Vacancy Loops Research Articles

Revealing the critical role of vanadium in radiation damage of tungsten-based alloys

Refractory tungsten-based medium- and high-entropy alloys form a promising class of strong, heat- and radiation-resistant materials for nuclear applications. Here, we systematically explore the radiation tolerance of Mo–Nb–Ta–V–W alloys using molecular dynamics simulations and a machine-learned interatomic potential. Going from pure W to W-based equiatomic binaries, ternaries, quaternary, and the quinary high-entropy alloy, we simulate the radiation damage accumulation up to 0.4–0.8 dpa through cumulative collision cascades. We find that the radiation damage and evolution are controlled by a combination of cascade-induced clustering, the balance in migration of vacancies and interstitials, and defect cluster binding energies. These mechanisms are strongly influenced by atom size, among which vanadium as the smallest atom is decisive. In pure W and alloys without V, the microstructure is characterised by large and growing interstitial dislocation loops. In stark contrast, in alloys containing V, vacancy dislocation loops are formed directly in collision cascades and the balanced migration rate of vacancies and interstitials promotes recombination and prevents growth of interstitial loops. The atom size differences also lead to clear segregation, with small atoms (V) in interstitial clusters and larger atoms (Ta, Nb) segregating around vacancy clusters. Furthermore, the small cluster sizes, formation of vacancy loops, segregation, and balanced migration in V-containing alloys lead to low swelling and an exceptionally efficient defect annealing compared to pure W and V-free alloys. Our results highlight WTaV as a promising low-activation material, where almost 90% of defects are annealed at 2000 K during 5 ns compared to <20% in pure W.

Spatially-resolved cluster dynamics modeling of irradiation growth

We develop here a spatially resolved, three-dimensional continuum model coupling cluster dynamics (SR-CD) and crystal plasticity to investigate irradiation growth in zirconium. The model uses scale separation to divide the population of the irradiation cluster into mobile and immobile families. Small interstitial and vacancy clusters are modeled using anisotropic reaction–diffusion equations. Among the immobile clusters, an atomistically-informed vacancy cluster to vacancy loop transition is taken into account. The coupling between the evolution equation of CD and the plastic deformation of the material is two-fold, with stress-informed bias factors and local inelastic strains computed from the evolution of the evolving cluster population. The numerical implementation of the model utilizes the finite element method to analyze both single-crystal and polycrystalline samples. The growth strains that are computed align well with the experimental data provided by Carpenter for single-crystal Zr. Furthermore, the transformation of a vacancy cluster into a complete vacancy loop, occurring at a size of 14 nm, is in agreement with experimental observations and atomistic simulations. The density, size, and growth rate of the dislocation loops, denoted as 〈c〉 and 〈a〉, also exhibit good agreement with transmission electron microscopy (TEM) analysis of irradiated Zr and its alloys. Our findings demonstrate that there is a spatial correlation between the growth of these dislocation loops and growth strains, significantly influenced by the crystal size. To explain the expansion of the 〈a〉 axis and the contraction of the 〈c〉 axis in irradiated Zr, it is necessary to consider the diffusion anisotropy difference (DAD) of mobile interstitial species. We show that the PWR Kearns parameters, specifically fr = 0.63, ft = 0.32, fa = 0.05, confer enhanced irradiation resistance to Zr along the principal directions when compared to single crystals. Additionally, reducing the grain size to nanograins further enhances the resistance to irradiation-induced growth, particularly along the direction with the highest volume fraction of basal poles [0001].

A hybrid rate theory model of radiation-induced growth

Differences in the diffusivity of radiation-produced defects along zirconium’s prismatic and basal planes result in radiation-induced growth (RIG) and creep. The difference in anisotropy of diffusion (DAD) model explains this behavior by assuming vacancies and self-interstitial atoms (SIAs) possess dissimilar ratios of in-basal-plane vs out-basal-plane diffusion coefficients. The self-interstitial cluster diffusion (SICD) model was proposed as an alternative to DAD, and relates growth to the formation of self-interstitial clusters which diffuse solely along the 〈a〉 direction. Here, we propose a hybrid model, in which the contribution of both effects are considered, which provides additional flexibility as compared to DAD or SICD taken individually. In this model, both anisotropic diffusing point defects and 1-dimensional (1-D) glissile SIA clusters are considered, which are removed in the internal and boundary sinks. Thirty-two DAD, SICD and hybrid models are fitted to a set of thirty-two RIG experiments. Good agreement between DAD and the experiments can be reached only by assuming unrealistically large SIA bias factors. In 9 of the 32 scenarios, good agreement between SICD and experiments could not be reached, indicating that the model lacks flexibility. Good agreement between the hybrid model and the experiments can be reached using realistic SIA bias factors; however, it requires assuming considerably lower vacancy bias factors than those found by ab initio calculations aimed at mono-vacancies, suggesting small vacancy clusters and loops play a more important role in RIG than previously thought.

