Fig. 3: Strut interconnectivity, surface and copper-pore interface analysis upon sintering.

a 3D tortuosity analysis in the y direction to quantify the connectivity of the copper along the direction from the surface to the substrate, with high tortuosity (blue) and low tortuosity (black). b Evolution of the averaged tortuosity upon sintering for HPA (blue), HPB (gold) and NPC (red). For the analysis we average the values of the last 25% of the volume, as highlighted for the 3D volume for HPB at 175 °C in five directions (see Supplementary Note 5). c Specific surface area analysis for HPA (blue), HPB (gold) and NPC (red), respectively. All samples indicate a reduction of the specific surface area. d The complexity of the sintering process is illustrated by joint distributions of the Gaussian (G) and mean (M) curvatures. All materials’ tails stretch in the first quadrant (QI) and second quadrant (QII). The QI tails show the presence of small radii convex regions, inversely related to the magnitudes. Consequently, the low temperature plots show the early stage of sintering. In contrast, the QII tails show the progress of sintering when the particles are joining. This progress indicates the formation of necks and concave radii. Interestingly as temperature increases, the QI tails tend to get shorter and the QII tails tend to get denser and longer. The intensity maximums/peaks show negative Gs for all samples at low temperatures. As the temperature increases, the necks become flattened, i.e., G becomes less negative.