Atomistic modeling of the solid-liquid interface of metals and alloys

Solidification is a phase transformation of utmost importance in material science, for it largely controls materials' microstructure on which a wide range of mechanical properties depends. Almost every human artifact undergoes a transformation that leads to a solid phase, be it via well-established manufacturing processes as casting or forging, or more recent technological advances such as 3D printing. This thesis aims to study some fundamental aspects of solidification, focussing in particular on metals and alloys.

Despite being a phenomenon investigated for a long time with both experiments and theoretical models, solidification still involves a very complex set of phenomena that requires a multi-scale approach to provide useful insights. For example, properties relating to the thermodynamics and kinetics of solid-liquid interfaces play a crucial role in micro-scale modeling of solidification, yet are particularly challenging to assess with experimental techniques. Our main instrument of investigation has been a set of well-established computer simulation techniques at the atomic scale, and we applied and extended some of these methods, with the primary goal of improving the reliability of some results related to the properties of solid-liquid interfaces and being able to study systems whose level of complexity comes closer to that of interest to some real manufacturing processes.

The approach of atomistic simulations involves several technical and theoretical problems. A first issue is related to the size of the systems that it is necessary to simulate to obtain results of some relevance despite an inherent statistical error that is often substantial. Moreover, some theoretical subtleties, such as the arbitrariness in the definition of the interface, inevitably emerge from an approach at the atomic scale, and they lead to problems whose solution is anything but univocal; often, in fact, different formulations of these problems provide different results. The first contribution of this thesis focused on extending a computational method that serves to calculate a fundamental quantity known as interface free energy and, in particular, to decrease its computational cost by reducing the number of particles of the simulated systems. The second contribution addressed the study of crystal-melt interface properties of a particular metallic binary alloy. The idea behind this part of the work was to combine different techniques of atomistic simulations whose outcomes make it possible to obtain an exhaustive description of both the thermodynamics and the dynamics of the interfaces. We have based this approach on a precise definition of dividing surface, and we have derived all our results in a consistent way allowing us to eliminate some arbitrary choices that similar kinds of simulations usually entail. A part of the results obtained confirmed the reliability of our approach, showing satisfactory agreement with some other established results. However, challenges remain associated with the accuracy of the interatomic potential, the presence of significant finite-size effects, and the difficulty in converging to satisfactory statistical accuracy the thermodynamic and dynamical properties of solid-liquid interfaces.

Transferable machine-learning models of complex materials: the case of GaAs

Giulio Imbalzano

Molecular simulations allow to investigate the behaviour of materials at the atomistic level, shedding light on phenomena that cannot be directly observed in experiments. Accurate results can be obtained with ab initio methods, while simulations of large-scale systems are usually possible only with coarse approximations of the molecular interactions. Machine learning interatomic potentials (MLIP) combine the strengths of the two methods in a framework that allows iterative refinement, opening the doors to the investigation of complex systems.Currently, the training of a MLIP is still human-centered. The success or failure is often dictated by the complexity of the system and by the experience of the user with the software. In this thesis, we want to provide some methods that would make the training and validation of the potentials easier and more general, even for complex, heterogeneous systems.We begin by comparing the learning ability of three widely adopted frameworks that have been developed by the community, proving that a well-constructed set of input features allow to learn at similar accuracy datasets of water dimers and trimers. Then, we compare heuristic methods based on the intrinsic correlations of the dataset to automatically identify the "best" inputs out of a larger set of candidates, which results in an accurate description of the system at a low computational cost. This allows to simplify the construction of potentials that use symmetry functions or smooth overlap of atomic positions as inputs.Finally, we introduce and implement a method to cheaply compute the uncertainty of the thermodynamic properties obtained through MD simulations with MLIPs. This method can be used either to assess the confidence of a given result obtained with a MLIP -necessary when we make quantitative predictions of properties- or to safely explore the phase space of interest, with the aid of a fall-back potential that takes over when the MLIP cannot be trusted.We showcase these methods with a real example, in which we train a potential for the complex GaAs system. The MLIP that we have developed is able to accurately predict the behavior across the whole phase diagram, spanning liquid and solid, metallic and semiconducting phases. In this endeavour we investigate a variety of methods to obtain a comprehensive dataset of structures that are fed into the MLIP.To demonstrate the transferability of the potential, we compute multiple properties, some of which (e.g. the liquid surface tension) are well beyond the limits of ab initio methods. We compare these results to our reference calculations and to experiments, finding a good agreement, within the limits of the selected level of theory (DFT at the GGA level). Finally, we use our GaAs MLIP to investigate the behaviour of liquid gallium in contact with the polar [111] surface of solid GaAs. Recent experimental findings assign an important role to the pre-ordering of the liquid at the interface during the growth of GaAs nanowires, pointing to the polarity as one of the main drivers for the correct growth. Our simulations allow to investigate this pre-ordering with increased detail, supporting and complementing the experimental observations. Furthermore, we explore the free energy of As atoms in the liquid Ga, to understand the behaviour of As atoms during the growth to help identifying the ideal growth conditions.