Formation of large loop-hydrogen complexes and related effects on mechanical properties of Zirconium investigated with molecular dynamics method

Using molecular dynamics (MD) method, interaction between hydrogen (H) atoms and interstitial or vacancy dislocation loops in Zr is extensively studied. The results show that the binding of hydrogen atoms to dislocation loops is anisotropic (attractive or repulsive), depending on the position of the hydrogen atoms with respect to the loop’s core. The anisotropy is governed by excess volume and stress field induced by the loop. For a 1/321̅1̅0interstitial dislocation loop, hydrogen atoms preferentially segregate near the outside of the loop and close to the decomposition knots of the loop. While for a 1/321̅1̅0or 1/6[202̅3] vacancy loop, hydrogen atoms prefer to segregate near the inside of the loop. The present work indicates large loop-hydrogen complexes could form in Zr. The binding of hydrogen to loops is stable up to 600 K, while dissociation is observed at 900 K. Formation of loop-hydrogen complexes affect the activation of slip system, resulting in higher yield stress of Zr. The effect increases with the increasing ratio of H to vacancies or interstitials in the vacancy or interstitial loops. The results imply the effects of large loop-hydrogen complexes should be considered to fully understand radiation damage in Zr.

Stress states and point defect capture radii of dislocation a-loops and c-loops in alpha-zirconium

Improving the predictive capability of microstructure evolution in irradiated α-zirconium requires a thorough understanding of the interaction rates between mobile defects and the existing, and evolving, microstructure. One of the parameters necessary to calculate these rates is the defect capture radii of dislocation loops. In order to better quantify this parameter, atomistic binding energy maps of point defects to interstitial a-loops, vacancy a-loops, and vacancy c-loops have been constructed using large-scale molecular statics simulations. Point defect capture radii have been correlated to the decay of binding energies with increasing distance using two criteria: spontaneous and thermal drift capture. Considering the spontaneous capture criteria, SIAs exhibit biased capture to all dislocation loops. However, when thermal drift capture is considered, the local stress state of dislocation loops imparts an inherent bias for the capture of same-type defects (i.e. vacancies to vacancy loops and vice versa). This phenomenon may drive the co-existence of vacancy and interstitial a-loops in irradiated α-Zr microstructure, an aspect that is poorly captured by most current models. The capture radii reported here will directly improve the predictive capability of microstructure evolution modeling in neutron-irradiated α-Zr.

An empirical potential for simulating hydrogen isotope retention in highly irradiated tungsten

We describe the parameterization of a tungsten-hydrogen empirical potential designed for use with large-scale molecular dynamics simulations of highly irradiated tungsten containing hydrogen isotope atoms, and report test results. Particular attention has been paid to getting good elastic properties, including the relaxation volumes of small defect clusters, and to the interaction energy between hydrogen isotopes and typical irradiation-induced defects in tungsten. We conclude that the energy ordering of defects changes with the ratio of H atoms to point defects, indicating that this potential is suitable for exploring mechanisms of trap mutation, including vacancy loop to plate-like void transformations.

Direct Observation of Vacancy-Cluster-Mediated Hydride Nucleation and the Anomalous Precipitation Memory Effect in Zirconium.

Controlling the heterogeneous nucleation of new phases is of importance in tuning the microstructures and properties of materials. However, the role of vacancy-a popular defect in materials that is hard to be resolved under conventional electron microscopy-in the heterogeneous phase nucleation remains intriguing. Here, this work captures direct in situ experimental evidences that vacancy clusters promote the heterogeneous hydride nucleation and cause the anomalous precipitation memory effect in zirconium. Both interstitial and vacancy dislocation loops form after hydride dissolution. Interestingly, hydride reprecipitation only occurs on those vacancy loop decorated sites during cooling. Atomistic simulations reveal that hydrogen atoms are preferentially segregated at individual vacancy and vacancy clusters, which assist hydride nucleation, and stimulate the unusual memory effect during hydride reprecipitation. The finding breaks the traditional view on the sequence of heterogeneous nucleation sites and sheds light on the solid phase transformation related to vacancy-sensitive alloying elements.

