We used density-functional-theory simulations to examine the structural and electronic properties of the $\Sigma 180{\deg}(100)[001] $ grain boundary in monoclinic ZrO$_2$, which is a very low-energy (0.06Jm$^{-2}$) twin boundary present in experimental oxide texture maps, with suggested special properties. This equilibrium structure was compared with a metastable structure (with a boundary energy of 0.32Jm$^{-2}$), which was considered to be representative of a more general oxide boundary. The interaction of oxygen vacancies, substitutional Sn and Nb defects (substituting host Zr sites) with both structures - and their effect on the boundary properties - were examined. We found that the equilibrium structure energetically favours V$_\textrm{O}^{2+}$ and Nb$_\textrm{Zr}^{2-}$, whereas the metastable structure favours V$_\textrm{O}^{2+}$ and Sn$_\textrm{Zr}^{2-}$. Tin was further found to bind strongly with oxygen vacancies in both structures, and introduce gap states in the band gap of their electronic structure. Sn$_\textrm{Zr}^{2-}$ was, however, found to increase the segregation preference of V$_\textrm{O}^{2+}$ for the metastable structure, which might contribute to increased oxygen and electron transport down this interface, and therefore other more general boundaries, compared to the equilibrium structure of the studied monoclinic twin boundary.

Data-driven machine learning (ML) models of atomistic interactions are often based on flexible and non-physical functions that can relate nuanced aspects of atomic arrangements to predictions of energies and forces. As a result, these potentials are only as good as the training data (usually the results of so-called ab initio simulations), and we need to ensure that we have enough information to make a model sufficiently accurate, reliable and transferable. The main challenge stems from the fact that descriptors of chemical environments are often sparse, high-dimensional objects without a well-defined continuous metric. Therefore, it is rather unlikely that any ad hoc method for selecting training examples will be indiscriminate, and it is easy to fall into the trap of confirmation bias, where the same narrow and biased sampling is used to generate training and test sets. We will show that an approach derived from classical concepts of statistical planning of experiments and optimal design can help to mitigate such problems at a relatively low computational cost. The key feature of the method we will investigate is that it allows us to assess the quality of the data without obtaining reference energies and forces-a so-called offline approach. In other words, we are focusing on an approach that is easy to implement and does not require sophisticated frameworks that involve automated access to high performance computing.

Understanding the nature of irradiation damage often requires a multi-scale and multi-physics approach, i.e. it requires a significant amount of information from experiments, simulations and phenomenological models. This paper focuses on the initial stages of irradiation damage, namely neutron-induced displacement cascades in zirconium, as nuclear-grade zirconium alloys are widely used in fuel assemblies. We provide results of large-scale molecular dynamics (MD) simulations based on existing inter-atomic potentials and the two-temperature model to include the effect of electron-phonon coupling. Our data can be used directly in higher scale methods. Furthermore, we analysed summary statistics associated with defect production, such as the number of defects produced, their distribution and the size of clusters. As a result, we have developed a generative model of collision cascades. The model is hierarchical, as well as stochastic, i.e. it includes the variance of the considered features. This development had three main objectives: to establish a sufficient descriptor of a cascade, to develop an interpolator of data obtained from high-fidelity simulations, and to demonstrate that the statistical model of the data can generate representative distributions of primary irradiation defects. The results can be used to generate synthetic inputs for longer length- and time-scale models, as well as to build fast approximations relating dose, damage and irradiation conditions.

Irradiation induced dislocation loops and lattice dislocations produced by plastic deformation have very different dipole characters, dislocation contrasts and range of strain fields. To determine partial dislocation densities of the different dislocation types from X-ray or neutron diffraction patterns, all differences in dislocation properties should be considered. We have extended the convolutional multiple whole profile line profile analysis method to convolve different strain profiles with different effective outer cut-off radii, corresponding to different dislocation type, into a single size profile. The extended procedure is applied to determine the (a) loop and lattice dislocation densities in a neutron irradiated and tensile deformed Zr-2.5 %Nb alloy and in a proton or neutron irradiated Zircaloy-2 alloy. We show that when the dislocation densities are very different the effective outer cut-off radius of dislocations is a better descriptor of dislocation character than the dislocation arrangement parameter, which was used previously in line profile analysis. Our results show that the combination of line profile analysis and electron microscopy methods provides a detailed and comprehensive description of defect structures in deformed and irradiated materials.

