Nanoporous gold: 3D structural analyses of representative volumes and their implications on scaling relations of mechanical behaviour

Abstract

We present a quantitative study of the salient structural parameters identified from so-called ‘representative volumes’ of the bicontinuous nanoporous gold (NPG) network, and examine the validity of self-similarity in describing its evolution. The approach is based on 3D-focused ion beam tomography applied to as-dealloyed and isothermally annealed NPG samples. After identifying sufficiently large representative volumes, we show that the ligament width distributions coarsen in a sufficiently self-similar, time-invariant manner, while the scaled connectivity density shows a self-similar ligament network topology. Using these critical parameters, namely mean ligament diameter and connectivity density, the Gibson–Ashby scaling laws for the mechanical response of cellular materials are revisited. The inappropriateness of directly applying the Gibson–Ashby model to NPG is demonstrated by comparing finite element method compression simulations of both the NPG reconstruction and that of the Gibson–Ashby solid model; rather than the solid volume fraction, we show that an effective load-bearing ring structure governs mechanical behaviour.

Keywords:

• Cellular structures
• nanomechanics
• micromechanics
• structure analysis

Acknowledgments

ETL is grateful to Jürgen Markmann and Jörg Weissmüller for lively discussions, which helped strengthen the work.