Primary Knock-on Atom Research Articles

An insight into radiation resistance of D019 Ti3Al intermetallics

A molecular dynamics study of radiation damage created in collision cascades in D019 Ti3Al intermetallic compound and a Ti-Al binary disordered solid solution with the same chemical composition is carried out. Collision cascades are initiated by either Al or Ti primary knock-on atoms (PKA) with PKA energy 5 keV ≤EPKA≤ 20 keV in the two materials at temperature T ranging from 100 K to 900 K. A series of at least 32 different cascades for each (EPKA, T) set was simulated in order to imitate an isotropic spatial and random temporal distribution of PKAs, generate representative sampling and obtain statistically reliable quantitative results. The numbers of Frenkel pairs, 〈NFPα2〉 and 〈NFPα〉, formed in D019 Ti3Al intermetallics and Ti-25at.%Al disordered solid solution, respectively, were averaged over collision cascades with the same (EPKA, T) and used to quantify the radiation resistance against primary damage formation. It is shown that the relationship 〈NFPα2〉≤〈NFPα〉 is satisfied under all simulation conditions, i.e. D019 ordered crystal structure of Ti3Al intermetallics is an important feature affecting its radiation tolerance. Nevertheless, a relatively high resistance against the formation of primary radiation defects has been retained even after complete disordering of D019 Ti3Al, which points out to the existence of additional mechanisms governing its radiation tolerance.

An MD study of primary damage formation in aluminium

Molecular dynamics simulations were applied to study primary damage formation in collision cascades initiated by primary knock-on atoms (PKA) with energy EPKA=5, 10, 15 and 20 keV in aluminum at temperature T=100, 300 and 600 K. A series of 24 collision cascades for each EPKA,T set was simulated in order to assure statistical reliability of the obtained results. The number of Frenkel pairs, fraction of vacancies σvac and self-interstitials (SIA) σSIA in point defect clusters, the average vacancy Nvac and SIA NSIA cluster size, the average vacancy Yvac and SIA YSIA cluster per cascade yield and the average cascade relaxation time τc were evaluated as a function of EPKA,T. It was established that collision cascades in aluminium split into subcascades along the projectile trajectory. As a result, σvac,σSIA,Nvac,NSIA and τc do not depend on EPKA.

Study on the self-shielding and temperature influences on the neutron irradiation damage calculations in reactors

Displacement per Atom (DPA) is conventionally computed using the DPA cross sections in reactor applications. The DPA cross sections can be influenced by temperature through the Primary Knocked-on Atom (PKA) energy and the Doppler broadening of reaction cross sections. The former is shown not important due to the threshold energy of atomic displacement and the small value of thermal kinetic energy. For 56Fe, the Doppler broadening has limited influence on DPA cross sections due to high resonance energies. On the other hand, the self-shielding should be considered in the computation of DPA, which depends not only on the cross sections but also the corresponding recoil energies of the PKA. ECCO 1968-group calculations show that the self-shielding corrections on DPA cross sections are necessary for the computation of atomic displacement. In addition, the total DPA rate calculated by self-shielding corrected total cross sections is smaller than the sum of partial components. The recommended method to compute DPA is the calculation of each reaction, especially for coarse energy structures. The total DPA rate in ASTRID reactor inner core is 25 DPA/year, for which the contributions of the elastic scattering, total inelastic scattering, and disappearance reactions are 81.9%, 18.0%, and 0.1%, respectively. The corresponding relative reductions due to the corrections of multi-group cross sections are 11.3%, 5.9%, and 20.5%, respectively.

