## 3 Results  
The results of studying the rheological properties of YSZ powder during the SPS process with various pressing schemes are presented in Table 1. Spark Plasma Sintering of YSZ ceramics is satisfactorily described by Equation (1). The use of a collector pressing scheme in the SPS process can significantly increase the intensity of compaction of the test material (coefficient b). It allows decreasing the critical pressing pressure \(P_{c}\) by half and reducing the critical temperature \(T_{c}\) of material flow by more than one hundred degrees Celsius. The graphical representation of the seal surface (Figure 2) described by Equation (1) makes it possible to assess the possibilities of achieving a nonporous state of the consolidated material and to optimize the SPS sintering modes by combining increasing pressure and temperature. The optimal line is the most intense gradient descent from an arbitrary point lying on the top of the seal surface. The development of a line for the transcendental surface, Equation (1), presents a certain problem. Nevertheless, numerical methods make it possible to develop this line with an accuracy sufficient for practical applications. The algorithm for the line developing at the most intense descent on the seal surface takes into account the direction of the local gradient using the normal isoline (dashed line in Figure 3a) and the density isoline at a given point, Equation (1). The intersection point of this normal isoline with the next density isoline was selected with an extremely small step from the previous isoline. The sequential execution of these actions allows the curve (path) of the most intense gradient descent (red circles in Figure 3b) to be drawn on the seal surface as a set of intersection points of normal isolines to the density isoline with the next density isoline. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pressing Scheme** & \(\mathbf{b}\) & \(\mathbf{P_{c}}\)**MPa** & \(\mathbf{n}\) & \(\mathbf{T_{c}}\)**, \({}^{\circ}\)C** \\ \hline Uniaxial pressing & 0.0280 & 11.687 & 59.30 & 1498 \\ Collector pressing & 0.0444 & 5128 & 54.14 & 1378 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rheological characteristics of the sintered ceramics under Spark Plasma Sintering (SPS) conditions. Figure 2: Compaction surfaces of yttrium-stabilized zirconia (YSZ) powder during consolidation by the SPS technique using various pressing schemes: (**a**) uniaxial pressing and (**b**) collector pressing. The results of the study of the rheological properties of the YSZ powder quantitatively confirm that the combination of SPS with rational methods of deformation is promising for the fabrication of transparent YSZ ceramics. The proposed technique for developing the line of the most intense gradient descent on the surface (1) can be effectively used to optimize the SPS consolidation of ceramics. X-ray phase analysis (Figure 4) showed that the YSZ ceramics consisted of cubic zirconium dioxide with a lattice parameter \(a\) in the range from 5.144 to 5.146 A. The sizes of the coherent scattering regions (CSRs) of the cubic phase (crystalline sizes \(D\)) and their relative microstresses \(\epsilon\) were determined from the broadening of the reflections in the diffraction pattern. The parameters of the crystal structure are the weighted profile R-factor (_Rwp_) characterized the reliability of microstructure parameters by the Rietveld method [15] and microhardness of YSZ ceramics (see Table 2). Figure 4: Typical XRD patterns of YSZ ceramics sintered by SPS at 1300 \({}^{\circ}\)C.  
Figure 3: Graphical representation of the algorithm for developing the line of the most intense gradient descent (**a**—red line) and an example of the seal surface at SPS process with this line; (**b**—noted by red markers). The Vickers microhardness of ceramics, with an increase in height from 2 to 5 mm, changed nonmonotonically within the range of values from 14.2 \(\pm\) 0.1 to 15.5 \(\pm\) 0.3 GPa for specimens made using uniaxial pressing, respectively.