Metrics for the characteristic length scale in the random bicontinuous microstructure of nanoporous gold

Nanoporous gold (NPG) made by dealloying exemplifies materials with random bicontinuous microstructures that can be approximated by leveled-wave type models. As a distinguishing feature, the characteristic length scale – often quantified by the “ligament size” L – of NPG may be tuned over several orders of magnitude while the microstructural geometry retains a high degree of self-similarity. It is therefore essential to have at hand accurate procedures for determining the size by experiment and to match it to analogous size metrics of model scenarios. Working with a set of NPG samples of widely different size, we compare ligament size distributions determined by analysis of scanning electron micrographs to those of the leveled-wave model. The model is representative of various material types with random bicontinuous microstructures. The size distribution is remarkably uniform over the cross-section of experimental samples. Furthermore, the distribution evolves self-similarly upon coarsening, and the normalized distribution width agrees closely to that of the model. A measure for size determined by the electrochemical capacitance ratio method correlates well with L. This supports a protocol for converting between the two measures. As a dimensionless factor characteristic of the microstructural geometry of random dual phase microstructures, the product of L and the specific surface area is found consistent between experiment and model. The findings suggest conversion factors between the various metrics, and they advertise the combination of NPG and the leveled-wave model as a showcase for characterizing the characteristic length scale of random bicontinuous microstructures.