Stanislav I Golubov

One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper

Atomic-scale computer simulation has been used to study the thermally activated atomic transport of self-interstitial atoms (SIAs) in the form of planar clusters in pure Cu and f-Fe. There is strong evidence that such clusters are commonly formed in metals during irradiation with high-energy particles and play an important role in accumulation and spatial distribution of surviving defects. An extensive study of the mobility of SIA clusters containing two to 331 interstitials has been carried out using the molecular dynamics simulation technique for the temperature range from 180 to 1200 K. The results obtained show that clusters larger than three to four SIAs are one-dimensionally mobile in both Cu and Fe. Large clusters of more than 100 SIAs in Cu and 300 SIAs in Fe have significantly reduced mobility. The problem of describing one-dimensional (1D) motion in three-dimensional space is discussed. An attempt is made to describe the mobility of SIA clusters within the approximation of 1D diffusion. For clusters in both metals the effective migration energy of 1D diffusion as estimated via the jump frequency of the cluster centre of mass is found to be independent of the number of SIAs in the clusters, although the cluster jump frequency decreases with increasing cluster size. Mechanisms of 1D mobility of interstitial clusters are discussed.

Aspects of microstructure evolution under cascade damage conditions

Abstract The conventional theoretical models describing the damage accumulation, particularly void swelling, under cascade damage conditions do not include treatments of important features such as intracascade clustering of self-interstitial atoms (SIAs) and one-dimensional glide of SIA clusters produced in the cascades. Recently, it has been suggested that the problem can be treated in terms of ‘production bias’ and one-dimensional glide of small SIA clusters. In the earlier treatments a ‘mean size approximation’ was used for the defect clusters and cavities evolving during irradiation. In the present work, we use the ‘size distribution function’ to determine the dose dependence of sink strengths, vacancy supersaturation and void swelling as a function of dislocation density and grain size within the framework of production bias model and glide of small SIA clusters. In this work, the role of the sessile-glissile loop transformation (due to vacancy supersaturation) on the damage accumulation behaviour is included. The calculated results on void swelling are compared with the experimental results as well as the results of the earlier calculations using the ‘mean size approximation’. The calculated results agree very well with the experimental results.

Structure and properties of clusters of self-interstitial atoms in fcc copper and bcc iron

Abstract Static and molecular dynamics simulations have been used with different types of interatomic potentials to investigate the structure, properties and stability of self-interstitial atom (SIA) clusters produced during irradiation. In α-iron (Fe), faulted clusters of <110> dumbbells are unstable for all the potentials. The most stable SIA clusters are sets of parallel <111> crowdions. Large clusters of this type form perfect dislocation loops with Burgers vector b = ½⟨111⟩. Small clusters (less than 9 SIAs) of ⟨100⟩ crowdions are stable at 0K, but transform into a set of ⟨111⟩ crowdions on annealing. Larger ⟨100⟩ clusters are stable and form perfect dislocation loops with b = ⟨100⟩. Both types of loops are glissile. In copper (Cu), clusters of parallel ⟨100⟩ dumbbells and ⟨110⟩ crowdions are stable. Large clusters of these types form faulted and perfect dislocation loops with b = ⅓ ⟨111⟩ and ½ ⟨110⟩ respectively. Small faulted clusters (less than 7 SIAs) of irregular shape can transform into a set of ⟨110⟩ crowdions during annealing. Larger faulted clusters are stable as hexagonal ⅓ ⟨111⟩ Frank loops at temperatures of about up to 1050K for a period of several hundred picoseconds. All faulted clusters are sessile. Clusters of ⟨110⟩ crowdions and ½ ⟨110⟩ perfect loops are glissile and stable at all temperatures. When large enough (more than 49–64 SIAs) they can dissociate on their glide prism. Symmetric three-dimensional clusters of ⟨100⟩ dumbbells are stable at 0K but during annealing they transform into sets of ⟨110⟩ crowdions. The results for both iron and copper are discussed and compared with experimental data and provide a basis for investigating and explaining the observed differences in radiation damage accumulation behaviour between fcc and bcc metals.

