## 4 Discussion
At the same time, no traces of significant agglomeration were found, and areas of the formed ceramic structure are without significant defects or large pores. Thus, it can be concluded that the diffusion process dominates for the Z0 sample which may be due to the larger carbon concentration gradient between the powder bed and the ceramic sample. From that point of view, the diffusion of SiC during sintering of Z0.25 and Z1 composites should be less pronounced. Indeed, the Z0.25 and Z1 samples have higher relative density and the most uniform structure without loosening in the bulk or large pores but have the near-surface layer. This assumption could also explain the shape and structure of the near-surface layers by the means of two-times different thermal expansion coefficients (CTE) for SiC (\(\approx\)4.5\(\cdot\)10\({}^{-6}\) K\({}^{-1}\) at 873 K [40]) and for YSZ (\(\approx\)9.2\(\cdot\)10\({}^{-6}\) K\({}^{-1}\) at 873 K [41]). When heated, YSZ ceramic grains have a compressive effect on diffusing silicon carbide, which, when cooled, leads to the formation of elongated pores. In addition, the uniform distribution of rGO in the intergranular space should limit grain growth and hinder oxygen vacancy transfer. Composite Z0.25 has the same type of microstructure but lower microhardness and higher conductivity, which indicates the presence of rGO in the intergranular space. The microstructure features obtained for the Z1 sample are in accordance with the decreased grain boundary conductivity and high activation energy. Finally, the Z1 sample has the highest microhardness among all the samples sintered. The addition of 1 wt.% of rGO prevents both significant agglomeration and SiC diffusion into the bulk; i.e., it is close to the optimal concentration for powder bed sintering of sol-gel synthesized YSZ powder. In order to reveal the nature of the carbon concentration gradient, let us consider the possible mechanisms of silicon carbide degradation during sintering from the thermodynamic point of view. In the presence of oxygen, reactions (3)-(5) are allowed:  
\[\text{SiC(s)}+1/2\text{O}_{2}\text{(g)}\ \rightarrow\ \text{CO(g)}+\text{SiO(g)}\ \Delta G _{r}=-460.8\ kJ/mol \tag{3}\]  
\[\text{SiC(s)}+1/2\text{O}_{2}\ \text{(g)}\ \rightarrow\ \text{C(s)}+\text{SiO(g)}\ \Delta G _{r}=-191.6\ kJ/mol \tag{4}\]  
\[\text{SiO(g)}+1/2\text{O}_{2}\ \text{(g)}\ \rightarrow\ \text{SiO}_{2}\text{(s)}\ \ \Delta G _{r}=-514.8\ kJ/mol \tag{5}\]  
where (s) and (g) are solid and gaseous phases, respectively. All reactions are characterized by significantly negative free Gibbs energy (\(\Delta G_{r}\)). The \(\Delta G_{r}\) values were calculated using reliable data [42] taking into account the dependences of entropies, enthalpies and heat capacities of all the reactants and products on temperature. Despite that reaction (3) has a more negative \(\Delta G_{r}\) value than reaction (4), no Si is present in the EDX data of all samples studied (see Supplementary Materials). One can suggest that reaction (5) resulting in gaseous SiO and solid C is more favorable from the point of view of kinetics. The resulted SiO is removed from the ceramic matrix, readily transforms into SiO\({}_{2}\) according to reaction (6) and stays in the powder bed. Thus, the reaction (4) and (5) sequence takes place during sintering. Thus, it can be concluded that the diffusion of SiC from a powder bed to the ceramic matrix followed by its decomposition takes place during annealing at 1550 \({}^{\circ}\)C. Its effects on the microstructure and electrical properties of the sintered samples depend on the initial rGO concentration in the composite powder. In summary, the suggested powder bed sintering technique in a three-layer graphite/SiC/graphite powder bed allows one to obtain well-formed dense YSZ-rGO ceramics and can become a suitable alternative to existing equilibrium (conventional sintering) and non-equilibrium (SPS, flash sintering) methods for various oxide ceramic composite fabrication.