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Article

Phase Stability and Transport Properties of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x Crystals (x = 0–0.01)

by
Mikhail Borik
1,
Galina Korableva
2,
Alexey Kulebyakin
1,*,
Irina Kuritsyna
2,
Nataliya Larina
3,
Elena Lomonova
1,
Filipp Milovich
1,4,
Valentina Myzina
1,
Polina Ryabochkina
3,
Nataliya Sidorova
3,
Nataliya Tabachkova
1,4 and
Tatyana Volkova
3
1
Prokhorov General Physics Institute of the Russian Academy of Sciences, 38 Vavilov str., 119991 Moscow, Russia
2
Institute of Solid State Physics of the Russian Academy of Sciences, 2 Academician Osip’yan str., 142432 Chernogolovka, Moscow District, Russia
3
Institute of Physics and Chemistry, National Research Mordovia State University, 68 Bolshevistskaya str., 430005 Saransk, Republic of Mordovia, Russia
4
Department of Materials Science of Semiconductors and Dielectrics, National University of Science and Technology (MISIS), 4 Leninskiy prospekt, 119049 Moscow, Russia
*
Author to whom correspondence should be addressed.
Crystals 2021, 11(2), 83; https://0-doi-org.brum.beds.ac.uk/10.3390/cryst11020083
Submission received: 10 December 2020 / Revised: 12 January 2021 / Accepted: 14 January 2021 / Published: 21 January 2021
(This article belongs to the Special Issue Selected Papers from the 2nd International Online Conference on Crystals)
Browse Figures
Versions Notes

Abstract

:
Phase stability and transport properties of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x crystals (x = 0–0.01) have been studied before and after air annealing at 1000 °C for 400 h. The crystals have been grown by radio frequency (RF) heating in a cold crucible. The microstructure, phase composition, and electrical conductivity of the crystals have been studied using optical microscopy, X-ray diffraction, Raman spectroscopy, and impedance spectroscopy. Phase stability and degradation of ionic conductivity of the crystals upon long-term high-temperature heat treatment have been discussed. We show that the stabilization of ZrO2 co-doped with 9 mol.% Sc2O3 and 1 mol.% Yb2O3 provides transparent uniform crystals with the pseudocubic t″ phase structure having high phase stability. Crystals of this composition had the highest conductivity in the entire temperature range. Long-term high-temperature annealing of these crystals did not lead to conductivity degradation.

