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Recent molecular dynamics (MD) computer simulations of pure copper and iron have shown that clusters consisting of up to a few tens of self-interstitial atoms (SIAs) are highly mobile along close-packed crystallographic directions. This effect has important consequences for microstructure evolution in irradiated metals and so it is desirable to investigate the mechanisms of cluster motion. In the present paper, results of MD modelling of the thermally-activated motion of clusters of three, nine and 17 SIAs in α-iron in the temperature range from 90 to 1400 K are analysed. The correlation between the motion of the centre of mass of a cluster and the individual jumps of its constituent SIAs is revealed. It is found that the SIAs in a cluster jump almost independently and their jump frequency depends on the number of SIAs in the cluster. This leads to a simple relationship between the jump frequency of a cluster and the number of SIAs in it. The reason for the deviation of the cluster jump frequency...

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...

The damage produced in the hcp metal α-zirconium at 100 K by displacement cascades with energy in the range from 0.3 to 5keV has been investigated by molecular dynamics using a many-body interatomic potential. Comparisons have been made with the results of a recent study by Wooding et al. of α-titanium, a hcp metal with a much smaller atomic mass. There is no discernible effect of primary-knock-on-atom direction, and individual replacement sequences make only a minor contribution to the final damage state. In comparison with titanium, fewer atoms in zirconium are displaced temporarily to interstitial sites during the collisional phase and the cascade core size is smaller. Nevertheless, the core temperature during the thermal spike is higher. The number of Frenkel pairs, produced in the final damage state is smaller in zirconium than in titanium, and the efficiency of their production declines with increasing cascade energy in a similar fashion to that found for all other metals. Some interstitial...

Computer simulations have shown that a nearby surface can engender a significant increase in the number of vacancy defects produced by high-energy displacement cascades in metals of cubic crystal structure. In the present work, the influence of a surface on the production of lattice defects in the bulk by displacement cascades of up to 10 keV in energy in α-Zr has been studied. The basal- or prism-plane surfaces were considered, with the direction of the primary recoil atom making either a high or a low angle to the surface normal. This hcp metal is of interest because self-interstitials migrate preferentially along the basal planes, and so the crystallographic orientation of the surface can influence the final defect state of cascade damage. Surface and subsurface damage increases with increasing energy. The surface damage is much larger for the prism-plane surface. Whereas stable interstitial defects are more readily generated below a basal-plane surface, they are deposited at greater depth bel...

Calculations on point-defect clusters in Zn are performed using a static simulation technique in conjunction with a many-body potential. The results are compared with the available experimental observations, theoretical estimates and previous computations in hcp metals with c/a ratios below the ideal value. Both monovacancy and divacancy defects demonstrate an anisotropic migration with almost the same activation energy, corresponding to that observed in recovery stage IV. Small vacancy clusters are found to favour three-dimensional agglomerates. Stability conditions for vacancy clusters to nucleate or break up (recovery stage V) are discussed. Small clusters of interstitials are shown to grow on the basal plane in forms based on the octahedral point defect, although the most stable single interstitial is the non-basal crowdion. Large single- and double-layer interstitial clusters are assigned to embryos of the experimentally observed dislocation loops.

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...

Computer simulation has been used to study the interaction of a perfect, basal dislocation with a {1012} twin boundary in a hcp metal for the situation where the 1/3{1120} Burgers vector is inclined at 60° to the interface. It is found that slip is not transferred from one crystal to the other with a residual dislocation left at the interface. Instead, the matrix dislocation decomposes into interfacial defects. We show that as a result of this decomposition the matrix dislocation becomes a new source of twinning dislocations that produce twin growth when the appropriate stress is applied to the crystal. The mechanism described does not require twinning dislocations to multiply by a pole process.

The damage produced by displacement cascades in the h.c.p. metal α-titanium at 100K has been investigated by molecular dynamics using a many-body interatomic potential. This has been the first simulation of cascades in the h.c.p. structure. 32 cascades ranging in energy from 0.3 to 5 keV were generated in order to study the effects of the crystal structure and cascade energy. Computer-generated plots have been used to visualize the nature and arrangement of the point defects produced in the cascade events. There is no discernible effect of the primary knock-on atom direction, and individual replacement sequences make only a minor contribution to the final damage state. Views of the displaced atoms looking along the basal planes show very clearly regions with a liquid-like disorder, but they are small, even at 5 ke V, and do not lead to vacancy clustering when crystalline order is restored. The efficiency of production of Frenkel pairs declines with increasing cascade energy in a similar fashion t...

