Migration Energies Of Point Defects Research Articles

Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials – also known as force fields – is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.

Evolution of Irradiation Defects in W and W-Re Systems: A Density Functional Theory and Rate Theory Study

In a fusion environment, tungsten, a plasma-facing material in a reactor, is subject to the irradiation of high-energy neutrons, generating a large amount of displacement damage and transmutation products (such as rhenium, Re). We studied the evolution of defects under irradiation in W and W-Re systems using the density functional theory (DFT) and rate theory (RT) method. The results indicate that the evolution of irradiation defects is mainly affected by the irradiation dose, dose rate, and temperature. During irradiation, loops form first in W, followed by the generation of voids, which are due to the different migration energies of point defects. Higher dose rates result in a higher density and larger size of defects in tungsten. Higher temperatures cause a decrease in void density and an increase in size. The results obtained at 600 °C were in good agreement with the reported TEM data. In W-Re alloys, it is indicated that the formation of loops is delayed because Re suppresses the nucleation of loops. The dynamic introduction of Re in W stabilizes the growth of defects compared to W-Re alloys, suggesting that transmuting elements have less detrimental effects on irradiation than alloying. As defect densities and sizes were quantified under different irradiation conditions, the results provide data for the multi-scale simulation of the radiation damage and thermal/mechanical properties in plasma-facing materials under fusion conditions.

A Set of Moment Tensor Potentials for Zirconium with Increasing Complexity.

Machine learning force fields (MLFFs) are an increasingly popular choice for atomistic simulations due to their high fidelity and improvable nature. Here we propose a hybrid small-cell approach that combines attributes of both offline and active learning to systematically expand a quantum-mechanical (QM) database while constructing MLFFs with increasing model complexity. Our MLFFs employ the moment tensor potential formalism. During this process, we quantitatively assessed the structural properties, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, free surface energies, and generalized stacking fault (GSF) energies of Zr as predicted by our MLFFs. Unsurprisingly, the model complexity has a positive correlation with prediction accuracy. We also find that the MLFFs were able to predict the properties of out-of-sample configurations without directly including these specific configurations in the training dataset. Additionally, we generated 100 MLFFs of high complexity (1513 parameters each) that reached different local optima during training. Their predictions cluster around the benchmark DFT values, but subtle physical features such as the location of local minima on the GSF energy surface are washed out by statistical noise.

Efficiency of the vacancy pipe diffusion along an edge dislocation in MgO

This study focuses on the mechanisms of pipe diffusion and the kinetic of point defect diffusion along dislocation line in MgO. We developed a numerical approach, based on atomic scale calculations and the use of the elasticity theory, to determine the migration energies of point defects. The kinetic of diffusion along the dislocation is then evaluated according to a on-lattice atomistic kinetic Monte Carlo algorithm informed by atomistic simulations. We show that edge dislocation in MgO behaves as a strong sink for vacancies which, combined with a lower migration energy at dislocation core region, strongly enhances the diffusion of point defect in the vicinity of the dislocation with respect to the bulk material. At low and intermediate temperatures, pipe diffusion results in an increase of the diffusivity of several order of magnitude. Accounting more precisely for the effect of pipe diffusion may therefore be a key to reconcile the experimentally measured scattering of diffusivity in MgO.

Vacancy migration in α-iron investigated using in situ high-voltage electron microscopy

ABSTRACT Modeling the microstructural evolution of irradiated materials requires knowledge of the migration energies of point defects, which results from energetic particle radiation. Herein, we measured the growth rate of self-interstitial atom (SIA) clusters in electron-irradiated α-iron at 275–320 K using in situ high-voltage electron microscopy. To improve the statistical accuracy of the measurement, we used photographic films and video data. This enabled analysis of a considerable amount of data by extracting several SIA clusters and tracking their size growth using image processing techniques. By fitting the temperature-dependent cluster growth rate to the Arrhenius relations derived using rate theory analysis, we obtained vacancy migration energy of eV. The validity of the estimation method was confirmed from the consistency of the dependence of the damage rate on the cluster growth rate using the applied rate theory analysis. We also investigated the possible roles of faster motion of tri-vacancies compared to those of mono- and di-vacancies, as demonstrated by first-principles calculations, on the obtained migration energy using a kinetic analysis model. In addition, the effects of impurities leading to decrease in the cluster growth rate were briefly discussed.