1. Introduction

The use of stabilizing scandium oxide in zirconia based solid electrolytes provides high ionic conductivity material. Electrolytic membranes of these materials significantly reduce the working temperature of the electrochemical devices while retaining their high electrical conductivity, which is of high importance for service life and reliability of electrochemical reactors, solid oxide fuel cells, electrolyzers, and sensors [1,2,3,4,5].
Polycrystalline ceramic materials are typically used in these devices. Ceramic technologies impose only little limitations on the shape and dimensions of final devices. However, zirconia based ceramic solid state electrolytes obtained using different methods exhibit quite different electrical conductivities [6,7,8,9,10]. This difference has been reported to originate from differences in the microstructure, impurity content, and thermal history of the materials, arising from technological aspects.
Zirconia based materials can be produced using not only ceramic technologies, but also directional melt crystallization [11,12]. This method is characterized by high productivity and makes it possible to obtain up to several hundred kilograms of single crystals in one technological cycle (24 h). The cold crucible design does not require any special devices limiting the number of grown crystals, e.g., devices used in hot crucibles. Directional melt crystallization process produces an ingot consisting of multiple columnar single crystals whose number and sizes depend on growth process parameters. Another advantage of this method is the fast in-melt synthesis from the raw oxides, which does not require any intermediate or preliminary stages at which the raw materials might be contaminated. The high melting points (~3000 °C) accelerate the removal of volatile impurities from the melt. Furthermore, directional melt crystallization removes a number of impurities, e.g., silicon, aluminum, titanium, tungsten, molybdenum, etc., which are displaced during directional crystallization because their distribution coefficients in zirconia are less than 1 [12]. The conductivity of crystals grown by directional melt crystallization only depends on the initial composition and crystallization conditions, unlike for materials obtained using ceramic technologies.
Different authors reported that solid solutions with the composition ZrO2 – (9–10) mol.% Sc2O3 have the highest ionic conductivity [13,14,15,16,17]. However, the structural and electrical properties of these materials are very sensitive to the Sc2O3 content [13,18]. For example, it was reported [18] that ceramics with 9.3 mol.% Sc2O3 has the highest ionic conductivity whereas above 9.5 mol.% Sc2O3 the rhombohedral phase forms and coexists with the cubic phase at room temperature. In comparison with the cubic phase, the rhombohedral phase has a low conductivity. Upon heating, the rhombohedral phase transforms to the cubic phase in the temperature range 400 to 600 °C. For scandia stabilized zirconia the phase boundaries have been determined only approximately, because metastable phases exist in this system and, therefore, the phase composition of the material depends on its synthesis method and conditions.
An important problem limiting the use of ZrO2-Sc2O3 solid solutions as solid electrolytes is the instability of the transport characteristics of the material during long-term device operation. The reasons for this behavior of conductivity in this system have been studied in a number of articles [19,20,21,22]. The instability originates from the metastability and multiphase composition of the materials causing phase transformations of the most conducting compositions at operation temperatures and, hence, reduction of oxygen-ionic conductivity of the materials. One method to provide stable phase composition and transport properties is additional doping of the ZrO2-Sc2O3 solid solution with rare earth oxides which favor the formation of single-phase solid solutions that are stable at solid state electrolyte operation temperatures [23]. This additional doping should not lead to a noticeable decrease in the conductivity of the material. The Yb2O3 is one of the promising oxides that stabilize the cubic phase in ZrO2-Sc2O3 solid solutions. Currently, there is interest in studying the structure and transport characteristics of ceramic and crystalline samples of ZrO2-Sc2O3 solid solutions additionally doped with Yb2O3 [24,25,26]. The effect of long-term annealing at 650 °C in air on the properties of ZrO2 solid solutions containing 8–9 mol% Sc2O3 and additionally co-doped with 1 mol% Yb2O3 has been studied [27]. It was shown that the introduction of 1 mol% Yb2O3 reduces the degradation of the conductivity of ZrO2-Sc2O3 solid solutions. However, since the operating temperatures of ZrO2-based solid electrolytes are ~900 °C, it is of interest to study the structural and electrophysical characteristics of ZrO2-Sc2O3 solid solution samples additionally stabilized with Yb2O3, which were subjected to heat treatment at higher temperatures.
The aim of this work is to study the effect of long-term annealing (at a temperature of 1000 °C for 400 h) on the phase composition and conductivity of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x crystals.

2. Materials and Methods

The (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x solid solution single crystals where x = (0; 0.005; 0.01) were synthesized using directional melt crystallization in a cold crucible. The raw materials were high purity powdered zirconia, scandia and ytterbia containing at least 99.96 wt.% of the respective materials. The raw materials were mechanically mixed, loaded into a water-cooled tube container and melted by direct RF heating. The RF generator frequency was 5.28 MHz and its power was 60 kW. Metal zirconium was used for initial melting. Melt crystallization in a cold skull produced an ingot consisting of single crystals.
The as-grown crystals were heat treated at 1000 °C in air for 400 h in an HT 04/16.2 high-temperature furnace.
The phase composition of the crystals was analyzed by X-ray diffraction on a Bruker D8 diffractometer in CuKα radiation and using Raman spectroscopy with a 633 nm excitation laser. The density of the crystals was measured by hydrostatic weighing on a Sartorius instrument. The microstructure of the specimens was studied for 1.5 mm thick plane-parallel wafers cut along the crystal growth axis using polarized transmitted light optical microscopy under a Carl Zeiss Axio Imager Z2 microscope.
The conductivity of the crystals was studied at 300‒900 °C using a Solartron SI 1260 frequency analyzer in the 1 Hz–5 MHz frequency range with an alternating current signal amplitude of 24 mV. The test wafers were 7 × 7 mm2 squares 0.5 mm in thickness. The current contacts were formed on opposite sides of the crystals from platinum paste annealed at 950 °C in air for 1 h. The impedance spectra were processed with the ZView version 2.8 software. The conductivity of the crystals was calculated from the impedance spectra processing data taking into account the specimen dimensions.

