Vacancy Loops Research Articles

Hierarchical computational approaches of the effects of interstitial and vacancy loops on plastic deformation

ABSTRACTHierarchical modeling based on atomistic and continuum simulations were established to describe the fundamental characteristics of plastic deformation in irradiated materials. Typical irradiation defects of a self-interstitial atom (SIA) loop and vacancy loop are considered. At first atomic models, including a SIA loop and a vacancy as well as a straight dislocation loop in single crystals were constructed. Constant strain is applied to each model and the equilibrium configuration under deformation is calculated by a molecular statics simulation. Maximum shear stresses in various radii of irradiated defects are stored in a database for the continuum mechanics analysis. Then local interaction events between glide dislocation and irradiation defects were introduced through crystal plasticity finite element analysis. In this model the effect of radiation hardening was considered by referring to the experiment. We found that softening after the first yield event is caused by annihilation of irradiation defects resulting from unfaulting of the radiation defects.

Experimental study and numerical modelling of the irradiation damage recovery in zirconium alloys

Neutron irradiation damage in zirconium alloys used as fuel cladding tubes for Pressurized Water Reactors in the nuclear industry consists mainly in a high density of small prismatic dislocation loops. During post-irradiation heat treatment thermal annealing of loops occurs. This phenomenon has been investigated by transmission electron microscopy and microhardness tests. It has been shown that the loop density decreases while their mean size increases. Furthermore it was demonstrated that only vacancy loops remain present in the material after a long term annealing at high temperature. A mechanism based on vacancies diffusion has been proposed to explain the loop evolution during annealing. A cluster dynamic model, originally developed to compute the evolution of the microstructure under irradiation, has been adapted to the modelling of the annealing for zirconium alloys. This physically based model reproduces the loop size and density evolution during a large variety of heat treatments and also provides a better understanding of the mechanisms involved in the loop recovery.

Generation of c-component edge dislocations in α-zirconium during neutron irradiation – An atomistic study

The nucleation and multiplication of c-component edge dislocation segments during neutron irradiation in zirconium and its alloys is known to have important consequences to their in-reactor deformation behavior. Although there are ample experimental observations showing the close correlation between the edge-type and the screw-type of c-dislocations, the relation between them is unclear. In this paper, we performed atomistic study of the interaction between a [0 0 0 1] screw dislocation and a vacancy cluster in the form of a platelet on the basal plane. The local minimum-energy configuration was obtained using the conjugate-gradient method, with boundary relaxation achieved via a modified Green’s function method. Under stress-free conditions, the vacancy clusters maintained their cavity nature. With a [0 0 0 1] screw dislocation in the close neighborhood, vacancy clusters containing more than 23 vacancies collapse into faulted vacancy loops. Interaction at even closer range leads to the disappearance of the vacancy cluster and the development of an edge component on the originally straight screw dislocation in the form of a helical line. The implications of these findings are discussed in relation to the experimentally observed behavior of growth acceleration in zirconium and its alloys.

Cluster Dynamics modelling of irradiation growth of zirconium single crystals

This paper aims at modelling irradiation growth of zirconium single crystals as a function of neutron fluence. The Cluster Dynamics approach is used, which makes it possible to describe the variation of irradiation microstructure (dislocation loops) with neutron fluence. From the irradiation microstructure, the strain can be calculated along the axes of the lattice structure. The model is applied to the growth of annealed zirconium single crystals at 553 K measured by Carpenter and Rogerson in 1981 and 1987. The model is found to fit the experimentally measured growth of Zr single crystals very nicely, even at large neutron fluence where the ‘breakaway growth’ occurs. This was made possible by considering in the model the growth of vacancy loops in the basal planes. This growth of vacancy loops in the basal planes could be modelled by taking into account that diffusion of self-interstitial atoms (SIA) is anisotropic and that there exist in the basal planes some nucleation sites for vacancy loops (iron clusters), the density of which is considered constant over time.