Atomistic modeling of interface strengthening in Al-Si eutectic alloys

Al-Si cast alloys are usually composed of α-Al and Al-Si eutectic. Si flakes and Al matrix generally hold cube-on-cube orientation relationship with the primary interface (111)Al∥(111)Si. Extensive experimental studies demonstrated that Si flakes cannot significantly improve mechanical properties of Al-Si cast alloys. We hypothesize that the weak strengthening effect associated with Si flakes might be attributed to thermomechanical properties of Al-Si interfaces besides their morphologies. To characterize Al-Si interfaces with a large lattice mismatch (> 30%), we proposed the quasi-coincident site lattice (Q-CSL) as reference lattice, and demonstrated that the Q-CSL Al-Si coherent interface has three characteristic coherent structures, one stable and low energy structure and two metastable and high energy structures. The translation vectors for the same type of coherent Q-CSL structures are consistent with three displacement shift complete (DSC) vectors. The two metastable structures can be obtained by shifting the low energy structure with three partial DSC vectors. Semi-coherent interface is composed of the low energy Q-CSL patches and three sets of interface misfit dislocations with Burgers vectors same as the DSC vectors. Atomistic simulations revealed that Al-Si interface exhibits low shear resistance. Ideal shear strength of the Q-CSL coherent interface is 110 MPa and semi-coherent interface is 20 MPa. The low shear resistance is attributed to the glide of interface misfit dislocations. Al-Si interface also exhibits low formation and migration energies of point defects. Owing to low shear strength and low formation and migration energies of point defects, interface sliding or shear readily happen under mechanical loading or during dislocation-interface interactions. Lattice dislocations can cross slip onto or climb along Al-Si interfaces. These reactions decrease the number of accumulated dislocation loops around Si flakes and promote nucleation and emission of lattice dislocations from Al-Si interfaces to matrix, consequently reduce the repulsive force on approaching dislocations and weaken Si flakes strengthening effect. In situ tension and compression tests in a scanning electron microscope reveal relatively weak strengthening effect due to Si flakes, consistent with the computed dislocation interaction with interfaces and shear behavior of interfaces.

Anti-radiation mechanisms in nanoporous gold studied via molecular dynamics simulations

The radiation resistance performance of nanoporous (NP) gold is investigated by cascade simulations of a gold nanowire using molecular dynamics. The role of the surface on primary defect production was clarified: the mean size of the vacancy clusters (VCs) near the surface in the nanowire becomes larger compared to that of a single crystal. In the surface region, the reduction of the formation and migration energies of point defects leads to a continuous flux of point defects towards the free surface, which retards the formation and growth of defect clusters, resulting in a good anti-radiation performance. In the cascade region, however, the retained vacancies tend to form larger sessile VCs due to their low migration energies and large attractive forces, resulting in radiation damage. The competition between these two factors determines the anti-radiation behavior of NP gold.

Formation Energy of Intrinsic Point Defects in Si and Ge and Implications for Ge Crystal Growth

The formation energies of intrinsic point defects in Si and Ge were calculated by means of Density Functional Theory applying thin film models. The obtained formation energy for a Ge vacancy is close to the value calculated by means of a hybrid exchange correlation potential (HSE06). Well accepted experimental data exist for the sum of the formation and migration energies of vacancies and self-interstitials in Si. Taking into account recent values for the migration energies of point defects, the results of the present study are in excellent agreement with the experimental data. Applying the thin film model for both Si and Ge, one can compare formation energies of intrinsic point defects for both semiconductors. The thermal equilibrium concentration of Ge self-interstitials is more than one order of magnitude lower than that of Si interstitials while the vacancy concentrations are of similar magnitude. Contrary to Si, the diffusivity of Ge self-interstitials cannot recover the unbalance of the thermal equilibrium concentrations even if the growth rate is reduced to very low values. Therefore, Ge crystals grown from a melt are always vacancy-rich which results in void formation independent of the growth condition.

Analysis of helium and hydrogen effect on RAFS by means of multi-beam electron microscope

Effects of helium and hydrogen gas on microstructural evolution in pure iron, Fe–8Cr, and F82H IEA were investigated by means of a multi-beam electron microscope. Growth rate and saturated number density of dislocation loops were measured to calculate migration energies of point defects. In all irradiation temperature conditions, both the size and the number density of dislocation loops were increased as a function of dose. Irradiation with helium and hydrogen showed an increase in the temperature dependence of the dislocation loop growth rate compared to irradiation without helium and hydrogen. On the other hand, little difference was observed in the saturated loop number density at each irradiation temperature. The migration energy of interstitials was determined to be 0.3eV for both types of irradiation. The migration energy of vacancies was determined to be 0.9eV for electron irradiation. This in situ experiment indicated that the net migration energy of vacancies could be increased due to trapping by helium and hydrogen. Irradiation experiments indicated that net migration energy of vacancy in F82H IEA irradiated with helium or hydrogen tended to be higher compared to that in pure iron and Fe–8Cr, which could relate not only to helium and hydrogen, but also to carbon and nitrogen concentration in matrix.

