Showing 1–27 of 27 results for author: Moody, M

A formal framework for higher-order spin models via hypergraphs, polymatroids, and the Tutte polynomial

Authors: Khallil Berrekkal, Joanna A. Ellis-Monaghan, Merijn Moody, Clélia de Mulatier

Abstract: We develop a rigorous mathematical framework for statistical mechanics models on hypergraphs, and give conditions for lifting the classical connection between Potts model partition functions and the Tutte polynomial from graphs to hypergraphs. We define hypergraphical models and their associated partition functions, and extend these to special classes of models induced by families of interaction f… ▽ More We develop a rigorous mathematical framework for statistical mechanics models on hypergraphs, and give conditions for lifting the classical connection between Potts model partition functions and the Tutte polynomial from graphs to hypergraphs. We define hypergraphical models and their associated partition functions, and extend these to special classes of models induced by families of interaction functions. For boolean interaction families, whose interaction functions map to $\{0,1\}$, we show that the partition function is determined by a combinatorial rank function, and we establish sufficient conditions for a hypergraph deletion-contraction recurrence and for when the rank function defines a polymatroid. We illustrate the theory by applying it to three hypergraph interaction families: Parity Ising, Delta Potts, and And Ising. The induced hypergraphical models are not isomorphic to each other, but the first two reduce to the same graphical Ising models. We identify three polymatroids naturally associated with hypergraphs for these models: respectively, the binary matroid of the incidence matrix over $\mathbb{F}_2$, the hypergraphical polymatroid, and the boolean polymatroid. For graphs, the first two reduce to the classical graphical matroid, and their partition functions recover the multivariate Tutte polynomial. The Tutte polynomial thus admits at least two distinct generalizations for hypergraphs, both satisfying a deletion-contraction recurrence: the Tutte polynomial of the binary matroid of the hypergraph incidence matrix, and a multivariate version of the Poincaré polynomial of the hypergraphical polymatroid. The partition functions of And Ising models are likewise multivariate versions of the Poincaré polynomial, here of the boolean polymatroid. These examples illustrate the much greater range of hypergraphical models and underscore the need for the unifying theory. △ Less

Submitted 23 July, 2026; originally announced August 2026.

MSC Class: 82B20; 05C31; 05C65; 05B35

Modeling Discrete Data with High-Order Vector Potts Models

Authors: Aaron De Clercq, Merijn Moody, Clélia de Mulatier

Abstract: Modeling high-dimensional data is challenging, yet essential to understanding many complex systems. Maximum entropy models such as Ising and Potts models have been used extensively to capture pairwise interactions from correlation patterns in data, allowing to infer graphical representations of complex systems from observations (e.g., from protein sequences or neural population activity). Recently… ▽ More Modeling high-dimensional data is challenging, yet essential to understanding many complex systems. Maximum entropy models such as Ising and Potts models have been used extensively to capture pairwise interactions from correlation patterns in data, allowing to infer graphical representations of complex systems from observations (e.g., from protein sequences or neural population activity). Recently, there has been growing interest in modeling higher-order correlation patterns involving simultaneously three or more variables. While progress has been made in binary data with high-order Ising models, we extend this framework to the more general case of discrete data. We introduce q-state spin models, a complete family of maximum entropy models that generalize the vector Potts model to include long-range and arbitrary high-order interactions. In the pairwise case, our models allow for more diverse interaction types compared to the standard vector Potts model. We discuss their statistical interpretation with examples and relate them to discrete Fourier analysis. Using a loop expansion of the partition function, we show that the statistical properties of spin models are fully captured by the algebraic structure of their interactions. We define gauge transformations under which this structure, and thus the partition function, remains invariant. Models equivalent under gauge transformations can be seen as different representations of the same abstract statistical model, despite generally having interactions of different orders, extending results from the binary case. For practical application to data analysis, we focus on a subset of models known in the binary case as Minimally Complex Models, generalizing them to discrete data. We obtain a closed-form expression for the marginal likelihood of these models, enabling fast model selection. We illustrate their use with simple real-world examples. △ Less

Submitted 2 June, 2026; originally announced June 2026.

Comments: 89 pages, 16 figures

Corrosion Evolution of T91 Steel in Static Lead-Bismuth Eutectic Under an Oxidising Environment

Authors: Minyi Zhang, Weiyue Zhou, Michael P. Short, Paul A. J. Bagot, Michael P. Moody, Felix Hofmann

Abstract: Understanding corrosion in liquid metal-cooled nuclear systems is essential in order be able to control it. While much literature exists detailing corrosion rates and mechanisms of structural materials in liquid metals, much still remains to be discovered in new regimes of temperature, chemistry, and impurity content. We focus on a less-studied set of conditions, specifically to investigate how li… ▽ More Understanding corrosion in liquid metal-cooled nuclear systems is essential in order be able to control it. While much literature exists detailing corrosion rates and mechanisms of structural materials in liquid metals, much still remains to be discovered in new regimes of temperature, chemistry, and impurity content. We focus on a less-studied set of conditions, specifically to investigate how liquid lead-bismuth eutectic (LBE) corrodes ferritic/martensitic steels under high-temperature oxidizing conditions. We find that the evolution of corrosion is determined by the formation of protection layer on the surface. The area without effective protection layer experiences oxidation along martensite grain boundaries, transitioning from intergranular attack to broader area corrosion as it progresses. The area a stable, coherent oxide scale will slow the corrosion process and then is oxidized along pre-austenite grain boundaries. Both chromium and oxygen diffusion play vital roles in this process. Most surprisingly, a layer of iron enriched body-centred cubic phase forms on the surface of LBE-corroded T91, contradicting previous studies, which reported only oxide-based surface layers. △ Less

Submitted 4 June, 2026; v1 submitted 23 February, 2026; originally announced February 2026.

