Atomic-scale analysis of light alloys using atom probe tomography

Introduction

As the title suggests, the present paper focuses on three-dimensional, atom-by-atom analysis of light alloys using the technique of atom probe tomography (APT). The challenge in characterising atomistic-level structures is that it pushes the limits of resolution and detection of most microscopy and characterisation techniques, hence the drive for multitechnique, correlative approaches that also cover multiple length scales. Atom probe microscopy is a tomographic technique that fits into the atomic-scale end of this spectrum and provides a unique combination of highly resolved chemical and spatial information in three dimensions. ¹ Several review articles, special issues of journals, and books are available on the topic.^1–13 So far, this technique is the closest to achieving the ultimate goal in microscopy, i.e. to accurately locate and identify every atom in the specimen and provide capacity to reveal both composition and crystallographic structure at the atomic scale. ¹⁴

In APT, atoms are progressively removed from the surface of a cryogenically cooled, needle-shaped specimen under ultrahigh vacuum conditions, through a process of field evaporation. A schematic of the experimental set-up is shown in Fig. 1. By the application of a high DC voltage, a very intense electrostatic field is produced at the apex of the specimen tip, having a radius of curvature of a few tens of nanometres. In a controlled manner, using either voltage or laser pulsing, the surface atoms are field ionised and evaporated, atom by atom, layer by layer, towards a position-sensitive detector, where their chemical identity is determined by time-of-flight mass spectrometry. It is noted that the mechanism of field evaporation is different between the two pulsing modes. Voltage pulsing increases the applied electric field, whereas laser energy increases the thermal energy to overcome the barrier to field ionisation. Subsequently, the evaporated volume is reconstructed in three dimensions using an inverse projection reconstruction algorithm and the sequence of detected events. The result is a tomographic data set, typically spanning some tens to hundreds of nanometres in depth and containing the spatial coordinates and elemental identities of tens to hundreds of millions of atoms with near atomic resolution (∼0.1–0.3 nm in depth and 0.3–0.5 nm laterally). ¹⁵

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Schematic of APT (reprinted from Ref. 14 with permission from Elsevier)

From a materials science perspective, APT has enabled the characterisation of many important microstructural features occurring in physical metallurgy, providing new insights into structure–property relationships. ¹⁶ These atomic and nanoscale microstructural features include solute clustering and precipitation, and interfacial segregation, such as at the phase boundary between a precipitate and the matrix, grain boundaries, and point and line defects. Many of these are detailed in the various sources already cited here and occur numerously within the light alloy systems based on Al, Mg and Ti, for which review articles also exist in the literature.^17–21 Hence, the purpose of the present paper is, rather, to highlight some of the atomic-scale characterisation circumstances where APT has made a unique contribution within the field of light alloys and also to outline some recent developments and future directions.

Atom-by-atom analysis of solid solution

Compared to other microscopy techniques, APT is particularly suited to characterising the chemical architecture of a solid solution, which is recognised as a key factor in engineering the formation and evolution of nanostructure within an alloy. In some cases, solid solution nanostructure can directly affect the material properties, and in other cases, their effect is indirect. For example, clusters of solute atoms can provide intrinsic strengthening upon their direct interaction with moving dislocations during deformation.^22–47 Solute clusters can also indirectly affect the material properties by cluster assisted nucleation of second phase, strengthening precipitates,^48,49 either intrinsically by having seeded the development of the aforementioned precipitates^50–53 or extrinsically by heterogeneous nucleation, where the solute species of the initial cluster are not strict constituents of the precipitate.^54–57Atom-by-atom analysis afforded by APT data is also well suited to characterisation of short-range order (SRO), which is another characteristic of a solid solution that can affect the physical and mechanical properties of an alloy by, for example, the influence on phase transformation phenomena. It is also noteworthy that APT is the only characterisation technique that can provide direct atomic-scale measurement and determination of the matrix composition of the solid solution, ⁵⁸ having equal detection sensitivity to all the elements. Specific methods exist for doing this, including solute–solute nearest-neighbour (NN) distance analysis, ⁵⁹ which is particularly useful for dilute alloys, e.g. precipitation hardened Al alloy systems,^59–61where the information about the solute composition in the matrix can also be used to indirectly derive the stoichiometry of the precipitates and their volume fraction. ⁶²