First-principles study of defect behavior in irradiated uranium monocarbide

Ab initio electron theory based on the projector-augmented-wave method in the generalized gradient approximation of the density functional theory is used for calculating formation and migration energies of point defects in uranium monocarbide (UC). The use of the Hubbard term to describe the 5$f$ electrons of uranium is discussed on the basis of the density of states and cohesive energies. A formalism allowing the ``raw'' calculated energies to be normalized is proposed to take into account the compositional dependence of defective crystals. Such formation energies are then used to determine the population of predominant defects as a function of nonstoichiometry. We identify the most stable defects as uranium antisites and carbon vacancies for UC${}_{1\ensuremath{-}x}$, and dimers ${\mathrm{C}}_{2}$ for UC${}_{1+x}$. The most stable thermal defects are obtained, in turn, by formation of complex defects associating dimer ${\mathrm{C}}_{2}$ and carbon vacancies whereas carbon Frenkel pairs and Schottky defects require larger formation energies. The migration energies are also calculated for different mechanisms, using as diffusion vectors both thermal vacancy sources and preexisting constitutional defects in the case of off-stoichiometric alloys. We compare the calculated diffusion paths with available experimental data proposed by Matzke [J. Less-Common Met. 121, 537 (1986)].

Multiple-beam irradiation effects in electron-beam-welded F82H joint

Electron-beam-welded reduced-activation ferritic/martensitic steel F82H, which is one of prime candidate materials for experimental fusion reactors, have been irradiated by electron and helium ion beams using a High Voltage Electron Microscope (HVEM) as the experimental evaluation of the modeling and simulations. Growth rate and saturated number density of dislocation loops have been measured to calculate the migration energies of point defects. Electron irradiation experiment indicated that net migration energy of vacancy in the welded metal of F82H tended to be lower compared to that in base metal, which could be relating to difference of carbon concentration in matrix. In the case of dual beam (electron and helium) irradiation, net migration energies of vacancy were slightly higher than that in electron beam irradiation. This result indicates that vacancy would be trapped by implanted helium due to their strong interaction and appeared to have higher migration energy.

Object Kinetic Monte Carlo calculations of irradiated Fe–Cr dilute alloys: The effect of the interaction radius between substitutional Cr and self-interstitial Fe

Object Kinetic Monte Carlo models allow for the study of the evolution of the damage created by irradiation to time scales that are comparable to those achieved experimentally. Therefore, the essential Object Kinetic Monte Carlo parameters can be validated through comparison with experiments. However, this validation is not trivial since a large number of parameters is necessary, including migration energies of point defects and their clusters, binding energies of point defects in clusters, as well as the interaction radii. This is particularly cumbersome when describing an alloy, such as the Fe–Cr system, which is of interest for fusion energy applications. In this work we describe an Object Kinetic Monte Carlo model for Fe–Cr alloys in the dilute limit. The parameters used in the model come either from density functional theory calculations or from empirical interatomic potentials. This model is used to reproduce isochronal resistivity recovery experiments of electron irradiated dilute Fe–Cr alloys performed by Abe and Kuramoto. The comparison between the calculated results and the experiments reveal that an important parameter is the capture radius between substitutional Cr and self-interstitial Fe atoms. A parametric study is presented on the effect of the capture radius on the simulated recovery curves.

A Multicomponent Model of Radiation-induced Segregation for Commercial Stainless Steels

A radiation-induced segregation model of the Fe-Cr-Ni-Si-Mo system was developed to predict the change in grain boundary composition in commercial stainless steels under neutron irradiation. Parametric survey showed that there were strong influences on segregation behavior for the binding of Si to an interstitial and the jump frequency of Ni and Si via interstitial mechanisms. Careful setting of these parameters using effective point defect migration energies resulted in a good agreement between calculated results and measured data for SUS316 stainless steels irradiated to 74 dpa in light water reactor. Model calculation qualitatively reproduced the effects of dose rate, temperature, and bulk composition reported in the literature.