Defects and Impurity Properties of VN precipitates in ARAFM Steels: Modelling using a Universal Machine Learning Potential and Experimental Validation

Authors: R. S. Stroud, C. Reynolds, T. Melichar, J. Haley, M. Carter, M. Moody, C. Hardie, D. Bowden, D. Nguyen-Manh, M. R. Wenman

Abstract: VN precipitates used to strengthen ARAFM steels for fusion applications dissolve under high Fe ion irradiation (100 dpa at 10^-3 dpa s^-1, 600 C). This study examined point defects and solute substitutions using atom probe tomography, machine learning interatomic potentials, and density functional theory. Combined with transmission electron microscopy, results show N-vacancies and substitutional C… ▽ More VN precipitates used to strengthen ARAFM steels for fusion applications dissolve under high Fe ion irradiation (100 dpa at 10^-3 dpa s^-1, 600 C). This study examined point defects and solute substitutions using atom probe tomography, machine learning interatomic potentials, and density functional theory. Combined with transmission electron microscopy, results show N-vacancies and substitutional Cr exist in VN precipitates before irradiation. Monte Carlo simulations and collision cascade simulations confirm ordered vacancies at operating temperatures help mitigate irradiation damage. However, solute additions disrupt vacancy ordering and enhance irradiation-induced damage, potentially accelerating dissolution. △ Less

Submitted 23 January, 2026; v1 submitted 25 March, 2025; originally announced March 2025.

Comments: 14 pages, 4 figures

How precisely are solute clusters in RPV steels characterized by atom probe experiments?

Authors: N. Castin, P. Klups, M. Konstantinovic, G. Bonny, M. I. Pascuet, M. Moody, L. Malerba

Abstract: Atom probe tomography (APT) is a powerful microscopy technique to characterize nano-sized clusters of the alloying elements in the bulk of reactor pressure vessel (RPV) steels. These clusters are known to dominantly determine the evolution of mechanical properties under irradiation. The results are conventionally summarized as the overall number density N and the average diameter D of the solute c… ▽ More Atom probe tomography (APT) is a powerful microscopy technique to characterize nano-sized clusters of the alloying elements in the bulk of reactor pressure vessel (RPV) steels. These clusters are known to dominantly determine the evolution of mechanical properties under irradiation. The results are conventionally summarized as the overall number density N and the average diameter D of the solute clusters identified in the material. Here, we demonstrate that these descriptors are intrinsically imprecise because they are steered by the parameters involved in the measurement and data processing, some of which are directly under the control of the operators, but some others not. Consequently, a direct comparison between data derived at different laboratories is compromised, and key trends such as the evolution with dose, are masked. This study relies on a state-of-the-art physical model for neutron irradiation in steels to make reliable estimates of the true microstructure before the measurement is performed, which allows the prediction of the population of solute clusters that are not seen by APT. We mimic APT measurements from simulated microstructures, performing a detailed study of the effects of the parameters of the analysis. We show that the values of N and D reported in the scientific literature can be matched by the predictions of our theoretical model only if specific sets of parameters are used for each laboratory that issued the measurements. We also show that if, on the contrary, all studied cases are analyzed in a consistent way, the scatter of N and D values is reduced. △ Less

Submitted 5 June, 2024; originally announced June 2024.

Testing Outlier Detection Algorithms for Identifying Early-Stage Solute Clusters in Atom Probe Tomography

Authors: R S. Stroud, A. Al-Saffar, M. Carter, M P. Moody, S. Pedrazzini, M R. Wenman

Abstract: Atom probe tomography is commonly used to study solute clustering and precipitation in materials. However, standard techniques, such as the density based spatial clustering applications with noise (DBSCAN) perform poorly with respect to small clusters of less than 25 atoms. This is a fundamental limitation of density-based clustering techniques due to the usage of Nmin, an arbitrary lower limit pl… ▽ More Atom probe tomography is commonly used to study solute clustering and precipitation in materials. However, standard techniques, such as the density based spatial clustering applications with noise (DBSCAN) perform poorly with respect to small clusters of less than 25 atoms. This is a fundamental limitation of density-based clustering techniques due to the usage of Nmin, an arbitrary lower limit placed on cluster sizes. Therefore, this paper attempts to consider atom probe clustering as an outlier detection problem of which KNN, LOF, LUNAR algorithms were tested against a simulated dataset and compared to the standard method, for a range of cluster sizes. The decision score output of the algorithms was then auto thresholded by the Karcher mean to remove human bias. Each of the major models tested outperforms DBSCAN for cluster sizes of less than 25 atoms but underperforms for sizes greater than 30 atoms. However, the new combined kNN and DBSCAN method presented was able to perform well at all cluster sizes. The combined kNN and DBSCAN method is presented as a possible new standard approach to identifying solute clusters in atom probe tomography. △ Less

Submitted 21 February, 2024; originally announced February 2024.

