Size Of Interstitial Clusters Research Articles

An Object Kinetic Monte Carlo Simulation for Defect Evolution of Neutron‐Irradiated Reactor Pressure Vessel Steels: Carbon Sensitive Study

Herein, the defect evolution in the FeCMnNi model alloy is investigated by the gray‐alloy method in an object kinetic Monte Carlo (OKMC) model. Based on the parameters of the Fe–C system, the influence of Mn and Ni is implicitly considered, and the migration energy of mobile defects is modified. The number density of interstitial clusters and vacancy clusters in simulation has a good agreement with experimental results. The defect evolution features versus carbon and solutes concentration are also studied. The simulation results show that the number density of defect clusters increases with increasing carbon or solutes concentration. The average size of interstitial clusters decreases, while the average size of vacancy clusters is hardly affected by increasing impurity/solutes concentration. The defect features do not show a saturation tendency with increasing carbon/solutes concentrations. It also seems the influence of solutes concentration is more sensitive on defect features than carbon concentration in this FeCMnNi alloy.

Effects of oversized tungsten on the primary damage behavior in Fe-W alloys

Tungsten (W) is proposed to replace molybdenum (Mo) as an alternative minor alloying element in iron (Fe) based ferritic alloys to reduce the activation time upon irradiation. Tungsten, which is about 10.5% larger in atomic radius or 34.8% larger in atomic volume than Fe, can induce both global volume expansion and local lattice distortion in the Fe matrix. To understand how oversized W influences the defect production behavior in Fe-based alloys, molecular dynamics simulations are conducted to study the primary damage in three systems at 300 K: (a) unstrained pure Fe, (b) Fe-5at.%W (Fe-5W) alloy, and (c) strained pure Fe with the same volume expansion as the Fe-5W. Compared to the unstrained pure Fe, both Fe-5W and strained pure Fe result in producing more Frenkel pairs at high irradiation energies, indicating that the global volume expansion may lead to enhanced defect production. Meanwhile, the damaged Fe-5W alloy contains many C15 Laves-phase-like interstitial clusters, while the interstitial clusters in the unstrained and strained pure Fe systems are mainly crowdion bundles or dislocation loops. The average size of vacancy clusters in the Fe-5W alloy is much smaller than its counterparts in the two pure Fe systems. The average size of interstitial clusters in the Fe-5W alloy is also smaller than those in the two pure Fe systems. These results indicate that the local lattice distortion induced by oversized W can significantly influence the morphologies and size distributions of defect structures. Finally, defect formation energies are calculated to interpret the different defect production behaviors in these systems.

Primary radiation damage near grain boundary in bcc tungsten by molecular dynamics simulations

Molecular dynamics (MD) cascade simulations of single crystal and five bi-crystal structures in bcc tungsten (W) are conducted to investigate the role of grain boundaries (GBs) on defect production and the size distribution of defect clusters. The cascades in W with cascade energies of 10keV and 20keV are simulated at different distances from the GB plane at 4.2K, 300K and 900K, respectively. The results indicate that the defect production is sensitive to the specific distance between the PKA and the nearby GB. The size of vacancy clusters becomes larger when the overlap region between the cascade and GB is small. Meanwhile, the mean size of interstitial clusters becomes smaller. The number of interstitials decreases with increasing temperature, whereas the number of vacancies is independent of the temperature.

Molecular dynamics simulations of displacement cascades in Fe-10%Cr systems

Molecular dynamics simulations of the displacement cascades in Fe−10%Cr systems are used to simulate the primary knocked-on atom events of the irradiation damage at temperatures 300, 600, and 750 K with primary knocked-on atom energies between 1 and 15 keV. The results indicate that the vacancies produced by the cascade are all in the central region of the displacement cascade. During the cascade, all recoil Fe and Cr atoms combine with each other to form Fe—Cr or Fe—Fe interstitial dumbbells as well as interstitial clusters. The number and the size of interstitial clusters increase with the energy of the primary knocked-on atom and the temperature. A few large clusters consist of a large number of Fe interstitials with a few Cr atoms, the rest are Fe—Cr clusters with small and medium sizes. The interstitial dumbbells of Fe—Fe and Fe—Cr are in the (111) and (110) series directions, respectively.

Synergistic effects of PKA and helium on primary damage formation in Fe–0.1%He

Molecular dynamics (MD) simulation of displacement cascades in Fe–0.1%He are used to investigate the synergistic effects of primary knock-on atoms (PKA) and He on the irradiation damage production at temperatures between 10 K and 523 K. The results indicate that the vacancies produced by cascades are all in the central region of displacement cascade. The presence of He does not influence Frenkel pair production. During cascade evolution all displaced Fe and He atoms combine with each other to form Fe–He or Fe–Fe interstitials dumbbell as well as interstitial clusters. The number and size of interstitial clusters increase with the PKA energy and temperature. A few large clusters consisting of a large number of Fe interstitials with a few helium atoms are formed, the rest being Fe–He clusters at small and medium sizes. The interstitial dumbbell of Fe–Fe and Fe–He are in the 〈1 0 0〉 and 〈1 1 0〉 lattice direction, respectively.