Vacancy defects in Fe: Comparison between simulation and experiment

The evolution of radiation damage under heavy-ion irradiation in thin foils of pure bcc Fe has been investigated by simulation and experiment. Simulations showed that vacancy loops are about as mobile as interstitial loops, and can be lost to the surface of a foil. Consistent with this, in situ real-time dynamic observations of the damage evolution showed that loops, many of which are believed to be of vacancy nature, were mobile and were often lost during irradiation. Atomistic simulations of vacancy defects in Fe showed that spherical voids, rather than vacancy loops, represent the lowest energy configurations for clusters of vacancies of any size. The simulations also indicated that the stability of loops strongly varies depending on their size. Closed loops above a critical diameter (∼2 nm) are highly metastable due to the difficulty of their transformation into voids. The greater stability of voids explains why the loop yield in Fe and other ferritic materials is very low.

Model for evolution of crystal defects in UO 2 under irradiation up to high burn-ups

The model for dislocations evolution under irradiation conditions in UO 2 is developed and implemented in the MFPR code. Being combined with the MFPR set of microscopic equations for the evolution of point defects and their interactions with gas bubbles, a self-consistent consideration of the whole system of point and extended defects in irradiated fuel, including point defects (vacancies, interstitials and gas atoms), as well as extended defects (bubbles, dislocations, vacancy loops and pores), is attained. The MFPR code with the new defect evolution model is successfully validated against steady-irradiation experiments, in which the dislocation density and the bubble concentration and mean size were directly measured as functions of burn-up at ≈1000 K. Being applied to higher temperatures, the code allows mechanistic interpretation of the temperature threshold for the fuel restructuring observed in the rim-zone of high burn-up UO 2 fuel.

Cluster-dynamics modelling of defects in α-iron under cascade damage conditions

We report the calibration of a rate theory numerical code capable to reproduce the agglomeration of point-defects produced in α-iron by irradiation under cascade damage conditions. The input parameters are obtained by performing transmission electron microscopy (TEM) experiments in α-iron. It was irradiated at temperatures between 200 and 400 °C with high flux krypton ion under resolvable point-defect cluster conditions. The TEM analyse of the sample irradiated at the highest temperature reveals the presence of two dislocation loop populations: large ones are decorated with small ones, both vacancy and interstitial in type. The vacancy loops are proposal to be located in the compressive side of the large interstitial loops.

Structure and metastability of mesoscopic vacancy and interstitial loop defects in iron andtungsten

The most recent observations of dynamical time-dependent fluctuating behaviour ofmesoscopic radiation defects in body-centred cubic metals (Arakawa et al 2006Phys. Rev. Lett. 96 125506; 2007 Science 318 956–9; Yao et al 2008 Phil. Mag. at press) havehighlighted the need to develop adequate quantitative models for the structural stability ofdefects in the mesoscopic limit where defects are accessible to direct in situ electronmicroscope imaging. In pursuit of this objective, we investigate and compare several typesof mesoscopic vacancy and interstitial defects in iron and tungsten by simulating themusing recently developed many-body interatomic potentials. We show that themesoscopic vacancy dislocation loops observed in ion-irradiated materials are,without exception, metastable with respect to the transformation into sphericalvoids, but that the rate of this transformation and even the specific type of thetransformation mechanism depend on the defect size and the properties of thematerial.

Experimental and Modeling Approach of Irradiation Defects Recovery in Zirconium Alloys: Impact of an Applied Stress

Abstract During neutron irradiation, both interstitial and vacancy loops are formed in high concentration in zirconium alloys. Due to this high density of loops, the material is considerably hardened, but the recovery of the radiation damage during a heat treatment leads to a progressive softening of the irradiated material. The recovery of the radiation induced hardening has been investigated using microhardness tests. Transmission electron microscopy (TEM) observations performed on irradiated foils have also shown that the loop density falls while the loop size increases during the thermal annealing. Furthermore, the TEM analysis has revealed that only vacancy loops are present in the material after long term annealing, the interstitial loops having entirely disappeared. A numerical cluster dynamic modeling has also been used in order to reproduce the material recovery for various annealing conditions. The microstructural evolution during mechanical testing with various loading conditions has also been studied. It has been shown that during a creep test with low applied stress (130 MPa) and high temperature (450°C), the microstructure evolution can essentially be explained by the thermal recovery of the loops leading to glide of dislocations as found for an non-irradiated material. At intermediate temperature (400°C), it is shown that for low stress level (130 MPa) the microstructure evolution can also be explained by the thermal recovery of loops, whereas for higher stress (250 MPa), sweeping of loops by gliding dislocations can also occur. In addition, for an applied stress of 130 MPa and a temperature of 400°C, dislocation density is higher in the irradiated material than in the non-irradiated material deformed in the same conditions. It is also shown that secondary slip systems are more activated in the irradiated material than in the non-irradiated material. From this detailed analysis, the mechanical behavior during creep is interpreted in terms of microscopic deformation mechanisms.