Multi-model quantification of defects in irradiated lithium titanate

Lithium based ceramics (Li2TiO3, Li4SiO4 etc.) in the packed pebble form, used in breeder blankets to breed tritium, are promising candidates for future fusion reactors. Neutron induced trap sites in the ceramic breeder affect the diffusion and inventory of tritium and thereby influence the quantity of tritium recovered. In the present work, a multi model framework has been employed to quantify the number of defects, which can be used to evaluate trap-sites, due to neutron irradiation in porous Li2TiO3 pebbles. This framework is based on a three stage calculation viz. (i) radiation transport, (ii) obtaining the primary knock-on atom (PKA) energy spectrum and (iii) quantifying the ensuing damage by collision cascade simulations. The output of one stage is coupled to the next stage and finally the defect distribution is obtained. We use radiation transport calculations to obtain the neutron spectrum in ceramic pebbles. This is used as an input to SPECTER, a code that uses evaluated cross-sections, to obtain the Primary Knock-on Atom (PKA) energy spectrum. The PKA energy spectrum is then used to find the number and distribution of vacancies and displacements in porous Li2TiO3 pebbles using binary collision approximation (BCA) based Monte Carlo simulations. The vacancy distribution and the number of vacancies in Li2TiO3 have been evaluated for the ITER neutron source using the above frame work. The PKA energy spectrum of Li, Ti and O PKAs, have been obtained using SPECTER, and their average energies are 680, 120 and 320 keV respectively. The collision cascade simulations shows the expected Bragg peak for the number of defects created and has a range of 6–8 microns for O and Li PKA respectively and a fraction of a micron for Ti PKA. The total number of displaced atoms which is equal to the number of vacancies, at the end of the collision cascades, obtained using the above framework has also been used to estimate the displacements per atom (dpa) in Li2TiO3 and this shows a good agreement with the dpa calculated using the NRT model.

Atomistic simulation of the effect of carbon content and carbon-rich region on irradiation response of α-Fe on picosecond timescale

α-Fe with low carbon content is a base material which is commonly used in manufacturing of Reactor Pressure Vessel (RPV) of commercial nuclear power plants. Carbon is generally diffused to α-Fe matrix to improve some of its mechanical properties. The presence of carbon may alter the irradiation response of the steel. In the current study, using molecular dynamics simulations, we have investigated the influence of carbon (∼in either dispersed form or carbon-rich region as chain) in the primary damage states of α-Fe low carbon steels. It is found that carbons in dispersed form have no significant effect on the self-interstitial atoms (SIAs) in α-Fe. While, carbon-rich (C-rich as pseudo-precipitation) region clearly increased the number of SIAs in bulk. A simple power formula was proposed to estimate the number of defects as a function of primary knock-on atom (PKA) energy and the number of atoms in the C-rich region.Cluster analyses of the defects formed in α-Fe containing 0–0.1 at.% dispersed carbon and with a C-rich region (with carbon chain of 0–100 atoms positioned in octahedral positions) showed that the presence of carbon in dispersed form had no effect on the average number of defect clusters (both the SIAs and the vacancies) in α-Fe containing 0–0.1 at.%. On the other hand, the average number of defect clusters for the α-Fe containing C-rich region apparently increases with increasing the number of carbon atoms in carbon chain. In addition, the average number of the interstitial clusters was significantly higher than that of the vacancy clusters.

Interactions between displacement cascade and dislocation and their influences on Peierls stress in Fe-20Cr-25Ni alloys

The interactions between dislocations and displacement cascades are investigated using molecular dynamics simulations. The primary knock-on atoms (PKAs) are placed at different distances to edge and screw dislocation lines. Specifically, an fcc Fe-20Cr-25Ni system is studied; the alloy is the based alloy for Alloy 709. The number of defects is calculated using Wigner-Seitz analysis in order to illustrate the effect of dislocations on cascades. The displacement cascades in systems containing dislocations tend to generate more total defects compared with bulk systems, but eventually lead to less surviving defects in the materials matrix due to interactions with dislocations. The changes in atomic structures of the dislocations after interacting with cascades are analyzed to understand how the primary damage affects dislocations. The displacement cascade potentially causes dislocation climb in edge dislocations and cross-slip in screw dislocations, which could serve as additional mechanisms contributing to the radiation-induced hardening (RIH) compared with conventional RIH models. To reveal this, Peierls stresses are calculated before and after cascades using molecular static simulations. This study provides critical information of how defect production and dislocations are correlated, especially when total dose is high, which needs to be taken into account in upper scale models, such as mean-field rate theory.