3. Results and Discussion

The ZrO2 crystals grown using directional melt crystallization in a cold crucible and stabilized with 9 mol.% Sc2O3 and additionally doped with 0.5 mol.% Yb2O3 and 1 mol.% Yb2O3 are hereinafter denoted as 9ScSZ, 9Sc0.5YbSZ and 9Sc1YbSZ. The cross-section sizes of the crystals were 10 to 15 mm and their lengths were 30 to 45 mm. Figure 1 shows polarized light microstructure images of wafers cut from the crystals along the growth axis.
The as-grown 9ScSZ crystals were completely semitransparent and contained no cracks. The microstructure images of the crystals show elongated structural features which have different orientations in different crystal regions. This crystal microstructure is produced by transformation twins forming upon crystal cooling. There are several options of the ZrO2-Sc2O3 phase diagram which differ considerably, the differences being the greatest in the region of ZrO2-9 mol.% Sc2O3 composition. The equilibrium room temperature phase composition has not yet been determined authentically, but the phase diagrams suggest that the cubic phase may undergo transitions to the tetragonal and/or rhombohedral phases upon cooling [28,29]. The phase transition from the high-temperature cubic phase which exists at temperatures close to the crystallization point to the tetragonal phase or the rhombohedral phase during cooling of single crystals is accompanied by twinning which reduces the stress generated during the phase transition. Upon annealing, the sizes of the structural features observed in the 9ScSZ crystals became larger, and the boundaries between crystal regions with different structures became clearer. The as-annealed 9ScSZ crystals contained microcracks.
Addition of 0.5 mol.% Yb2O3 to the 9ScSZ solid solution produced discrete transparent regions in the crystals. The bottom part of the 9Sc0.5YbSZ crystal, i.e., the part from which crystallization began, contained a uniform transparent region. The middle part of the crystal had a fine twin structure with discrete inclusions of small transparent regions. The top part of the crystal contained large twins that crossed in different directions. The structure of the as-annealed crystals did not contain discrete transparent regions. The microstructure of the 9Sc0.5YbSZ crystals became similar to that of the 9ScSZ crystals. The as-annealed 9Sc0.5YbSZ crystals were uniform and semitransparent and exhibited strong light scattering.
Addition of 1 mol.% Yb2O3 to the 9ScSZ solid solution produced uniform transparent single crystals. The polarized light microstructure images of the 9Sc1YbSZ crystals exhibit an interference pattern caused by residual growth thermal stress in the crystals. Annealing of the crystals at 1000 °C did not relieve the residual thermal stress but the crystal remained transparent and contained no twins in the bulk.
The phase composition of the crystals was studied using X-ray diffraction for wafers cut from different crystal parts perpendicularly to the <100> direction. Table 1 shows data on the phase composition and density of the as-grown and the as-annealed crystals.
The as-grown 9ScSZ crystals were tetragonal according to X-ray diffraction data. The as-annealed 9ScSZ crystals contained two phases: tetragonal and rhombohedral. The growth of the tetragonal phase in the as-annealed crystals testifies to an unstable phase composition of the ZrO2 based solid solution if Sc2O3 is the only doping impurity.
The as-grown crystals co-doped with 0.5 mol.% Yb2O3 were mixtures of the tetragonal and cubic zirconia modifications. In the tetragonal phase of the 9Sc0.5YbSZ crystal the lattice parameter a increased and the lattice parameter c decreased as compared with the respective lattice parameters of the tetragonal phase of the 9ScSZ crystal. The tetragonality degrees of the t phase were 1.007 and 1.004 for the 9ScSZ and 9Sc0.5YbSZ crystals, respectively. The addition of 0.5 mol.% Yb2O3 to the 9ScSZ solid solution not only changed the lattice parameters of the tetragonal phase but also stabilized the cubic phase in some regions of the crystal. However, the cubic phase in these regions is unstable and transformed to the more stable tetragonal phase upon annealing. In the as-annealed 9Sc0.5YbSZ crystal the lattice parameter a of the tetragonal phase did not change whereas the lattice parameter c increased, indicating a shift of the oxygen atoms along the C axis.
The 9Sc1YbSZ crystals contained only the cubic zirconia modification. The phase composition and lattice parameters of the as-annealed cubic zirconia modification did not change.
The density of the crystals depends on the content of stabilizing oxides and on the phase composition of the crystals. The data summarized in Table 1 suggest that co-doping with Yb2O3, which has a higher density (9.17 g/cm3) than those of ZrO2 (5.68 g/cm3) and Sc2O3 (3.86 g/cm3) increases the density of the crystals. The as-annealed 9ScSZ crystal contains rhombohedral phase inclusions, which reduce the density of the crystals, because tetragonal zirconia based solid solution single crystals have the highest density, whereas crystals containing the cubic or rhombohedral phases have lower densities [30]. The density of the as-annealed 9Sc0.5YbSZ crystal increased but slightly, probably also due to the change in the phase composition of the crystals. The density of the as-annealed 9Sc1YbSZ crystals did not change.
