arXiv subjects

Dierk Raabe

Publications and source records attributed to Dierk Raabe.

At least 55 records · Page 3Linked to original sources

arXiv2022

Combined modeling and experimental characterization of Mn segregation and spinodal decomposition along dislocation lines in Fe-Mn alloys

Mn enrichment at dislocations in Fe-Mn alloys due to segregation and spinodal decomposition along the dislocation line is studied via modeling and experimental characterization. To model these phenomena, both finite-deformation microscopic phase-field chemomechanics (MPFCM) and Monte Carlo molecular dynamics (MCMD) are employed. MPFCM calibration is carried out with the same Fe-Mn MEAM-based potential used in MCMD, as well as CALPHAD data. Simulation results for Mn segregation to, and spinodal decomposition along, straight screw and edge dislocations as well as dislocation loops, are compared with characterization results from atom probe tomography (APT) for two Fe-Mn alloy compositions. In contrast to classical Volterra dislocation theory, both MPFCM and MCMD predict a non-zero hydrostatic stress field in screw cores. Being of much smaller magnitude than the hydrostatic stress in straight edge cores, much less solute segregates to screw than to edge cores. In addition, the segregated amount in screw cores is below the critical concentration of 0.157 for the onset of spinodal decomposition along the line. Results from MPFCM-based modeling imply that the concentration dependence of the solute misfit distortion and resulting dependence of the elastic energy density on concentration have the strongest effect. The maximum amount of Mn segregating to straight edge dislocations predicted by MPFCM agrees well with APT results. The MPFCM model for Fe-Mn predicts little or no variation in Mn concentration along a straight dislocation line, in contrast to the APT results. As shown by the example of a dislocation loop in the current work, a change in the hydrostatic stress along the line due to changing character of dislocation does lead to a corresponding variation in Mn concentration. Such a variation in Mn concentration can also then be expected along a dislocation line with kinks or jogs.

cond-mat.mtrl-sci↗

arXiv2022

A mechanically strong and ductile soft magnet with extremely low coercivity

Soft magnetic materials (SMMs) serve in electrical applications and sustainable energy supply, allowing magnetic flux variation in response to changes in applied magnetic field, at low energy loss1. The electrification of transport, households and manufacturing leads to an increase in energy consumption due to hysteresis losses2. Therefore, minimizing coercivity, which scales these losses, is crucial3. Yet, meeting this target alone is not enough: SMMs in electrical engines must withstand severe mechanical loads, i.e., the alloys need high strength and ductility4. This is a fundamental design challenge, as most methods that enhance strength introduce stress fields that can pin magnetic domains, thus increasing coercivity and hysteretic losses5. Here, we introduce an approach to overcome this dilemma. We have designed a Fe-Co-Ni-Ta-Al multicomponent alloy with ferromagnetic matrix and paramagnetic coherent nanoparticles (~91 nm size, ~55% volume fraction). They impede dislocation motion, enhancing strength and ductility. Their small size, low coherency and small magnetostatic energy create an interaction volume below the magnetic domain wall width, leading to minimal domain wall pinning, thus maintaining the soft magnetic properties. The alloy has a tensile strength of 1336 MPa at 54% tensile elongation, extremely low coercivity of 78 A/m (<1 Oe), moderate saturation magnetization of 100 Am2/kg, and high electrical resistivity of 103 μΩ u Ohm cm.

cond-mat.mtrl-sci↗

arXiv2022

Accelerating phase-field-based simulation via machine learning

Phase-field-based models have become common in material science, mechanics, physics, biology, chemistry, and engineering for the simulation of microstructure evolution. Yet, they suffer from the drawback of being computationally very costly when applied to large, complex systems. To reduce such computational costs, a Unet-based artificial neural network is developed as a surrogate model in the current work. Training input for this network is obtained from the results of the numerical solution of initial-boundary-value problems (IBVPs) based on the Fan-Chen model for grain microstructure evolution. In particular, about 250 different simulations with varying initial order parameters are carried out and 200 frames of the time evolution of the phase fields are stored for each simulation. The network is trained with 90% of this data, taking the $i$-th frame of a simulation, i.e. order parameter field, as input, and producing the $(i+1)$-th frame as the output. Evaluation of the network is carried out with a test dataset consisting of 2200 microstructures based on different configurations than originally used for training. The trained network is applied recursively on initial order parameters to calculate the time evolution of the phase fields. The results are compared to the ones obtained from the conventional numerical solution in terms of the errors in order parameters and the system's free energy. The resulting order parameter error averaged over all points and all simulation cases is 0.005 and the relative error in the total free energy in all simulation boxes does not exceed 1%.