A model to describe the disordering of ordered Cu3Au under irradiation is proposed. For the thermal spike phase of a displacement cascade, the processes of heat evolution and conduction in the cascade region are modelled by solving the thermal conduction equation by a discretization method for a medium that can melt and solidify under appropriate conditions. The model considers disordering to result from cascade core melting, with the final disordered zone corresponding to the largest molten zone achieved. The initial conditions for this treatment are obtained by simulation of cascades by the MARLOWE code. The contrast of disordered zones imaged in a superlattice dark-field reflection and projected on the plane parallel to the surface of a thin foil was calculated. The average size of images from hundreds of cascades created by incident Cu+ ions were calculated for different ion energies and compared with experimental transmission electron microscopy data. The model is in reasonable quantitative ...

A many-body interatomic potential has been developed for the h.c.p. metal α-zirconium using the same methodology as that used by Ackland for α-titanium. The repulsive pair part of the potential has been constructed so that the model can be employed for simulating atomic collisions. The favoured self-interstitial configurations are the 〈1120〉 crowdion and split defects, and they are highly mobile in the basal plane. The energy of surfaces is not strongly dependent on the crystallographic orientation, and the I2 stacking fault on the basal plane is not stable. The displacement threshold energy in a crystal at 0 K exhibits a similar orientation dependence to that computed recently for α-titanium by Bacon et al. and has the same minimum of 27·5 eV along the 〈1120〉 directions, but the mean value of 55 eV averaged over all orientations is higher than that of 30 eV in titanium.

The 76 displacement cascades in Ni3Al at 100 K simulated in part I have been analysed to investigate the influence of the energy E p of the primary knock-on atom on the kinetics of defect production, the degree of disorder and the atomic mixing of the different atomic species. The Ni atoms are more readily displaced during the ballistic phase, but they also return to lattice sites at a faster rate than do the Al atoms. The characteristic time of this recombination increases with increasing E p, an effect related to the development of a highly defective ‘molten’ zone, which has a radius given by R melt ≈ 3ao E p 1/3. The final concentration of antisite defects in this region is 2–5% for most cascades, consistent with an integrated long-range order parameter of 0.85–0.9 over the same region, and the value of this parameter in the cascde centre falls to 0.5–0.7 for all E p. The chemical short-range order is almost entirely lost at the peak in the number of ballistic displacements, particularly at hi...

The damage produced by displacement cascades in the L12 alloy Ni3Al at 100 K has been investigated by molecular dynamics using many-body interatomic potentials. 76 cascades ranging in energy from 0.15 to 5 keV have been simulated in order to study the effects of the energy and species of the primary recoil atom. Computer-generated colour plots have been used to visualize the nature and arrangement of the point defects produced in the cascade events. There is a change in cascade morphology at the end of the collisional phase for cascade energies in the range 1–2 keV, and separate subcascade regions can be seen in some cascades at 5 keV. Individual replacement sequences do not make a significant contribution to the final damage state. The efficiency of production of Frenkel pairs declines with increasing cascade energy in a similar fashion to that found recently for pure metals. Approximately 90% of the interstitials created in cascades are Ni-Ni dumbbell atoms, and the tendency of interstitials to...

The mechanism of redistribution of vacancies in the depleted zone of a displacement cascade in copper has been investigated by molecular dynamics simulations. A simplified model of the thermal spike was used, for which the calculation cell was cooled down along one axis after previously introducing into it vacancies and kinetic energy. The time evolution of the temperature profile and the vacancy concentration distribution was calculated, and it was found that in a nonuniform temperature field, vacancies are swept to the centre of the thermal spike as a result of the advance of the solid-liquid interface. This effect leads to the development of a zone where the average concentration of vacancies is several times larger than that produced before the onset of the thermal spike phase. The redistribution of density of the surrounding matrix which is realized in this way is analogous to ‘collapse’ of a vacancy platelet and the consequent formation of a vacancy loop, a feature which is characteristic o...

Molecular dynamics simulations with the many-body interatomic potentials used in part I have been employed to investigate the displacement threshold energy E d at 0 K and the defect structure created at the displacement threshold in the ordered alloy Ni3Al. The crystallography of the L12 structure requires four unit stereographic triangles to be considered: one for Al primary recoils and three for Ni. E d for Al is generally higher and has a much stronger orientation dependence than in pure Al. For Ni recoils, on the other hand, E d is similar to that in pure Ni in directions where Ni-Al interactions are not strong; exceptions occur along closely packed directions, for which replacement collision sequences (RCSs) are comparatively short in the ordered alloy. There are significant differences from pure Ni for directions where the Ni primary recoil makes close contact with an Al neighbour. The stable defect arrangement in Ni3Al is usually much more complex than for pure metals because of the requir...