Characterisation of Corrosion Damage in T91/F91 steel exposed to Liquid Lead-Bismuth Eutectic

Authors: M. T. Lapington, M. Zhang, M. P. Moody, W. Y. Zhou, M. P. Short, F. Hofmann

Abstract: T91 samples were exposed to static liquid lead-bismuth eutectic (LBE) at 700°C for 250-500 hours in either an oxidising or reducing environment. Corrosion damage was characterised using electron microscopy techniques, which identified networks of LBE intrusion beneath LBE-wetted surfaces. Under reducing conditions these networks are uniformly distributed, while they appear patchier and deeper unde… ▽ More T91 samples were exposed to static liquid lead-bismuth eutectic (LBE) at 700°C for 250-500 hours in either an oxidising or reducing environment. Corrosion damage was characterised using electron microscopy techniques, which identified networks of LBE intrusion beneath LBE-wetted surfaces. Under reducing conditions these networks are uniformly distributed, while they appear patchier and deeper under oxidising conditions. The individual intrusions preferentially follow microstructural features, initially along prior-austenite grain boundaries, followed by penetration down martensite lath boundaries. Local depletion of Cr was observed within 4 μm of the intrusions and along intersecting boundaries, suggesting local Cr dissolution as the main corrosion mechanism. △ Less

Submitted 7 February, 2023; originally announced February 2023.

Comments: 14 pages, 4 figures and graphical abstract, submitted to Scripta Materialia

Report number: NUMA_154687

Effect of alloying on the microstructure, phase stability, hardness and partitioning behavior of a new dual-superlattice nickel-based superalloy

Authors: C. Rodenkirchen, A. K. Ackerman, P. M. Mignanelli, A. Cliff, G. J. Wise, J. O. Douglas, P. A. J. Bagot, M. P. Moody, M. Appleton, M. P. Ryan, M. C. Hardy, S. Pedrazzini, H. J. Stone

Abstract: A novel y-y'-y" dual-superlattice superalloy, with promising mechanical properties up to elevated temperatures was recently reported. The present work employs state of the art chemical and spatial characterization techniques to study the effect systematic additions of Mo, W and Fe and variations in Nb and Al contents have on the phase fraction, thermal stability, elemental partitioning and mechani… ▽ More A novel y-y'-y" dual-superlattice superalloy, with promising mechanical properties up to elevated temperatures was recently reported. The present work employs state of the art chemical and spatial characterization techniques to study the effect systematic additions of Mo, W and Fe and variations in Nb and Al contents have on the phase fraction, thermal stability, elemental partitioning and mechanical properties. Alloys were produced through arc melting followed by heat treatment. Multi-scale characterization techniques and hardness testing were employed to characterize their microstructure, thermal stability and mechanical properties. Alterations in such properties or in elemental partitioning behaviour were then explained through thermodynamic modelling. A modest addition of 1.8 at.% Mo had a strong effect on the microstructure and thermal stability: it minimized microstructural coarsening during heat treatments while not significantly decreasing the y' solvus temperature. A reduction of Nb by 0.6 at.%, strongly reduced the y" volume fraction, without affecting the y' volume fraction. The reduced precipitate fraction led to a significant reduction in alloy hardness. Fe, added to achieve better processability and reduced material cost, decreased the y' solvus temperature and caused rapid microstructural coarsening during heat treatments, without affecting alloy hardness. A reduction of Al by 0.4 at.%, reduced the y' volume fraction and the y' solvus temperature, also without affecting alloy hardness. The addition of 0.9 at.% W decreased the y' solvus temperature but increased both precipitate volume fractions. These data will be invaluable to optimize current alloy design and to inform future alloy design efforts. △ Less

Submitted 19 September, 2022; originally announced September 2022.

Quantifying the effect of oxygen on micro-mechanical properties of a near-alpha titanium alloy

Authors: H. M. Gardner, P. Gopon, C. M. Magazzeni, A. Radecka, K. Fox, D. Rugg, J. Wade, D. E. J. Armstrong, M. P. Moody, P. A. J. Bagot

Abstract: Atom probe tomography (APT), electron probe microanalysis (EPMA) and nanoindentation were used to characterise the oxygen-rich layer on an in-service jet engine compressor disc, manufactured from the titanium alloy TIMETAL 834. Oxygen ingress was quantified and related to changes in mechanical properties through nanoindentation studies. The relationship between oxygen concentration, microstructure… ▽ More Atom probe tomography (APT), electron probe microanalysis (EPMA) and nanoindentation were used to characterise the oxygen-rich layer on an in-service jet engine compressor disc, manufactured from the titanium alloy TIMETAL 834. Oxygen ingress was quantified and related to changes in mechanical properties through nanoindentation studies. The relationship between oxygen concentration, microstructure, crystal orientation and hardness has been explored through correlative hardness mapping, EPMA and electron backscatter diffraction (EBSD). The role of microstructure on oxygen ingress has been studied and oxygen ingress along a potential alpha/ beta interface was directly observed on the nanoscale using APT. △ Less

Submitted 10 September, 2020; originally announced September 2020.

