A.D. Brailsford

Diffusion to a random array of identical spherical sinks

The effect of the insertion of one additional spherical sink on the steady state diffusion field of particles migrating to a random array of identical sinks of the same type is determined. The change in particle concentration as a function of the distance from the inserted sink, when averaged over all permissible configurations of the original array, is shown to be of the same form as that arising from insertion of a sink of the same type in a homogeneous lossy medium. The loss rate per atom in this effective medium is found to be of the form DkM2(c (r) − c), where D is the particle diffusivity, c(r) an ensemble-averaged concentration (atomic fraction) defined in the text, and c is the prescribed concentration at each sink surface. The sink strength, kM2, is calculated to be kM2 = λ2 {1 + λa − λ2a2 (16 + γ + ln 6λa)}, with λ2 = 4πCa and γ Eulers constant, C being the average volume concentration of sinks, a their common radius. These results are shown to substantiate the standard rate theory treatment of simultaneous diffusion to many sinks and confirm the existence of correction terms in λa to the sink strength normally employed in this method.

Effect of self-ion injection in simulation studies of void swelling

Abstract The rate theory of void swelling is generalized to incorporate the effect of excess interstitial production resulting from self-ion injection in simulation studies. The swelling rate is shown to be reduced at all temperatures, the fractional reduction being largest in the region where intrinsic recombination of irradiation-induced interstitials and vacancies dominates, provided there is no dislocation recovery at high doses. When such recovery processes are operative, however, the effect of self-ion injection is most important near the peak swelling temperature and can lead to a saturation in swelling with increasing dose which, in the model considered, would be absent under neutron irradiation. For this reason it is emphasized that the results of simulation experiments, without complementary microstructural data, should be viewed with caution as far as their quantitative relation to neutron damage is concerned.

Swelling with inhomogeneous point defect production — a cascade diffusion theory☆

A theoretical method is described for evaluating the effects of spatially and temporally discrete production in collision cascades on point defect concentrations and swelling in materials during irradiation. The concentrations of vacancies and interstitials at a point which result from their diffusion from all cascades in the material are calculated. Large fluctuations occur with time in the vacancy concentration. The interstitial concentration is nearly always zero except for extremely large spikes of very short duration, corresponding to the occurrence of a cascade anywhere within the sphere beyond which all generated defects are absorbed by sinks before reaching the reference point. The growth rate of a void in this cascade diffusion theory is compared to that given by the more approximate rate theory. The difference is small but increases rapidly at high temperature. Implications of this work for void nucleation, irradiation creep, and analysis of pulsed irradiations are mentioned.

An effect of solute segregation on void growth in irradiated dilute alloys

Abstract Void growth in an irradiated solid-solution or two-phase system can be inhibited if solute segregation near the void surface, induced, say, by a lowering of the surface free energy, simultaneously reduces the diffusion of vacancies relative to self-interstitials. The mechanism is found to be efficient in suppressing void growth when re-solution of second-phase precipitates leads to solute supersaturation, or impurity interstitials are generated by collisions cascades in the matrix. While the effect does not require a precipitated second phase for the impurity/interstitial process, changes in the size of precipitates are shown to provide an independent indication of the solute redistribution.

Point defect trapping and void growth

Abstract Trapping of point defects at solute atoms or on the surfaces of coherent precipitates is known to reduce the void swelling of irradiated materials. It is shown here, however, that the dominant physical processes in these two situations are different. For atomic traps, defect capture is mainly balanced by defect emission in the steady state. For precipitate trapping, on the other hand, the balance is mainly achieved by on-site recombination with the anti-defect. Isomorphisms between interstitial and vacancy trapping are derived in the two cases through the development of a semi-quantitative analytical model. Substantial agreement is obtained with the prior numerical analyses of other workers.

On the meaning of sink capture efficiency and sink strength for point defects

Abstract The concepts of sink capture efficiency and sink strength for point defects are central to the theory of point defect reactions in materials undergoing irradiation. Two fundamentally different definitions of the capture efficiency are in current use. The essential difference can be stated simply. The conventional meaning denotes a measure of the loss rate of point defects to sinks per unit mean point defect concentration. A second definition of capture efficiency, introduced recently, gives a measure of the point defect loss rate without normalization to the mean point defect concentration. The relationship between the two capture efficiencies is here derived. By stating the relationship we hope to eliminate confusion caused by comparisons of the two types of capture efficiencies at face value and to provide a method of obtaining one from the other. Internally consistent usage of either of the capture efficiencies leads to the same results for the calculation of measuable quantities, as is required physically.

The sink strength of permeable sinks — a distribution of dislocation tangles

Abstract Following a suggestion implicit in the recent work of Lewthwaite, the sink strength associated with a dispersion of localized regions of high sink density has been investigated. The analysis is based upon some minor extensions of the Effective Medium method of rate theory. It yields the sink strength of such regions for any volume fraction of them. Lewthwaites model of a dislocation tangle is treated as a specific example. In addition to extending this to large volume fraction of tangles, the influence of different point defect production rates and or different point defect diffusivities in the tangled dislocation regions is investigated. A semi-quantitative analysis of the growth rate of voids in such a system reveals an extreme sensitivity to physical features of the model, thus rendering unequivocal quantitative predictions of anticipated behavior very difficult to obtain.

The effects of cascade damage and self-ion injection on the swelling of irradiated materials

Abstract The effects on the void swelling of irradiated materials of cascade damage and (for self-ion bombardment) of self-ion injection are derived in a unified manner by means of rate theory. The collapse of vacancy clusters within cascades to form vacancy edge dislocation loops follows the general model investigated by Bullough, Eyre and Krishan, although in contrast with this previous development that given here is entirely analytical. The dependence upon macroscopic measurable quantities is thereby exposed and the complementary effects of cascade damage and self-ion injection are made evident.

The vacancy dislocation loop microstructure formed during heavy-particle bombardment

Abstract The magnitude of the steady-state vacancy loop dislocation density resulting from the partial collapse of collision cascades, and the irradiation dose necessary to attain this state, are estimated by means of rate theory. The effects of dislocations of other than vacancy-loop type, of voids, and of the simultaneous injection of self-ions (such as occurs in a simulation experiment) are incorporated within the model. Analytical approximations for the vacancy loop dislocation density and time to steady are presented for various limiting cases of dose rate and temperature. The implications of the results for the void growth rate are presented in a companion paper.

Influence of point defect trapping on sink strengths

Abstract Under constant irradiation, immobile point defect trapping sites acquire a steady state occupation probability. The value of this probability depends upon the proximity of other sinks or sources. This in turn modifies the steady state point defect flux to (from) the sink (source) in question, thereby influencing its strength. An approximate theory of this effect is developed for a void embedded in a sea of point-impurity-associated trapping sites and of dislocations distributed at random. The sink strength of a set of such voids is determined. The theory is compared at length with the results of an earlier analysis in which the boundary layer phenomenon was not included.