Understanding corrosion mechanisms is of importance for reducing the global cost of corrosion. While the properties of engineering components are considered at a macroscopic scale, corrosion occurs at micro or nano scale and is influenced by local microstructural variations inherent to engineering alloys. However, studying such complex microstructures that involve multiple length scales requires a multitude of advanced experimental procedures. Here, we present a method using correlated electron microscopy techniques over a range of length scales, combined with crystallographic modelling, to provide understanding of the competing mechanisms that control the waterside corrosion of zirconium alloys. We present evidence for a competition between epitaxial strain and growth stress, which depends on the orientation of the substrate leading to local variations in oxide microstructure and thus protectiveness. This leads to the possibility of tailoring substrate crystallographic textures to promote stress driven, well-oriented protective oxides, and so to improving corrosion performance.

Finding efficient means of quantitatively describing material microstructure is a critical step towards harnessing data-centric machine learning approaches to understanding and predicting processing-microstructure-property relationships. Current quantitative descriptors of microstructure tend to consider only specific, narrow features such as grain size or phase fractions, but these metrics discard vast amounts of information. Since the gain in traction of machine learning and computer vision, more abstract methods for describing image data in a concise and quantitative manner have become available, but have yet to be fully exploited within materials science. The main aim of this paper is to investigate some of these methods as tools for constructing compressed numerical descriptions of microstructural image data, which are here referred to as "microstructural fingerprints". A statistical framework is developed to combine some of these methods which includes some classical computer vision methods as special cases.The effectiveness of fingerprints, in this case, is assessed via a series of classification tasks, which take the fingerprints as input along with some label to describe the microstructure, and aim to predict the class label. The classification tasks are a simple way to assess the information content of differently constructed fingerprints, using readily available data. However, the potential applications for such fingerprints, in theory, extend far beyond this, provided a suitably labelled training dataset. For example, fingerprints constructed from image data labelled with some processing parameters or mechanical properties could be fed into regression based tasks to predict properties from microstructure or predict the processing parameters required for a target microstructure. The ultimate purpose is to rapidly fingerprint sample images in the context of various high-throughput design/make/test scenarios. Such fingerprints would enable, for example, quantification of the disparity between microstructures for quality control, classifying microstructures, predicting materials properties from image data and identifying potential processing routes to engineer new materials with specific properties.Here, the approach is applied to two distinct datasets to illustrate various aspects of the fingerprints and some recommendations are made based on the findings. In particular, methods that leverage transfer learning with convolutional neural networks (CNNs), pretrained on the ImageNet dataset, are generally shown to outperform other methods. Additionally, dimensionality reduction of these CNN-based fingerprints is shown to have negligible impact on classification accuracy for the supervised learning approaches considered. In situations where there is a large dataset with only a handful of images labelled, graph-based label propagation to unlabelled data is shown to be favourable over discarding unlabelled data and performing supervised learning. In particular, label propagation by Poisson learning is shown to be highly effective at low label rates. The supplementary code is available on GitHub (White and Tarakanov, 2021).

We present object kinetic Monte Carlo simulations that have been developed to understand a number of experimentally observed facts related to the growth of high-purity recrystallized zirconium alloys under irradiation. In this modeling, the irradiation growth is the sum of the elemental deformations generated by defects resulting from irradiation. Such deformations were determined using atomic-scale (ab initio and empirical potential) calculations. According to our results, breakaway growth is strongly related to the vacancy diffusion anisotropy: in agreement with ab initio calculations, vacancies diffuse faster in the basal planes than in planes perpendicular to them. Conversely, the diffusion of interstitials is taken as almost isotropic, as shown by recent ab initio calculations. This combination of point-defect diffusion anisotropy leads to the formation of layers of interstitial prismatic dislocation loops, which are parallel to the basal plane. These layers have been reported experimentally, but the rafts are made of interstitial and vacancy loops. Their formation is also correlated with the growth of vacancy loops that are introduced in the model by the collapse of stacking-fault pyramids. This collapse could explain why the diameter of the loops has never been experimentally observed below a size of the order of 9 nm and before a certain threshold of fluence. Thus, the “breakaway” results from the development of vacancy loops and the rafting of prismatic loops. In a previous work these observations were reproduced, but rafts were only compounded of interstitial loops in the simulation box.