Radiation Defects in Aluminum: MD Simulations of Collision Cascades in the Bulk of Material

The molecular dynamics method has been used to simulate displacement cascades created by primary knock-on atoms (PKAs) with energies EPKA= 5, 10, 15, and 20 keV in aluminum at temperatures T = 100, 300, and 600 K. A series of 24 cascades was simulated for each pair of the parameters (EPKA, T) to ensure a representative sampling. The number of Frenkel pairs, the fraction of vacancies (evac) and self-interstitial atoms (SIA) (eSIA) in point defect clusters, the average yield of vacancy (Yvac) and SIA (YSIA) clusters per cascade, and the average relaxation time τc have been determined as a function of (EPKA, T). It has been shown that displacement cascades of in aluminum decompose into several sub-cascades along PKA trajectory. Such a spatial structure of cascades is responsible for the absence of the dependence of the values of 〈evac〉, 〈eSIA〉, 〈Nvac〉, 〈NSIA〉, and τc on the energy of PKAs.

Radiation Defects in Aluminum. Simulation of Primary Damage in Surface Collision Cascades

Molecular dynamics method has been applied to simulate collision cascades initiated by primary knock-on atoms (PKAs) with energy EPKA = 5, 10, 15, and 20 keV at temperatures T = 100, 300, and 600 K on the aluminum surface. A series of 48 cascades has been simulated for each pair of parameters (EPKA, T), providing a representative statistical sampling. The number of Frenkel pairs NFP, the fraction of vacancies evac and self-interstitial atoms (SIA) eSIA in clusters of point defects, the average size of vacancy 〈Nvac〉 and self-interstitial 〈NSIA〉 clusters, the average number of vacancy 〈Yvac〉 and self-interstitial 〈YSIA〉 cluster per cascade yield, and the average time τc of cascade relaxation as a function (ЕPKA, T) have been found. The level of primary damage, 〈evac〉, 〈eSIA〉, 〈Nvac〉, 〈NSIA〉, 〈Yvac〉 and 〈YSIA〉 have been found to be higher in surface cascades than those in displacements cascades in the bulk of material under the same simulation conditions. The morphology of surface cascades and the spatial separation of self-interstitial atoms and vacancies has been studied. Icosahedral self-interstitial clusters have been identified in displacement cascades in aluminum for the first time.

Develop a Model to Study the Energy Distribution of Cascades of Atomic Collisions

In this paper, based on the solution of the Boltzmann kinetic equation, we determine the energy distribution function describing the steady-state deceleration of the cascade of moving atoms taking into account their multiplication at the power interaction potential U∼1/rn.A new approach to the solution of the kinetic equation based on the extended concept of primary knocked-on atoms (PKA) is used for its calculation. One of the advantages of using the power interaction potential is that in this case it is possible to obtain simple analytical formulas for the distribution function of the cascade of slowing-down atoms taking into account their multiplication and demonstrate the simplicity and convenience of the proposed new approach to the solution of the kinetic equation. On the other hand, based on the obtained results it is possible to estimate the accuracy of various approximate solutions. It is shown that this approach will be applicable to other interatomic interaction potentials, if the average PKA energy loss in individual collisions decreases monotonically with decreasing energy, and the relative PKA energy loss in individual collisions will be small.

Application of special relativity in damage calculations

The Displacement per Atom (DPA) is one of the most important factors that influence the mechanical behaviors of materials during and after irradiation. However, the relativistic effect is not accounted for in typical calculations of DPA cross sections and Primary Knock-on Atom (PKA) spectra. The present work shows the computation of relativistic recoil energy. For incident energy lower than 20 MeV, the relativistic corrections are within 1% for neutron scattering reactions of 56Fe and nuclei with mass larger than 56Fe. The corresponding corrections on damage energy (equivalent to DPA with standard DPA metrics) is smaller than 0.5%. However, the relativistic effect is of importance for high incident energies, such as 200 MeV. For example, the relativistic recoil energy of continuum inelastic scattering is 10% higher than the classical one for all nuclei. The consideration of relativistic effect increases the recoil energy for the elastic scattering. Both positive and negative relativistic corrections are possible for both discrete and the inelastic scatterings. A consequent result is the broadening of PKA spectra.

