The isothermal evolution of nanoporous gold from the ring perspective - an application of graph theory

The ring structures of five isothermally annealed nanoporous gold (npg) samples were analyzed explicitly by applying results and algorithms from graph theory to skeletonized 3D reconstructions from focused ion beam (FIB) tomography data. Simplified skeletons of the reconstructions were utilized, in which the real ligaments are reduced to straight edges between the branching points of the npg microstructure. So-called minimum weight cycle bases of each skeleton graph’s cycle vector space were calculated, assigning different weight functions to these straight edges: equal weights, Euclidean lengths, and the real ligament lengths from backmapping the Euclidean skeleton edges to the skeletonized real ligament sections. These cycle bases contain the maximum number of linearly independent rings that cannot be generated by smaller rings via the ring sum specified in the cycle vector space. Such a decomposition of the npg network structures into the fundamental ring building blocks served to provide a new perspective of the isothermal evolution of npg, since the coarsening of the npg network structure could be examined from analyzing the local ring topologies and the classification of the ring topological classes. Our results suggest an increasing relative dominance of ligament pinch-off events over ring collapse events, manifesting in a broadening of the distribution of topological classes, and leading to a small but steady increase of the average number of ring edges. Furthermore, self-similar evolution of the investigated sample series cannot be stated. The implications on the topological evolution of npg as a function of the solid volume fraction are discussed.