Zirconium alloys are widely used as the fuel cladding material in pressurized water reactors, accumulating a significant population of defects and dislocations from exposure to neutrons. We present and interpret synchrotron microbeam X-ray diffraction measurements of proton-irradiated Zircaloy-4, where we identify a transient peak and the subsequent saturation of dislocation density as a function of exposure. This is explained by direct atomistic simulations showing that the observed variation of dislocation density as a function of dose is a natural result of the evolution of the dense defect and dislocation microstructure driven by the concurrent generation of defects and their subsequent stress-driven relaxation. In the dynamic equilibrium state of the material developing in the high dose limit, the defect content distribution of the population of dislocation loops, coexisting with the dislocation network, follows a power law with exponent α≈2.2. This corresponds to the power law exponent of β≈3.4 for the distribution of loops as a function of their diameter that compares favourably with the experimentally measured values of β in the range 3≤β≤4.

Cu rich precipitates (CRPs) are commonly observed to form core-shell structures in neutron irradiated pressure vessel steels. The core region is typically composed of pure Cu whilst the shell is formed of other solute elements including Ni and Si. In this work we calculate the segregation energies for Ni and Si substitutional defects segregating to coherent Fe-Cu interfaces decorated with different types of point defect (vacancies and other solute substitutional defects). By comparing these values to those found for Ni and Si segregation to clean Fe-Cu interfaces we can establish how the presence of point defects on the interface influences solute segregation behaviours. Interestingly we find that the segregation of Ni to Si decorated interfaces and the segregation of Si to Ni decorated interfaces demonstrate a relatively strong co-segregation interaction. We additionally observe that both solute species experience more attractive segregation to vacancy decorated Fe-Cu interfaces. These findings suggest that mixed solute interactions and the presence of vacancies may both play an important role in assisting the formation of large solute shell regions in CRPs. We further observe that the presence of Ni and vacancies on coherent Fe-Cu interfaces both result in substantial reductions in interfacial energy density. These findings support experimental predictions and indicate both features may significantly contribute to CRP formation.

Materials modelling at the atomistic scale provides a useful way of investigating the widely debated fundamental mechanisms of hydrogen embrittlement in materials like aluminium alloys. Density functional theory based tensile tests of grain boundaries (GBs) can be used to understand the hydrogen enhanced decohesion mechanism (HEDE). The cohesive zone model was employed to understand intergranular fracture from energies obtained in electronic structure calculations at small separation increments during ab initio tensile tests of an aluminium Σ11 GB supercell with variable coverages of H. The standard rigid grain shift (RGS) test and a quasistatic sequential test, which aims to be faster and more realistic than the RGS method, were implemented. Both methods demonstrated the effects of H on the cohesive strength of the interface. The sequential method showed discrete structural changes during decohesion, along with significant deformation in general compared to the standard rigid approach. H was found to considerably weaken the GB, where increasing H content led to enhanced embrittlement such that, for the highest coverages of H, GB strength was reduced to approximately 20% of the strength of a pure Al GB—it is proposed that these results simulate HEDE. The possibility of finding H coverages required to induce this effect in real alloy systems is discussed in context by using calculations of the heat of segregation of H.

Whilst substantial progress has been made in understanding the influence that hydrides have on the mechanical properties of zirconium alloys, there is currently an urgent need for a transparent, reproducible image analysis workflow for their characterisation. In this study, an open-source software package for the analysis of hydride networks, HAPPy (Hydride Analysis Package in Python), is introduced to calculate the radial hydride fraction (RHF) and mean hydride length, as well as characterising the connectivity of the microstructure both quantitatively and qualitatively. In this study, we used the Hough line transform to calculate the orientation distribution of the hydride segments within a micrograph, and its projection on to the radial direction is used to determine the RHF. The proposed methodology is validated, and its robustness is demonstrated over a wide range of microstructures. The image processing prior to analysis as well as the projection method used has been shown to have a significant influence on the calculated RHF, highlighting the need for standardized image analysis workflows to facilitate accurate comparisons and correlations across different studies in the literature. Finally, this paper introduces a new damage susceptibility parameter termed the branch length fraction, which can be used in conjunction with a path of lowest cost algorithm to visualise the most plausible crack path as well as the connectivity evolution over an entire micrograph.