Solute clustering analysis

Despite many attempts to understand solute clustering phenomena in light alloys, as detailed variously in the literature, inconsistency surrounds the description of the early stages of decomposition of a supersaturated solid solution with respect to solute cluster formation and the influence of these clusters both directly and indirectly on the evolution of the microstructure and the mechanical properties of the material. Part of the issue is definition and discrimination between atomic-scale constituents of the microstructure or, rather, nanostructure.^48,49 The other part relates to the ability to accurately and quantitatively characterise such nanostructure. This is understandable because of the acute difficulties associated with the characterisation of solute clustering processes, where even statistical/random compositional fluctuations in the solid solution may seem like clusters. Thus, the analysis of these results can be subject to different interpretations.

Experimental studies that attempt to characterise solute clustering can be broadly categorised into three groups based on the type of characterisation method/technique. The first group includes bulk, non-local measurements such as differential scanning calorimetry, ⁶³ electrical resistivity ⁶⁴ and of course mechanical property testing (hardness and tensile), all of which provide globally averaged information. The second group consists of techniques that probe the local environment, but again the information is obtained from a bulk averaged point of view. These include nuclear magnetic resonance, ⁶⁵ small-angle scattering^66,67 of both X-rays (SAXS) ⁶⁸ and neutrons, ⁶⁹ and positron annihilation spectroscopy, ⁷⁰ referring to both positron annihilation lifetime spectroscopy and coincidence Doppler broadening. The third group pertains to direct imaging methods, which are essentially APT and high-resolution aberration-corrected transmission electron microscopy (TEM). The latter can provide a two-dimensional projection image of the three-dimensional (3D) lattice with atomic column resolution (Fig. 2a); however, convolutions in the electron scattering processes from different elements, in addition to limited elemental Z-contrast from solute species close to each other in the periodic table, make it near impossible to unambiguously distinguish between the various atomic species in a multicomponent solid solution with non-periodic solute architecture. ⁷² Atom probe tomography, on the other hand, is the only technique capable of performing direct microscopy of the atomic-scale clustered microstructure by resolving both the 3D position and the chemical identity of individual atoms (Fig. 2b). ¹ Various cluster-finding algorithms are available for the analysis of atom probe data^2,73–80 including various strategies for their deployment and parameter selection.^1,36,81–90 There is no universally applicable methodology or ‘one size fits all’ approach, ⁷⁶ but it is clear that using a heuristic parameter choice or some optimisation technique is emerging as best practice (Fig. 3). ⁹¹ Additionally, random labelling^76,91,92 is a valuable method for parameter selection^36,45,81,91 and to establish the extent to which the observed clustering occurs over and above that which may be expected in a corresponding random configuration.^36,91

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a high-resolution TEM of a solute cluster within an Al–1.1Cu–1.7Mg (at.-) alloy, demonstrating its coherence with matrix: left side, high-angle annular dark field scanning TEM image; right side, bright-field scanning TEM image (reprinted from Ref. 71 with permission from Elsevier) and b APT map of an equivalent solute cluster in the same alloy, clearly showing the 3D location of Cu and Mg atoms (Al atoms have been omitted for clarity) ²⁸

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Frequency histograms of both the experimental and the randomly labelled first and fifth NN distance distributions of Mg, Si and Cu solute atoms in a 6111 aluminium alloy after natural aging at room temperature for 1 week; comparison of 1NN (blue) and 5NN (red) distributions shows that the latter is more sensitive to fine-scale clustering, since there is a larger difference between experimental and random (where the experimental curve shifts to smaller distances), which is the heuristic basis for selection of the distance parameter often used in cluster-finding algorithms

