with automated high-throughput studies of the latent crystallographic information a difficult task with APT data. To improve the situation, the existing methods are reviewed and how they link to the methods currently used by the electron and X-ray diffraction communities is discussed. As a result of this, some of the APT methods are modified to yield more robust descriptors of the atomic arrangement. Also reported is how this enables the development of an open-source software tool for strong scaling and automated identification of a crystal structure, and the mapping of crystal orientation in nanocrystalline APT data sets with multiple phases.

Development of Wide Field of View Three-Dimensional Field Ion Microscopy and High-Fidelity Reconstruction Algorithms to the Study of Defects in Nuclear Materials

This article presents a fast and highly efficient algorithm developed to reconstruct a three-dimensional (3D) volume with a high spatial precision from a set of field ion microscopy (FIM) images, and specific tools developed to characterize crystallographic lattice and defects. A set of FIM digital images and image processing algorithms allow the construction of a 3D reconstruction of the sample at the atomic scale. The capability of the 3D FIM to resolve the crystallographic lattice and the finest defects in metals opens a new way to analyze materials. This spatial precision was quantified on tungsten, analyzed at different analyzing conditions. A specific data mining tool, based on Fourier transforms, was also developed to characterize lattice distortions in the reconstructed volumes. This tool has been used in simulated and experimental volumes to successfully locate and characterize defects such as dislocations and grain boundaries.

Role of dislocation elastic field on impurity segregation in Fe-based alloys

Dislocation engineering in crystalline materials is essential when designing materials for a large range of applications. Segregation of additional elements at dislocations is frequently used to modify the influence of dislocations on material properties. Thus, the influence of the dislocation elastic field on impurity segregation is of major interest, as its understanding should lead to engineering solutions that improve the material properties. We report the experimental study of the elastic field influence on atomic segregation in the core and in the area surrounding edge dislocations in Fe-based alloys. Each element is found either to segregate in the edge dislocation core or to form atmospheres. The elastic field has a strong effect on the segregation atmosphere, but no effect on the dislocation core segregation. The theory is in good agreement with experiments, and should support dislocation engineering.

Size-dependent diffusion controls natural aging in aluminium alloys

A key question in materials science is how fast properties evolve, which relates to the kinetics of phase transformations. In metals, kinetics is primarily connected to diffusion, which for substitutional elements is enabled via mobile atomic-lattice vacancies. In fact, non-equilibrium vacancies are often required for structural changes. Rapid quenching of various important alloys, such as Al- or Mg-alloys, results for example in natural aging, i.e. slight movements of solute atoms in the material, which significantly alter the material properties. In this study we demonstrate a size effect of natural aging in an AlMgSi alloy via atom probe tomography with near-atomic image resolution. We show that non-equilibrium vacancy diffusional processes are generally stopped when the sample size reaches the nanometer scale. This precludes clustering and natural aging in samples below a certain size and has implications towards the study of non-equilibrium diffusion and microstructural changes via microscopy techniques.

Aluminium alloys can naturally age and form microstructural clusters that affect their mechanical properties. Here, the authors show that nanosized samples do not under undergo natural aging because diffusion-controlled clustering processes are inhibited.

Correlative study of lattice imperfections in long-range ordered, nano-scale domains in a Fe-Co-Mo alloy

Recent advancements in data mining methods in atom probe microscopy have enabled new quantitative chemical and microstructural characterization beyond the standard three-dimensional reconstruction. For example, spatial distribution maps have been developed to enable visualisation of the local lattice occupation of a selected region of interest. However, the precision of such studies yet remains unknown as correlation with complementary methods would be required. Therefore, a correlative study of atom probe microscopy, neutron diffraction and microstructural modelling of long-range ordered, nano-scale domains in a well-researched Fe-Co-Mo Maraging-type steel is presented here. Its microstructure consists of Mo-enriched µ-phase (Fe,Co)₇Mo₆ particles embedded into a body-centred cubic FeCo matrix. Previous research has shown that under slow cooling conditions, this matrix partially decomposes into nano-scale B2 long-range ordered domains surrounded by disordered regions, resulting in reduced toughness in potential cutting applications. Usually, a long-range order parameter S referring to ideal B2 long-range order is assumed within such domains according to neutron diffraction. However, atom probe microscopy and modelling results presented in the current study indicate lattice imperfections with a partial substitution of atoms on the Fe- and Co-sublattices. After considering preferential retention effects during the atom probe experiment, a model unit cell is presented to define the observed imperfect B2 long-range order as pseudo-D0₃ long-range order, and the potential impact on the materials properties is discussed.

