## 2 Materials and Methods  
### YSZ-GO Composite Manufacturing  
Composites were obtained from the individual powders of 8 mol.% yttria-stabilized zirconia (YSZ) and reduced graphene oxide (rGO). YSZ precursor powder was synthesized by a sol-gel method in a variant of reversed co-precipitation. Precipitation of the 0.1 M aqueous solution of mixed nitrate hydrates Y(NO\({}_{3}\))\({}_{3}\):6H\({}_{2}\)O (Acros Organics, Geel, Belgium, 99.9%) and ZrO(NO\({}_{3}\))\({}_{2}\):6H\({}_{2}\)O (Acros Organics, Geel, Belgium, 99.5%) was realized by dropwise addition of 1 M ammonia solution (LenReactiv Ltd., St Petersburg, Russia, c.p.). The obtained gel was washed to a neutral pH then freeze-dried (Laboconco, 1 L chamber, Kansas City, MO, USA; 293 K, 24 h, P 0.018 mm Hg) and annealed at 700 \({}^{\circ}\)C for 3 h (to start the formation of cubic solid solution) and then milled in a planetary ball mill (Pulverisette 6, Fritsch, Germany, 420 rpm, 24 reverse cycles of 5 min each) to diminish powder agglomerate size. A detailed description of used synthesis procedures is provided elsewhere [9].  
Oxidation/reduction route was chosen for the reduced graphene oxide (rGO) production. Oxidation from the commercial highly oriented pyrolytic graphite (Active-nano Ltd., Russia) was performed via Hummers technique [23]. The obtained graphite oxide was washed by distilled water until the neutral pH of filtrate, treated in an ultrasonic bath for 30 min (bath Sapphire 2.3 TTC, Russia, frequency 35 kHz, 0.1 kW power) for the delamination of individual graphene oxide layers then dried at 100 \({}^{\circ}\)C for 3 h and then thermally reduced in two steps: exposure at 300 \({}^{\circ}\)C for 1 h with the following microwave irradiation treatment (household microwave oven, 2.45 GHz, 750 W, 30 s) in the argon atmosphere. Additional microwave irradiation step allows one to increase the quality of the graphene basal plane and to decrease the number of defects [24]. Thus, the individual components were obtained.  
YSZ and rGO powders were mixed in 4 different ratios (see Table 1) and milled in the planetary ball mill to prepare powder composites, break particle agglomerates and reach homogeneous distribution of the carbon additive in the ceramic matrix. The optimal amount of the graphene additive providing the formation of a \"core-shell\" type composite with YSZ agglomerate covered with the single rGO layer was calculated using simple mathematical model proposed in recent papers [8; 9].  
Composite powders were compacted into pellets with the diameter of \(\sim\)8 mm and thickness of \(\sim\)5 mm by cold uniaxial pressing with a force of 49 kN (Mega kck-50A, 50 t, Spain) and exposure time of 5 min and then additionally compressed by cold isostatic pressure with a force of 152 MPa. The obtained green body samples were placed into a three-layer powder bed (Figure 1) and sintered at 1550 \({}^{\circ}\)C for 3 h in air. Sintering conditions (time and temperature) were chosen according to recent work of authors [9], where the YSZ-rGO samples were sintered without the use of a powder bed. Silicon carbide was chosen as a main component of the powder bed because of its inertness against YSZ and ability to bind oxygen with the formation of SiO\({}_{2}\) continuous layer preventing further O\({}_{2}\) diffusion and oxidation process [25]. Top graphite layer was added to bind oxygen at low temperatures, where SiC remains relatively inert. Bottom graphite layer was added to preserve carbon concentration excess and limit its diffusion out of specimens.