cond-mat.mtrl-sci↗

arXiv2022

Phase-Field Modeling of Coupled Brittle-Ductile Fracture in Aluminum Alloys

Fracture in aluminum alloys with precipitates involves at least two mechanisms, namely, ductile fracture of the aluminum-rich matrix and brittle fracture of the precipitates. In this work, a coupled crystal plasticity-phase field model for mixed ductile-brittle failure modes is formulated and used to investigate the effect of precipitate morphology and size distribution on damage evolution in aluminum alloys. A thermodynamically consistent framework for elastic and plastic work dissipation in the fracture process zone is used to formulate the coupled constitutive behavior for brittle and ductile damage, respectively. Representative Volume Elements (RVE) with varying particle morphology and orientation were generated and their uni-axial loading was simulated to assess the damage resistance of the different model microstructures. For critical energy release rate $G_c$ values of the aluminum matrix ranging from 4 to 8~Jm$^{-2}$ for single crystals and from 10 to 16~Jm$^{-2}$ for polycrystals, the model predicts a change in failure modes from particle debonding to cracking followed by ductile matrix failure. The change of particle failure mechanism as a result of increased $G_c$ is observed for both, single and polycrystalline model microstructures. For the case of particle debonding, microstructures with circular or ellipsoidal particles (with the major axis perpendicular to the loading direction) show a higher ductility and fracture work compared to the other studied cases. In the case of particle cracking, microstructures with ellipsoidal particles aligned parallel to the loading axis show a higher ductility and fracture work among the investigated cases. The simulations qualitatively reproduce the experimentally observed particle failure mechanisms (cracking and debonding) for two different matrix alloy classes (commercially pure and 2xxx alloys) reinforced with ceramic particles.

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arXiv2022

Machine learning-enabled high-entropy alloy discovery

High-entropy alloys are solid solutions of multiple principal elements, capable of reaching composition and feature regimes inaccessible for dilute materials. Discovering those with valuable properties, however, relies on serendipity, as thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. Here, we propose an active-learning strategy to accelerate the design of novel high-entropy Invar alloys in a practically infinite compositional space, based on very sparse data. Our approach works as a closed-loop, integrating machine learning with density-functional theory, thermodynamic calculations, and experiments. After processing and characterizing 17 new alloys (out of millions of possible compositions), we identified 2 high-entropy Invar alloys with extremely low thermal expansion coefficients around 2*10-6 K-1 at 300 K. Our study thus opens a new pathway for the fast and automated discovery of high-entropy alloys with optimal thermal, magnetic and electrical properties.

cond-mat.mtrl-sci↗

arXiv2022

Green steel at its crossroads: hybrid hydrogen-based reduction of iron ores

Iron- and steelmaking cause ~7% of the global CO2 emissions, due to the use of carbon for the reduction of iron ores. Replacing carbon by hydrogen as the reductant offers a pathway to reduce emissions. However, production of hydrogen using renewable energy will remain a bottlenecks, because making the annual crude steel production of 1.8 billion tons sustainable requires a minimum amount of ~97 million tons of green hydrogen per year. Another fundamental aspect to make ironmaking sector more sustainable lies in an optimal utilization of green hydrogen and energy, thus reducing efforts for costly in-process hydrogen recycling. We therefore demonstrate here how the efficiency in hydrogen and energy consumption during iron ore reduction can be dramatically improved by the knowledge-based combination of two technologies: partially reducing the ore at low temperature via solid-state direct reduction (DR) to a kinetically defined degree, and subsequently melting and completely transforming it to iron under a reducing plasma (i.e. via hydrogen plasma reduction, HPR). Results suggest that an optimal transition point between these two technologies occurs where their efficiency in hydrogen utilization is equal. We found that the reduction of hematite through magnetite into wustite via DR is clean and efficient, but it gets sluggish and inefficient when iron forms at the outermost layers of the iron ore pellets. Conversely, HPR starts violent and unstable with arc delocalization, but proceeds smoothly and efficiently when processing semi-reduced oxides. We performed hybrid reduction experiments by partially reducing hematite pellets via DR at 700°C to 38% global reduction (using a standard thermogravimetry system) and subsequently transferring them to HPR, conducted with a gas mixture of Ar-10%H2 in an arc-melting furnace, to achieve conversion into liquid iron.