The population of dislocation defects in a crystalline material strongly influences its properties, so the ability to analyse this population in experimental samples is of great utility. As a complement to direct counting in the transmission electron microscope, quantitative analysis of x-ray diffraction line profiles is an important tool. This is an indirect approach to quantification and so requires careful validation of the physical models that underly the inferential process. Here we undertake to directly evaluate the ability of line profile analysis to quantify aspects of the dislocation and stacking fault populations by exploiting atomistic models of deformed copper single crystals. We directly analyse these models to determine exact details of the defect content (our "ground truth"). We then generate theoretical line profiles for the models and analyse them using the same procedures used in experimental analysis. This leads to inferred measures of the defect content which we are able to compare with the exact data. We show that line profile analysis is able to provide sound predictions of both dislocation density and stacking fault fraction across two orders of magnitude. We further show how the outer cut-off radius in the mean-square strain of a dislocation distribution invoked by Warren and Averbach corresponds to the cell size in an artificially constructed restrictedly-random distribution of dislocations according to the model of Wilkens. Overall, our results lend important new support to the use of line profile analysis for the quantification of line and planar defects in crystalline materials.

We present the results of first-principles calculations of selected structural and thermodynamic properties of a set of grain boundaries (GBs) in zirconium, spanning a range of misorientation angles and boundary planes. We performed plane-wave density functional theory calculations on low-sigma grain boundaries - five symmetric tilt GBs (STGBs) and three twist GBs; all with misorientation axes about [0001] and in optimised microscopic configurations - to gain insight into the associated atomistic structures. From studying the interface energetics, we found that higher GB excess volumes tended to be associated with higher GB energies. Furthermore, we examined how the interplanar spacing, volume per atom, and local atomic coordination at the GB deviated from equivalent quantities in bulk. We also defined a grain boundary width according to a threshold value of volume per atom, allowing us to rank the GBs by their relative thickness. We found the twist GBs to exhibit similar energetic and structural properties, whereas the STGBs demonstrated more variation. Our comprehensive analysis demonstrates how all five dimensions of GB space are crucial in determining properties such as the work of ideal separation and the length scale over which atoms are perturbed by the presence of the GB. So that our results can be useful for further investigations, we have published our data to a public repository (Zenodo). This data includes the optimised and initial structures, in addition to the computed interface energetics and structural properties.

Quantitative measurements of extended defects in crystalline materials are important in understanding material behaviour. X-ray line profile analysis provides a complement to direct counting in the electron microscope, but is an indirect method and requires validation. Previous studies have focused on comparing x-ray analysis to electron microscopy results. Instead, we use simulated defective material with known defect content and apply line profile analysis to calculated diffraction profiles to directly show that line profile analysis can reliably quantify dislocations and stacking faults.

Neutron irradiation progressively changes the properties of zirconium alloys: they harden and their average c/a lattice parameter ratio decreases with fluence [1, 2, 3, 4]. The bombardment by neutrons produces point defects, which evolve into dislocation loops that contribute to a non-uniform growth phenomenon called irradiation-induced growth (IIG). To gain insights into these dislocation loops in Zr we studied them using atomistic simulation. We constructed and relaxed dislocation loops of various types. We find that the energies of 〈a〉 loops on different habit planes are similar, but our results indicate that they are most likely to form on the 1st prismatic plane and then reduce their energy by rotating onto the 2nd prismatic plane. By simulating loops of different aspect ratios, we find that, based on energetics alone, the shape of 〈a〉 loops does not depend on character, and that these loops become increasingly elliptical as their size increases. Additionally, we find that interstitial 〈c/2+p〉 loops and vacancy 〈c〉 loops are both energetically feasible and so the possibility of these should be considered in future work. Our findings offer important insights into loop formation and evolution, which are difficult to probe experimentally.

Understanding the in-reactor corrosion behavior of zirconium alloys is essential for optimizing the lifetime of fuel assemblies. Recent advances in available experimental methods have enabled the characterization of oxide morphology, crystallography, and chemical heterogeneity with unprecedented detail for both autoclave and reactor formed oxides. Advanced high-resolution techniques have already improved the understanding of zirconium alloy corrosion performance. However, they are carried out on small volumes of material and require preparation of thin samples, which can lead to changes in the phase distribution in the oxide and often show varied results from different regions of a single bulk specimen. The present study utilizes high-spatial-resolution electron backscatter diffraction (EBSD) performed on bulk samples to produce spatially resolved microtexture data from nanograined zirconium oxide over a large area, which has not previously been possible. This advanced method of plan-view oxide texture analysis, alongside targeted focused ion beam cross-section measurements and substrate EBSD analysis, has revealed well-defined regions of monoclinic oxide grains that exhibit different textures depending on the orientation of the substrate grain on which they have formed. The observed variations in oxide texture have significant implications on any conclusions drawn solely from methods that are limited to the characterization of small areas—especially where sampling areas are smaller than the substrate grain size. Two competing mechanisms of oxide grain growth and nucleation are discussed, and detailed EBSD analysis illustrates a correlation between local oxide texture and corrosion rate. This analysis is performed on specimens of autoclave-tested Zircaloy-2 and ZIRLO and highlights differences in oxide texture development between the two alloys, indicating the significance of material composition and thermomechanical processing on corrosion behavior.