Atom probe characterisation of segregation driven Cu and Mn-Ni-Si co-precipitation in neutron irradiated T91 tempered-martensitic steel

Authors: T. P. Davis, M. A. Auger, N. Almirall, P. Hosemann, G. R. Odette, P. A. J. Bagot, M. P. Moody, D. E. J. Armstrong

Abstract: The T91 grade and similar 9Cr tempered-martensitic steels (also known as ferritic-martensitic) are leading candidate structural alloys for fast fission nuclear and fusion power reactors. At low temperatures (300 to 400 $^\circ$C) neutron irradiation hardens and embrittles these steels, therefore it is important to investigate the origin of this mode of life limiting property degradation. T91 steel… ▽ More The T91 grade and similar 9Cr tempered-martensitic steels (also known as ferritic-martensitic) are leading candidate structural alloys for fast fission nuclear and fusion power reactors. At low temperatures (300 to 400 $^\circ$C) neutron irradiation hardens and embrittles these steels, therefore it is important to investigate the origin of this mode of life limiting property degradation. T91 steel specimens were separately neutron irradiated to 2.14 dpa at 327 $^\circ$C and 8.82 dpa at 377 $^\circ$C in the Idaho National Laboratory Advanced Test Reactor. Atom probe tomography was used to investigate the segregation driven formation of Mn-Ni-Si-rich (MNSPs) and Cu-rich (CRP) co-precipitates. The precipitates increase in size and, slightly, in volume fraction at the higher irradiation temperature and dose, while their corresponding compositions were very similar, falling near the Si(Mn,Ni) phase field in the Mn-Ni-Si projection of the Fe-based quaternary phase diagram. While the structure of the precipitates has not been characterized, this composition range is distinctly different than that of the typically cited G-phase. The precipitates are composed of CRP with MNSP appendages. Such features are often observed in neutron irradiated reactor pressure vessel (RPV) steels. However, the Si, Ni, Mn, P and Cu solutes concentrations are lower in the T91 than in typical RPV steels. Thus, in T91 precipitation primarily takes place in solute segregated regions of line and loop dislocations. These results are consistent with the model for radiation induced segregation driven precipitation of MNSPs proposed by Ke et al. Cr-rich alpha prime ($α$') phase formation was not observed. △ Less

Submitted 21 July, 2020; originally announced July 2020.

Comments: Pre-print (not peer reviewed)

DF-Fit : A robust algorithm for detection of crystallographic information in Atom Probe Tomography data

Authors: Daniel Haley, Paul A. J. Bagot, Michael P. Moody

Abstract: We report on a new algorithm for detection of crystallographic information in 3D, as retained in Atom Probe Tomography (APT), with improved robustness and signal detection performance. The algorithm is underpinned by 1D distribution functions, as per existing algorithms, but eliminates an unnecessary parameter as compared to current methods. By examining traditional distribution functions in an au… ▽ More We report on a new algorithm for detection of crystallographic information in 3D, as retained in Atom Probe Tomography (APT), with improved robustness and signal detection performance. The algorithm is underpinned by 1D distribution functions, as per existing algorithms, but eliminates an unnecessary parameter as compared to current methods. By examining traditional distribution functions in an automated fashion in real space, rather than using Fourier transform approaches, we utilise an error metric based upon the expected value for a spatially random distribution for detecting crystallography. We show cases where the metric is able to successfully obtain orientation information, and show that it can function with high levels of additive and displacive background noise. We additionally compare this metric to Fourier transform methods, showing fewer artefacts when examining simulated datasets. An extension of the approach is used to aid the automatic detection of high-quality data regions within an entire dataset, albeit with a large increase in computational cost. This extension is demonstrated on acquired Aluminium and Tungsten APT datasets, and shown to be able to discern regions of the data which have relatively improved spatial data quality. Finally, this program has been made available for use in other laboratories undertaking their own analyses. △ Less

Submitted 17 January, 2019; originally announced January 2019.

A gas-phase reaction cell for modern Atom Probe systems

Authors: Daniel Haley, Ingrid McCarrol, Paul. A. J. Bagot, Julie. M. Cairney, Michael P. Moody

Abstract: In this work, we demonstrate a new system for the examination of gas interactions with surfaces via Atom Probe Tomography. This system provides the capability to examine the surface and subsurface interactions of gases with a wide range of specimens, as well as a selection of input gas types. This system has been primarily developed to aid the investigation of hydrogen interactions with metallurgi… ▽ More In this work, we demonstrate a new system for the examination of gas interactions with surfaces via Atom Probe Tomography. This system provides the capability to examine the surface and subsurface interactions of gases with a wide range of specimens, as well as a selection of input gas types. This system has been primarily developed to aid the investigation of hydrogen interactions with metallurgical samples, to better understand the phenomenon of hydrogen embrittlement. In its current form, it is able to operate at pressures from 10^-6 to 1000 mbar (abs), can operate using a variety of gasses, and is equipped with heating and cryogenic quenching capabilities. We use this system to examine the interaction of hydrogen with Pd, as well as the interaction of water vapour and oxygen in Mg samples. △ Less

Submitted 17 January, 2019; originally announced January 2019.

