A. V. Barashev

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.

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.

On the correlation between self-interstitial cluster diffusivity and irradiation-induced swelling in Fe–Cr alloys

It is shown that the dependence of self-interstitial cluster diffusivity in Fe–Cr alloys on Cr concentration correlates with that of swelling in these alloys under neutron irradiation; namely, with increasing chromium concentration the cluster diffusivity first decreases and then increases. The origin of such behaviour lies in a relatively long-ranged, ∼1 nm, attractive interaction between Cr atoms and crowdions. The minimum diffusivity is realized for ∼11 at.% Cr, where all crowdions constituting the cluster interact with Cr atoms, but the interaction fields of different Cr atoms do not overlap.

Grouping method for the approximate solution of a kinetic equation describing the evolution of point-defect clusters

Abstract An approximate method for the numerical solution of a kinetic equation describing the nucleation, growth and coarsening of point-defect clusters or second-phase precipitates is of interest for many applications in solid-state physics. In the present paper the validity of a grouping method developed by Kiritani (1973, J. phys. Soc. Japan 35, 95) is examined. In this method, which is the only one proposed up to now, a group of equations is replaced by an ‘averaged’ equation. Significant disagreement between the group kinetic equation and the original kinetic equation is revealed and the reasons for this are specified. A new grouping method based on the original equation is proposed and application of the method for the solution of two problems is demonstrated by comparing the results of numerical and analytical calculations.

Monte Carlo modelling of Cu atom diffusion in α-Fe via the vacancy mechanism

Monte Carlo calculations of copper atom diffusion via the vacancy mechanism in bcc iron are presented. The activation energy of atomic jumps is taken from recent ab initio calculations. It is shown that the vacancy–copper atom cross-diffusion coefficient is positive at all temperatures, for which the bcc crystal structure is preserved. This is shown to be opposite to the description obtained using data calculated with an empirical interatomic potential for the Fe–Cu system. The sensitivity of the results to the values of the activation energy within the uncertainty of ab initio calculations is analysed. Implications of the results for the features of copper precipitation in ferritic steels under neutron irradiation are discussed.

Mechanism of one-dimensional glide of self-interstitial atom clusters in α-iron

Abstract 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 from a simple Arrhenius relationship is discussed. It is shown that such clusters only exhibit an effectively random walk, that is a correlation factor of one, when the jump length defining diffusion is taken to be 3b to 4b, where b is the magnitude of the vector ½(111).

Modelling the diffusion of self-interstitial atom clusters in Fe-Cr alloys

The results of molecular dynamics simulations of the diffusion of self-interstitial atom clusters in Fe–Cr alloys of different Cr content are presented. It is shown that, with increasing Cr concentration, the cluster diffusivity first decreases and then increases, in accordance with the predictions of a model developed recently and based on molecular static calculations. The minimum diffusivity is found at about 10 at% Cr for small clusters and it shifts towards lower concentration with increasing cluster size. The migration energy of SIA clusters is found to lie in between the binding energy of a Cr atom with a crowdion and half of it. This indicates that the mechanism of cluster migration is via the movement of individual crowdions from one Cr atom to another. The values obtained statically are much higher and are argued to be more reliable due to better sampling of different configurations in a bigger simulation box.

Reaction kinetics of glissile interstitial clusters in a crystal containing voids and dislocations

Abstract It has been shown in recent years that one-dimensional (1D) atomic transport plays an important role in radiation damage accumulation in metallic materials under cascade irradiation conditions. This transport is due to clusters of self-interstitial atoms (SIAs) that form directly in cascades and migrate along close-packed crystallographic directions. The reaction kinetics of 1D migrating clusters are known to be qualitatively different from those of three-dimensional diffusing point defects. It has been suggested that deviation of the reaction kinetics of SIA clusters from those for pure 1D diffusion is important for the further development of the theory of radiation damage. In the present paper, an analysis of the change in the reaction kinetics of SIA clusters with voids and dislocations due to spontaneous changes of the cluster glide direction is presented. Two forms of spatial distribution of voids, namely random and in the form of a lattice, are considered.

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.

Effect of mass of the primary knock-on atom on displacement cascade debris in α-iron

Results are presented from molecular dynamics (MD) simulations of displacement cascades created in α-iron (Fe) by primary knock-on atoms (PKAs) with energy from 5 to 20 keV and mass chosen to represent C, Fe and Bi. The PKA-Fe interaction potential at short range has been varied, and damage by molecular Bi2 has been simulated using two Bi PKAs. Four effects are reported. First, the PKA mass has a major effect on the damage produced in individual cascades while the PKA-Fe potential has little influence. Second, the total number of point defects produced in a cascade decreases with increasing PKA mass. This fact is not accounted for in models used conventionally for estimating damage. Third, interstitial loops of type and both vacancy and interstitial loops of ⟨100⟩ type are formed, the latter being observed in MD simulation for the first time. The probability of ⟨100⟩ loop appearance increases with increasing PKA mass as well as energy. Finally, there is a correlation between production of large vacancy and interstitial clusters in the same cascade.