Atomic Displacement Cascades Research Articles

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers, and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.

МОДЕЛИРОВАНИЕ ЗАРОЖДЕНИЯ ПЛАСТИЧЕСКОЙ ДЕФОРМАЦИИ В МЕХАНИЧЕСКИ НАГРУЖЕННЫХ КРИСТАЛЛИТАХ ПРИ РАДИАЦИОННОМ ВОЗДЕЙСТВИИ

The investigation of plastic deformation nucleation in metals and alloys under irradiation and mechanical loading is one of the topical issues of materials science. Specific features of nucleation and evolution of the defect system in stressed and irradiated iron, vanadium, and copper crystallites were studied by molecular dynamics simulation. Mechanical loading was performed in such a way that the modeled crystallite volume remained unchanged. The energy of the primary knock-on atom initiating a cascade of atomic displacements in a stressed crystallite was varied from 0.05 to 50 keV. It was found that atomic displacement cascades might cause global structural transformations in a region far larger than the radiation-damaged area. These changes are similar to the ones occurring in the process of mechanical loading of samples. They are implemented by twinning (in iron and vanadium) or through the formation of partial dislocation loops (in copper).

Generation of shock waves in iron under irradiation

Molecular dynamics simulation is employed to study peculiarities of the formation and propagation of shock waves generated by atomic displacement cascades in iron crystallites under irradiation. The interaction of shock waves with point defects and their clusters is investigated. Atomic interactions are described with the use of the pair central-symmetric potential. Parameters of shock waves generated by atomic displacement cascades are evaluated and their dependence of the crystallographic direction, energy of a primary knock-on atom, and crystallite temperature is determined. These waves are shown to cause point defect clusters to rearrange.

Long term simulation of point defect cluster size distributions from atomic displacement cascades in Fe70Cr20Ni10

We have used an Object Kinetic Monte Carlo (OKMC) model to simulate the long term evolution of the primary damage in Fe70Cr20Ni10 alloys. The mean number of Frenkel pairs created by different Primary Knocked on Atoms (PKA) was estimated by Molecular Dynamics using a ternary EAM potential developed in the framework of the PERFORM-60 European project. This number was then used to obtain the vacancy–interstitial recombination distance required in the calculation of displacement cascades in the Binary Collision Approximation (BCA) with code MARLOWE (Robinson, 1989). The BCA cascades have been generated in the 10–100keV range with the MARLOWE code and two different screened Coulomb potentials, namely, the Molière approximation to the Thomas–Fermi potential and the so-called “Universal” potential by Ziegler, Biersack and Littmark (ZBL). These cascades have been used as input to the OKMC code LAKIMOCA (Domain et al., 2004), with a set of parameters for describing the mobility of point defect clusters based on ab initio calculations and experimental data. The cluster size distributions have been estimated for irradiation doses of 0.1 and 1dpa, and a dose rate of 10−7dpa/s at 600K. We demonstrate that, like in the case of BCC iron, cluster size distributions in the long term are independent of the cascade energy and that the recursive cascade model suggested for BCC iron in Souidi et al. (2011) also applies to FCC Fe70Cr20Ni10. The results also show that the influence of the BCA potential is sizeable but the qualitative correspondence in the predicted long term evolution is excellent.

Field ion microscopy of cascades of atomic displacements in metals and alloys after various types of irradiation

Experimental results on atomic-spatial investigation of radiative defect formation in surface layers of materials, initiated by neutron bombardment (of Pt, E > 0.1 MeV) and ion implantation (in Cu3Au: E = 40 keV, F = 1016 ion/m2, j = 10−3 A/cm2), are considered. Quantitative estimates are obtained for the size, shape, and volume fraction of cascades of atomic displacements formed under various types of irradiation in the surface layers of the materials. It is shown that the average size of radiation clusters after irradiation of platinum to a fast neutron fluence of 6.7 × 1022 m−2 (E > 0.1 MeV) is about 3.8 nm. The experimentally established average size of a radiation cluster (disordered zone) in the alloy after ion bombardment is 4 × 4 × 1.5 nm.

MD Simulation of Atomic Displacement Cascades in Random Fe-9at.%Cr Binary Alloy with Twin Grain Boundaries

The present paper is devoted to radiation damage simulation of Fe-9at.%Cr binary alloy with twin grain boundaries (GBs) by the molecular dynamics method. Evaluations of specific energy of five GBs and sizes of corresponding GB regions have been obtained for iron and FeCr alloy at temperatures of 0 and 300 K. The binding energies of the vacancy, self-interstitial atom (SIA) and substitutional Cr atom to the GB in pure Fe have been estimated. The results showed that GB regions are energetically preferable for the point defects. Interaction of 10 keV displacement cascades with the GBs has been studied. The tendency to accumulate at the GB region has been shown for produced defects. Some quantitative results which describe features of radiation damage nearby the GB have been obtained. It is revealed that Cr fraction in SIAs inside the GB region is slightly lower than that in the initial alloy matrix. Cr fraction in interstitial configurations outside the GB region is almost three times as high. However, no remarkable chromium redistribution nearby the GB has been detected.