Computer simulation of vacancy and interstitial clusters in bcc and fcc metals

Interstitial clusters in bcc-Fe and fee-Cu and vacancy clusters in fcc-Cu have been studied by computer simulation using different types of interatomic potentials such as a short-ranged empirical pair potential of Johnson type, short-ranged many-body potentials of Finnis-Sinclair type and long-ranged pair potentials obtained within the generalized pseudopotential theory. The stability of a self interstitial in bcc-Fe was found to be dependent on the range of potential but not on the type. Thus, both short-ranged potentials simulated [110] dumb-bell as a stable configuration while in the cast of the long-ranged potential the stable configuration Is the [111] crowdion. Nevertheless the structure and properties of interstitial clusters were found to be qualitatively the same with all the potentials. Up to 50 interstitials. the most stable clusters were found as perfect dislocation loops with Burgers vector (b) over right arrow = 1/2[111]. The stability of interstitial clusters in Cu also does not depend on the potential and fer the same sizes the most stable configurations are faulted Frank loops 1/3[111]{111} and edge loops in die {110} plane. The structure and stability of vacancy clusters in fcc-Cu were found to be dependent mainly on bath the range of potential and equilibrium conditions. Thus for long-ranged non-equilibrium pair potentials vacancy clusters in the {111} plane collapsed and formed vacancy loops or stacking fault tetrahedra depending on the shape of the initial vacancy platelet. For the short-ranged equilibrium many-body potential vacancy clusters do not collapse into loops or tetrahedra. The process of vacancy clustering in the cascade region has been studied by molecular dynamics. This study has been done for the case of a PKA energy of about 20-25 keV. We found thar the processes simulated with the short-ranged many-body potential and the lone-ranged pair potential are qualitatively different. Thus for the many-body potential we have observed melting and crystallization of the central part of the cascade region, sweeping of vacancies inside due to the moving of the liquid-solid interface and increasing of vacancy concentration in the centre of the cascade region: however no significant clustering was observed. Contrarily for the long-ranged pair potential we have observed a very fast diffusion in the solid crystallite and the formation of stacking fault tetrahedra. The results obtained have been discussed and compared with the experimental data

Atomistic studies of helium defect properties in bcc iron: Comparison of He–Fe potentials

In the fusion irradiation environment, helium created by transmutation will play an important role in the response of structural materials to neutron radiation damage. Atomistic simulations have been carried out using a new three-body He–Fe interatomic potential and the results have been compared to those obtained using two He–Fe pair potentials. In simulations with the three-body potential, helium interstitials are very mobile and multiple He interstitials can coalesce to form interstitial clusters which are also mobile. The He interstitial cluster binding energy is in good agreement with DFT calculations. If the He cluster is sufficiently large, it can create additional free volume by ejecting an Fe interstitial atom, creating a Frenkel pair. The corresponding vacancy is incorporated into the existing He cluster, and the resulting helium–vacancy cluster is not mobile. The ejected self-interstitial atom is mobile, but is trapped by the He–vacancy cluster. If additional helium atoms join a He–vacancy cluster, more Fe interstitials can be ejected and they are observed to form small interstitial clusters (nascent dislocation loop). Although multiple helium atoms can be trapped in a single vacancy, a vacancy containing only a small number of helium atoms can recombine with an Fe interstitial to recreate a helium interstitial cluster. The He binding energy with one of the He–Fe pair potentials (Wilsons) is much higher, leading to more rapid He clustering and Frenkel pair formation. Very little He clustering occurs with the second He–Fe pair potential.

Vacancy loops and stacking-fault tetrahedra in copper - II. Growth, shrinkage, interactions with point defects and thermal stability

The interaction of vacancy loops (VLs) and stacking-fault tetrahedra (SFTs) with point defects and the processes of growth and shrinkage of VLs and SFTs have been studied using computer simulation and a long-range pair potential for copper. It was found that there is a qualitative difference in the mechanism of growth of VLs and SFTs. While VLs can grow without limitations, the growth of SFTs containing more than 91 vacancies is rather difficult. The structure of small vacancy loops (N-v less than or equal to 217; N-v is the number of vacancies) may change during its growth and the loop can transform, in turn, to a completely dissociated loop with six small truncated SFTs, a faulted Frank loop with Burgers vector b = 1/3(111) and several intermediate configurations of a partly dissociated loop. The problem of estimation the binding energy of a vacancy in a VL or SFT as a function of their size has been discussed and several approximations have been tested. Furthermore, the thermal stability of small VLs of different shapes has been studied by molecular dynamics and the VL-to-SFT transformation has been observed.