Atomistic simulation of helium-defect interaction in alpha-iron

Molecular dynamics (MD) methods are utilized to study the formation of vacancy clusters created by displacement cascades in α-Fe containing different concentrations of substitutional He atoms. Primary knock-on atom energies, Ep, from 500eV to 20keV are considered at a temperature of 100K, and the results are compared with those performed in pure α-Fe. There are distinct differences in the number and size of vacancy clusters within displacement cascades with and without substitutional helium atoms. It is found that many large vacancy clusters can be formed within cascade cores in α-Fe with helium atoms, in contrast to a few small vacancy clusters observed in pure α-Fe. The number and size of helium/vacancy clusters generally increase with increasing helium concentration and PKA energy. One of the striking results is that the number of self-interstitial atoms (SIAs) and the size of interstitial clusters are much smaller than those in pure α-Fe.

Migration and directional change of interstitial clusters in α-Fe: searching for transition states by the dimer method

The interstitial clusters produced by cascades in metals have very high mobility and exhibit thermally activated, one-dimensional glide along ⟨111⟩ directions. Only small interstitial clusters (<4) are observed to change their glide direction during the period of molecular dynamics (MD) simulations (∼10 ns), but the directional change for larger clusters is inaccessible to MD due to the limited time-scale. In order to overcome the ‘time barrier’ in MD simulations, the dimer method is employed to search for possible transition states of interstitials and small interstitial clusters in α-Fe. The method uses only the first derivatives of the potential energy to find saddle points without knowledge of the final state of the transition. The possible transition states are studied as a function of interstitial cluster size, and the lowest energy barriers correspond to defect migration along ⟨111⟩ directions, as seen in MD simulations. Small clusters change their direction by a ⟨110⟩ fragment mechanism involving rotation of each crowdion into and out of the ⟨110⟩ dumbbell configuration, whereas the directional change for larger clusters is a two-step process consisting of translation along a ⟨100⟩ direction and rotation into an equivalent ⟨111⟩ direction. The mechanism of changing direction for a tri-interstitial cluster is also investigated using MD simulations.

Finding possible transition states of defects in silicon-carbide and alpha-iron using the dimer method

Energetic primary recoil atoms from ion implantation or fast neutron irradiation produce isolated point defects and clusters of both vacancies and interstitials. The migration energies and mechanisms for these defects are crucial to successful multiscale modeling of microstructural evolution during ion-implantation, thermal annealing, or under irradiation over long periods of time. The dimer method is employed to search for possible transition states of interstitials and small interstitial clusters in SiC and α-Fe. The method uses only the first derivatives of the potential energy to find saddle points without knowledge of the final state of the transition. In SiC, the possible migration pathway for the C interstitial is found to consist of the first neighbor jump via a Si site or second neighbor jump, but the relative probability for the second neighbor jump is very low. In α-Fe, the possible transition states are studied as a function of interstitial cluster size, and the lowest energy barriers correspond to defect migration along 〈1 1 1〉 directions. However, this paper addresses whether migrating interstitial clusters can thermally change their direction, and the activation energies and corresponding mechanisms for changing the direction of these clusters are determined.

Study of fundamental features of bias effect in metals under irradiation

Studies on bias mechanisms, such as the dislocation bias and production bias have so far been made in the Fe and Ni model crystals. In the present work the interaction between an edge dislocation and interstitial clusters has been mainly studied by computer simulation from the viewpoint of the production bias for Fe and Ni. Capture zones for interstitial clusters I n (bundles of n crowdions, n=1, 2, 3, 5) to an edge dislocation line have been obtained, with the definition of the capture zone as the region where the binding energy is larger than kT=0.067 eV ( T=500 °C). This shows increasing capture areas on the expansion side of the edge dislocation line with increasing size of interstitial clusters both in Fe and Ni. The energy change from the as-trapped state of the interstitial cluster to the absorbed state into the edge dislocation core was also calculated. This showed that the final stable configuration is a jogged state in Fe. This is also correct in Ni but only when the size of the interstitial cluster is larger than a certain value. These results give a confirmed basis to the production bias mechanism.

The effect of free surfaces on cascade damage production in iron

The first results have been obtained from a study intended to provide a quantitative measure of the effect of free surfaces on cascade damage evolution. A sufficient number of 10 keV iron cascades were completed to statistically evaluate variations between surface-influenced and bulk cascades. Two sets of near-surface cascades were completed; surface atoms served as the primary knockon atom (PKA) in the first set, while the PKA were located 10 lattice parameters below the surface in the second. Relative to bulk cascades, stable point defect production increased for cascades 10 a o below the surface. Stable vacancy production increased further for cascades initiated at the surface, while the number of surviving interstitials decreased. The difference between the surviving vacancies and interstitials arises from sputtering and surface absorption of mobile interstitial defects. The fraction of vacancies contained in clusters increased as the cascade initiation site approached the surface, and larger vacancy clusters were formed. Conversely, no significant change in the in-cascade interstitial clustering fraction or the interstitial cluster size distribution was observed.