We also studied the phase composition of the crystals using Raman spectroscopy. Different from the long-range ordered structure reflected by XRD, the Raman spectrum is sensitive to the short-range ordered structure such as chemical bonds of the internal structure, so it is used to further study the cell distortion [31]. This method reveals even minor changes in the local structure of crystals upon long-term annealing. Figure 2 shows the Raman spectra of the as-grown and as-annealed crystals.
According to our Raman data the structure of the as-grown 9ScSZ crystals is tetragonal which is indicated by the presence of the typical ~150 cm−1, 260 cm−1, 470 cm−1, and 630 cm−1 bands [32]. However, these bands are quite broadened and shifted toward smaller Raman shift. The Raman spectra of the as-annealed 9ScSZ crystal also contain rhombohedral phase bands [14]. The Raman spectra of the as-grown 9Sc0.5YbSZ crystal are typical of tetragonal structures, but the bands are significantly broadened indicating the presence of the cubic phase along with the tetragonal phase. In the Raman spectra of the as-annealed 9Sc0.5YbSZ crystal, the tetragonal phase bands are clearer. The 600 cm−1 band is heavily broadened, but does not split in bands typical of the tetragonal and rhombohedral phases as is the case for the as-annealed 9ScSZ crystal.
The spectra of 9Sc1YbSZ crystals exhibits the cubic phase bands and an additional tetragonal phase band near ~ 470 cm−1. According to Raman spectroscopy data, the structure of the 9Sc1YbSZ crystals contains the pseudocubic tʺ phase [33,34]. This phase was described as having a degree of tetragonality c/a = 1, but belonging to the space group of symmetry P42/nmc due to the displacement of oxygen atoms in the anionic sublattice. Thus, according to Raman spectroscopy data, 9Sc1YbSZ crystals are tetragonal (tʺ phase), and not cubic, as follows from X-ray diffractometry data. After annealing, the spectrum of 9Sc1YbSZ crystals does not change.
Thus X-ray diffraction and Raman spectroscopy phase composition data suggest that the phase composition of the as-grown 9ScSZ crystals stabilized with only Sc2O3 is unstable. Annealing causes the formation of the rhombohedral phase along with the tetrahedral phase. The crystals contain conjugating phases having different volumes and, therefore, stress accumulating at phase boundaries may fracture the crystals. Co-doping of the ZrO2 – 9 mol.% Sc2O3 solid solutions with 0.5 mol.% ytterbia stabilizes the high-temperature phase but does not stabilize the cubic phase in the entire crystal. In the 9Sc0.5YbSZ crystals, the co-doping oxide content is insufficient and upon annealing regions with an unstable cubic structure undergo a phase transition to the more stable tetragonal phase, and possibly part of the cubic phase transforms to the rhombohedral phase according to our Raman data. The pseudocubic tʺ phase stabilizes in the entire bulk of the 9Sc1YbSZ crystals. Co-doping of the ZrO2 – 9 mol.% Sc2O3 solid solutions with 1 mol.% ytterbia produces single-phase single crystals with the pseudocubic tʺ phase which is stable upon long-term air annealing.
Figure 3a shows the conductivity of the test crystals vs temperature in Arrhenius coordinates. Figure 3b shows the conductivity of the test crystals vs Yb2O3 concentration.
As can be seen from Figure 3, the 9ScSZ crystals stabilized only with scandia have the lowest conductivity in the whole test temperature range. Co-doping of the crystals with 0.5 mol.% Yb2O3 increases the ionic conductivity. Phase composition analysis showed that the as-grown 9Sc0.5YbSZ crystals contain the cubic phase along with the tetragonal phase and therefore their conductivity in the entire temperature range is higher than that of the tetragonal 9ScSZ crystals. The single-phase 9Sc1YbSZ crystals that contain the tʺ phase have the highest conductivity.
Figure 4 shows the conductivity of the as-grown and as-annealed crystals as a function of temperature.
The conductivity vs temperature curve of the as-annealed 9ScSZ crystal shows an abrupt increase in the conductivity at ~ 600 °C caused by the rhombohedral to cubic phase transition. The conductivity of the as-annealed 9Sc0.5YbSZ crystal decreases slightly. The conductivities of the as-grown and as-annealed 9Sc1YbSZ crystals are almost the same in the entire temperature range. Figure 5 shows the 1173 K conductivity of the as-grown and as-annealed crystals.
After air annealing at 1000 °C for 400 h the 1173 K conductivity of the 9ScSZ crystal decreased by 35%, the 1173 K conductivity of the 9Sc0.5YbSZ crystal decreased by less than 10% and the 1173 K conductivity of the 9Sc1YbSZ crystal did not decrease.