Nevertheless, beyond basic scientific interest, it is important to understand the relation between cluster formation and the resulting yield strength of an alloy because, for example, it is critical not only for performance during end application but also for handling of the alloy during processing and fabrication of components. The characterisation of clusters is challenging as they are dynamic in nature, i.e. subject to change by vacancy-mediated diffusional processes that in some cases, e.g. Al alloys, occur even at room temperature, which therefore adds to the experimental difficulty of making an absolute quantification of the clustered state at any one point in time. ⁴⁵ However, with a robust cluster-finding approach applied consistently to a series of atom probe data containing changes in solid solution microstructure as a function of applied processing (e.g. thermomechanical or aging heat treatment), quantitative information about the change in clustered state can be ascertained in order to progress the understanding of the materials science.

In addition to the yield strength derived directly from the interaction of a moving dislocation with a solute cluster, there also exist cases where the solute distribution, necessarily analysed by APT, can affect other aspects of microstructural development in light alloys. These aspects refer to the suggestion that solute clusters (particularly of rare-earth elements) are a potent modifier of recrystallisation texture in magnesium alloys^93,94 and that their presence or absence in the Mg solid solution will also influence the crystal deformation mode (slip or twinning) and the evolution of deformation microstructure, notably the appearance of certain twin types. ⁹⁵ Both of these aspects critically impact the room temperature formability of magnesium. Factors that could be affected by solute atoms during twinning include the movement of the twinning dislocation, the shuffle/shear motion of atoms during the twinning event, and the migration of the twin/matrix interface. Hence, solute strengthening of twinning dislocations in Mg alloys is a very complex situation, and although the solute arrangements that cause hardening of twins may be similar to that which causes hardening of slip, the mechanisms could be different. While recent theoretical modelling combined with first principles based simulation input is making significant progress in predicting the strengthening response from particular solute elements, ⁹⁶ the role of experimental APT towards understanding how solute configuration determines twinning mechanics at the atomistic scale (and hence deformation/formability performance) is still not well defined. This represents opportunity for future research.

Overcoming limitations of atom probe data

It is well known that atom probe detector efficiency is less than 100, which means that not all the atoms are detected. This is a stochastic loss due to the current state-of-the-art in detector design, ¹² but because it is independent of atomic identity, this does not affect composition determination. Additionally, the undetected atoms are taken into account for accurate reconstruction of tomographic volumes.¹ Furthermore, while the 3D spatial resolution of APT can be extremely high,^1,15,103,104 with near-atomic resolution in the depth direction attributed to an ordered evaporation sequence, it is not perfectly exact. As such, the locations of the atoms in the reconstructed image are offset slightly from their true positions. Limited detector efficiency alone does not affect nano-scale measurements or analysis of APT data, but the combination of the aforementioned factors means that there remain challenges for truly atom-by-atom, atomic-scale analyses. Recent work is beginning to address these issues with respect to NN analysis techniques such as cluster-finding and GM-SRO analysis.

In the latter case, the accuracy of the GM-SRO analysis at higher order coordination shells has been improved by lattice rectification of the reconstructed atom probe data, carried out before application of the GM-SRO analysis. ¹⁰² Lattice rectification is a technique that uses crystallographic information from the reconstructed APT data to restore the lattice-specific atomic configuration of the original specimen (Fig. 4).^105–108 Initial tests carried out on simulated APT data indicate that lattice rectification can improve the atomic position information sensitivity and also provide an estimation of the spatial noise tolerance. ¹⁰²

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Lattice rectification of an Al–1.1Cu–1.7Mg (at.-) alloy a 5 nm thick two-dimensional section of the raw APT data, b complementary section after lattice rectification, c close-up 3D subvolume from b, where vacant lattice sites in the rectified reconstruction have also been highlighted, and d radial distribution function analysis of the rectified experimental data as compared to that of the theoretical lattice, the ratio of which indicates the detector efficiency (reproduced from Ref. 105 with permission from Cambridge University Press)

