## 3 Results and Discussion
It is known that zinc oxide is also effectively reduced with hydrogen ZnO + H\({}_{2}\) (g) \(\rightarrow\) Zn (g) + H\({}_{2}\)O (g) [40] followed by complete evaporation of Zn at the temperature of 700 \({}^{\circ}\)C [41]. Probably, similar processes take place in our experiments. Figure 5: Scanning electron microscope (SEM) images of the surface of printed lines made of nanoparticles on alumina, borosilicate glass, and silicon substrates sintered in a reducing atmosphere at temperatures equal to (**a**) 350, (**b**) 450, (**c**) 550, and (**d**) 650 \({}^{\circ}\)C, respectively. However, despite the high proportion of copper, the electrical resistivity of the sintered lines is 10-15 times higher than the electrical resistivity of the bulk material \(\sim\)1.7 \(\upmu\Omega\cdot\)cm. The main reason for this low resistance may be the large number of pores in the sintered lines. In the case of the presence of pores in the volume of the line, it can be difficult to understand the quality of their sintering, examining only the surface morphology. For this reason, additional studies on the degree of shrinkage \(S\) of the line depending on the sintering temperature were performed. The degree of shrinkage \(S\) of the line, which is responsible for the change in the cross-sectional area before and after sintering, was determined using the following Equation (2):  
\[S=\frac{A_{0}-A}{A_{0}} \tag{2}\]  
where \(S\), \(A_{0}\) and \(A\) are the shrinkage, cross-sectional areas of the initial and sintered lines, respectively. Figure 6b shows, as an example, the change in the cross-sectional profile of a line on an alumina substrate at different reductive sintering temperatures. The general result of determining the degree of shrinkage of lines on substrates of Al\({}_{2}\)O\({}_{3}\), BG, and Si, depending on the sintering temperature, is presented in Table 2 as the average value of measurements of five lines on one type of substrate for each sintering temperature. The Table 2 shows that the degree of shrinkage of the lines after sintering at 350 \({}^{\circ}\)C is insignificant and amounts to 12-15%. At the same time, a significant shrinkage of the printed lines equal to 45-59% is observed with an increase in the sintering temperature to 450 \({}^{\circ}\)C, and reaches a maximum value of about 70% at a temperature of 650 \({}^{\circ}\)C. In \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sintering Temperature** & **Alumina (Al\({}_{2}\)O\({}_{3}\))** & **Borosilicate Glass (BG)** & **Silicon (Si)** \\ \cline{2-3} \(T_{\text{sint}}\)\({}^{\circ}\)**C** & & **Shrinkage \(S\), \%** & \\ \hline
350 & \(15\pm 7\) & \(12\pm 7\) & \(14\pm 7\) \\
450 & \(45\pm 8\) & \(59\pm 8\) & \(54\pm 6\) \\
550 & \(48\pm 5\) & \(65\pm 7\) & \(61\pm 7\) \\
650 & \(59\pm 6\) & \(69\pm 9\) & \(63\pm 8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Shrinkage of printed lines as a function of sintering temperature on various substrates. Figure 6: (a) Changes in the elemental composition (results of EDX analysis) and (b) the cross-sectional profile of lines based on copper nanoparticles with the temperature of reductive on alumina substrate as an example. this regard, it can be seen that the degree of shrinkage (Table 2) and electrical resistivity (Figure 4a) of the lines correlate with each other. Thus, incomplete shrinkage or high residual porosity of the samples can be the reason for their high electrical resistivity. It is known from sintering theory that sintered agglomerate structures contain a large number of closed pores [42]. Considering this, additional experiments were performed on the formation and sintering of lines from spherical nanoparticles instead of fractal-like agglomerates in order to obtain denser and highly conductive microstructures. Spherical nanoparticles were produced using a spark discharge as shown in Figure 1, but the aerosol nanoparticles were additionally passed through a tube furnace prior to deposition onto a substrate.