Temperature effects on defect production and disordering by displacement cascades in Ni3Al

Abstract Molecular dynamics simulations are used to obtain detailed information on defect production and disordering produced in the primary cascade state of radiation damage in Ni3Al as a function of irradiation temperature Tirr, Although the number of Frenkel pairs decreases with increasing Tirr, the size of interstitial clusters and the interstitial clustering fraction increase with temperature. Temperature has a strong effect in enhancing the production of antisite defects, for the number per cascade increases by about 20% as Tirr increases from 100 K to 600 K, and then by about 90% as it increases further to 900 K. These effects are believed to be due to the increase in the intensity and lifetime of the thermal spike. The average size of disordered zones at different temperatures in the simulations is compared with experimental transmission electron microscopy data and the results are in reasonable agreement. The long range order parameter in the cascade region is found to be consistent with values o...

Md Investigation of Thermal Spike Effects on Defect Production and Disordering by Displacement Cascades in Nl3AL

AbstractMolecular dynamics (MD) simulations are used to obtain detailed information on defect production and disordering produced in the primary cascade state of radiation damage in Ni3AI as a function of irradiation temperature, Tirr Although the number of Frenkel pairs decreases with increasing Tirr, the size of interstitial clusters and the interstitial clustering fraction increase with Tirr. The number of antisites defects per cascade increases by about 20% as Tir increases from 100 to 600K, and then by about 90% from 600 to 900K due to the increase in the intensity and lifetime of the thermal spike. The average size of disordered zones at different Tir, is compared with experimental transmission electron microscopy data and the results are in reasonable agreement. The long-range order parameter in the cascade region is found to be consistent with values obtained experimentally on Ni3A1 irradiated by ions to a similar dose. The chemical short-range order parameter is about 0.6 over the whole range of Tirr, considered, suggesting that the cascade core retains some short-range order at high temperature due to local reordering.

Investigation of Frenkel defects in electron irradiated copper by Huang scattering of X-rays. II. Thermal annealing

For pt. I see ibid., vol.4, no.10, 1575 (1974). After low temperature electron irradiation of copper single crystals the thermal recovery behaviour has been investigated by measurements of the diffuse scattering of X-rays close to the Bragg reflections and by measurements of the electrical resistivity change. At the end of recovery stage I an increase of the scattering intensity per interstitial was observed. This gives direct evidence that the interstitials agglomerate during their free migration. In recovery stage II a further increase of the scattering intensity per interstitial suggests an increase of the average interstitial cluster size throughout this stage. The mean number of interstitials per cluster can be estimated. These results can be compared with observations in the electron microscope.

Investigation of Interstitials in Electron-Irradiated Aluminum by Diffuse-X-Ray Scattering Experiments

The diffuse scattering of x rays ($\mathrm{Cu}{K}_{\ensuremath{\alpha}l}$) from single crystals of aluminum has been investigated after low-temperature electron irradiation (defect concentrations 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ and 5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$). The measurements were made near the (200), (400), (220), and (222) Bragg reflections in directions both parallel and perpendicular to the scattering vector. These measurements were repeated after a number of steps in an isochronal-recovery program. The data taken immediately after the irradiation showed all the characteristic features predicted by the theory for scattering from point defects with weak displacement fields (Huang scattering). The conclusions are the following: (i) The interstitial in Al has slightly tetragonal or cubic symmetry; the crowdion configuration can be excluded. (ii) By comparing the diffuse-scattering intensities with measurements of the lattice parameter the absolute defect concentration and the volume change $\ensuremath{\Delta}V$ per defect was determined. ($\ensuremath{\Delta}V=1.9\ifmmode\pm\else\textpm\fi{}0.2$ atomic volumes per Frenkel defect.) From the absolute concentration and from electrical-resistivity change measurement on the same sample, the resistivity change was determined to be ${\ensuremath{\rho}}_{F}=3.9\ifmmode\pm\else\textpm\fi{}0.6$ \ensuremath{\mu}\ensuremath{\Omega} cm per atomic percent Frenkel defects. In the recovery measurements an increase of the scattering intensity per defect was observed at the end of stage I. This gives direct evidence that the interstitials agglomerate during their free migration in stage I. In stage II a further increase of the scattering intensity per interstitial is observed close to the Bragg peaks, suggesting an increase of the average interstitial cluster size throughout this stage. The changes in the intensity distribution around the reflections were in good agreement with the predictions of the scattering theory for defects with strong displacement fields (Stokes-Wilson approximation). From the data, the mean number of interstitials per cluster can be estimated. It is 2 at the end of stage I and increases to about 10 at the beginning of stage III. There is good indication that the larger interstitial clusters are dislocation loops.

The behaviour of point defect clusters in irradiated metals

>A simple model, where clusters of interstitial atoms compete with the equlvalent number of vacancies left in the crystal for subsequent interstitial atoms, is used to discuss the rate of accumulation of the vacancies and the conditions governing the size of the interstitial atom clusters. Recombination becomes important at an interstitial cluster size which is dependent upon the relative interaction distances of interstitial atoms with vacancies and dislocation lines. (auth)