Multiscale Modeling of Helium-Vacancy Cluster Nucleation under Irradiation: A Kinetic Monte-Carlo Approach

AbstractWe applied ab initio calculation and an object kinetic Monte Carlo modeling to the study of He-vacancy cluster nucleation under irradiation in bcc and fcc Fe, which are surrogate materials for ferritic/martensitic and austenitic steels, respectively. The ab initio calculations provided parameters for the object kinetic Monte Carlo model, such as the migration energies of point defects and the dissociation energies of He and vacancy to He-vacancy clusters. We specially focused on the simulation of high He/dpa irradiation such as He-implantation into the materials and tracked the nucleation of clusters and the fate of point defects such as SIAs, vacancies, and He atoms. We found no major difference of He-vacancy cluster nucleation between bcc and fcc Fe when we ignore the intracascade clustering even if the migration energies of point defects are significantly different between the two crystals.

Use of computational intelligence for the prediction of vacancy migration energies in atomistic kinetic monte carlo simulations

In this work, we try to build a regression tool to partially replace the use of CPU-time consuming atomic-level procedures for the calculation of point-defect migration energies in Atomistic Kinetic Monte Carlo (AKMC) simulations, as functions of the Local Atomic Configuration (LAC). Two approaches are considered: the Cluster Expansion (CE) and the Artificial Neural Network (ANN). The first is found to be unpromising because of its high computational complexity. On the contrary, the second provides very encouraging results and is found to be very well behaved.

Modelling irradiation effects in fusion materials

We review the current status of the European fusion materials modelling programme. We describe recent findings and outline potential areas for future development. Large-scale density functional theory (DFT) calculations reveal the structure of the point defects in α-Fe, and highlight the crucial part played by magnetism. The calculations give accurate migration energies of point defects and the strength of their interaction with He atoms. Kinetic models based on DFT results reproduce the stages of radiation damage recovery in iron, and stages of He-desorption from pre-implanted iron. Experiments aimed at validating the models will be carried out in the future using a multi-beam ion irradiation facility chosen for its versatility and rapid feedback.

Migration energies of point defects during electron irradiation of hydrogenated Si crystals

To study both generation rates and mobilities of point defects due to electron irradiation, we measured and analyzed optical-absorption spectra of complexes of hydrogen and point defects generated by low-temperature electron irradiation of hydrogenated Si crystals. Specimens were doped with H by heating in ${\mathrm{H}}_{2}$ gas at 1300 \ifmmode^\circ\else\textdegree\fi{}C followed by quenching. They were then irradiated with 6-MeV electrons at 270, 200, 130, and 77 K. We measured their optical-absorption spectra at 7 K with an Fourier transform infrared spectrometer. We observed many optical absorption peaks which are due to localized vibrational modes of H bound to various point defects. The irradiation temperature dependence of concentrations of some H-point defect complexes was not monotonic contrary to the prediction of metastable Frenkel pair models. Relative intensities of those peaks depended on the irradiation temperature and were interpreted to be due to the relative mobilities of various point defects. The migration energies of a self-interstitial and a Frenkel pair relative to that of a vacancy were determined.

Radiation damage process of vanadium and its alloys during electron irradiation

Microstructural change and the migration energies of point defects in V, V4Ti4Cr and oxide dispersion strengthened vanadium were examined by high voltage electron microscopy. Irradiation was performed up to 7.2 dpa at room temperature to 773 K. To protect the specimens from surface contamination, some specimens were coated with Ti and Cr by the evaporation process. During irradiation of low dose, interstitial-type dislocation loops were initially nucleated and grown. Micro-voids were observed in oxide dispersion strengthened vanadium at 723 K. The migration energies of interstitials and vacancies were estimated from the number density and the growth rate of the loops, as a function of temperature. The microstructure change is explained by the effect of the interaction between impurities and solute atoms.

Molecular dynamics calculations of defect energetics in β-SiC

The molecular dynamics (MD) method is used to calculate defect energetics in β-silicon carbide. Many-body interaction effects in this covalent material are accounted for by using a hybrid of two-body and three-body potentials. Pearson's potential is modified to accurately fit the sublimation energy of β-SiC, and interatomic potentials among silicon, carbon, and helium atoms are also developed. A microcrystal is constructed to represent the computational cell, and external forces are applied to its boundaries so that it behaves as a part of an infinite medium. The potential energy for the unperturbed computational cell is first calculated. The cell is then set at a chosen defect configuration and relaxed, and the potential energy of the relaxed cell is computed. The difference between the potential energies of the unperturbed cell and that of the defect-containing cell is used to calculate the formation energies of point defects and defect clusters in SiC. Binding energies, and migration energies of point defects are then deduced. Preexponential factors of point defect diffusion coefficients are derived from the calculated potential energy profile. Activation energies and preexponential factors of thermal diffusion through the vacancy mechanism are compared to corresponding experimental data.