Limited detector efficiency will affect cluster-finding analysis ¹⁰⁹ and Stephenson et al.^110,111 have employed an analytical model using an expectation maximisation algorithm to determine the original cluster size and number density distribution with 100 detector efficiency. Another approach by Ceguerra et al. ¹⁰¹ takes GM-SRO values measured from the original APT data to drive atomistic Monte Carlo simulations, instead of the common practice of using interaction energy values, to generate statistically equivalent, 100 efficient systems. ⁹¹ More recently, Moody et al. ¹¹² have taken this latter methodology another step forward by creating a novel hybrid data format that blends experimental APT and predictive Monte Carlo simulations, together with lattice rectification techniques, ¹⁰⁵ to overcome limitations from detector efficiency in combination with spatial resolution. The result is atomically complete, chemically resolved and lattice-bound data that can then be used as a direct input into computer simulations to predict bulk material properties, bridging the gap to create a true nexus between microscopy and atomistic simulations. The method has been demonstrated on an Al–Ag–Cu alloy to create hybrid APT data that directly inform the starting geometrical models for density functional theory simulations to calculate local energetics and elastic properties. ¹¹² These exciting new developments open the door for a wealth of new information at the atomic scale to inform light alloy design by understanding nanostructure–property relationships.

Modelling and simulation of cluster strengthening

Significant strengthening in aluminium alloys due to the formation of clusters during natural and artificial aging has been known since the 1960s, ¹¹³ whereas modelling of the strengthening has received relatively early attention. Deschamps et al. ⁶⁸ adapted a classical hardening model for shearable precipitates from Friedel ¹¹⁴ to estimate the contribution of cluster hardening to yield strength, based on quantitative measurement of their size and volume fraction using a combination of nuclear magnetic resonance and in situ SAXS. Starink et al.^115,116 have used a thermodynamic model based on a single interaction energy (estimated by differential scanning calorimetry) of dissimilar NN interaction to define the strengthening from clusters. More recently, Zhao et al.^117,118 have considered the elastic effect of clusters (about < 1 nm in diameter) and propose a size misfit strengthening model, where the size misfit of clusters is assumed to be the sum of elementary atomic misfits. From the point of view of the effect of the spatial distribution of weak obstacles (e.g. solute atoms and small clusters thereof), areal glide simulations by de Vaucorbeil et al. ¹¹⁹ suggest that this does not affect the resultant strength (critically resolved shear stress). Subsequently, Marceau et al. ⁴⁵ have estimated the contribution of cluster strengthening by directly incorporating the cluster distribution (size and volume fraction) determined by APT into a randomly arranged areal glide plane model for strengthening. Here, the strength of each cluster was assumed to be proportional to its radius on the glide plane, while the solid solution strengthening contribution from the non-clustered solute atoms, obtained from recent ab initio density functional theory calculations of Leyson et al., ¹²⁰ is summed with the aforementioned cluster strengthening contribution using a new addition law for the superposition of strengthening components. ¹²¹ Importantly, the role of experimental APT and quantitative cluster-finding analysis has been crucial in providing key input data for the prediction of light alloy mechanical properties by simulation and modelling of the strengthening effect exerted by solute clusters.

While these approaches are becoming better at accurately modelling cluster strengthening, there are aspects of the situation that are not represented, which are likely to bring strengthening predictions closer to experimentally measured strength values. ⁴⁵ For example, the precise shape/configuration in terms of chemical bonding of the solute atoms in a cluster can vary significantly including their orientation with respect to the glide plane and an oncoming dislocation. The possibility of different interface strengthening mechanism/effects from clusters having the same number of atoms and the same composition, but different configuration and orientation, deserves further research from a simulation and modelling perspective. It is envisaged that APT can assist this process by generating complete, hybrid experimental–analytical data sets, ¹¹² ready to be seeded directly into atomistic molecular dynamics simulations of the interaction of a dislocation(s) with experimentally measured cluster configurations that are known to produce different mechanical properties. There has also been recent simulation work of the development of early-stage clustering and precipitation in binary and ternary Al alloys using the phase field crystal method,^122–124 which could also serve as a very useful starting point for molecular dynamics simulations involving interaction with dislocations.