Cascade defect evolution processes: Comparison of atomistic methods

Determining defect evolution beyond the molecular dynamics (MD) time scale is critical to bridging the gap between atomistic simulations and experiments. The recently developed self-evolving atomistic kinetic Monte Carlo (SEAKMC) method provides new opportunities to simulate long-term defect evolution with MD-like fidelity to the atomistic processes involved. To demonstrate this capability, three examples are presented in which SEAKMC has been used to investigate the evolution of typical radiation-induced defects in bcc iron. Depending on the particular example, SEAKMC results are compared with those obtained using two other on-the-fly KMC techniques, object KMC, and MD. The three examples are: (1) evolution of a vacancy-rich region similar to the core of a displacement cascade, (2) the stability of recently reported interstitial clusters with a structure similar to the C15 Laves phase, and (3) long-term aging of atomic displacement cascade debris. In the various examples, the SEAKMC approach provides better agreement with MD simulations, highlights the importance of the underlying atomistic processes, and provides new information on long-term defect evolution in iron.

Ejection of Au and Si nanocrystals from Au implanted Si(1 0 0) by MeV heavy ion irradiation

Si(100) substrates implanted with 32keV Au− ions, were irradiated with 3MeV Au3+ ions at an angle of 60°. Transmission electron microscopy (TEM) studies on sputtered particles collected on catcher grids revealed the presence of Au and Si nanocrystals. The size distribution of collected Au nanocrystals exhibited inverse power law dependence with a decay exponent of 2. Atomic force microscopy (AFM) analysis of irradiated sample showed the presence of surface craters along with hillocks. The formation of Au and Si nanocrystals in MeV ion irradiated Au doped amorphous Si layer can be attributed to the localized melting due to thermal spike phase of atomic displacement cascades produced by MeV Au ion impacts.

On the use of SRIM for computing radiation damage exposure

The SRIM (formerly TRIM) Monte Carlo simulation code is widely used to compute a number of parameters relevant to ion beam implantation and ion beam processing of materials. It also has the capability to compute a common radiation damage exposure unit known as atomic displacements per atom (dpa). Since dpa is a standard measure of primary radiation damage production, most researchers who employ ion beams as a tool for inducing radiation damage in materials use SRIM to determine the dpa associated with their irradiations. The use of SRIM for this purpose has been evaluated and comparisons have been made with an internationally-recognized standard definition of dpa, as well as more detailed atomistic simulations of atomic displacement cascades. Differences between the standard and SRIM-based dpa are discussed and recommendations for future usage of SRIM in radiation damage studies are made. In particular, it is recommended that when direct comparisons between ion and neutron data are intended, the Kinchin–Pease option of SRIM should be selected.

Radiation damage in cubic-stabilized zirconia

Cubic yttria-stabilized zirconia (YSZ) can be used for nuclear applications as an inert matrix for actinide immobilization or transmutation . Indeed, the large amount of native oxygen vacancies leads to a high radiation tolerance of this material owing to defect recombination occurring in the atomic displacement cascades induced by fast neutron irradiation or ion implantations , as showed by molecular dynamics (MD) simulations. Amorphization cannot be obtained in YSZ either by nuclear-collision or electronic-excitation damage, just like in urania. A kind of polygonization structure with slightly disoriented crystalline domains is obtained in both cases. In the first steps of damage, specific isolated point defects (like F + -type color centers) and point-defect clusters are produced by nuclear collisions with charged particles or neutrons. Further increase of damage leads to dislocation-loop formation then to collapse of the dislocation network into a polygonization structure. For swift heavy ion irradiations , a similar polygonization structure is obtained above a threshold stopping power value of about 20–30 keV nm −1 .

MD simulation of atomic displacement cascades near chromium-rich clusters in FeCr alloy

The paper reports simulation of cascades in Fe–9at.%Cr binary alloy containing chromium-rich clusters. The simulation is performed by the molecular dynamics method at the initial temperature of 300K and primary knock-on atom energy of 15 and 20keV. Spherical clusters containing 95at.% of Cr with diameter of 1–5nm have been considered. The properties of cascade evolution in the presence of chromium-rich cluster are studied. It is shown that these clusters tend to dissolve in collision cascades. However, clusters with diameter of ⩾3nm exhibit only slight modifications and can be considered stable. Parameters of small (1–2nm) clusters can change significantly and, in some cases, a 1nm cluster can be totally dissolved.