cond-mat.mtrl-sci↗

arXiv2022

Hierarchical nature of hydrogen-based direct reduction of iron oxides

Fossil-free ironmaking is indispensable for reducing massive anthropogenic CO2 emissions in the steel industry. Hydrogen-based direct reduction (HyDR) is among the most attractive solutions for green ironmaking, with high technology readiness. The underlying mechanisms governing this process are characterized by a complex interaction of several chemical (phase transformations), physical (transport), and mechanical (stresses) phenomena. Their interplay leads to rich microstructures, characterized by a hierarchy of defects ranging across several orders of magnitude in length, including vacancies, dislocations, internal interfaces, and free surfaces in the form of cracks and pores. These defects can all act as reaction, nucleation, and diffusion sites, shaping the overall reduction kinetics. A clear understanding of the roles and interactions of these dynamically-evolving nano-/microstructure features is missing. Gaining better insights in these effects could enable improved access to the microstructure-based design of more efficient HyDR methods, with potentially high impact on the urgently needed decarbonization in the steel industry.

cond-mat.mtrl-sci↗

arXiv2022

Hydrogen trapping and embrittlement in high-strength Al-alloys

Ever more stringent regulations on greenhouse gas emissions from transportation motivate efforts to revisit materials used for vehicles. High-strength Al-alloys often used in aircrafts could help reduce the weight of automobiles, but are susceptible to environmental degradation. Hydrogen (H) "embrittlement" is often pointed as the main culprit, however, the mechanisms underpinning failure are elusive: atomic-scale analysis of H inside an alloy remains a challenge, and this prevents deploying alloy design strategies to enhance the materials' durability. Here we successfully performed near-atomic scale analysis of H trapped in second-phase particles and at grain boundaries in a high-strength 7xxx Al-alloy. We used these observations to guide atomistic ab-initio calculations which show that the co-segregation of alloying elements and H favours grain boundary decohesion, while the strong partitioning of H into the second-phases removes solute H from the matrix, hence preventing H-embrittlement. Our insights further advance the mechanistic understanding of H-assisted embrittlement in Al-alloys, emphasizing the role of H-traps in retarding cracking and guiding new alloy design.

cond-mat.mtrl-sci↗

arXiv2021

A cracking oxygen story: a new view of stress corrosion cracking in titanium alloys

Titanium alloys can suffer from halide-associated stress corrosion cracking at elevated temperatures e.g., in jet engines, where chlorides and Ti-oxide promote the cracking of water vapour in the gas stream, depositing embrittling species at the crack tip. Here we report, using isotopically-labelled experiments, that crack tips in an industrial Ti-6Al-2Sn-4Zr-6Mo alloy are strongly enriched (>5 at.%) in oxygen from the water vapour, far greater than the amounts (0.25 at.%) required to embrittle the material. Surprisingly, relatively little hydrogen (deuterium) is measured, despite careful preparation and analysis. Therefore, we suggest that a combined effect of O and H leads to cracking, with O playing a vital role, since it is well-known to cause embrittlement of the alloy. In contrast it appears that in alpha+beta Ti alloys, it may be that H may drain away into the bulk owing to its high solubility in beta-Ti, rather than being retained in the stress field of the crack tip. Therefore, whilst hydrides may form on the fracture surface, hydrogen ingress might not be the only plausible mechanism of embrittlement of the underlying matrix. This possibility challenges decades of understanding of stress-corrosion cracking as being related solely to the hydrogen enhanced localised plasticity (HELP) mechanism, which explains why H-doped Ti alloys are embrittled. This would change the perspective on stress corrosion embrittlement away from a focus purely on hydrogen to also consider the ingress of O originating from the water vapour, insights critical for designing corrosion resistant materials.

cond-mat.mtrl-sci↗

arXiv2021

Chemo-Mechanical Phase-Field Modeling of Iron Oxide Reduction with Hydrogen

The reduction of iron ore with carbon-carriers is one of the largest sources of greenhouse gas emissions in the industry, motivating global activities to replace the coke-based blast furnace reduction by hydrogen-based direct reduction (HyDR). Iron oxide reduction with hydrogen has been widely investigated both experimentally and theoretically. The process includes multiple types of chemical reactions, solid state and defect-mediated diffusion (by oxygen and hydrogen species), several phase transformations, as well as massive volume shrinkage and mechanical stress buildup. In this work, a chemo-mechanically coupled phase-field (PF) model has been developed to explore the interplay between phase transformation, chemical reaction, species diffusion, large elasto-plastic deformation and microstructure evolution. Energetic constitutive relations of the model are based on the system free energy which is calibrated with the help of a thermodynamic database. The model has been first applied to the classical core-shell (wüstite-iron) structure. Simulations show that the phase transformation from wüstite to alpha-iron can result in high stress and rapidly decelerating reaction kinetics. Mechanical stresses can contribute elastic energy to the system, making phase transformation difficult. Thus slow reaction kinetics and low metallization are observed. However, if the stress becomes comparatively high, it can shift the shape of the free energy from a double-well to a single-well case and speed up the transformation. The model has been further applied to simulate an actual iron oxide specimen with its complex microstructure, characterized by electron microscopy. The simulation results show that isolated pores in the microstructure are filled with water vapor during reduction, an effect which influences the local reaction atmosphere and dynamics.