Correlating Atom Probe Crystallographic Measurements with Transmission Kikuchi Diffraction Data

Correlative microscopy approaches offer synergistic solutions to many research problems. One such combination, that has been studied in limited detail, is the use of atom probe tomography (APT) and transmission Kikuchi diffraction (TKD) on the same tip specimen. By combining these two powerful microscopy techniques, the microstructure of important engineering alloys can be studied in greater detail. For the first time, the accuracy of crystallographic measurements made using APT will be independently verified using TKD. Experimental data from two atom probe tips, one a nanocrystalline Al-0.5Ag alloy specimen collected on a straight flight-path atom probe and the other a high purity Mo specimen collected on a reflectron-fitted instrument, will be compared. We find that the average minimum misorientation angle, calculated from calibrated atom probe reconstructions with two different pole combinations, deviate 0.7° and 1.4°, respectively, from the TKD results. The type of atom probe and experimental conditions appear to have some impact on this accuracy and the reconstruction and measurement procedures are likely to contribute further to degradation in angular resolution. The challenges and implications of this correlative approach will also be discussed.

Detecting Clusters in Atom Probe Data with Gaussian Mixture Models

Accurately identifying and extracting clusters from atom probe tomography (APT) reconstructions is extremely challenging, yet critical to many applications. Currently, the most prevalent approach to detect clusters is the maximum separation method, a heuristic that relies heavily upon parameters manually chosen by the user. In this work, a new clustering algorithm, Gaussian mixture model Expectation Maximization Algorithm (GEMA), was developed. GEMA utilizes a Gaussian mixture model to probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via expectation maximization: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. GEMA outperforms the maximum separation method in cluster detection accuracy when applied to several realistically simulated data sets. Lastly, GEMA was successfully applied to real APT data.

Automated Atom-By-Atom Three-Dimensional (3D) Reconstruction of Field Ion Microscopy Data

An automated procedure has been developed for the reconstruction of field ion microscopy (FIM) data that maintains its atomistic nature. FIM characterizes individual atoms on the specimen's surface, evolving subject to field evaporation, in a series of two-dimensional (2D) images. Its unique spatial resolution enables direct imaging of crystal defects as small as single vacancies. To fully exploit FIM's potential, automated analysis tools are required. The reconstruction algorithm developed here relies on minimal assumptions and is sensitive to atomic coordinates of all imaged atoms. It tracks the atoms across a sequence of images, allocating each to its respective crystallographic plane. The result is a highly accurate 3D lattice-resolved reconstruction. The procedure is applied to over 2000 tungsten atoms, including ion-implanted planes. The approach is further adapted to analyze carbides in a steel matrix, demonstrating its applicability to a range of materials. A vast amount of information is collected during the experiment that can underpin advanced analyses such as automated detection of "out of sequence" events, subangstrom surface displacements and defects effects on neighboring atoms. These analyses have the potential to reveal new insights into the field evaporation process and contribute to improving accuracy and scope of 3D FIM and atom probe characterization.

Idealized vs. Realistic Microstructures: An Atomistic Simulation Case Study on γ/γ' Microstructures

Single-crystal Ni-base superalloys, consisting of a two-phase γ/γ′ microstructure, retain high strengths at elevated temperatures and are key materials for high temperature applications, like, e.g., turbine blades of aircraft engines. The lattice misfit between the γ and γ′ phases results in internal stresses, which significantly influence the deformation and creep behavior of the material. Large-scale atomistic simulations that are often used to enhance our understanding of the deformation mechanisms in such materials must accurately account for such misfit stresses. In this work, we compare the internal stresses in both idealized and experimentally-informed, i.e., more realistic, γ/γ′ microstructures. The idealized samples are generated by assuming, as is frequently done, a periodic arrangement of cube-shaped γ′ particles with planar γ/γ′ interfaces. The experimentally-informed samples are generated from two different sources to produce three different samples—the scanning electron microscopy micrograph-informed quasi-2D atomistic sample and atom probe tomography-informed stoichiometric and non-stoichiometric atomistic samples. Additionally, we compare the stress state of an idealized embedded cube microstructure with finite element simulations incorporating 3D periodic boundary conditions. Subsequently, we study the influence of the resulting stress state on the evolution of dislocation loops in the different samples. The results show that the stresses in the atomistic and finite element simulations are almost identical. Furthermore, quasi-2D boundary conditions lead to a significantly different stress state and, consequently, different evolution of the dislocation loop, when compared to samples with fully 3D boundary conditions.

Nano sculpt: A methodology for generating complex realistic configurations for atomistic simulations

Atomistic simulations have now become commonplace in the study of the deformation and failure of materials. Increase in computing power in recent years has made large-scale simulations with billions, or even trillions, of atoms a possibility. Most simulations to-date, however, are still performed with quasi-2D geometries or rather simplistic 3D setups. Although controlled studies on such well-defined structures are often required to obtain quantitative information from atomistic simulations, for qualitative studies focusing on e.g. the identification of mechanisms, researchers would greatly benefit from a methodology that helps realize more realistic configurations. The ideal scenario would be a one-on-one reconstruction of experimentally observed structures. To this end, we propose a new method and software tool called nano sculpt with the following features:•The method allows for easy sample generation for atomistic simulations from any arbitrarily shaped 3D enclosed volume.•The tool can be used to build atomistic samples from artificial geometries, including CAD geometries and structures obtained from simulation methods other than atomistic simulations.•The tool enables the generation of experimentally informed atomistic samples, by e.g. digitization of micrographs or usage of tomography data.