MD Simulations and first principles to evaluate the role of binary Fe–V alloys layer on the radiation resistance in the alpha-iron

ABSTRACTRadiation damage in reactor materials caused by the collision of the fast neutrons has a great impact on the reliability and safety of nuclear reactors. The element vanadium has attracted interest in many fields due to its advantageous properties in alloys. Thus, molecular dynamics simulation (MD) and first-principles calculation have been executed here to explore the radiation-resistant properties of five materials adding a layer in the bulk (pure iron and four types of Fe–V alloys containing 10%-40% V). The following results were inferred from these simulations. Firstly, the number of Frenkel pairs (FPs) at the stable quenching stage in the bulk decreases when the Fe–V alloy is added as an anti-radiation layer to the bulk. These benefits are evident for the Fe80V20 and alloy layers with more vanadium. The main reason is that the Fe–V binding energy is greater than the Fe-Fe binding energy, which can make the Primary Knock-On atom (PKA) lose more energy at the Fe–V alloy layer. Secondly, the average value of point-defect, cluster and defect clustered fractions in the bulk of Fe–V alloy is smaller than that in the pure iron at the stable quenching stage, especially for the Fe80V20 alloy.

Investigation of primary radiation damage near free surfaces in iron nanofoam with a model cylindrical nanovoids structure

In this research, in order to investigate primary radiation damage in iron nanofoam, simulation of displacement cascade near cylindrical nanovoids is performed using molecular dynamics. A primary knocked-on atom with 3, 6 and 9 keV energies and velocity parallel to the cylinder axis at 300 K is considered. 1–4 nanovoids are used as the model structure for free surfaces. It is identified that interaction between the displacement cascades and free surfaces is very sensitive to PKA energy and the distance of free surfaces. Near-surface cascade mechanism is observed when the displacement cascade interacts with a single cylindrical free surface, where clusters of bulk vacancies and a rim of adatoms are formed. In this case, based on the location of these defects rather free surface, two sub-mechanisms are identified. It is recognized that the degree of the penetration of the cascade into the cylindrical surfaces, plays an important role in forming vacancies and vacancy clusters in the ligament after the cooling of the cascade. Results show that when the PKA energy is 9 keV, enhancement of number of nanovoids increases the number of vacancies in the bulk. In this case, formation of vacancy planes is observed between the cylindrical nanovoids. The absorption of bulk vacancy clusters by the free surfaces is observed when displacement cascade is generated by a 6 keV PKA in close vicinity of four cylindrical surfaces.

Features of plasticity nucleation in deformed vanadium crystallite under irradiation

Molecular dynamics simulation of the defect structure nucleation in deformed vanadium crystallites under irradiation was carried out taking into account their internal structure. The crystallites studied contained grain boundaries of different types. The behavior of crystallites deformed to values close to the limit of elasticity under irradiation was simulated by the generation of atomic displacement cascades. The energy of the primary knock-on atoms which generated atomic displacement cascades was 5 keV. It was found that atomic displacement cascades in elastically deformed crystallites can lead not only to the formation of radiation defects, but also cause plasticity. It is shown that the nucleation of plasticity in crystallite is associated with elastic waves. These waves are formed in the region of atomic displacement cascade development. Their generation is due to the high-speed thermal expansion of the region in which atomic displacement cascade develops.