Journal ref: Microsc Microanal 25 (2019) 410-417

On the effect of Ti on Oxidation Behaviour of a Polycrystalline Nickel-based Superalloy

Authors: S. Pedrazzini, B. S. Rowlands, A. Turk, I. M. D. Parr, M. C. Hardy, P. A. J. Bagot, M. P Moody, E. Galindo-Nava, H. J. Stone

Abstract: Titanium is commonly added to nickel superalloys but has a well-documented detrimental effect on oxidation resistance. The present work constitutes the first atomistic-scale quantitative measurements of grain boundary and bulk compositions in the oxide scale of a current generation polycrystalline nickel superalloy performed through atom probe tomography. Titanium was found to be particularly detr… ▽ More Titanium is commonly added to nickel superalloys but has a well-documented detrimental effect on oxidation resistance. The present work constitutes the first atomistic-scale quantitative measurements of grain boundary and bulk compositions in the oxide scale of a current generation polycrystalline nickel superalloy performed through atom probe tomography. Titanium was found to be particularly detrimental to oxide scale growth through grain boundary diffusion. △ Less

Submitted 24 October, 2018; originally announced October 2018.

Reflections on the analysis of interfaces and grain boundaries by atom probe tomography

Authors: Benjamin M. Jenkins, Frédéric Danoix, Mohamed Gouné, Paul. A. J. Bagot, Zirong Peng, Michael P. Moody, Baptiste Gault

Abstract: Interfaces play critical roles in materials, and are usually both structurally and compositionally complex microstructural features. The precise characterization of their nature in three-dimensions at the atomic-scale is one of the grand challenges for microscopy and microanalysis, as this information is crucial to establish structure-property relationships. Atom probe tomography is well-suited to… ▽ More Interfaces play critical roles in materials, and are usually both structurally and compositionally complex microstructural features. The precise characterization of their nature in three-dimensions at the atomic-scale is one of the grand challenges for microscopy and microanalysis, as this information is crucial to establish structure-property relationships. Atom probe tomography is well-suited to analyzing the chemistry of interfaces at the nanoscale. However, optimizing such microanalysis of interfaces requires great care in the implementation across all aspects of the technique, from specimen preparation to data analysis and ultimately the interpretation this information. This article provides critical perspectives on key aspects pertaining to spatial resolution limits and the issues with compositional analysis that can limit the quantification of interface measurements. Here, we use the example of grain boundaries in steels, however the results are applicable for the characterization of grain boundaries and transformation interfaces in a very wide range of industrially relevant engineering materials. △ Less

Submitted 29 October, 2019; v1 submitted 11 June, 2018; originally announced June 2018.

The Kinetics of Primary Alpha Plate Growth in Titanium Alloys

Authors: Abigail K Ackerman, Alexander J. Knowles, Hazel M. Gardner, Andre A N Nemeth, Ioannis Bantounas, Anna Radecka, Michael P. Moody, Paul A. J. Bagot, Roger C. Reed, David Rugg, David Dye

Abstract: The kinetics of primary alpha-Ti colony/Widmanstatten plate growth from the beta are examined, comparing model to experiment. The plate growth velocity depends sensitively both on the diffusivity D(T) of the rate-limiting species and on the supersaturation around the growing plate. These result in a maxima in growth velocity around 40 K below the transus, once sufficient supersaturation is availab… ▽ More The kinetics of primary alpha-Ti colony/Widmanstatten plate growth from the beta are examined, comparing model to experiment. The plate growth velocity depends sensitively both on the diffusivity D(T) of the rate-limiting species and on the supersaturation around the growing plate. These result in a maxima in growth velocity around 40 K below the transus, once sufficient supersaturation is available to drive plate growth. In Ti-6246, the plate growth velocity was found to be around 0.32 um min-1 at 850 oC, which was in good agreement with the model prediction of 0.36 um min-1 . The solute field around the growing plates, and the plate thickness, was found to be quite variable, due to the intergrowth of plates and soft impingement. This solute field was found to extend to up to 30 nm, and the interface concentration in the beta was found to be around 6.4 at.% Mo. It was found that increasing O content will have minimal effect on the plate lengths expected during continuous cooling; in contrast, Mo approximately doubles the plate lengths obtained for every 2 wt.% Mo reduction. Alloys using V as the beta stabiliser instead of Mo are expected to have much faster plate growth kinetics at nominally equivalent V contents. These findings will provide a useful tool for the integrated design of alloys and process routes to achieve tailored microstructures. △ Less

Submitted 31 July, 2019; v1 submitted 24 May, 2018; originally announced May 2018.