Molecular dynamics simulation of cascade-induced ballistic helium resolutioning from bubbles in iron

Molecular dynamics simulations have been used to assess the ability of atomic displacement cascades to eject helium from small bubbles in iron. This study of the ballistic resolutioning mechanism employed a recently-developed Fe–He interatomic potential in concert with an iron potential developed by Ackland and co-workers. The primary variables examined were: irradiation temperature (100 and 600K), cascade energy (5 and 20keV), bubble radius (0.5 and 1.0nm), and He-to-vacancy ratio in the bubble (0.25, 0.5 and 1.0). Systematic trends were observed for each of these variables. For example, ballistic resolutioning leads to a greater number of helium atoms being displaced from larger bubbles and from bubbles that have a higher He/vacancy ratio (bubble pressure). He resolutioning was reduced at 600K relative to 100K, and for 20keV cascades relative to 5keV cascades. Overall, the results indicate a modest level of He removal by ballistic resolutioning. The results may be particularly relevant to fusion irradiation conditions which produces high levels of helium by transmutation. They can be used to provide initial guidance in selection of a “resolution parameter” that can be employed in kinetic models to predict the bubble size distribution that evolves under irradiation.

Mechanisms of radiation damage of zircons deduced from computer simulation

The radiation resistance of zircon (ZrSiO4) was comparatively tested with computer simulations of four different sets of parameters of interatomic potentials. The energies of Frenkel pairs (FP) for Zr, Si, and O atoms were calculated using the Mott-Littleton method in approximation of isolated defects. The difference between the FP energies calculated for four potentials and the FP energies obtained ab initio is the least in the one of the four calculated potentials that takes into account the ab initio data for Zircon 3. The formation of an atomic displacement cascade (ADC) after the passage of the initially knocked-out Th atom with energy of 20 keV was investigated using the molecular dynamics method. The number of FP in ADC reaches 5300 to 61 900, depending on the chosen potential. The number of FP at the end of the simulation varies from 480 to 4970. The distribution of internodal oxygen atoms in zircon has been studied. It is shown that within a time (t) interval of 0–0.1 ps (ballistic stage), the internodal oxygen atoms knocked-out from the initial equilibrium site are predominant (O1 defects). Thereby the Si-O bond is ruptured. The mean displacement of those defects is 2–3 A. The probability of their survival is 34–73% depending on the chosen potential. After t = 0.1 ps (onset of the thermal stage), many SiO4 tetrahedra in zircon are displaced with formation of a great amount of internodal oxygen atoms, because the Si-O bond is not ruptured. The mean displacement of those O2 defects is 1 A; the probability of their survival is insignificant: 1.5–3.0% depending on the chosen potential. The total amount of internodal oxygen atoms consists of O2 defects (19–25%) and largely of O1 defects. A parameter characterizing that part of the energy of the initially knocked-out atom, which is consumed for FP, has been introduced. The physically acceptable values of this parameter (<1) are obtained only for Zircon 3 potential. The results show that a substantial discrepancy in relative amounts of Si and O atoms with displacements for 0.3–0.5 A from the equilibrium site exists for different potentials. In particular, the number of FP in zircon diminishes with decrease in mobility of atoms. It has been established that the lower the mobility of atoms, the lower the number of FP, and the most reasonable consistency with the preset conditions of the computer simulation is provided by Zircon 3 potential.

Resonant charging and stopping power of slow channelling atoms in a crystalline metal

Fast moving ions travel great distances along channels between low-index crystallographic planes, slowing through collisions with electrons, until finally they hit a host atom initiating a cascade of atomic displacements. Statistical penetration ranges of incident particles are reliably used in ion-implantation technologies, but a full, necessarily quantum-mechanical, description of the stopping of slow, heavy ions is challenging and the results of experimental investigations are not fully understood. Using a self-consistent model of the electronic structure of a metal, and explicit treatment of atomic structure, we find by direct simulation a resonant accumulation of charge on a channelling ion analogous to the Okorokov effect but originating in electronic excitation between delocalized and localized valence states on the channelling ion and its transient host neighbours, stimulated by the time-periodic potential experienced by the channelling ion. The charge resonance reduces the electronic stopping power on the channelling ion. These are surprising and interesting new chemical aspects of channelling, which cannot be predicted within the standard framework of ions travelling through homogeneous electron gases or by considering either ion or target in isolation.