Characterization of radiation damage in TiO2 using molecular dynamics simulations

Molecular dynamics simulations are carried out to characterize irradiation effects in TiO2 rutile, for wide ranges of temperatures (300–900 K) and primary knock-on atom (PKA) energies (1–10 keV). The number of residual defects decreases with increased temperature and decreased PKA energy, but is independent of PKA type. In the ballistic phase, more oxygen than titanium defects are produced, however, the primary residual defects are titanium vacancies and interstitials. Defect clustering depends on the PKA energy, temperature, and defect production. For some 10 keV PKAs, the largest cluster of vacancies at the peak of the ballistic phase and after annealing has up to ≈1200 and 100 vacancies, respectively. For the 10 keV PKAs at 300 K, the energy storage, primarily in residual Ti vacancies and interstitials, is estimated at 140–310 eV. It decreases with increased temperature to as little as 5–180 eV at 900 K. Selected area electron diffraction patterns and radial distribution functions confirm that although localized amorphous regions form during the ballistic phase, TiO2 regains full crystallinity after annealing.

Monte Carlo simulation of PKA distribution along nanowires under ion radiation

Abstract An open-source and full-3D Monte Carlo simulation code, Mat-TRIM, was developed in MATLAB to study the primary knock-on atom (PKA) statistics along nanowires under ion radiation. It is based on TRIM/SRIM’s physics; however, compared to TRIM/SRIM, it enables us to properly handle the 3D geometry of a cylindrical nanowire and a planar source of ions. In this paper, we first discuss the mechanism of Mat-TRIM, followed by some validation examples. Then the distributions of ion density, PKA density, PKA total energy, and PKA average energy in nanowires are explored. Significant differences have been found between the slab and the nanowire simulations. The relative error of a 1D slab and the assumption of a point beam source can be more than 1000% when the nanowire is around 20 nm in diameter. In addition, collisions with electrons is demonstrated to be the dominant mechanism of energy loss in narrow nanowires. Our results reveal that full-3D simulations which correctly treat ion leakage at sample boundaries are necessary to properly simulate PKA production in nano-sized targets.

Molecular dynamics simulations of the primary irradiation damage in Zirconium

Atom-scale numerical calculations were performed to investigate the damage behavior in close-packed hexagonal zirconium (HCP-Zr) by primary irradiation through a molecular dynamics (MD) study. The influences of Primary Knock-on Atom (PKA) energy (EPKA), the PKA incident direction and the ambient temperature (T) on the cascade collision were studied comprehensively. The results show that the athermal recombination corrected displacements per atom (arc-dpa) model is more accurate in comparison with the Norgett-Robinson-Torrens (NRT) model when predicting the steady vacancy (Ns). It was found that the vacancy peak (Npeak), the peak time (tpeak), and the steady time (ts) increase as EPKA and T increase. The steady vacancy also increases with the increase of EPKA. It was also found that Ns increases and subsequently decreases by increasing T, suggesting that there is a suitable temperature to maximize Ns when EPKA is constant. In addition, it was discovered that the PKA incident direction has little effect on vacancy dynamic history. It was proved that EPKA can worsen the irradiation damage in crystal Zr, but T can relieve such damage. In addition, the incident direction was found to have an insignificant effect on the damage. This study highlights that the steady vacancy concentration (C) can characterize the material irradiation damage.

Effects of stacking fault energies on formation of irradiation-induced defects at various temperatures in face-centred cubic metals

ABSTRACTBy using the six sets of interatomic potentials for face-centred cubic metals that differ in the stacking fault energy (SFE) while most of the other material parameters are kept almost identical, we conducted molecular dynamics simulations to evaluate the effects of SFE on the defect formation process through collision cascades. The simulations were performed at 100, 300 and 600 K, with a primary knock-on atom energy of 50 keV. The number of residual defects is not dependent on the SFE at all the temperatures. For clusters of self-interstitial atoms (SIAs), their clustering behaviour does not depend on the SFE, either. However, the ratio of glissile SIA clusters tends to decrease with increasing SFE. This is because perfect loops, the edges of which split into two partial dislocations with stacking fault structures between them in most cases, prefer to form at lower SFEs. The enhanced formation of glissile SIA clusters at lower SFEs can also be observed even at increased temperature. Because most large vacancy clusters have stacking fault structures, they preferentially form at lower SFE; however, it is observed only at the lowest temperature, where the mean size increases with decreasing SFE. At higher temperatures, because of their extremely low number density, the vacancy clustering behaviour does not depend on the SFEs.

