A. V. Barashev

Evans's comments are related only loosely to the main body of our paper, which is devoted to the onset of void ordering: his Monte Carlo simulations of this early stage of ordering are in a qualitative agreement with our results. They question, however, the basic mechanisms of damage accumulation revealed by a number of scientists using various techniques over the years. Here we argue that his views are erroneous due to overlooking some essential features of one-dimensional defect transport.

Formation of void lattices is observed in a number of metals and alloys under high-energy particle bombardment. The conditions were derived for destabilisation of homogeneous void arrangement using an approach developed for the description of lane formation in pedestrian crowds. The model is based on the Foreman's mechanism of void alignment due to one-dimensionally migrating clusters of self-interstitial atoms. The results show that spatial correlations between voids should exist above some very small size, unless correlations with other defects prevail. It is shown that spatial correlations of voids with dislocations and second-phase precipitates should also evolve and provide a powerful driving force for further swelling.

Some lattice defects, such as dislocations, interact with migrating species, e.g. vacancies, interstitial atoms and their clusters, via long-range strain fields. An equation for the mean dissociation time of a migrating particle from a trap is derived in terms of the potential well function for the interaction energy. The distribution of dissociation times is studied by the Monte Carlo method, and the problem of particle exchange between spatially separated traps is considered.

The classical transition state theory for calculating complex dissociation rates requires separation of time scales. It is shown here that this condition is satisfied for complexes with long-range interaction, such as an edge dislocation and a cluster of self-interstitial atoms in metallic materials. Hence, one can apply the equations for first-order reactions with a rescaled mean dissociation time and the cross-section of complex formation. The rescaling coefficient is the Eyring transmission coefficient. A general expression for this coefficient through the first two moments of the distribution function of dissociation times is derived. It is shown that it is equal to unity if the dividing surface between ‘bound’ and ‘free’ states is defined as that where the interaction energy is equal to the thermal energy.

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.

Segregation of solute atoms such as P to grain boundaries (GBs) in reactor pressure vessel steels can cause intergranular embrittlement. We study the segregation kinetics at low temperatures, where the thermal effects are negligible and the solute atoms are fully adhesive to GBs. An analytical dependence of the GB coverage of segregant atoms on the irradiation dose is derived.

Changes in the near-surface region of V-5Fe alloy after irradiation at room temperature with 50 keV V⁺ ions to fluences in the range from 10¹⁹ to 10²¹ ion/m² have been investigated. Radiation-induced segregation profiles were measured by means of XPS with ion sputtering. Calculations of the segregation profiles were performed using diffusion equations modified for the case of ion irradiation at temperatures where the vacancies are immobile. The difference in the interstitial diffusion coefficients of alloy components were considered as the main driving force for the component redistribution. By fitting the experimental data the ratio of iron to vanadium interstitial diffusion coefficients δ_i has been evaluated. Assuming the equality of the pre-exponential factors in the diffusion coefficients, a temperature dependence of δ_i has been found. An analytical expression for δ_i has been derived.