## 3 Results and Discussion
For instance, NP Au can have a specific surface area as large as 85 m2 g-1 when its ligaments are about 7 nm in size [35]. From pore volume evaluation, a porosity of 40% can be estimated, relative to those pores smaller than 300 nm. The presence of nanosized ligaments and pores represents a fundamental aspect of a NP materials. However, it is well known that the performances of this kind of material also depend on larger-scale cavities by influencing various parameters, such as the mass transport of fluids, mechanical properties, and electrical and thermal conductivity [38; 39]. Thus, aiming at investigating the overall porous structure of the specimen, a technique capable of revealing its internal 3D structure appeared of pivotal importance. As a consequence, an SBF-SEM experiment was carried out on it. By this technique, the sample 3D structure along the entire 270 \(\upmu\)m cross-section profile was determined (example images of the cross-section at two different magnifications are shown in the Supplementary Materials, Figure S2) and the obtained micrographs allow analysis of NP Al at different scales with a resolution of 300 nm. From the SBF-SEM measurements, the 3D reconstruction and a representative video of the porous structure evolution during the subsequent cuts of the entire cross-section profile are shown in Figure 4 and in Video S1, respectively. Quantitative analysis of SBF images was focused near the surfaces and in the interior of the sample (see Figure S3). Indeed, it can be observed that the two surfaces have smaller pores and a higher overall porosity with respect to the inner part of the sample, as can also be clearly seen by the 3D reconstructions at a low (Figure 4) and higher (Figure S4) magnification. Moreover, the dense areas of the sample manifest different brightness levels, associated with a higher concentration of Zn in the brightest areas (and a lower one in the inverted images in Figures S2 and S3). The  
Figure 3: (**a**) SEM-SE micrograph of the NP Al cross-section showing a quite large internal pore. (**b**) N2 physisorption isotherms obtained from the whole NP Al specimen. Zn-richest areas are found to be more prevalent in the interior of the specimen due to the slower Zn removal in the inner part of the sample. From SBF-SEM analysis and by using IA techniques, it has been possible to estimate an additional porosity of 10% related to pores larger than 300 nm, which cannot be estimated by N\({}_{2}\) physisorption measurements. Therefore, by adding this value to the porosity relative to pores smaller than 300 nm, a rough estimation of the overall porosity lies at around 50%. IA of SBF-SEM images was also carried out to elaborate pore cumulative curves for voids with characteristic lengths higher than 300 nm. Consequently, in order to reproduce these experimental findings, an IFU model (see Figure 5) has been applied and input data has been reported in Table 1. In Figure 6a, a cumulative curve obtained by IA elaborations has been compared with fractal pore structure. It is possible to observe that the proposed model can reproduce the experimental data. Moreover, IA allows calculating the fractal dimension (Dt) of pores that is about 1.17 \(\pm\) 0.02. By using Equation (8), it is possible to estimate the length of the tortuous profile of each pore. Furthermore, in this case, the measured and calculated data, referred per unit of surface, are very comparable, 0.33 \(\upmu\)m\({}^{-1}\) and 0.30 \(\upmu\)m\({}^{-1}\), respectively. However, the pore fraction relative to IA observation is only 1/5 of the total porosity (equal to 50%). In order to have an overall description of porosity, IFU models have been used to design possible pore size distributions. These designed cumulative curves are built considering pore size ranges from SEM observations and overall porosity from SBF-SEM stacks and N\({}_{2}\) physisorption measurements. In Figure 6b, pore size distributions designed by using input data reported in Table 2 have been shown.