EPFL2021

Analysis of nano-sized irradiation-induced defects in Fe-base materials by means of small angle neutron scattering and molecular dynamics simulations

Gang Yu

Thermonuclear fusion of light atoms is considered since decades as an unlimited, safe and reliable source of energy that could eventually replace classical sources based on fossile fuel or nuclear fuel. Fusion reactor technology and materials studies are important parts of the fusion energy development program. For the time being, the most promising materials for structural applications in the future fusion power reactors are the Reduced Activation Ferritic/Martensitic (RAFM) steels for which the greatest technology maturity has been achieved, i.e., qualified fabrication routes, welding technology and a general industrial experience are almost available. The most important issues concerning the future use of RAFM steels in fusion power reactors are derived from their irradiation by 14 MeV neutrons that are the product, together with 3.5 MeV helium ions, of the envisaged fusion reactions between deuterium and tritium nuclei. Indeed, exposure of metallic materials to intense fluxes of 14 MeV neutrons will result in the formation of severe displacement damage (about 20-30 dpa per year) and high amounts of helium, which are at the origin of significant changes in the physical and mechanical of materials, such as hardening and embrittlement effects, for instance. This PhD Thesis work was aimed at investigating how far the Small Angle Neutron Scattering (SANS) technique could be used for detecting and characterizing nano-sized irradiation-induced defects in RAFM steels. Indeed, the resolution limit of Transmission Electron Microscopy (TEM) is about 1 nm in weak beam TEM imaging, and it is usually thought that a large number of irradiation-induced effects have a size below 1 nm in RAFM steels and that these very small defects actually contribute to the irradiation-induced hardening and embrittlement of RAFM steels occurring at irradiation temperatures below about 400°C. The aim of this work was achieved by combing SANS experiments on unirradiated and irradiated specimens of RAFM steels with Molecular Dynamics (MD) simulations of main expected nano-sized defects in irradiated pure Fe and Fe-He alloys, as model materials for RAFM steels, and simulations of their corresponding TEM images and SANS signals. In particular, the SANS signal of various types of defects was simulated for the first time. The methodology used in this work was the following: SANS experiments were performed by applying a strong saturating magnetic field to unirradiated and irradiated specimens of three types of RAFM steels, namely the European EUROFER 97, the Japanese F82H and the Swiss OPTIMAX A steels. The available irradiated specimens included specimens which had been irradiated with 590 MeV protons in the Proton IRradiation EXperiment (PIREX) facility at the Paul Scherrer Institute (PSI) at temperatures in the range of 50-350°C to doses in the range of 0.3-2.0 dpa. SANS spectra as well as values of the so-called A ratio, which represents the ratio of the total scattered intensity to the nuclear scattered intensity, were obtained for the various irradiation doses and temperatures investigated. MD simulations of atomic displacement cascades in pure Fe and in Fe-He alloys were performed using Embedded Atom Method (EAM) many-body interatomic potentials. The main nano-sized defects that should be produced in RAFM steels under irradiation were created by means of MD in pure Fe. These included dislocation loops of various types, voids, helium bubbles with various He concentration and Cr precipitates. TEM images of cascade damage and all the defects created by MD were simulated in the dark field/weak beam imaging modes by using the Electron Microscopy Software (EMS) developed by P.A. Stadelmann (EPFL) and analyzed in terms of variations of contrast intensities versus depth inside the specimen. The SANS signal provided by cascade damage and all the defects created by MD was simulated by using a slightly modified version of EMS, accounting for neutrons instead of electrons. The SANS technique has been proven in this work to be a very powerful tool for detecting nano-sized irradiation-induced defects and a tool well complementary to TEM for characterizing such very small irradiation-induced defects. Indeed, TEM appears most adapted to investigate structural defects, such as dislocation loops and helium bubbles with high helium concentration, which yield significant lattice deformation of the surrounding matrix, while SANS is most adapted to investigate phase defects, such as voids, helium bubbles with low helium concentration and Cr precipitates. By combining the results of SANS experiments with those of MD simulations, TEM image simulations and SANS signal simulations, the nano-sized irradiation-induced defects were tentatively identified as small helium bubbles. While the radiation hardening measured for RAFM steels cannot be explained by accounting only for the defects observed in TEM, it could be successfully modeled by accounting also for a reasonable number density of the nano-sized defects evidenced using the SANS technique.