Effect of mass of the primary knock-on atom on displacement cascade debris in α -iron

Results are presented from molecular dynamics (MD) simulations of displacement cascades created in α-iron (Fe) by primary knock-on atoms (PKAs) with energy from 5 to 20 keV and mass chosen to represent C, Fe and Bi. The PKA-Fe interaction potential at short range has been varied, and damage by molecular Bi2 has been simulated using two Bi PKAs. Four effects are reported. First, the PKA mass has a major effect on the damage produced in individual cascades while the PKA-Fe potential has little influence. Second, the total number of point defects produced in a cascade decreases with increasing PKA mass. This fact is not accounted for in models used conventionally for estimating damage. Third, interstitial loops of type and both vacancy and interstitial loops of ⟨100⟩ type are formed, the latter being observed in MD simulation for the first time. The probability of ⟨100⟩ loop appearance increases with increasing PKA mass as well as energy. Finally, there is a correlation between production of large vacancy and interstitial clusters in the same cascade.

Interface microstructure between Ni base-metal electrode and BaTiO3 dielectric

The interface microstructure in a simulated sandwich structure of Ni base-metal electrode and BaTiO3 dielectric has been studied by transmission electron microscopy. Some Ni grains have been oxidized to NiO; most of them although coarsened and poorly densified remained Ni metal. NiO formed during the reoxidation step at 1000 °C because the partial pressure of oxygen (pO2 ≈ 10−6 atm) in the controlled-sintering atmosphere was higher than the thermodynamic equilibrium value of pO2 = 4.68 × 10−11 atm. Crystallographic orientation relationships between NiO and BaTiO3 at the interface were determined. The BaTiO3–NiO interface was both twist and tilt boundaries that are characterized by dislocations of a mixed nature with Burgers vectors b = ½ ⟨0 0 1⟩ and ½ ⟨1 1 0⟩ and ⟨1 1 1⟩, described in the indices of pseudo-cubic BaTiO3. Dislocation loops were also found in BaTiO3 as well as along the NiO–BaTiO3 interface; the latter with was a vacancy loop formed by condensation of intrinsic Schottky defects. The Ni–BaTiO3 interface is built on and a configuration with opposite-charged ions stacked upon each other was energetically more favourable. The lattice mismatch was accommodated by misfit partials with b = ½ ⟨1 1 0⟩ that were dissociated from perfect dislocations with b = ⟨1 1 0⟩ probably by glide in on the metal–dielectric interface.

Molecular dynamics study on the formation of stacking fault tetrahedra and unfaulting of Frank loops in fcc metals

Critical conditions have been determined for intrinsic transformation of a vacancy Frank loop into a stacking fault tetrahedron in a face centered cubic metal by the molecular dynamics method. We found that a stacking fault tetrahedron can be formed from the scalene hexagonal vacancy Frank loops of wide range of sizes due to the dissociation of dislocations. We have also found atomistically the dynamical process in which vacancy and interstitial faulted Frank loops transform into perfect loops by the application of the external shear stress or by raising the temperature. We have determined numerically the critical shear stress and temperature for the initiation of unfaulting. The simulation results clearly unveiled the important role of temperature in the unfaulting mechanism of an interstitial Frank loop.