Modelling of zirconium growth under irradiation and annealing conditions

Modelling zirconium growth under irradiation is a difficult task due to the different types of defects formed which all contribute to the macroscopic deformation. An Object Kinetic Monte Carlo model parameterized using state-of-the-art atomic-scale calculations and experimental data is presented. It is able to reproduce a good macroscopic deformation, the coexistence of all types of defects: 〈a〉 interstitial and vacancy loops, 〈c〉 vacancy loops and the alignments of 〈a〉 loops parallel to the basal plane. A large parametric study is performed in order to understand thoroughly in which conditions these microstructural features can be observed. The model is then applied to study flux effects and the microstructure evolution during annealing. It can be concluded that 〈a〉 loop alignments are phenomena which are very sensitive to the flux. During annealing, the defects can recover in a non-monotonous way and 〈a〉 loops inside the alignments disappear at last, which illustrates their strong stability.

Effect of radiation damage on liquid Pb corrosion at the Fe/Pb solid-liquid interface

The interaction between liquid Pb and irradiation defects at structural materials/liquid metal interface is fundamental to understand the irradiation-enhanced corrosion of structure materials in nuclear system. The primary damage to iron surfaces and the density profiles, lateral structure, and interfacial diffusion profiles of the irradiated Fe/Pb solid-liquid interfaces are investigated using the molecular dynamics method. We find that the vacancy clusters predominate on the surfaces, and the vacancy loops emerge under Fe(110) surface with higher probability compared with Fe(100) surface under Fe particle irradiation. The liquid Pb could accelerate the migration of irradiation damages, mainly the vacancies, to the surface. Those vacancies could promote the corrosion of Pb on the Fe surface in turn by combining with Pb atoms. The Pb atoms near the interface exhibit a two-dimensional diffusion mechanism and anisotropy in the transport properties due to the different structural symmetry of the Fe/Pb interfaces.

Molecular dynamics simulations of displacement cascades in vanadium: Generation and types of dislocation loops

Vanadium(V)-based alloys have received extensive attention as promising first-wall and blanket candidates for fusion reactors. In the present study, molecular dynamics (MD) simulations have been performed to study the displacement cascades in V bulk with the recoil energy up to 80 keV at 300 K. The results indicate that the clustering fraction and cluster size of vacancies are higher than those of interstitials. The nucleation, evolution, and energy of dislocation loops are studied. It’s found that 1/2 〈1 1 1〉 interstitial and vacancy dislocation loops are the primary ones, while low concentration 〈1 0 0〉 vacancy loops are also formed. In addition, the nucleation of 1/2 〈1 1 1〉 interstitial dislocation loops is earlier than that of 1/2 〈1 1 1〉 vacancy ones. The reason for the appearance of 1/2 〈1 1 1〉 vacancy dislocation loops is that the formation energy of the 1/2 〈1 1 1〉 vacancy dislocation loops is close to that of voids containing the same number of vacancies. These results provide a new understanding of applying V-based alloys in fusion reactors.

On the theory of dislocation loop nucleation in irradiated crystals

The theory of dislocation loop nucleation in irradiated crystals is critically analysed and revised. The key parameters of the nucleation model are reassessed within the traditional (mean field) rate theory for irradiation defects. In the new approach, it is shown that at relatively low irradiation temperatures all interstitial loops are supercritical (due to the absence of a critical nucleus) and grow until they coalesce with other loops or with the dislocation network. In the transition temperature range, a large critical size of interstitial loops arises and the nucleation rate decreases significantly. At higher temperatures, all interstitial loops become subcritical and shrink, in qualitative agreement with experimental observations in irradiated steels. The vacancy loops are shown to be subcritical at all irradiation temperatures and thus shrink and disappear, in agreement with observations. To further improve the predictions of the nucleation theory, possible modifications of the mean field rate theory for irradiation defects are discussed.

Impact of micro-alloying in ion-irradiated nickel: From the inhibition of point-defect cluster diffusion by thermal segregation to the change of dislocation loop nature