The energy and volume change associated with the creation of point defects in Ni3Al have been calculated by computer simulation using a modified version of the many-body potentials of Vitek, Ackland and Cserti. The potentials have been adjusted to provide a better description of the interaction between atoms at separations inside the normal nearest-neighbour spacing. This region is important for interstitial properties and the interaction of atoms in displacement events associated with radiation damage. The properties of point defects in the pure metals Al and Ni are in good agreement with known values. For Ni3Al, the properties of the Ni defects are very close to those found by Caro, Victoria and Averback with the embedded-atom potentials for Ni3Al of Foiles and Daw, and the most stable interstitial, in particular, is the Ni-Ni⟨100⟩ dumbbell centred on a Ni site in the {100} planes which contain only Ni atoms. For the Al and antisite defects, however, the model used here gives different results....

Atomic-scale computer simulations using many-body interatomic potentials have been carried out to investigate the energy changes and equilibrium configurations associated with the dissociation of perfect and Lomer dislocations in copper and silver. The state of minimum energy is close in both cases to that given by the use of linear elasticity theory, and the Lomer dislocation adopts the asymmetric Lomer-Cottrell arrangement predicted by the same approach. The absolute energy values obtained from elasticity for the equilibrium dissociated configurations agree well with those found by computer simulation, but the elastic model does not accurately describe the energy changes associated with dissociation of the Lomer dislocation, thus confirming the conclusions drawn recently by Saada and Douin.

The influence of boundaries on vacancy properties in interfaces has been considered for the case of twin boundaries in the h.c.p. structure. Twinning is a common occurrence in the h.c.p. metals and the atomic structure of several boundaries has been well characterized by recent computer modelling. In the present work, the formation and migration energies of vacancies have been investigated in {1011}, {1012}, {1121} and {1122} boundaries in a model with nearideal c/a ratio. It is found that, even though the atomic density at these interfaces is close to perfect, the vacancy formation energy can be reduced by up to 27% and the migration energy by up to 50% from the single-crystal values. These results are discussed in terms of the crystallography of the interfaces and the hydrostatic component of internal stress at individual atomic sites, but these features provide only a partial explanation of the results found.

Twinning is an important plastic deformation mechanism in the response of h.c.p. metals to applied stress, and in the present paper the atomic processes associated with {1011}, {1012}, {1121} and {1122} twinning in Mg are considered. The technique of atomic-scale computer modelling has been used, with atomic interactions described by the many-body potential of the Finnis–Sinclair type recently derived by Igarashi, Khantha and Vitek. The atomic structure, energy and stress state of planar twin interfaces, and the structure and energy of twinning dislocations in these boundaries, have been determined. The ease of glide of these dislocations has also been studied. It is found that the energy and mobility are related to the width of the dislocation core rather than to its height. Hence, dislocations in {1012} and {1121} boundaries are wide, have a low energy and are very glissile, whereas those in {1011} and {1122} boundaries have the opposite characteristics. These results support conclusions drawn ...

The production of vacancy loops by the collapse of displacement cascades is of particular importance in radiation damage, for these loops are known to play a major role in subsequent microstructural development, and yet little is known of the cascade processes in them. In this study, attention has been focused on cascade collapse to form vacancy loops in five of the h.c.p. metals, namely Ti, Co, Re, Ru and Mg, chosen for their wide-ranging material properties. Sb+ ions of either 100 of 150 keV have been used to produce cascades, which may collapse to form vacancy dislocation loops. These loops have been studied using transmission electron microscopy, and this has enabled detailed analysis to be undertaken of loop geometry, size and number density. For the foil orientation used, all the loops observed lay on the prism planes, and from the size distributions of faulted and perfect loops we have estimated values for the prism plane stacking-fault energy. The efficiency of collapse varies dramaticall...

Vacancy loop formation in cascades formed during heavy-ion irradiation of the h.c.p. metal ruthenium at room temperature has been investigated by transmission electron microscopy. The ion energy and the ion mass were varied between 10 and 100 keV and 84 (Kr+) to 184 (W+) respectively to produce a wide variety of cascade morphologies. Information about the cascade collapse process has been obtained from the measurement of defect yield and cascade efficiency values. The former defines the probability that an incident ion forms a visible loop, and the latter the proportion of vacancies per cascade that remain in the form of a dislocation loop. The defect yield increases with increasing ion energy and has a complex dependence on ion mass, first increasing and then decreasing with increasing mass at low and high energies respectively. Cascade efficiency is not as complex and increases with increasing ion mass and decreasing ion energy. These effects have been interpreted in terms of current cascade co...