Implementation of a new Fe–He three-body interatomic potential for molecular dynamics simulations

A recently developed interatomic potential for He–Fe interactions includes a three-body term to stabilize the interstitial He defect in the tetrahedral position in the Fe bcc matrix and provides simultaneous agreement with the forces and energies of different atomic configurations as computed by first principles. This term makes a significant contribution to the static and dynamic properties of He in Fe. The implementation of this potential for atomistic simulations using molecular dynamics (MD) presented certain challenges which are discussed here to facilitate its further use in materials research, particularly to investigate the behavior of iron-based alloys that may be employed in fusion energy systems. Detailed results of an MD study comparing the new potential and alternate He–Fe pair potentials with different iron matrix potentials have been presented elsewhere to illustrate the impact of the He–Fe potential on He diffusion, helium clustering and the dynamics of He-vacancy clusters.

The evolution of copper precipitates in binary FeCu alloys during ageing and irradiation

Abstract The evolution of copper precipitates in FeCu alloys during thermal ageing and irradiation, assuming the domination of Ostwald ripening, has been theoretically investigated. It is assumed that copper atoms diffuse via a vacancy mechanism and copper clusters are homogeneously nucleated. The diffusion coefficient and the binding energy of copper atom with a cluster as a function of cluster size, that fit satisfactorily the available experimental data for thermally aged FeCu alloys, have been obtained. It was taken into account that the crystal lattice of copper precipitates changes from bee at small sizes to fee at large ones via an intermediate martensitic stage. The results of calculations are in agreement with the observed evolution of copper precipitates in FeCu alloys during thermal ageing and irradiation.

Unlimited damage accumulation in metallic materials under cascade-damage conditions

Most experiments on neutron or heavy-ion cascade-produced irradiation of pure metals and metallic alloys demonstrate unlimited void growth as well as development of the dislocation structure. In contrast, the theory of radiation damage predicts saturation of void size at sufficiently high irradiation doses and, accordingly, termination of accumulation of interstitial-type defects. It is shown in the present paper that, under conditions of steady production of one-dimensionally (1-D) mobile clusters of self-interstitial atoms (SIAs) in displacement cascades, any one of the following three conditions can result in indefinite damage accumulation. First, if the fraction of SIAs generated in the clustered form is smaller than some finite value of the order of the dislocation bias factor. Second, if solute, impurity or transmuted atoms form atmospheres around voids and repel the SIA clusters. Third, if spatial correlations between voids and other defects, such as second-phase precipitates or dislocations, exist that provide shadowing of voids from the SIA clusters. The driving force for the development of such correlations is the same as for void lattice formation and is argued to be always present under cascade-damage conditions. It is emphasised that the mean-free path of 1-D migrating SIA clusters is typically at least an order of magnitude longer than the average distance between microstructural defects; hence, spatial correlations on the same scale should be taken into consideration. A way of developing a predictive theory is discussed. An interpretation of the steady-state swelling rate of ∼1%/displacement per atom (dpa) observed in austenitic steels is proposed.

Kinetic Monte Carlo studies of the effects of Burgers Vector Changes on the Reaction Kinetics of One-Dimensionally Gliding Interstitial Clusters

Kinetic Monte Carlo simulations of one-dimensionally diffusing interstitial clusters (dislocation loops) are used to gain insight into their role in microstructure evolution under irradiation. The simulations investigate the changes in reaction kinetics of these defects as a function of changes in the Burgers vector and variation in the size and density of randomly or periodically distributed sinks. In this paper we report on several kinetic Monte Carlo studies intended to elucidate the effects of mixed 1-D/3-D migration relative to pure 3-D and pure 1-D migration. We have investigated the effects of variation of the average distance traveled between Burgers vector changes (L) on the absorption of individual defects into absorbers of varying size and varying concentration, as well as the effects of variatioin in (L) on the time dependence of absorption of a collection of defects into an array of absorbers. Significant effects of Burgers vector changes on the reaction kinetics of the diffusing interstitial clusters are clearly demonstrated. Even when (L) is larger relative to the size and spacing of microstructural features, significant effects of mixed 1-D/3-D migration on reaction kinetics are evident.