cond-mat.mtrl-sci↗

arXiv2021

Laser-equipped gas reaction chamber for probing environmentally sensitive materials at near atomic scale

Numerous metallurgical and materials science applications depend on quantitative atomic-scale characterizations of environmentally-sensitive materials and their transient states. Studying the effect upon materials subjected to thermochemical treatments in specific gaseous atmospheres is of central importance for specifically studying a material's resistance to certain oxidative or hydrogen environments. It is also important for investigating catalytic materials, direct reduction of an oxide, particular surface science reactions or nanoparticle fabrication routes. This manuscript realizes such experiments upon a thermochemical reaction chamber called the Reacthub and allows for transferring treated materials under cryogenic & ultrahigh vacuum workflow conditions for characterisation by either atom probe or scanning Xe+/electron microscopies. Two examples are discussed in the present study. One protocol was in the deuterium gas charging (25 kPa D2 at 200 °C) of a high-manganese twinning-induced-plasticity steel and characterization of the ingress and trapping of hydrogen at various features (grain boundaries in particular) in efforts to relate this to the steel's hydrogen embrittlement susceptibility. Deuterium was successfully detected after gas charging but most contrast originated from the complex ion FeOD+ signal and the feature may be an artefact. The second example considered the direct deuterium reduction (5 kPa D2 at 700 °C) of a single crystal wuestite sample, demonstrating that under a standard thermochemical treatment causes rapid reduction upon the nanoscale. Further studies are required for complete confidence about these phenomena, but these experiments successfully demonstrate that how an ex-situ thermochemical treatment can be realised that captures environmentally-sensitive transient states that can be analysed by atomic-scale by atom probe microscope.

cond-mat.mtrl-sci↗

arXiv2021

Lossless Multi-Scale Constitutive Elastic Relations with Artificial Intelligence

The elastic properties of materials derive from their electronic and atomic nature. However, simulating bulk materials fully at these scales is not feasible, so that typically homogenized continuum descriptions are used instead. A seamless and lossless transition of the constitutive description of the elastic response of materials between these two scales has been so far elusive. Here we show how this problem can be overcome by using Artificial Intelligence (AI). A Convolutional Neural Network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from Molecular Statics (MS), as output. Trained with the atomistic data, the CNN model captures the size- and pore-dependency of the material's elastic properties which, on the physics side, can stem from surfaces and non-local effects. Such effects are often ignored in upscaling from atomistic to classical continuum theory. To demonstrate the accuracy and the efficiency of the trained CNN model, a Finite Element Method (FEM) based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with that by a full atomistic simulation. The good agreement between the atomistic simulations and the FEM-AI combination for a system with size and surface effects establishes a new lossless scale bridging approach to such problems. The trained CNN model deviates from the atomistic result by 9.6\% for porosity scenarios of up to 90\% but it is about 230 times faster than the MS calculation and does not require to change simulation methods between different scales. The efficiency of the CNN evaluation together with the preservation of important atomistic effects makes the trained model an effective atomistically-informed constitutive model for macroscopic simulations of nanoporous materials and solving of inverse problems.

cond-mat.mtrl-sci↗

arXiv2021

Discovery and implications of hidden atomic-scale structure in a metallic meteorite

Iron and its alloys have made modern civilisation possible, with metallic meteorites providing one of the human's earliest sources of usable iron as well as providing a window into our solar system's billion-year history. Here highest-resolution tools reveal the existence of a previously hidden FeNi nanophase within the extremely slowly cooled metallic meteorite NWA 6259. This new nanophase exists alongside Ni-poor and Ni-rich nanoprecipitates within a matrix of tetrataenite, the uniaxial, chemically ordered form of FeNi. The ferromagnetic nature of the nanoprecipitates combined with the antiferromagnetic character of the FeNi nanophases give rise to a complex magnetic state that evolves dramatically with temperature. These observations extend and possibly alter our understanding of celestial metallurgy, provide new knowledge concerning the archetypal Fe-Ni phase diagram and supply new information for the development of new types of sustainable, technologically critical high-energy magnets.