Evaluation of damage in neutron irradiated boron carbide

When irradiated in a reactor, neutron absorber materials undergo two different damages induced, first, by the elastic scattering of neutrons; second by the neutron absorption reactions. In boron carbide irradiated in a fast neutron flux, neutron scattering and the slowing-down of He and Li arising from the (n,α) absorption reaction both lead to the displacement of B and C atoms which energy ranges up to a few MeV. Simulating the neutron damage by ion irradiation requires the calculation of the damage produced in both cases. In this paper we propose an estimation of the actual defect production rate resulting from the fast neutron irradiation. For this, we first estimate the energy spectra of both the primary knocked-on atoms and atoms created by the absorption reactions, here in a Phenix-like neutron spectrum. We then deduce from SRIM calculations the actual energy distribution of all the atoms displaced along the displacements cascades induced by those primary projectiles. At last, we obtain an estimation of the number of displaced atoms per produced helium, about 305, most of them resulting from neutron scattering. This is far from a Kinchin-Pease or NRT estimation, of the order of several thousands, this arising from the fact that most of the energy is dissipated through electronic interactions. Such results are then used in order to perform ion irradiations aiming at a realistic simulation of synergetic effects of helium implantation and damage production.

A combined BCA-MD method with adaptive volume to simulate high-energy atomic-collision cascades in solids under irradiation

We present a method combining the Binary Collision Approximation (BCA) and Molecular Dynamics (MD) with adaptive volume to simulate high-energy collision cascades in solids under irradiation. The results obtained with the BCA-MD method with adaptive volume are in very good agreement with those obtained with full MD calculations. The BCA-MD predicts very well in a broad range of Primary Knock-on Atom (PKA) energies the different phases of evolution of the cascade, the number of Frenkel pairs, the fraction of point defects in clusters and their size distribution. The BCA-MD method proposed here achieves a considerable acceleration of MD simulations with a speedup factor that increases with the PKA energy. For a PKA energy of 80 keV in Fe, the speedup measured is higher than 30. For a PKA energy of 0.5 MeV in Fe, by comparison with MD simulations performed by other authors, we estimate that the BCA-MD accelerates MD simulations by a factor 312.

Propagation of uncertainties in basic nuclear reaction data to uncertainties in the parameters of primary radiation damage by neutrons

The primary radiation damage formation in materials subjected to neutron radiation is very sensitive to the energy spectra of primary knock-on atoms (PKAs) and their collision cascade in the crystal lattice. The estimated values of the primary radiation damage metrics, such as displacements per atom (dpa) cross sections, integrated dpa, PKA spectrum and spectrum averaged PKA energy are uncertain because of uncertainties present in both the basic nuclear reaction data and the displacement damage model parameters. The Total Monte Carlo (TMC) methodology, which uses the random evaluated nuclear data files for nuclides, is well recognized to propagate the uncertainties in basic nuclear data to the derived quantities in nuclear reactor physics. The uncertainties in the above mentioned primary radiation damage parameters are obtained in this study by propagating the uncertainties in basic evaluated nuclear data, following the TMC methodology. The knowledge of uncertainties in the spectrum averaged PKA energies also enables us to ascertain the uncertainties in the production of vacancies through self-ion simulations using SRIM-2013 code. The present study is an outcome of our systematic approach towards establishing the procedure. This includes pre-processing a large number of TENDL nuclear data random files using NJOY-2016, developing an indigenous code CRaD for handling these point and multigroup data libraries and computing primary radiation damage metrics and their associated uncertainties including energy-energy and nuclear reaction channel-channel correlation matrices. The uncertainties in dpa cross sections and PKA spectra due to uncertainties in basic nuclear data are found to be comparatively larger than the uncertainties in respective integrated parameters; viz. dpa and average PKA energy. This study also confirms the non-Gaussian distributions of derived primary radiation damage parameters.