Internal Probe to Detect Defects from Cascades—In-situ Ion Irradiation Experiments Revisited

Abstract Our understanding of the evolution of extended defects during irradiation has progressed considerably since 1990 following the proposal of production bias by Bachu Singh and C. H. Woo. One of the important phenomena underlying this concept is that self-interstitials and interstitial clusters can migrate a long distance via one-dimensional motion. There have been a number of indirect experimental evidences supporting this mode of migration. However, the direct evidence has not necessarily been sufficient. In this paper, we revisit our former experimental results of in-situ observation of ion irradiation damage from the stand point of an internal probe for detecting point defect fluxes in an irradiation environment or those coming from nearby cascades. Surfaces, giving rise to specimen size effects, preexisting dislocations, intentionally preintroduced vacancy loops with stacking fault, irradiation induced vacancy clusters and loops, precipitates and precipitate-matrix interfaces, etc., are utilized to monitor the influx of point defects, particularly those of interstitials nature. Some of the reanalysis of the former results will be presented.

Dislocation Loops in Pressureless‐Sintered Undoped BaTiO3 Ceramics

Dislocation loops in pressureless‐sintered undoped BaTiO3 ceramics have been analyzed by transmission electron microscopy. The Burgers vector of the loops and its sense b=+1/2[010] were determined using the g·b=0 invisibility criteria, combined with the inside–outside contrast technique using (g·b)sg>0 or<0, keeping the deviation parameter sg>0. The edge‐vacancy nature was further ascertained by determining the loop habit plane normal n=[010]. Weak‐beam dark‐field imaging reveals that loops contained no stacking fault fringes; they are edge‐vacancy partial dislocation loops lying in {020} or {010} where parts of the TiO2 or BaO layer are vacant. It is suggested that the extrinsic defects of both cations and oxygen vacancies generated by non‐stoichiometry have condensed during sintering in air and are responsible for the formation of such vacancy loops.

Mechanism of recovery of the mechanical properties of neutron-irradiated metals in the course of thermocycling

The mechanism of recovery of the strength and strain characteristics of neutron-irradiated metals and alloys (up to their initial values observed prior to irradiation) during periodic quenching in the temperature range below the irradiation temperature is considered. It is assumed that the removal of radiation-induced defects (interstitial and vacancy loops) from radiation-hardened metals is associated with the formation of defect-free channels along the slip planes (the phenomenon of dislocation channeling) under the thermal stresses arising in each cycle of quenching. The relationships describing both the kinetics of the decrease in the yield strength σY and in the ultimate strength σU and the kinetics of the increase in the uniform strain eU of a preliminarily irradiated material with increasing number of quenching cycles are derived using the equations of dislocation kinetics. The theoretical results obtained are compared with experimental data on the kinetics of recovery of the mechanical properties of neutron-irradiated samples (the austenitic FeNiCr and ferritic FeCrMo structural steels and the titanium alloy TiAlZr) in the course of periodic quenching.

Modeling of the Simultaneous Evolution of Vacancy and Interstitial Dislocation Loops in hcp Metals Under Irradiation

Abstract We present a model of the homogeneous nucleation and growth of vacancy and interstitial loops in irradiated hcp metals, which allows one to find the size distribution function, the dose dependence of the mean parameters of the dislocation system, and to describe effects due to temperature, material parameters, and initial microstructure. The model is based on a hierarchy of coupled ordinary differential equations. The first two equations are the rate equations for vacancy and interstitial concentrations. Other equations describe random walks of interstitial and vacancy clusters in a size space, i.e., the time dependence of loop densities. As an input, the model contains the capture efficiencies of point defects by loops, which depend self-consistently on the loop size and dislocation density. We have considered two possible scenarios depending on the point defect dilatation volume ratio: (i) dislocation bias for interstitial atoms and (ii) dislocation bias for vacancies. The model results are qualitatively consistent with experimental observations of a coexistence of interstitial and vacancy dislocation loops on the same habit planes in Zr and other hcp metals. The temperature dependence of the resulting loop size distributions depends strongly on the material properties and the initial microstructure.

