Graph Theory Based Approach to Characterize Self Interstitial Defect Morphology

Abstract

Morphology of self interstitial atom (SIA) clusters formed after a collision cascade is an important aspect of radiation damage. We present a method to characterize the morphology of a cluster by precisely identifying its constituent homogeneous components. The constituent components are identified as parallel bundles of SIAs, rings and other configurations based on the properties of alignment of the SIA lines and their neighborhood relationships. We reduce the problem of decomposition of a cluster into components and characterizing them into graph theory problems of finding connected components and finding cycles in a graph representation of a cluster.The method is used to study over 1000 clusters formed in W collision cascades for energies ranging from 50 keV to 200 keV. We show the typical cluster shapes for each morphology type identified using the method and compare the structural description with the results from dislocation analysis. The description is found to be in agreement for components with big parallel bundle of SIA. We demonstrate with examples that for other cases such as a mixed cluster, the presented method provides a better description of the structural details. The study gives statistical distribution of different morphologies across energies and their properties such as component sizes and orientations.

Comparison of SIA Defect Morphologies from Different Interatomic Potentials for Collision Cascades in W

“…Figure 1 (e) shows a cluster with one parallel component augmented with a planar hexagonal ring. In such structures the parallel component can appear as a dislocation loop and the relatively smaller ring may or may not be identified as a complex arrangement adjoining it [38]. Same can be observed for clusters with multiple parallel components (Figure 2 (c)) where some parallel components are small and are not identified as a loop.…”

“…For identifying a C15-like 3D-ring or its constituent planar ring basis viz. hexagonal ring and tripod / triangle configurations [23,38], we can check if the angles between the dumbbells correspond to the angles in the basis configurations. A graph adjacency matrix defines the connections between the nodes based on a desired relationship.…”

“…To further verify ring morphology, we check for cycles in the graph, wherein, neighboring lines within a specified angle to the original line are traversed, and during the course of the traversal, if the initial line is reached, a cycle is said to have been completed. The computational method is described in [38]. It can be used to search for a specific cluster morphology or a specific combination of morphologies composing a cluster.…”

“…Figure 1 shows the different possible morphologies that have been obtained from our analysis of MD simulations of collision cascades in W [38,21]. A sessile cluster can be a combination of different sessile and glissile configurations.…”

“…Their rare occurrence implies that these change to known stable forms. We have developed a method based on graph theory [39] to define the morphology of a cluster based on the constituent homogeneous components it is composed of [38]. The method is applied to study and compare clusters formed in W collision cascades at 100 keV and 200 keV using three different potentials viz.…”