## 2 Materials and Methods  
The investigated yttria-stabilized zirconia (hereinafter YSZ) was prepared using commercial powders of yttria and zirconia fabricated at the Vol'nogorskii Mining and Smelting Plant, Vol'nogorsk, Ukraine. Corresponding powders were characterized by the average particle sizes as follows: 10-30 nm for Y\({}_{2}\)O\({}_{3}\) and 100-150 nm for ZrO\({}_{2}\). Rectangle beam samples of YSZ ceramics doped with 3 and 6 mol% Y\({}_{2}\)O\({}_{3}\) (hereinafter 3 YSZ and 6 YSZ), of the size 4.2 \(\times\) 4.2 \(\times\) 50 mm\({}^{3}\), were produced by sintering for 2 h at 1450 \({}^{\circ}\)C, 1500 \({}^{\circ}\)C, and 1550 \({}^{\circ}\)C in an electric resistance furnace in argon. Preparation of powder mixture and selection of sintering modes have been thoroughly described in our earlier paper [39]. Slow polishing of the samples was carried out with a metallographic polishing machine to avoid phase transformations and reach the required surface quality.  
Standard preparation techniques were utilized to prepare samples for imaging and chemical analysis. They were cut on Struers Accutom 50 with a diamond disk, mounted in epoxy resin, and polished using a Struers Tegramin machine (Struers, Copenhagen, Denmark) with a set of SiC papers and diamond suspensions. The samples were analyzed without etching or coating.  
Both optical Olympus DSX1000 (Olympus, Tokyo, Japan) and scanning electron microscope (SEM) Hitachi SU3500 (Hitachi, Tokyo, Japan) were used for the microstructure and fracture surface characterizations of ceramics. In an assemble with the last one, Oxford energy dispersive X-ray spectroscopy system (EDS) was provided. Additionally, Hitachi SU3900 SEM with Bruker EDS and Esprit software (Bruker, Billerica, MA, USA) and Aztec software (Oxford Instruments, Abingdon, UK) were used. For each material variant, we manually measured 625 grains, 510 pores, 100 cleavage facets, and 310 fracture voids. For a several small and large grains, the yttrium concentration was estimated in each material variant in relation to the yttria fraction, sintering temperature, and grain size. During EDS analysis, acceleration voltage of 20 keV was applied.  
X-ray diffraction (XRD) analysis of as-sintered samples was carried out using a diffractometer DRON-4.07M (Bourcevetsnik, St Petersburg, Russia). A software package WinCSD (WinCSD, [[https://www.wincsd.eu/](https://www.wincsd.eu/)]([https://www.wincsd.eu/](https://www.wincsd.eu/)), accessed on 21 March 2021) was utilized for performing the indexing, refining the profile, and determining the phase balance (weight percentage). The following reference codes were used for the marked ZrO\({}_{2}\) phases (c--cubic,t--tetragonal, m--monoclinic): COD ID 2101234, COD ID 2300612, and COD ID 1528984, respectively.  
A testing machine MTS E43.004 (MTS Systems Corporation, Eden Prairie, USA) with a unit for three-point bend loading was used for performing the bend test of the beam samples at 20 \({}^{\circ}\)C in air. The loading unit was set with 14 mm distance between the supporting rollers. The material strength in flexure was calculated using the equation [45]:  
\[\sigma_{f}=1.5\frac{P\cdot s}{b\cdot h^{2}} \tag{1}\]  
where \(\sigma_{f}\) is the strength (MPa), \(P\) is the fracture load (N), \(s\) is the distance between the supporting rollers (mm), and \(h\) and \(b\) are the height and width (mm) of a beam sample, respectively.  
For each material variant, five samples were tested, and the flexural strength was calculated as the average value.