A.F. Calder

Computer simulation of point defect properties in dilute Fe-Cu alloy using a many-body interatomic potential

Abstract The behaviour of copper atoms in dilute solution in α-iron is important for the microstructural changes that occur in ferritic pressure vessel steels under fastneutron irradiation. To investigate the properties of atomic defects that control this behaviour, a set of many-body interatomic potentials has been developed for the Fe—Cu system. The procedures employed, including modifications to ensure suitability for simulating atomic collisions at high energy, are described. The effect of copper on the lattice parameter of iron in the new model is in good agreement with experiment. The phonon properties of the pure crystals and, in particular, the influence of the instability of the metastable, bcc phase of copper that precipitates during irradiation are discussed. The properties of point defects have been investigated. It is found that the vacancy has lower formation and migration energy in bcc copper than in α-iron, and the self-interstitial atom has very low formation energy in this phase of coppe...

A comparison of displacement cascades in copper and iron by molecular dynamics and its application to microstructural evolution

Abstract The use of molecular dynamics simulation and improved many-body potentials make it possible to compare displacement cascade evolution in different materials. However, the extreme variability between individual cascades requires multiple simulations at nominally identical conditions of temperature and energy in order to assure that the comparison is statistically valid. We describe such a comparison of copper and iron in this paper. Over 600 cascades have been investigated, with simulation energies in the range 60 eV to 10 keV and temperatures from 100 to 900 K. The evolution of the cascades is similar in both materials, with the development of a highly disordered core and the emission of focusons and replacement collision sequences during the collisional phase of the cascade. The majority of vacancy-type defects are found in the cascade core when in-cascade recombination is complete, while the interstitial-type defects tend to be distributed around the periphery of this region. The final defect structure has been characterized by the total surviving defect fraction, and the number and size of the point defect clusters produced. Since these parameters have significant implications for the nuclear industry in its assessment of radiation damage, we show how they depend on cascade energy and temperature. To illustrate their importance, we provide an example of how the molecular dynamics results can be used in a rate theory model of ferritic steel embrittlement.

A molecular dynamics study of displacement cascades in α-iron

Abstract The mechanisms of defect production in displacement cascades in α-iron have been investigated by computer simulation. Cascades of up to 5 keV in energy have been simulated by molecular dynamics in crystals with atomic interactions described by a many-body potential. The effects of lattice temperature have been studied by using block temperatures of either 100 or 600 K. 80 cascades have been modelled overall. The morphology of cascades during the collisional phase changes at about 1–2 keV, due to the collective nature of atomic displacements at higher energy. This transition is reflected in the relaxation time during the subsequent recombination phase, and it also decreases the efficiency factor for defect production. This factor is similar in size to that obtained from recent modelling of copper, an fcc metal. Although the cascade zone contains a large number of displaced atoms, true melting was not observed in α-Fe, and vacancy clustering did not occur in the thermal spike phase. Interstitial clustering has been analysed, and found to be less pronounced than in copper. One large cluster was observed to grow by interstitial movement during the thermal spike, and visual analysis has shown that it formed a perfect dislocation loop: it was not nucleated by the Eyre-Bullough mechanism, however. Statistics on the cascade parameters are presented, and comparisons with work on other crystal structures are drawn where possible.

Computer simulation of defect production by displacement cascades in metals

Abstract MD simulations of displacement cascades in a variety of pure metals and alloys of different crystal structure are reviewed. For low recoil energies, these simulations have provided extensive results on the orientation-dependence and mean value of the displacement threshold energy in different crystal systems, and this information is tabulated. Large numbers of recoils have been simulated at true cascade energies, and the results show that Frenkel-pair production at the end of the cascade process is well below the NRT theoretical value in all metals and alloys. A new empirical relationship between Frenkel-pair number and damage energy is proposed. In contrast with this, antisite production efficiency in ordered alloys increases with increasing energy. Clustering of interstitials is a feature of cascade processes for all metals, but the degree of clustering is material-dependent. Atomic mixing in cascades is strongly dependent on cascade energy and is shown to be independent of crystal structure. The mechanisms underlying these results are discussed, particularly in relation to the highly disordered zone formed at the end of the thermal spike.

Defect production due to displacement cascades in metals as revealed by computer simulation

Computer simulation using molecular dynamics (MD) can provide information on the mechanisms and final state of defect production in displacement cascades in metals that cannot be obtained by other means. Recent progress in a number of areas in this field is reviewed here. It includes research dealing with the effect on defect formation of primary knock-on atom (PKA) energy, irradiation temperature, the spatial overlap of cascades and alloy additions (solid solutions, ordered alloys and precipitates). It is shown that a rather firm view on dependencies and trends is emerging in all these areas. Improvements still need to be made in some aspects of the simulations for metals, particularly with regard to the accuracy of the interatomic potentials that have to be employed and the neglect of coupling between the ion and electron systems. Nevertheless, the current knowledge of defect numbers, arrangements and properties provided by MD simulation paves the way for future development of models of the evolution of damage beyond the stage of the cascade process.