We use quantum mechanical ab initio simulation to inform a model which predicts the structures of coherent Cu nanoprecipitates that are thought to form in low-alloy reactor pressure vessel (RPV) steels. Using density functional theory (DFT) we calculated the interfacial energy densities of {100}, {110}, {111}, {210}, {211} and {221} orientated Fe-Cu interfaces. These energy density values were used in an optimisation model to predict low energy Cu nanoprecipitate geometries for nominal radii ranging from 1 to 5 nm. Strain states parallel to the Fe-Cu interface were calculated using an embedded atom method (EAM) potential for similarly sized Cu nanoprecipitates. Fe-Cu interfacial energy densities under equivalent strains were calculated using DFT allowing comparison with the predictions of the EAM potential. The DFT calculations revealed the lowest energy Fe-Cu interface orientation to be the {110}. Accordingly, the geometry prediction optimisations found that regardless of size the predicted Cu nanoprecipitate surface geometries were dominated by the {110} orientation. Notably, as the Cu nanoprecipitates increased in size the ratio of the surface made up of non-{110} orientations was observed to proportionally increase. This allows the nanoprecipitate to take a more spherical form so reducing its total surface area. Additionally, the Fe-Cu interface strains predicted by the EAM potential for all Cu nanoprecipitate radii are sufficiently small that they do not significantly alter the calculated interfacial energy density values. This finding suggests interfacial strain does not play a significant role in determining the morphology of Cu nanoprecipitates.

Iodine-induced stress corrosion cracking (I-SCC) has long been proposed as a primary cause of pellet cladding interaction failures in light water reactors. The I-SCC process has been studied in great detail but its precise mechanism and the influence of local microstructure remains uncertain. In this study, a large-scale investigation was undertaken of a sample produced by a novel rig for I-SCC using analytical three-dimensional characterization and then it was related to atomistic simulations describing the orientation dependence of iodine segregation and its influence on various types of boundaries. In situ monitoring capability enabled an I-SCC crack to be arrested in a compact tension specimen machined from Zircaloy-4 plate before failure, and serial sectioning by a plasma-focused ion beam allowed detailed characterization of an entire cracked region consisting of nearly 1,000 grains. By relating the crack path to the local microstructure three-dimensionally, new insights could be gained about the crack propagation during I-SCC. The crack was observed to be primarily transgranular in nature, progressing along basal planes; but away from the crack tip, a significant proportion of intergranular cracking was also observed. By careful analysis, this study was able to relate the nature of the crack progression directly to the individual grain orientations and their level of deformation. Particular grain orientations were observed to be resistant to I-SCC attack and resulted in crack deflection. The formation of twins in the vicinity of the crack was also observed and the role of twins discussed. Complementary density functional theory modeling examined the effects of iodine impurities at different positions within the microstructure. Simulations suggested that transgranular basal cleavage was energetically accessible and might be preferable to cleavage on prismatic planes, even if this would result in significant deviation of the crack path. These results are discussed with respect to the experimental observations.

We report a rapid solution-phase strategy to synthesize alloyed PtNi nanoparticles which demonstrate outstanding functionality for the oxygen reduction reaction (ORR). This one-pot coreduction colloidal synthesis results in a monodisperse population of single-crystal nanoparticles of rhombic dodecahedral morphology with Pt-enriched edges and compositions close to Pt1Ni2. We use nanoscale 3D compositional analysis to reveal for the first time that oleylamine (OAm)-aging of the rhombic dodecahedral Pt1Ni2 particles results in Ni leaching from surface facets, producing aged particles with concave faceting, an exceptionally high surface area, and a composition of Pt2Ni1. We show that the modified atomic nanostructures catalytically outperform the original PtNi rhombic dodecahedral particles by more than two-fold and also yield improved cycling durability. Their functionality for the ORR far exceeds commercially available Pt/C nanoparticle electrocatalysts, both in terms of mass-specific activities (up to a 25-fold increase) and intrinsic area-specific activities (up to a 27-fold increase).