EPFL2008

Multiscale Modelling of Irradiation Induced Effects on the Plasticity of Fe and Fe-Cr

Seyed Masood Hafez Haghighat

Degradation of mechanical properties due to nanometric irradiation induced defects is one of the challenging issues in designing ferritic materials for future nuclear fusion reactors. Various types of defects, namely dislocation loops, voids, He bubbles and Cr precipitates may be produced in ferritic materials due to high doses of irradiation with the 14 MeV neutrons stemming from the deuterium-tritium fusion reaction. Multiscale modelling methods, namely molecular dynamics (MD) and dislocation dynamics (DD) methods, are used here to study the impact of radiation-induced defects on the mechanical properties of model ferritic material. MD simulation is used to study the state of a nanometric helium bubble in α-Fe as a function of temperature, 10 to 700 K, and He content, 1 to 5 He atoms per vacancy. It appears that up to moderate temperatures the Fe lattice can confine He to solid state, in good agreement with known solid-liquid transition diagram of pure He. However, while for a given temperature and He density range where an fcc structure is expected, He in the bubble forms an amorphous phase. He bubble forms a polyhedron whose morphology depends on either the surface energy or elastic-plastic properties of Fe at either low or high pressure, respectively. At high He contents the bubble surface breaks down at the mechanical stability limit of the Fe crystal, leading to a pressure decrease in the bubble. The basic mechanisms of the interaction in α-Fe between a moving dislocation and a nanometric defect, as a function of temperature, interatomic potentials, interaction geometry and size are investigated using MD simulation. The stress-strain responses are obtained under imposed strain rate and using different interatomic potentials for Fe-Fe and Fe-He interactions. It appears that voids and He bubbles are strong obstacles to dislocation, which induce hardening and loss of ductility. A nanometric void is a stronger obstacle than a He bubble at low He contents, whereas at high He contents, the He bubble becomes a stronger obstacle. It also appears that different potentials give different strengths and rates of decrease of obstacle strength with increasing temperature. Temperature eases the dislocation release, due to the increased mobility of the screw segments appearing on the dislocation line upon bowing from the void or He bubble. Concerning the obstacle size at low content He bubble, where it is penetrable defect, size increase from 1 to 5 nm make them harder in agreement with the elasticity of continuum. At high He contents a size dependent loop punching is observed, which at larger bubble sizes leads to a multistep dislocation-defect interaction. Atomistic simulations reveal that the He bubble induces an inhomogeneous stress field in its surroundings, which strongly influences the dislocation passage depending on the geometry of the interaction. Fe-Cr alloys are also studied using MD simulations as model alloys for the ferritic base steels. Studying the flow stress of a moving edge dislocation in Fe(Cr) shows that the flow stress is not sensitive to temperature and strain rate, while it increases with Cr concentration. The flow stress of a screw dislocation is temperature dependant and its value is much higher than that of edge dislocation. Interaction in a pure Fe matrix of an edge dislocation with a nanometric Cr precipitate having various Cr content inside (Cr/Fe ratio) indicates that with the Cr/Fe ratio the obstacle strength increases, with a strong sensitivity to the short-range order. Temperature induces a monotonous decrease of the strength for all studied Cr/Fe ratios. DD calculation coupled to finite element method (FEM) is used to simulate the interaction of an edge dislocation with a void. DD calculations present a good match to the MD simulation results for the impact of image forces on the dislocation due to the free internal surface of the void. Using DD simulation, hardening due to the presence of nanometric defects, as immobile dislocation segments and spherical defect, are considered. The results of MD simulations for the strength of different defects are introduced in DD simulation. It appears that the presence of both immobile dislocation segments and nanometric defects may lead to the hardening of α-Fe. However, the defect density has more significant importance on the DD simulation, obtained here, than the strength of a single defect. TEM in-situ straining is used to validate simulations, in particular on the dislocation interaction mechanisms. Experiments were performed in ultra high purity Fe specimens. It appears that the microstructure of the material consists mainly in elongated screw dislocations. The in-situ straining tests led to the observation of the formation of screw dislocation dipoles in consistency with the MD simulation results. The interaction between a dislocation and an obstacle, as nanometric defect or immobile dislocations, leading to their shear or to Orowan loop formation were successfully observed. This work shows that using of different simulation methods can assist in the understanding of nano- and meso-scale phenomena occurring due to the presence of irradiation induced defects upon deformation of α-Fe. The information obtained from various microstructure mechanisms at lower scale simulations can be passed to higher scale simulation methods in order to realize the simulated phenomena. Experimental observations may validate what is observed in simulations provided the simulation scale is reachable in experimental observations.

EPFL2010