Statistical analysis of a library of molecular dynamics cascade simulations in iron at 100 K

Abstract An extensive database of atomic displacement cascades in iron has been developed using molecular dynamics (MD) simulations. Simulations have been carried out at temperatures of 100, 600, and 900 K, and at energies between 0.10 and 50 keV. The results presented here focus on the simulations conducted at 100 K. A sufficient number of cascades has been completed under each condition of cascade energy and temperature to obtain statistically significant average values for the primary damage production parameters. The statistical analysis has been used to examine the influence of primary knockon direction, simulation cell-size, and lattice heating by the high energy recoil. A surprising effect of primary knockon atom (PKA) direction was observed up to 1 keV, but little effect of lattice heating was detected. We have previously reported preliminary results indicating that the ratio of surviving point defects to the number calculated by the Norgett–Robinson–Torrens (NRT) displacement model appears to pass through a minimum value of about 20 keV. The present analysis supports the statistical significance of this minimum, which can be attributed to the onset of extensive subcascade formation.

On the Origin of Large Interstitial Clusters in Displacement Cascades

Displacement cascades with wide ranges of primary knock-on atom (PKA) energy and mass in iron were simulated using molecular dynamics. New visualisation techniques are introduced to show how the shock-front dynamics and internal structure of a cascade develop over time. These reveal that the nature of the final damage is determined early on in the cascade process. We define a zone (termed ‘spaghetti’) in which atoms are moved to new lattice sites and show how it is created by a supersonic shock-front expanding from the primary recoil event. A large cluster of self-interstitial atoms can form on the periphery of the spaghetti if a hypersonic recoil creates damage with a supersonic shock ahead of the main supersonic front. When the two fronts meet, the main one injects atoms into the low-density core of the other: these become interstitial atoms during the rapid recovery of the surrounding crystal. The hypersonic recoil occurs in less than 0.1 ps after the primary recoil and the interstitial cluster is formed before the onset of the thermal spike phase of the cascade process. The corresponding number of vacancies is then formed in the spaghetti core as the crystal cools, i.e. at times one to two orders of magnitude longer. By using the spaghetti zone to define cascade volume, the energy density of a cascade is shown to be almost independent of the PKA mass. This throws into doubt the conventional energy-density interpretation of an increased defect yield with increasing PKA mass in ion irradiation.

A molecular dynamics study of high-energy displacement cascades in α-zirconium

Abstract The damage produced in α-zirconium at 100 K by displacement cascades with energy, E p , up to 20 keV has been investigated by molecular dynamics using a many-body interatomic potential. The results are compared with similar data for cascades of energy up to 10 keV in α-titanium. The production efficiency of Frenkel pairs falls to about 25% of the NRT value as E p rises above 10 keV in zirconium, and to about 30% at 10 keV in titanium. The power-law dependence of the number of Frenkel pairs, N F , on E p found previously is obeyed, i.e., N F = A ( E p ) m . Interstitial and vacancy clusters with sizes of the same order are created in the cascade process, and clusters containing up to 25 interstitials and 30 vacancies were formed in zirconium by 20 keV cascades. Two thirds of the SIAs are produced in clusters in zirconium at high cascade energy. Most interstitial clusters have dislocation character with perfect Burgers vectors of the form 1/3〈1120〉, but a few metastable clusters are formed and are persistent over the timescale of MD simulations. Collapse of the 30-vacancy cluster to a faulted loop on the prism plane was found to occur over a period of more than 100 ps. Annealing over this timescale has a stronger effect on the number and clustering of defects in cascades that are dispersed over a large region of crystal than in cascades that form a compact region of damage.

Computer simulation study of cascade overlap effects in α iron

Abstract The effects on defect production of the overlap of collision cascades in a-iron have been investigated by molecular dynamics computer sirriulations. A large number of cascades was simulated and this has provided clear evidence that fewer defects result when two cascades produced at different times overlap. A means of defining the spacing of cascades for the purposes of categorising overlap effects has been found. When the two cascade energies are very different, viz. 400 eV and 5 keV, the defects produced by the smaller cascade are effectively lost at complete overlap, regardless of which cascade occurs first. Even when the energies are similar, substantial defect loss arises when overlap occurs. Overlap also changes the distribution of interstitial clusters that results from the primary damage process of cascades, with a higher proportion of the defects occurring in larger clusters. The mechanisms that give rise to these effects have been found from computer visualisations.

Computer simulation of low-energy displacement events in pure bcc and hcp metals

Abstract Molecular dynamic simulation of low-energy atomic recoils has been carried out for α-Fe (bcc) and α-Ti (hcp). Many-body interatomic potentials have been employed with modifications suitable for short-range interactions. This is the first systematic study of atomic displacement events in the bcc and hcp structures using such potentials. The displacement threshold energy, E d , has been investigated in detail for Ti, and the strong dependence of E d on orientation has been interpreted in terms of the number of atoms temporarily displaced into interstitial positions during a threshold event. E d has also been obtained for Fe and is discussed in a similar manner. In addition, displacement cascades of up to 500 eV have been simulated for this metal, and the efficiency factor for defect production is found to be strongly dependent on recoil energy in this energy regime.