Displacement-cascade collapse to form vacancy loops is of fundamental importance to the development of damage structures in irradiated metals. In the present experiments, displacement cascades have been generated in ruthenium, a high melting-point hexagonal metal with a c/a ratio of 1.58, by irradiation with heavy ions having a range of masses and energies. A detailed transmission electron microscopy analysis of the vacancy loops formed by cascade collapse has shown that four distinct sets of loop geometries are present. In a majority of cases the cascades collapse initially on to the {1010} prism planes to form loops with Burgers vector b=½〈1010〉 and it is shown that these can subsequently unfault to form perfect ⅓ 〈1120〉-type loops. When the incident-ion-beam direction lies in the basal plane, a minority of the cascades collapse on to the basal planes to form faulted ½[0001] loops and these can transform to a lower-energy faulted loop with b of the type ⅙〈2023〉. From determination of the loop s...

Four pair-wise potentials have been found to be suitable for the simulation by computer of stacking faults and dislocation core configurations in model crystals having the hexagonal-close-packed structure. The potentials define stress-free perfect crystals and have markedly different ranges and shapes, but the crystals have very similar elastic properties. The stability of translational stacking faults on basal and non-basal planes has been investigated, and it is concluded that stable faults can exist on all the planes considered. The translation vectors and volume expansions associated with the faults are reasonably well understood in terms of the hard-sphere model of the structure, irrespective of the form of the potential, and changes in atom coordination at the non-basal faults may be used to estimate the fault energy. The potentials are used in parts II and III to investigate dislocation behaviour.

The four pair-wise potentials found in part I (Bacon and Liang 1986) to define model hexagonal-close-packed crystals in equilibrium have been used for the computer simulation of dislocation cores in the absence of external stress. Straight dislocations with Burgers vector b equal to either ⅓〈1120〉 or 1/3〈1123〉 have been considered. For the former, the screw and the edge lying along 〈1200〉 dissociate on the basal plane to a width expected from the stacking-fault energy found in part I, but not always to two Shockley partials. The screw in one crystal has a more stable core when the disregistry spreads on the {1100} prism plane. The stable core of the edge lying along 〈0001〉 is not dissociated in any of the models, and contains a microcrack in one case. The ⅓〈1123〉 edge dislocation lying along 〈1100〉 has two stable core states in all the crystals. One consists of combinations of {1121} and {1122} microtwins and microcracks, the precise form depending on the potential, and in the other the 〈1123〉 di...

The energy and atomic structure of {1121}, {1122) and {1012} twin boundaries in the hexagonal-close-packed (h.c.p.) metals have been investigated using computer simulation. Three distinctly different interatomic potential functions have been used in either equilibrium or non-equilibrium form. It is predicted that only one form of boundary can occur for {1121} and {1012} twins, but several interfaces may exist for (1122} twins. The stable boundaries are, with one exception, associated with one or both of the symmetry operations of reflection and 2-fold rotation defined in the conventional theory of twinning. The good agreement between the results for all six model crystals suggests that the structures found here have general relevance to twin boundaries in real h.c.p. metals.

Geometrical formulae for calculating the elastic field of a dislocation segment in an anisotropic medium are discussed. They have been derived from analyses for two-dimensional situations, and it is shown that one of them is also valid for three-dimensional problems. Ways in which this formula can be evaluated are described.

The properties of clusters of a small number (≤7) of self-interstitials in bodycentred-cubic transition metals have been studied by computer simulation using model interatomic potentials of the embedded-atom type. The potentials employed are empirically-based and include many-body forces between nearneighbour atoms: they were originally developed by Finnis and Sinclair (1984) and contain recent modifications of the repulsive cores by Ackland and Thetford (1987). The W, α-Fe and Mo potentials have been found to model distinct types of behaviour with regard to preferred cluster geometries, which seem to arise from the relative stability of the possible orientations of the single interstitial. The results are discussed in terms of the Eyre-Bullough mechanism of dislocation loop formation and unfaulting. For the W model a ⟨111⟩ orientation is favoured (even for the single interstitial). For α-Fe the ⟨111⟩ orientation quickly becomes dominant with increased cluster size, while for Mo there is some ten...

The effect of dissociation on the energy of a perfect dislocation in f.c.c. metals is considered using elasticity theory and is compared with the Peierls-model calculations of Prinz, Kirchner and Schoeck (1978). It is shown that the effect, which is significant, largely arises from the elastic energy, and that consequently models of strengthening, etc., can incorporate the influence of dissociation if suitable values of energy and line tension are used. Effective isotropic elastic constants which give these values for real metals are discussed.

The c/a ratio, vacancy-formation energy, elastic constants and phonon frequencies for metals having the h.c.p. structure are assessed and it is found that, although empirical potentials fo...

The N-body potentials of Finnis and Sinclair (1984) are investigated to gauge their usefulness in computer simulation work. Results on monovacancies, di-vacancies and (100) surfaces are presented.