Stochastic effects on dislocation structure development under cascade-damage irradiation

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Dislocation climb, loop growth, and void swelling in the presence of the continuous generation of intracascade primary clusters are considered in this paper. Due to the ran- dom nature of cascade initiation, annihilation of point defects at sinks undergoes continuous random fluctuations that of- ten have sizes comparable to the sizes of the primary clus- ters. This makes them particularly important to the evolution of small defect clusters. In this paper, a reaction kinetics approach is generalized to include the effects of stochastic fluctuations of point-defect fluxes introduced by the random point-defect production in discrete packages during cascade irradiation. The reaction constant consistent with this ap- proach is derived for the annihilation of immobile clusters by the climbing dislocations. Taking the immobile primary inter- stitial clusters (PICs) as the interstitial loop nuclei, the evolu- tion of loops and network dislocations, and the resulting void swelling are calculated as a function of dose. Using param- eters appropriate to stainless steel, the loop number density, loop size distribution, network line density, and correspond- ing swelling are calculated and compared with experimental observations. It is found that this calculation explains the ob- servations very well. One of the central issues in the study of the accumulation of damage produced by cascade irradiation, in the form of both free defects and defect clusters, is the reaction kinet- ics between the primary clusters and extended sinks such as dislocations. Indeed, it is immediately clear, from the con- tinuous generation of clusters in cascades, that if they are only produced and not annihilated, they will become domin- ant sinks at very low dose. Acting as recombination centers for point defects, they may suppress any further development of the microstructure. Therefore, the evolution of the primary clusters (particularly the thermally stable primary interstitial clusters (PICs)), as governed by reactions among themselves, and with extended dislocations (both loops and network), is an essential ingredient in any theory of irradiation-induced deformation. It is evident that reaction among the primary clusters, and between the primary clusters and the dislocations, can only take place when the reaction partners come within the reac- tion volumes of each other. In general, such reactions can be envisaged to occur in two steps. During the first step, the relative motion of the reaction partners brings them together in a position in which they are bound by the elastic inter- action. During the second step, one of the reaction partners, the primary cluster, is annihilated, with the absorption of its point-defect content accommodated by dislocation climb or