Aside from cluster strengthening, there is also much room for improvement with respect to properly understanding solid solution strengthening provided by non-clustered solute atoms. From an ab initio simulation point of view, further work by Leyson and Curtin ¹²⁵ has determined that the applicability of the strong pinning Friedel model ¹¹⁴ is very limited in dislocation core structure, temperature and solute concentration, so that use of the weak pinning Labusch-type model ¹²⁶ is more appropriate for most materials and engineering applications. However, the current state-of-the-art approaches aim rather at merging the advantages of both fully describing the interaction between the dislocation core and the solute atom(s) using the ab initio method (i.e. accurate but time consuming) and using the material properties calculated from ab initio calculations as the input to the solid solution strengthening models developed in the framework of linear elasticity theory (i.e. efficient but somewhat qualitative), to develop computationally efficient and quantitatively accurate predictions of solid solution strengthening. ¹²⁷ The question now is: how can state-of-the-art, hybrid experimental–analytical atom probe data, combined with modern theoretical approaches, further extend our atomistic level understanding of microstructure–property relationships to better engineer light alloy materials with advanced properties?

Application of APT to study corrosion

In addition to consideration of mechanical properties, improved performance of light alloys requires better understanding of how the structure and chemistry at the atomic scale impacts electrochemical processes related to corrosion. In this regard, APT can play a very important role and has only somewhat recently been used to investigate light alloys for this purpose. For example, Ralston et al. ⁷¹ have examined the effect of precipitate size on the correlation between yield strength and pitting corrosion in Al–Cu–Mg alloys, incorporating the use of APT. It is shown that nanoscale solute clusters and fine precipitates (∼3 to 8 nm) formed during the earlier stages of artificial aging strongly affect the yield stress of the alloy but do not contribute to its corrosion susceptibility. ¹²⁸ This is unlike the behaviour observed for larger precipitates developed after longer aging times, for which an order of magnitude increase in the pitting rate is observed. It is hypothesised that above this critical precipitate size it is not possible for the formation of a continuous protective passive oxide film to occur. ¹²⁸

At the other end of the scale, APT has also been recently applied to a commercial 2024 aluminium alloy to study the 3D local chemical structure at and around a large intermetallic dispersoid particle that was exposed to the atom probe tip surface and therefore influenced by the corrosive action of the electrolytic polishing solution during specimen preparation (Fig. 5). ¹²⁹ This situation represents a novel APT based method to investigate directly the effects of corrosion on the alloy microstructure. Additionally, the size of the various features described in this work bridge corrosion activity at the micrometre scale (e.g. constituent intermetallic particles) to the very beginning of corrosion at the nanoscale, where chemical heterogeneities can lead to local galvanic cells at which corrosion can initiate or propagate.

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Three-dimensional reconstruction of AA 2024 alloy sample after ‘corrosion’ treatment during electropolishing, showing the locations of Al, Cu, Mg and Mn atoms: purple isoconcentration surface highlights Al₂CuMg (S phase) precipitate, through which a one-dimensional compositional profile is taken (inset, bottom left); green isoconcentration surface shows segregation of H⁺ ions at a constituent intermetallic Al₂₀Mn₃Cu₂ particle exposed to the specimen surface (reprinted from Ref. 129 with copyright permission from American Chemical Society, 2014)