4. Summary

(ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x solid solution crystals (x = 0; 0.005; 0.01) were grown by directional melt crystallization in a cold crucible. The crystals were heat treated at 1000 °C for 400 h in air for determining the phase stability of the crystals and studying degradation of their conductivity.
The microstructure of the crystals was studied using polarized light optical microscopy for wafers cut along the growth axis. The 9ScSZ crystals that were stabilized only with scandia contained multiple twins in the entire bulk. The as-annealed 9ScSZ solid solutions contained larger structural features and microcracks in the bulk. Co-doping of the ZrO2 – 9 mol.% Sc2O3 solid solutions with 0.5 mol.% Yb2O3 produced discrete transparent regions in the crystals. However, the as-annealed 9Sc0.5YbSZ crystals were uniform and semitransparent and contained twins in the entire bulk. Co-doping of the ZrO2 – 9 mol.% Sc2O3 solid solutions with 1 mol.% Yb2O3 produced uniform and transparent single crystals. Annealing of the 9Sc1YbSZ crystals at the 1000 °C relieved the residual stress but the crystal remained transparent and did not contain twins.
The phase composition of the crystals was analyzed using X-ray diffraction and Raman spectroscopy. Co-doping of the ZrO2 – 9 mol.% Sc2O3 solid solutions with ytterbia stabilized the annealing-stable high-temperature pseudocubic tʺ phase but the stabilization was only achieved at a co-doping oxide concentration of 1 mol.%. At lower Yb2O3 concentrations the high-temperature phase stabilized but the cubic phase did not stabilize in the entire crystal bulk. In the 9Sc0.5YbSZ crystals, the content of the co-doping oxide is insufficient and after annealing the regions with the unstable cubic structure underwent a phase transition to the more stable tetragonal phase, and possibly part of the cubic phase transformed to the rhombohedral phase according to our Raman data.
Study of the transport properties of the crystals showed that the crystals stabilized only with scandia have the lowest conductivity in the entire test temperature range. Co-doping of the crystals with 0.5 mol.% Yb2O3 increased their ionic conductivity. The single-phase 9Sc1YbSZ crystals that contained the tʺ phase had the highest ionic conductivity. Long-term high-temperature annealing did not reduce the ionic conductivity of the ZrO2 – 9 mol.% Sc2O3 crystals co-doped with 1 mol% Yb2O3.