cond-mat.mtrl-sci↗

arXiv2021

Dopant-segregation to grain boundaries controls electrical conductivity of n-type NbCo(Pt)Sn half-Heusler alloy mediating thermoelectric performance

Science-driven design of future thermoelectric materials requires a deep understanding of the fundamental relationships between microstructure and transport properties. Grain boundaries in polycrystalline materials influence the thermoelectric performance through the scattering of phonons or the trapping of electrons due to space-charge effects. Yet, the current lack of careful investigations on grain boundary-associated features hinders further optimization of properties. Here, we study n-type NbCo1-xPtxSn half-Heusler alloys, which were synthesized by ball milling and spark plasma sintering (SPS). Post-SPS annealing was performed on one sample, leading to improved low-temperature electrical conductivity. The microstructure of both samples was examined by electron microscopy and atom probe tomography. The grain size increases from ~230 nm to ~2.38 μm upon annealing. Pt is found within grains and at grain boundaries, where it locally reduces the resistivity, as assessed by in situ four-point-probe electrical conductivity measurement. Our work showcases the correlation between microstructure and electrical conductivity, providing opportunities for future microstructural optimization by tuning the chemical composition at grain boundaries.

cond-mat.mtrl-sci↗

arXiv2021

Revealing in-plane grain boundary composition features through machine learning from atom probe tomography data

Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB-specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.

cond-mat.mtrl-sci↗

arXiv2021

Revealing atomic-scale vacancy-solute interaction in nickel

Imaging individual vacancies in solids and revealing their interactions with solute atoms remains one of the frontiers in microscopy and microanalysis. Here we study a creep-deformed binary Ni-2 at.% Ta alloy. Atom probe tomography reveals a random distribution of Ta. Field ion microscopy, with contrast interpretation supported by density-functional theory and time-of-flight mass spectrometry, evidences a positive correlation of tantalum with vacancies. Our results support solute-vacancy binding, which explains improvement in creep resistance of Ta-containing Ni-based superalloys and helps guide future material design strategies.

cond-mat.mtrl-sci↗

arXiv2021

CALPHAD-informed phase-field modeling of grain boundary microchemistry and precipitation in Al-Zn-Mg-Cu alloys

The grain boundary (GB) microchemistry and precipitation behaviour in high-strength Al-Zn-Mg-Cu alloys has an important influence on their mechanical and electrochemical properties. Simulation of the GB segregation, precipitation, and solute distribution in these alloys requires an accurate description of the thermodynamics and kinetics of this multi-component system. CALPHAD databases have been successfully developed for equilibrium thermodynamic calculations in complex multi-component systems, and in recent years have been combined with diffusion simulations. In this work, we have directly incorporated a CALPHAD database into a phase-field framework, to simulate, with high fidelity, the complex kinetics of the non-equilibrium GB microstructures that develop in these important commercial alloys during heat treatment. In particular, the influence of GB solute segregation, GB diffusion, precipitate number density, and far-field matrix composition, on the growth of a population of GB precipitates, was systematically investigated in a model Al-Zn-Mg-Cu alloy of near AA7050 composition. The simulation results were compared with scanning transmission electron microscopy and atom probe tomography characterisation of alloys of the similar composition, with good agreement.

cond-mat.mtrl-sci↗

arXiv2021

Teaching Solid Mechanics to Artificial Intelligence: a fast solver for heterogeneous solids

We propose a deep neural network (DNN) as a fast surrogate model for local stress (and in principle strain) calculation in inhomogeneous non-linear material systems. We show that the DNN predicts the local stresses with about 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical phase contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The speed-up arises from the fact that after training, the DNN predicts the stress without any iterations, as opposed to the iterative nature of standard non-linear solvers. The new DNN surrogate model also proves suited for general purposes: it is capable to reproduce the stress distribution in geometries topologically far different from those used for training, implying effective learning of scenarios described by the underlying partial differential equations. Even in the case of elasto-plastic materials with up to 2 times mechanical contrast in elastic stiffness and 4 times in yield stress among adjacent regions, where conventional solvers typically require a substantial number of iterations to arrive at stress predictions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation step of the network, i.e. without any iterative calculations even for the case of such a non-linear problem. The results reveal a completely new and highly efficient approach to solve non-linear mechanical boundary value problems and/or augment existing solution methods in corresponding hybrid variants, with an acceleration up to factor of 8300 for heterogeneous elastic-plastic materials in comparison to the currently fastest available solvers.

cond-mat.mtrl-sci↗