Spatial Instability in Dislocation Structure under Irradiation

Abstract

In many materials, the dislocation structure after irradiation is observed to be heterogeneous, with regions of high dislocation density separated by ones of low dislocation density. Using a simple rate theory model with onedimensional diffusion of point defects (vacancies and interstitials), we show that spatial instabilities can arise for a general class of models for dislocation evolution. The numerical results obtained for density oscillations and their wave-lengths reproduce qualitatively both the magnitudes and trends with temperature of observed heterogeneous structures.

Spatial ordering of primary defects at elevated temperatures

“…This explains why no peak coarsening was obtained in the previous numerical calculations. 20,24 Another consequence of the treatment of Refs. 23-25 is that the spatial heterogeneity developed at elevated temperatures is permanent, as long as the instability criteria ͑35͒ is fulfilled, while, according to the present approach, the spatial heterogeneity should be much less stable at these temperatures, and eventually disappears.…”

“…In this case the parameter N represents the line density of both the network dislocations and the interstitial loops. Although, this simplification return us to the original simplest model, 20,21 we are not aware of any detailed study of what actually follows from this model at low temperatures.…”

“…[16][17][18] Pattern formation due to the development of instability in the homogeneous vacancy loop population is one of the most actively studied cases. Investigations within the reactiondiffusion mode 16,[19][20][21][22][23][24][25][26] progress from the simplest case, in which only vacancy clusters, beside the Frenkel pairs, are considered, 20,21 to the more complicated cases that also include extended defects like interstitial loops and voids. [22][23][24][25] Krishan 6 showed numerically that under the continuous generation of vacancy clusters, the spatially homogeneous evolution of the damage microstructure may become unstable.…”

“…Numerical calculations in the one-dimensional case further demonstrated that the development of this instability leads to the spatial ordering of vacancy loops. 20 Analytical studies [21][22][23][24] in the weakly nonlinear regime, as well as numerical simulations in two dimensions, 24 show that the evolution of a homogeneous vacancy loop population is sometimes unstable, leading to the formation of planar wall defect structures, after transients corresponding to threedimensional patterns. Taking into account interstitial loops and voids in the reaction-diffusion model does not change this conclusion.…”

“…27 The evolution of the interstitial cluster population should therefore be described in a way similar to the shrinking vacancy clusters. 6,[19][20][21][22][23][24][25] In other words, the Bullough-Eyre-Krishan ͑BEK͒ model, 28 originally developed for the vacancy clusters should also be applied to the interstitials clusters. 29 Interstitial clusters directly produced in cascades are generally smaller in size than their vacancy counterpart.…”