Micro-alloying strongly affects the incubation period of void swelling in irradiated face-centered cubic materials. However, the underlying mechanism, which relates to the formation of dislocation loops, is still unclear. Here, we investigate pure Ni, Ni-0.4wt.%Cr and Ni-0.4/0.8/1.2wt.%Ti as model materials, to gain insight into the solute effects on the loops evolution in the early stage of irradiation. The dislocation loop characteristics (mobility, Burgers vector, nature) are studied using in-situ transmission electron microscopy and ex-situ irradiation with Ni+ ions at 450°C and 510°C for doses from 0.06 to 0.7 dpa. It appears that a tiny amount of Ti effectively increases the loop density, reduces the loop mobility and the stacking fault energy. It leads to an equal distribution among a/2<110> perfect loop families. It also stabilizes self-interstitial loops against vacancy loops depending on Ti content and temperature. Our modeling of radiation-induced segregation, based on experiments and recent ab initio calculations of flux couplings, predicts a Cr enrichment and a Ti depletion nearby dislocation loops. It is in good agreement with our observations by X-ray spectroscopy in TEM and by atom probe tomography. However, the lowered loop mobility must be the signature of a thermal segregation rather than the impact of radiation-induced depletion. Indeed, oversized Ti atoms subsequently trapped at strained lattice sites around the dislocation line of the loop due to thermal segregation would inhibit its diffusion. This opens new perspectives for future experimental investigations and radiation-effect modeling.

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

We develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch (1959). We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. (1999). Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

Molecular dynamics simulation to elucidate effects of spatial geometry on interactions between an edge dislocation and rigid, impenetrable precipitate in Cu

Molecular dynamics simulations were conducted to evaluate the interactions between an edge dislocation and a rigid, impenetrable precipitate in Cu by changing the distance between the glide plane of the dislocation and the center of the precipitate (ξ). In these calculations, the precipitate was introduced as a super particle that moved according to the total force exerted by the matrix atoms on the precipitate atoms. When the center of the precipitate was close to the glide plane, an Orowan loop was formed around the precipitate after the dislocation detached, and the critical resolved shear stress (CRSS) was similar to the value evaluated by the results at ξ = 0. However, when the glide plane was far from the center of the precipitate, either a vacancy loop or loops generated through the Hirsch mechanism were formed, depending on whether the center of the precipitate was below or above the glide plane. The magnitude of the CRSS was not symmetric about ξ = 0. This study confirmed that it is necessary to analyze the CRSS by changing ξ to construct a predictive model for the hardening caused by the formation of lattice defects, and that precipitate hardening appears to be smaller than the value estimated using the results at ξ = 0.

Interaction between collision cascades and nanocrack in hcp zirconium by molecular dynamics simulations

In this work, molecular dynamics simulations are performed to investigate the interaction between the collision cascades and nanocrack in hcp zirconium. When the thermal spike overlaps with the nanocrack, the collision cascades will induce the healing of the nanocrack. Higher PKA energy leads to higher degree of crack healing at the same separation distance between PKA and nanocrack. The PKA velocity direction changes the fraction of atoms entering the crack by influencing the shape and distribution of the thermal spike. Furthermore, both Zr #3 and #2 potentials show that the degree of crack healing drops as the distance between the nanocrack and PKA decreases. In particular, collision cascades induce the transformation of nanocrack in the basal plane into prismatic vacancy loop is captured due to the interaction between thermal spike with nanocrack. Lastly, the pre-existing nanocrack may induce cascade splitting of hcp Zr. This work provides a mechanistic understanding of the interaction between the nanocrack and irradiation damages in Zr and other hcp metals.

Direct transformation of equilateral hexagonal Frank vacancy loops to stacking fault tetrahedra under thermal fluctuation

Stacking fault tetrahedra (SFTs) are highly interesting three-dimensional vacancy defects in quenched, plastically deformed or irradiated face-centered-cubic metals and have a significant impact on the properties and subsequent microstructural evolution of the materials. Their formation mechanism and stability relative to two-dimensional vacancy loops are still debated. Equilateral hexagonal Frank vacancy loops (faulted, sessile) observed in microscopy have been considered unable to directly transform to SFTs due to separation of Shockley partial dislocations as well as embryonic stacking faults. Here using sufficiently long (up to tens of nanoseconds) molecular dynamic simulations, we demonstrate that such a transformation can in fact take place spontaneously at elevated temperatures under thermal fluctuation, reducing potential energy of defected atoms by <0.05 eV/atom. The transformation becomes easier with increasing temperature or decreasing loop size.