Radiation resistance of the xenotime YPO4 from the computer simulation data

The radiation resistance of the mineral xenotime YPO4 has been investigated using computer simulation methods. The optimal criteria for the appropriate choice of the parameters of the interatomic potentials used for the simulation of α-decay in minerals have been proposed. The formation of a cascade of displaced atoms in the structure of xenotime after the passage of a primarily knocked thorium atom with an energy of 20 keV has been studied using the molecular dynamics method. The specific features of the formation and annealing of individual defects in the structure of xenotime have been considered using the Mott-Littleton method. The dependences of the energy of formation of Frenkel pairs and the probability of their annihilation during the annealing of a cascade of atomic displacements on the distance between the vacancy and the interstitial site have been analyzed within the framework of the supercell approximation.

On the correlation between primary damage and long-term nanostructural evolution in iron under irradiation

Atomic displacement cascades in solids are complex phenomena, the outcome of which can be statistically characterised by properties such as their spatial extent, morphology and the spatial correlation of defects. Some properties scale in a simple way with parameters such as the cascade energy, others have limited variability with energy, for example point defect cluster size distributions. Taking advantage of the latter invariance, we use object kinetic Monte Carlo simulations to demonstrate that most properties of displacement cascade play no significant role in the evolution of point defect cluster size distributions after long enough time. It is suggested that reliable long-term predictions are possible, when using only the self-interstitial and vacancy cluster size distributions from low energy displacement cascades as building blocks to represent the complete spectrum of cascade energies obtained under neutron irradiation conditions. This is shown on the basis of recursive properties of displacement cascades evidenced for the first time and taking only approximately into account the average volumes in which vacancies and self-interstitial atoms are confined. The model has been successfully used to simulate the evolution of point defect clusters in iron for displacement rates in the range of 10 −6 dpa/s and doses of the order of 0.1 dpa. The applicability beyond this range and to more complex materials is discussed.

Molecular dynamics simulation of atomic displacement cascades in Fe-9 at % Cr and Fe-9 at % Cr-0.1 at % C alloys

The atomic displacement cascades in Fe-9 at % Cr and Fe-9 at % Cr-0.1 at % C alloys are studied by molecular dynamics simulation at an initial temperature of 600 K. The average fractions of defects that “survive” in a displacement cascade are calculated for primary knocked-on atom (PKA) energies of 0.1–20 keV, and the number and size of the vacancy and interstitial-atom clusters that form in a displacement cascade are determined. Carbon at the concentration under study is found not to affect the number of survived defects and the cascade efficiency. At PKA energies of 15 and 20 keV, the presence of carbon slightly decreases the fraction of point defects forming clusters.

Material degradation under DEMO relevant neutron fluences

In fusion power reactors, the plasma facing and breeding-blanket components will suffer intense irradiation by 14 MeV neutrons. These high-energy fusion neutrons will produce atomic displacement cascades and nuclear transmutation reactions inside the irradiated materials, and these will result in important radiation damage and effects. In the present paper, typical examples of radiation damage and effects on candidate materials for plasma facing components in fusion power reactors are presented and discussed.

Evolution of atomic collision cascades in vanadium crystal with internal structure

The formation of radiation-damage regions (radiation-damage cascades) in vanadium crystallites with internal structures (intergrain boundary) has been simulated by the molecular-dynamic method. The interatomic interaction is described within the embedded-atom method. A relatively small number of clusters of intrinsic point defects (vacancies and self-interstitial atoms) are formed both in ideal vanadium crystallites and in crystallites with boundaries after the relaxation of atomic-displacement cascades. The evolutionary character of atomic-displacement cascades is determined in many respects by the presence of extended boundaries in materials. The intergrain boundaries hinder the propagation of atomic-displacement cascades and store many radiation-induced defects.

MD simulation of atomic displacement cascades in Fe–10 at.%Cr binary alloy

Molecular dynamics simulation of atomic displacement cascades up to 20 keV has been performed in Fe–10 at.%Cr binary alloy at a temperature of 600 K. The N-body interatomic potentials of Finnis–Sinclair type were used. According to the obtained results the dependence of “surviving” defects amount is well approximated by power function that coincides with other researchers’ results. Obtained cascade efficiency for damage energy in the range from 10 to 20 keV is ≈0.2 NRT that is slightly higher than for pure α-Fe. In post-cascade area Cr fraction in interstitials is in range 2–5% that is essentially lower than Cr content in the base alloy. The results on size and amount of vacancy and interstitial clusters generated in displacement cascades are obtained. For energies of 2 keV and higher the defect cluster average size increases and it is well approximated by a linear dependence on cascade energy both for interstitials and vacancies.