Author Contributions

Conceptualization, E.L. and N.T.; Formal analysis, V.M.; Investigation, A.K., G.K., I.K., N.L., F.M., V.M., N.S. and T.V.; Methodology, P.R.; Resources, A.K.; Supervision, E.L.; Validation, P.R. and N.T.; Visualization, A.K. and F.M.; Writing—review and editing, A.K., M.B., E.L., P.R. and N.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Russian Science Foundation, grant number 19-72-10113.

Conflicts of Interest

The authors declare no conflict of interest.

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Crystals 11 00083 g001 550
Figure 1. Polarized light microstructure images of as-grown crystals: (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ.
Figure 1. Polarized light microstructure images of as-grown crystals: (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ.
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Crystals 11 00083 g002 550
Figure 2. Raman spectra of as-grown and as-annealed (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ crystals.
Figure 2. Raman spectra of as-grown and as-annealed (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ crystals.
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Crystals 11 00083 g003 550
Figure 3. (a) Conductivity of test crystals vs temperature in Arrhenius coordinates and (b) Conductivity of test crystals vs. Yb2O3 concentration.
Figure 3. (a) Conductivity of test crystals vs temperature in Arrhenius coordinates and (b) Conductivity of test crystals vs. Yb2O3 concentration.
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Crystals 11 00083 g004 550
Figure 4. Conductivity of as-grown and as-annealed (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ crystals as a function of temperature.
Figure 4. Conductivity of as-grown and as-annealed (a) 9ScSZ, (b) 9Sc0.5YbSZ, and (c) 9Sc1YbSZ crystals as a function of temperature.
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Crystals 11 00083 g005 550
Figure 5. 1173 K conductivity of crystals as-grown and as-annealed at 1000 C for 400 h.
Figure 5. 1173 K conductivity of crystals as-grown and as-annealed at 1000 C for 400 h.
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Table
Table 1. Phase composition, lattice parameters and density of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x crystals before and after annealing at 1000 °C for 400 h.
Table 1. Phase composition, lattice parameters and density of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x crystals before and after annealing at 1000 °C for 400 h.
SampleAs-GrownAs-Annealed
Phase *Lattice Parameters, nmDensity, g/cm3PhaseLattice Parameters, nmDensity, g/cm3
9ScSZta = 0.3595(1); c = 0.5122(1)5.786(3)ta = 0.3596(1); c = 0.5124(1)5.783(3)
ra = 0.3559(2); c = 0.9007(2)
9Sc0.5YbSZta = 0.3597(1); c = 0.5106(1)5.816(3)ta = 0.3597(1); c = 0.5110(1)5.818(3)
ca = 0.5092(1)
9Sc1YbSZca = 0.5094(1)5.863(3)ca = 0.5094(1)5.862(3)
* t, c and r are tetragonal, cubic, and rhombohedral modifications of scandia-stabilized zirconia.
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Borik, M.; Korableva, G.; Kulebyakin, A.; Kuritsyna, I.; Larina, N.; Lomonova, E.; Milovich, F.; Myzina, V.; Ryabochkina, P.; Sidorova, N.; et al. Phase Stability and Transport Properties of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x Crystals (x = 0–0.01). Crystals 2021, 11, 83. https://0-doi-org.brum.beds.ac.uk/10.3390/cryst11020083

AMA Style

Borik M, Korableva G, Kulebyakin A, Kuritsyna I, Larina N, Lomonova E, Milovich F, Myzina V, Ryabochkina P, Sidorova N, et al. Phase Stability and Transport Properties of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x Crystals (x = 0–0.01). Crystals. 2021; 11(2):83. https://0-doi-org.brum.beds.ac.uk/10.3390/cryst11020083

Chicago/Turabian Style

Borik, Mikhail, Galina Korableva, Alexey Kulebyakin, Irina Kuritsyna, Nataliya Larina, Elena Lomonova, Filipp Milovich, Valentina Myzina, Polina Ryabochkina, Nataliya Sidorova, and et al. 2021. "Phase Stability and Transport Properties of (ZrO2)0.91−x(Sc2O3)0.09(Yb2O3)x Crystals (x = 0–0.01)" Crystals 11, no. 2: 83. https://0-doi-org.brum.beds.ac.uk/10.3390/cryst11020083

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