The final remark in this section relates to the ability of APT to detect hydrogen in either its molecular or atomic form. This is of major interest for corrosion research because atomic hydrogen, which is generated as a result of hydrolysis reactions to produce protons, can cause embrittlement in many metals.^130–132 There are significant challenges involved in studying hydrogen using APT, ¹³³ namely the charging of samples with deuterium to a suitable degree, such that it is detectable during the APT experiment (as compared to sorption of hydrogen gas residual in the vacuum chamber) and has not diffused back out of the specimen in the meantime. As a result, there have been few APT studies dedicated to direct, nanoscale observations of the distribution of hydrogen in metallic systems.^133–139 However, it is recognised that while the source of hydrogen in APT experiments is not the same as in a corrosion experiment (as described above), the nature of the microstructural adsorption sites will be the same. ¹²⁹ Accordingly, there have been some APT studies of light alloy systems (Al-, ¹²⁹ Mg-^140,141 and Ti-based ¹⁴² ) where it has been found that certain microstructural features (e.g. intermetallic dispersoids and precipitates) particular to those systems have been observed to be capable of trapping hydrogen and acting as preferred sinks compared to other sites such as interfaces and defects (Fig. 5). These findings have received relatively little attention but have considerable implications for hydrogen embrittlement studies and demonstrate the utility of APT to serve as an extremely useful tool for mapping the atomic hydrogen distribution within the sample in the context of corrosion research. A necessary caveat to mention, however, is that while these results are promising and show the potential of APT in this area, continued fundamental work such as that in Refs. 133–136 is still required to be truly confident in characterisation of hydrogen that is unambiguously from the specimen itself.

Concluding remarks

It has been the purpose of the present paper to highlight instances of atomic-scale characterisation of light alloys where APT has made a unique contribution, beyond the scope of other microscopy and microanalysis techniques. The advantage of the APT technique is its capacity to enable investigation of 3D structure and chemistry at the atomic scale, with equal detection sensitivity to all the elements (including hydrogen), which makes it particularly amenable for atom-by-atom analyses of solid solution architecture, e.g. solute clustering and SRO. Importantly however, APT also lends itself well to correlative and complementary studies of light alloys, combining its advantages with that of other techniques, including, for example, TEM^62,141 and electron tomography,^143,144 to provide feedback for accurate geometric APT reconstruction (Fig. 6); positron annihilation spectroscopy,^36,51 which is the vacant space analogue to APT (which probes the atom space, of course); and SAXS,^62,145–147 where APT feeds its interpretation model with missing chemical information to allow real space determination of the expected size and volume fraction of precipitates from a kinetic development point of view.

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Tomographic image showing particle matching in an Al–Ag alloy from the combination of electron tomography (pink) and APT (yellow) results, acquired from the same sample: vertical dotted lines outline a smaller volume of APT data with respect to the ET data; horizontal dotted lines indicate a displacement of ∼7 nm due to a microfracture of the sample tip at the start of the atom probe experiment (reproduced from Ref. 143 with permission from Elsevier)

Another recent atomic-scale application of APT, in combination with TEM, has been the study of dynamic strain aging in Al–Mg, where the measurement of Mg enrichment and depletion at dislocations is helping to explain this macroscopic phenomenon. ¹⁴⁸ This relates to the potential application of APT for the investigation of solute strengthening of twinning in Mg alloys, as mentioned in the section on ‘Solute clustering analysis’. In fact, it has been recently stated in the literature that greater understanding of the role of solutes in room temperature deformation of rare-earth containing Mg alloys would benefit from application of APT by atomic-scale exploration of solute segregation to dislocations. ¹⁴⁹ In this context, the possible future merits of using correlated APT and electron microscopy are further reinforced, where atom probe would require additional complementary diffraction or similar structure information. Hence, methods that merge information obtained from electron microscopy and APT, yielded on the very same tip, will be of significant interest.^150–153

It is clear that there exist numerous opportunities for APT characterisation to contribute to the materials science and engineering design of light alloys. Future directions rely not only on further instrument advances, both incremental (e.g. improved detection efficiency) and major (e.g. environmental cell for in situ reactions, ¹⁵⁴ or combined TEM and APT^72,155,156), but also, as reflected by the some of the applications demonstrated in the present review, in the development of new data analysis tools and methodologies.^{91,92,112,156}