Comments: Revised version resubmitted to journal

Characterizing solute hydrogen and hydrides in pure and alloyed titanium at the atomic scale

Authors: Yanhong Chang, Andrew J. Breen, Zahra Tarzimoghadam, Philipp Kürnsteiner, Hazel Gardner, Abigail Ackerman, Anna Radecka, Paul A. J. Bagot, Wenjun Lu, Tong Li, Eric A. Jägle, Michael Herbig, Leigh T. Stephenson, Michael P. Moody, David Rugg, David Dye, Dirk Ponge, Dierk Raabe, Baptiste Gault

Abstract: Ti has a high affinity for hydrogen and is a typical hydride formers. Ti-hydride are brittle phases which probably cause premature failure of Ti-alloys. Here, we used atom probe tomography and electron microscopy to investigate the hydrogen distribution in a set of specimens of commercially pure Ti, model and commercial Ti-alloys. Although likely partly introduced during specimen preparation with… ▽ More Ti has a high affinity for hydrogen and is a typical hydride formers. Ti-hydride are brittle phases which probably cause premature failure of Ti-alloys. Here, we used atom probe tomography and electron microscopy to investigate the hydrogen distribution in a set of specimens of commercially pure Ti, model and commercial Ti-alloys. Although likely partly introduced during specimen preparation with the focused-ion beam, we show formation of Ti-hydrides along α grain boundaries and α/\b{eta} phase boundaries in commercial pure Ti and α+\b{eta} binary model alloys. No hydrides are observed in the α phase in alloys with Al addition or quenched-in Mo supersaturation. △ Less

Submitted 11 March, 2018; originally announced March 2018.

Comments: Published in Acta Materialia in 2018

Extending Continuum Models for Atom Probe Simulation

Authors: Daniel Haley, Paul A. J. Bagot, Michael P. Moody

Abstract: This work describes extensions to existing level-set algorithms developed for application within the field of Atom Probe Tomography (APT). We present a new simulation tool for the simulation of 3D tomographic volumes, using advanced level set methods. By combining narrow-band, B-Tree and particle-tracing approaches from level-set methods, we demonstrate a practical tool for simulating shape change… ▽ More This work describes extensions to existing level-set algorithms developed for application within the field of Atom Probe Tomography (APT). We present a new simulation tool for the simulation of 3D tomographic volumes, using advanced level set methods. By combining narrow-band, B-Tree and particle-tracing approaches from level-set methods, we demonstrate a practical tool for simulating shape changes to APT samples under applied electrostatic fields, in three dimensions. This work builds upon our previous studies by allowing for non-axially symmetric solutions, with minimal loss in computational speed, whilst retaining numerical accuracy. △ Less

Submitted 27 February, 2018; originally announced February 2018.

Atom Probe Analysis of Ex Situ Gas-Charged Stable Hydrides

Authors: Daniel Haley, Paul A. J. Bagot, Michael P. Moody

Abstract: In this work, we report on the atom probe tomography analysis of two metallic hydrides formed by pressurized charging using an ex situ hydrogen charging cell, in the pressure range of 200-500 kPa (2-5 bar). Specifically we report on the deuterium charging of Pd/Rh and V systems. Using this ex situ system, we demonstrate the successful loading and subsequent atom probe analysis of deuterium within… ▽ More In this work, we report on the atom probe tomography analysis of two metallic hydrides formed by pressurized charging using an ex situ hydrogen charging cell, in the pressure range of 200-500 kPa (2-5 bar). Specifically we report on the deuterium charging of Pd/Rh and V systems. Using this ex situ system, we demonstrate the successful loading and subsequent atom probe analysis of deuterium within a Pd/Rh alloy, and demonstrate that deuterium is likely present within the oxide-metal interface of a native oxide formed on vanadium. Through these experiments, we demonstrate the feasibility of ex situ hydrogen analysis for hydrides via atom probe tomography, and thus a practical route to three-dimensional imaging of hydrogen in hydrides at the atomic scale. △ Less

Submitted 17 November, 2017; originally announced November 2017.

Journal ref: Microscopy and Microanalysis, 23,2, 2017,pp. 307-313

A nexus between 3D atomistic data hybrids derived from atom probe microscopy and computational materials science: a new analysis of solute clustering in Al-alloys

Authors: Baptiste Gault, Xiang Yuan Cui, Michael P. Moody, Anna V. Ceguerra, Andrew J. Breen, Ross K. W. Marceau, Simon P. Ringer

Abstract: Solute clusters affect the physical properties of alloys. Knowledge of the atomic structure of solute clusters is a prerequisite for material optimisation. In this study, solute clusters in a rapid-hardening Al-Cu-Mg alloy were characterised by a combination of atom probe tomography and density functional theory, making use of a hybrid data type that combines lattice rectification and data complet… ▽ More Solute clusters affect the physical properties of alloys. Knowledge of the atomic structure of solute clusters is a prerequisite for material optimisation. In this study, solute clusters in a rapid-hardening Al-Cu-Mg alloy were characterised by a combination of atom probe tomography and density functional theory, making use of a hybrid data type that combines lattice rectification and data completion to directly input experimental data into atomistic simulations. The clusters input to the atomistic simulations are thus observed experimentally, reducing the number of possible configurations. Our results show that spheroidal, compact clusters are more energetically favourable and more abundant. △ Less

Submitted 9 January, 2017; originally announced January 2017.