Identification and morphology of point defect clusters created in displacement cascades in α-zirconium

Atomic scale computer simulation of high-energy displacement cascades in α-zirconium has been carried out for a wide range of primary knock-on atom energy (10–25keV) and temperature (100–600K). A large number of vacancy and self-interstitial atom (SIA) clusters of various shapes and sizes was generated in more than 240 cascades. In spite of the variety of cluster structures, they can be categorized into three distinct configurations for vacancy and SIA clusters. Internal atom arrangements for all point defect clusters have been established and the type of stacking faults that can be assigned to vacancy clusters identified. The explanation of different relaxation patterns of prismatic vacancy loops occupying either even or odd number of neighbouring close-packed planes is suggested. Transformation of the pyramid-like vacancy cluster with a basal-plane extrinsic fault into prismatic vacancy loop is considered.

Simulations of electron elastic diffuse scattering patterns from individual nanometre-sized dislocation loops. I. Kinematical methodology

A new experimental technique has recently been developed for characterizing small dislocation loops in the electron microscope by collecting elastic diffuse scattering patterns in the vicinity of Bragg reflections. In this paper we develop the theory and computational approaches for simulating such patterns. We apply the anisotropic elastic theory of displacement fields of planar dislocation loops of arbitrary shape to compute the distortion diffuse scattering amplitudes. To do this we extend methods based on kinematical scattering theory, previously used to simulate X-ray and neutron diffuse scattering patterns. We demonstrate significant differences in the diffuse scattering patterns for the electron scattering case that arise from the small width of the incident electron beam, and under weak-beam conditions. We show that the method may be used to distinguish between individual, very small, vacancy or interstitial loops. We also show that elastic anisotropy may have an influence on elastic diffuse scattering patterns from loops, to an extent that varies with the magnitude of the deviation parameter.

Effect of self-interstitial diffusion anisotropy in electron-irradiated zirconium: A cluster dynamics modeling

A model based on the cluster dynamics approach was proposed in [A. Hardouin Duparc, C. Moingeon, N. Smetniansky-de-Grande, A. Barbu, J. Nucl. Mater. 302 (2002) 143] to describe point defect agglomeration in metals under irradiation. This model is restricted to materials where point defect diffusion is isotropic and is thus not applicable to anisotropic metals such as zirconium. Following the approach proposed by Woo [C.H. Woo, J. Nucl. Mater. 159 (1988) 237], we extended in this work the model to the case where self-interstitial atoms (SIA) diffusion is anisotropic. The model was then applied to the loop microstructure evolution of a zirconium thin foil irradiated with electrons in a high-voltage microscope. First, the inputs were validated by comparing the numerical results with Hellio et al. experimental results [C. Hellio, C.H. de Novion, L. Boulanger, J. Nucl. Mater. 159 (1988) 368]. Further calculations were made to evidence the effect of the thin foil orientation on the dislocation loop microstructure under irradiation. The result is that it is possible to reproduce for certain orientations the ‘unexpected’ vacancy loop growth experimentally observed in electron-irradiated zirconium [M. Griffiths, M.H. Loretto, R.E. Sallmann, J. Nucl. Mater. 115 (1983) 313; J. Nucl. Mater. 115 (1983) 323; Philos. Mag. A 49 (1984) 613]. This effect is directly linked to SIA diffusion anisotropy.

Vacancy dislocation loops in zirconium and their interaction with self-interstitial atoms

The present work aims at predicting at the atomic scale, binding energies of vacancies to vacancy clusters in zirconium, preparing this way the modelling of their growth. Empirical laws established on the basis of simulation results are suggested, describing the size dependence of formation and binding energies of small voids (involving up to 1000 atoms) as well as basal, prismatic and pyramidal vacancy loops involving the same number of vacancies. The detailed atomic configurations of the loops are examined and characterized by means of areas where atoms are mis-coordinated and by strain fields. The importance of mis-coordinated areas is emphasized by an examination of self-interstitial atom (SIA) diffusion mechanisms in the vicinity of basal vacancy loops. The loops act as sinks for SIAs that, depending on the temperature, migrate one- or three-dimensionally to the mis-coordinated areas from which they cannot escape. By this mechanism, the annihilation of vacancy loops by SIA absorption is inhibited.