# A principle curvatures analysis of the isothermal evolution of nanoporous gold: Quantifying the characteristic length-scales

## Abstract

A study of the isothermal evolution of a nanoporous gold (npg) microstructure after dealloying has been performed. In order to adequately characterize its complex three-dimensional bicontinuous ligament-ring structure, an analysis of the scaled principle curvatures κ1 and κ2 based on representative volumes of meshed 3D reconstructions was applied. Five npg samples, as obtained from an electrolytical dealloying process, with different mean ligament diameters ranging from ca. 25 nm (as-dealloyed) to ca. 420 nm (from annealing at 300° C) were analyzed. The results indicate that ligament surface flattening effects lead to small but distinct morphological changes during the investigated early and mid-stages of coarsening, visible in the scaled κ1- and κ2- marginal distributions. Thus, strictly speaking, self-similar evolution of npg cannot be confirmed, but dependent on the specific application, the evolution might be seen as “sufficiently” self-similar. Moreover, it is shown that the inverse mean principle curvatures from the marginal distributions can be used to identify the mean sizes of the two salient structural features, namely the ligaments and the rings. Both inverse mean principle curvatures scale linearly with the mean ligament diameter. Thus, for the material used in this study, one parameter is sufficient to characterize its microstructure. Finally, it is shown that rings resembling the ones from the real samples can be generated computationally by applying modified torus parameterizations. Surprisingly, a calculation of the curvature distribution of only one ”average” ring is sufficient to approximate the scaled kappa distributions accumulated from the ring distributions of the real samples.