Comments: 16 pages, 4 figures, published in Scripta Materialia, Jan 2017

Behavior of molecules and molecular ions near a field emitter

Authors: Baptiste Gault, David W. Saxey, Michael V. Ashton, Susan B. Sinnott, Ann N. Chiaramonti, Michael P. Moody, Daniel K. Schreiber

Abstract: The cold emission of particles from surfaces under intense electric fields is a process which underpins a variety of applications including atom probe tomography (APT), an analytical microscopy technique with near-atomic spatial resolution. Increasingly relying on fast laser pulsing to trigger the emission, APT experiments often incorporate the detection of molecular ions emitted from the specimen… ▽ More The cold emission of particles from surfaces under intense electric fields is a process which underpins a variety of applications including atom probe tomography (APT), an analytical microscopy technique with near-atomic spatial resolution. Increasingly relying on fast laser pulsing to trigger the emission, APT experiments often incorporate the detection of molecular ions emitted from the specimen, in particular from covalently or ionically bonded materials. Notably, it has been proposed that neutral molecules can also be emitted during this process. However, this remains a contentious issue. To investigate the validity of this hypothesis, a careful review of the literature is combined with the development of new methods to treat experimental APT data, the modelling of ion trajectories, and the application of density-functional theory (DFT) simulations to derive molecular ion energetics. It is shown that the direct thermal emission of neutral molecules is extremely unlikely. However, neutrals can still be formed in the course of an APT experiment by dissociation of metastable molecular ions. △ Less

Submitted 7 February, 2016; v1 submitted 29 November, 2015; originally announced November 2015.

Atom probe microscopy investigation of Mg site occupancy within δ precipitates in an Al Mg Li alloy

Authors: Baptiste Gault, Xiang Yuan Cui, Michael P. Moody, Frederic De Geuser, Christophe Sigli, Simon P. Ringer, Alexis Deschamps

Abstract: The composition and site occupancy of Mg within ordered δ precipitates in a model Al Mg Li alloy have been characterized by atom probe microscopy and first-principles simulations. The concentration in the precipitates is found to be almost the same as that of the matrix, however, we show evidence that Mg partitions to the sites normally occupied by Li in the L12 structure. Density functional calcu… ▽ More The composition and site occupancy of Mg within ordered δ precipitates in a model Al Mg Li alloy have been characterized by atom probe microscopy and first-principles simulations. The concentration in the precipitates is found to be almost the same as that of the matrix, however, we show evidence that Mg partitions to the sites normally occupied by Li in the L12 structure. Density functional calculations demonstrate that this partition is energetically favorable, in agreement with experimental results. △ Less

Submitted 10 October, 2015; originally announced October 2015.

Journal ref: Scripta Materialia, Volume 66, Issue 11, June 2012, Pages 903 906

Spatial resolution in atom probe tomography

Authors: Baptiste Gault, Michael P. Moody, Frederic de Geuser, Alex La Fontaine, Leigh T. Stephenson, Daniel Haley, Simon P. Ringer

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

Submitted 10 October, 2015; originally announced October 2015.

Journal ref: Microscopy & Microanalysis 16, 99 110 2010

Estimation of the reconstruction parameters for Atom Probe Tomography

Authors: Baptiste Gault, Frederic De Geuser, Leigh T. Stephenson, Michael P. Moody, Barry C. Muddle, Simon P. Ringer

Abstract: The application of wide field-of-view detection systems to atom probe experiments emphasizes the importance of careful parameter selection in the tomographic reconstruction of the analysed volume, as the sensitivity to errors rises steeply with increases in analysis dimensions. In this paper, a self-consistent method is presented for the systematic determination of the main reconstruction paramete… ▽ More The application of wide field-of-view detection systems to atom probe experiments emphasizes the importance of careful parameter selection in the tomographic reconstruction of the analysed volume, as the sensitivity to errors rises steeply with increases in analysis dimensions. In this paper, a self-consistent method is presented for the systematic determination of the main reconstruction parameters. In the proposed approach, the compression factor and the field factor are determined using geometrical projections from the desorption images. A 3D Fourier transform is then applied to a series of reconstructions and, comparing to the known material crystallography, the efficiency of the detector is estimated. The final results demonstrate a significant improvement in the accuracy of the reconstructed volumes. △ Less

Submitted 10 October, 2015; originally announced October 2015.

Journal ref: Microscopy and Microanalysis Volume 14 Issue 04 2008 Pages 296 305

Dynamic reconstruction for atom probe tomography

Authors: Baptiste Gault, Shyeh Tjing Loi, Vicente J. Araullo-Peters, Leigh T. Stephenson, Michael P. Moody, Sachin L. Shrestha, Ross K. W. Marceau, Lan Yao, Julie M. Cairney, Simon P. Ringer

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

Submitted 9 October, 2015; originally announced October 2015.