Radiation-induced segregation on dislocation loops in austenitic Fe-Cr-Ni alloys

Radiation-induced segregation of alloying elements to crystallographic defects is commonly observed in irradiated austenitic stainless steels. The interaction between solutes and radiation-induced defects changes the physical distribution of solutes and thus affects the formation and growth of defects. The change of the microstructure consequently affects the mechanical properties of the material. A qualitative and quantitative understanding of the interaction between solutes and defects is desirable to better predict the service lifetime of nuclear materials. We used atom probe tomography to measure the distribution of solutes at dislocation loops in 304L stainless steel, irradiated with 2 MeV protons up to 1.5 displacements per atom at 373 and 633 K. No segregation at dislocation loops was found in samples irradiated at 373 K, whereas Ni and Si enrichment and Cr depletion were detected at dislocation loops irradiated at 633 K. The experimentally observed perfect and faulted dislocation loops in vacancy and interstitial types were reproduced by molecular dynamics (MD). A hybrid MD/Monte Carlo method was used to predict the redistribution of alloying atoms at all possible types of dislocation loops in face-centered cubic Fe-Cr-Ni alloys at the same irradiated temperatures (373 and 633 K). The simulations show that, at both temperatures, Cr clusters were formed and distributed randomly, and Ni atoms enriched or depleted at interstitial or vacancy dislocation loops, respectively. The change of solute concentration reaches the highest at the edge of the loop. Ni profiles exhibit characteristic behavior in terms of the stress field of the loops: tension inside of vacancy loops showing depletion of Ni atoms compared with compression inside of interstitial loops showing enrichment of Ni atoms. In addition, the stress field is reduced after solute redistribution. The absence of alloying segregation observed in experiments at a lower temperature (373 K) is explained by a rate theory model: Low-temperature irradiation requires significantly longer irradiation time to see the same amount of segregation as at high temperatures because of the extremely low diffusion of vacancies at low temperatures.

Atomistic structure and thermal stability of dislocation loops, stacking fault tetrahedra, and voids in face-centered cubic Fe

Irradiation-induced hardening and changes to mechanical properties can often lead to material degradation and can limit the operation of reactor components. In addition, changes to mechanical properties can be a precursor to other material environmental degradation. Dislocation loops, stacking fault tetrahedra (SFT), and voids are major irradiation-induced lattice defects that occur in structural materials and are often observed post-irradiation. However, these defects are often considered only as obstacles to dislocation motion, with hardening assumed to be dependent on the habit plane and Burgers vector of the defect. The stability and nature of dislocation loops and SFTs with temperature are often overlooked, and this may play a crucial role in the mechanical properties of structural materials. We combine high-resolution transmission electron microscopy (HR-TEM) and atomistic simulations to determine the atomistic configurations and thermal stability of dislocation loops and SFTs. Dislocation dissociations are observed in both vacancy and interstitial-type perfect dislocation loops as well as in vacancy-type Frank loops, whereas interstitial-type Frank loops remain stable and are the least influenced by temperature. Triangle-shaped intrinsic stacking faults are formed at the edges of Frank vacancy loops, and a direct transformation from triangle-shaped Frank vacancy loops to SFTs is observed in atomistic simulations. SFTs are energetically more stable than Frank vacancy loops based on formation energy calculations in pure face-centered cubic Fe, which may explain why vacancy-type Frank loops are infrequently observed experimentally. The motivation for this study is to develop a framework for the stability and nature of irradiation defects as a function of temperature, which will be subsequently used for more complex (alloy) systems.

Effect of Mn addition on the formation of vacancy-type dislocation loops in α-Fe

It has recently been established that vacancy loops of ~100 nm in maximum size could form in hydrogen pre-implanted α-Fe (Huang et al. Fusion Eng. Des., 2010). The formation temperature of these large loops is composition dependent, varying from ~500 °C in α-Fe, to ~450 °C in FeNi and ~ 620 °C in FeCr (Wan et al. J. Nucl. Mater., 2014; Du et al. Acta Metall. Sin., 2019). In this work, the effect of Mn addition upon vacancy loop formation has been investigated. Pure Fe and Fe-1.4 wt% Mn alloy specimens were irradiated with 30 keV H+ ions at room temperature. Radiation-induced loop production, size, population and nature were characterized based on diffraction contrast imaging using a combination of 1 MV high voltage electron microscope (HVEM) and 200 kV conventional transmission electron microscope (CTEM). Results of observation indicate that Mn addition gives rise to the increase of vacancy loop formation temperature in α-Fe, similar to the effect of Cr. A new criterion has been thus proposed, to classify the common alloying elements (Cr, Ni, Mn etc) found in Fe.

Strength properties and deformation structure of VT1-00 titanium under shock loading

We present the results of measurement of wave stress profiles of uniaxial shock compression of VT1-00 titanium samples under different loading conditions. The dependences of the spall strength on the strain rate and the Hugoniot elastic limit on the distance traveled by the shock wave in the material were obtained. It was shown that, at the investigated loading modes, the high-rate plastic deformation occurs by dislocation slip and twinning. A characteristic feature of the structure of deformed samples is the presence of a great number of dislocation vacancy loops.