Comments: 16 pages, 6 figures

Journal ref: Ultramicroscopy Volume 111 Issue 11 November 2011 Pages 1619 1624

Structural, electronic, and optical properties of $m$-plane InGaN/GaN quantum wells: Insights from experiment and atomistic theory

Authors: S. Schulz, D. P. Tanner, E. P. O'Reilly, M. A. Caro, T. L. Martin, P. A. J. Bagot, M. P. Moody, F. Tang, J. T. Griffiths, F. Oehler, M. J. Kappers, R. A. Oliver, C. J. Humphreys, D. Sutherland, M. J. Davies, P. Dawson

Abstract: In this paper we present a detailed analysis of the structural, electronic, and optical properties of an $m$-plane (In,Ga)N/GaN quantum well structure grown by metal organic vapor phase epitaxy. The sample has been structurally characterized by x-ray diffraction, scanning transmission electron microscopy, and 3D atom probe tomography. The optical properties of the sample have been studied by photo… ▽ More In this paper we present a detailed analysis of the structural, electronic, and optical properties of an $m$-plane (In,Ga)N/GaN quantum well structure grown by metal organic vapor phase epitaxy. The sample has been structurally characterized by x-ray diffraction, scanning transmission electron microscopy, and 3D atom probe tomography. The optical properties of the sample have been studied by photoluminescence (PL), time-resolved PL spectroscopy, and polarized PL excitation spectroscopy. The PL spectrum consisted of a very broad PL line with a high degree of optical linear polarization. To understand the optical properties we have performed atomistic tight-binding calculations, and based on our initial atom probe tomography data, the model includes the effects of strain and built-in field variations arising from random alloy fluctuations. Furthermore, we included Coulomb effects in the calculations. Our microscopic theoretical description reveals strong hole wave function localization effects due to random alloy fluctuations, resulting in strong variations in ground state energies and consequently the corresponding transition energies. This is consistent with the experimentally observed broad PL peak. Furthermore, when including Coulomb contributions in the calculations we find strong exciton localization effects which explain the form of the PL decay transients. Additionally, the theoretical results confirm the experimentally observed high degree of optical linear polarization. Overall, the theoretical data are in very good agreement with the experimental findings, highlighting the strong impact of the microscopic alloy structure on the optoelectronic properties of these systems. △ Less

Submitted 1 December, 2015; v1 submitted 23 September, 2015; originally announced September 2015.

Comments: 13 pages, 12 figures

From solid solution to cluster formation of Fe and Cr in $α$-Zr

Authors: P. A. Burr, M. R. Wenman, B. Gault, M. P. Moody, M. Ivermark, M. J. D. Rushton, M. Preuss, L. Edwards, R. W. Grimes

Abstract: To understand the mechanisms by which Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, a combination of experimental (atom probe tomography, x-ray diffraction and thermoelectric power measurements) and modelling (density functional theory) techniques are employed to investigate the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys. Cr occupies both… ▽ More To understand the mechanisms by which Fe and Cr additions increase the corrosion rate of irradiated Zr alloys, a combination of experimental (atom probe tomography, x-ray diffraction and thermoelectric power measurements) and modelling (density functional theory) techniques are employed to investigate the non-equilibrium solubility and clustering of Fe and Cr in binary Zr alloys. Cr occupies both interstitial and substitutional sites in the α-Zr lattice, Fe favours interstitial sites, and a low-symmetry site that was not previously modelled is found to be the most favourable for Fe. Lattice expansion as a function of alloying concentration (in the dilute regime) is strongly anisotropic for Fe additions, expanding the $c$-axis while contracting the $a$-axis. Defect clusters are observed at higher solution concentrations, which induce a smaller amount of lattice strain compared to the dilute defects. In the presence of a Zr vacancy, all two-atom clusters are more soluble than individual point defects and as many as four Fe or three Cr atoms could be accommodated in a single Zr vacancy. The Zr vacancy is critical for the increased solubility of defect clusters, the implications for irradiation induced microstructure changes in Zr alloys are discussed. △ Less

Submitted 10 October, 2015; v1 submitted 27 January, 2015; originally announced January 2015.

Comments: 15 pages including figure, 9 figures, 2 tables. Submitted for publication in Acta Mater, Journal of Nuclear Materials (2015)

Journal ref: Journal of Nuclear Materials, 467 (2015) 320-331

Direct observation of local K variation and its correlation to electronic inhomogeneity in (Ba1-xKx)Fe2As2 Pnictide

Authors: W. K. Yeoh, B. Gault, X. Y. Cui, C. Zhu, M. P. Moody, L. Li, R. K. Zheng, W. X Li, X. L. Wang, S. X. Dou, C. T. Lin, S. P. Ringer

Abstract: Local fluctuations in the distribution of dopant atoms are a suspected cause of nanoscale electronic disorder or phase separation observed within the pnictide superconductors. Atom probe tomography results present the first direct observations of dopant nano-clustering in a K-doped 122-phase pnictides. First-principles calculations suggest the coexistence of static magnetism and superconductivity… ▽ More Local fluctuations in the distribution of dopant atoms are a suspected cause of nanoscale electronic disorder or phase separation observed within the pnictide superconductors. Atom probe tomography results present the first direct observations of dopant nano-clustering in a K-doped 122-phase pnictides. First-principles calculations suggest the coexistence of static magnetism and superconductivity on a lattice parameter length scale over a large range of doping concentrations. Collectively, our results provide evidence for a mixed scenario of phase coexistence and phase separation originating from variation of dopant atom experiments distroibutions. △ Less

Submitted 18 May, 2011; v1 submitted 3 April, 2011; originally announced April 2011.

Comments: 4 pages, 4 figures and 1 table, accepted by Physical Review Letter 2011

Journal ref: Phys. Rev. Lett. 106, 247002 (2011)