Formation of Thick Immersion Coatings and Residual Stress Evaluation in the System ZrB2–ZrO2: Experimental and Numerical Investigation

The combination of various oxide ceramics in layered and functionally graded composites allows for the development of novel materials, including for high-temperature applications. This study demonstrates the possibility of obtaining a thick ZrO2-based coating on a ZrB2–SiC ceramic substrate by the immersion method. For better wettability, the porous ZrB2–SiC substrate is treated with cold plasma without changing the structure and phase composition of the surface. Immersion of the substrate in a ZrO2-based slurry results in the formation of a gradient transition layer due to ZrO2 particle penetration into the pore volume. The interfacial residual microstresses are evaluated experimentally. The residual macrostresses in the samples are calculated by finite element simulation. It is shown that the thermal residual stresses in the ZrB2–SiC substrate are compressive and do not exceed 43 MPa. In the ZrO2 coating and transition layers of the composite, the residual stresses are tensile. Their values increase as they get closer to the outer layer of the ZrO2 coating and reach 1525 MPa. This confirms the conclusions about the presence of tensile residual stresses made in the experimental part of the work when observing crack propagation in the surface layers during indentation.


Introduction
Ceramic coatings, including on ceramic substrates, are conventionally applied using PVD and CVD methods. The advantage of these technologies is that the thickness of the applied coating can be controlled with high accuracy. For some applications, however, this is a drawback because the thickness of such coatings can hardly reach several microns, while its increase can lead to the loss of adhesion between layers, delamination, cracking due to thermal residual stresses, and higher deposition costs [1,2].
A less trivial task is the formation of transition and gradient coatings with high adhesion strength and high spalling resistance. These issues were discussed in studies on ultra-high-temperature ceramics (UHTC), where laminated composites consisting of components with different thermal expansion coefficients were obtained by pressure cosintering of layers with different phase ratios, or by plasma spraying [3,4]. Such composites are important for the thermal protection of high-energy facilities, and further research in this area is aimed at reducing the thermal conductivity of the composite and increasing its fracture toughness due to the formation of numerous interfaces.
In recent years, the research focus in the field of UHTC has shifted from the characteristics and parameters of carbon/carbon composites and composites based on monolithic carbides and borides with uniformly distributed functional particles towards approaches of the modern structural design of composite materials. Some authors have shown that the consequently, to adjust their behavior during operation. At present, the residual stress measurements are the subject of extensive research. Various residual stress measurement methods have been proposed for experimental studies, including optical, X-ray, and other approaches [17,18]. Theoretical studies employ various numerical models [19][20][21] and analytical models [22][23][24][25].
This work presents a case study to validate the possibility of applying thick immersion ZrO 2 -based coatings to ZrB 2 ceramics and to evaluate the interfacial microstresses. Control over the zone of different-sign elastic stresses at the coating-substrate interface can help to modify the impact strength and cracking behavior of the composite. The advantage of such composites for practical applications is the abnormally low thermal conductivity of ZrO 2 , which is capable of acting as, e.g., the back layer of a ZrB 2 -based heat shield. The difficulty of the problem being solved lies in the different thermal expansion coefficients of these compounds, which inhibits their co-sintering and leads to low wettability, which prevents the build-up of immersion coating.

Materials
The investigation was performed on disk-shaped ceramic composite samples with a thickness of 5 mm and a diameter of 30 mm. The samples were fabricated from commercially available powders of ZrB 2 with an average particle size of 15.7 ± 11.2 µm and SiC, used as a sintering additive, with an average particle size of 3.1 ± 1.9 µm. Powder mixtures of ZrB 2 -30% SiC were mixed and activated in a planetary ball mill with ZrO 2 grinding media. The pre-sintered ceramic samples were compacted by cold uniaxial pressing of ZrB 2 -30% SiC powder mixture (hereinafter ZrB 2 -SiC) and 1 wt % polyvinyl alcohol solution, followed by sintering in a vacuum furnace at 1600 • C. The residual porosity of the pre-sintered samples was 48%.
The low wettability of ZrB 2 was overcome by air cold plasma treatment of the sample surfaces. The cold plasma treatment of pre-sintered samples was carried out in a laboratory setup at a frequency of 1000 Hz and a pulse energy of 0.32 J in air while rotating a glass drum with the samples at a speed of 60 rpm.
The contact angle variation was evaluated using a control ZrB 2 -SiC sample with a high relative density of 99.97% (Figure 1). Contact angle measurements of a water drop on the surface of the control ZrB 2 sample with high relative density showed a steady increase at treatment times up to 50 s ( Figure 1). Further exposure to cold plasma did not lead to noticeable changes in surface wettability. After several hours of sample exposure in air outside the protective gas atmosphere, the observed increase in contact angle vanished. Therefore, immersion coatings were applied to samples of pre-sintered porous ZrB 2 -SiC ceramics exposed to cold plasma for 50 s.
Coatings on the pre-sintered ceramic samples were formed by immersion in a slurry composed of ZrO 2 nanoparticles (10 g/30 mL), distilled water, and dispersant (0.2 g/30 mL) under sonication for 10 min (Figure 2). The ZrO 2 powder used in the study was obtained by plasma chemical synthesis and stabilized with 3 mol % MgO. The morphology of nanostructured ZrO 2 particles varied from hollow spheres and sphere fragments to agglomerates of size < 1 µm and spheroidized agglomerates of size up to 10 µm. The time between the end of cold plasma treatment of pre-sintered ZrB 2 -SiC samples and the complete immersion of the samples in the slurry was less than 10 s.
The samples coated with the ZrO 2 layer were placed in a graphite crucible on a surface coated with inert boron nitride to prevent sticking of the test sample to the substrate, and were then transferred to a vacuum furnace. The time of transfer of the coated samples to the vacuum furnace for sintering was no more than 30 min. The ZrB 2 -SiC samples coated with ZrO 2 were sintered in vacuum at a temperature of 1800 • C without isothermal holding. Coatings on the pre-sintered ceramic samples were formed by immersion in a slurry composed of ZrO2 nanoparticles (10 g/30 mL), distilled water, and dispersant (0.2 g/30 mL) under sonication for 10 min (Figure 2). The ZrO2 powder used in the study was obtained by plasma chemical synthesis and stabilized with 3 mol % MgO. The morphology of nanostructured ZrO2 particles varied from hollow spheres and sphere fragments to agglomerates of size < 1 m and spheroidized agglomerates of size up to 10 m. The time between the end of cold plasma treatment of pre-sintered ZrB2 -SiC samples and the complete immersion of the samples in the slurry was less than 10 s.
The samples coated with the ZrO2 layer were placed in a graphite crucible on a surface coated with inert boron nitride to prevent sticking of the test sample to the substrate, and were then transferred to a vacuum furnace. The time of transfer of the coated samples to the vacuum furnace for sintering was no more than 30 min. The ZrB2-SiC samples coated with ZrO2 were sintered in vacuum at a temperature of 1800 °C without isothermal holding.   Coatings on the pre-sintered ceramic samples were formed by immersion in a slurry composed of ZrO2 nanoparticles (10 g/30 mL), distilled water, and dispersant (0.2 g/30 mL) under sonication for 10 min (Figure 2). The ZrO2 powder used in the study was obtained by plasma chemical synthesis and stabilized with 3 mol % MgO. The morphology of nanostructured ZrO2 particles varied from hollow spheres and sphere fragments to agglomerates of size < 1 m and spheroidized agglomerates of size up to 10 m. The time between the end of cold plasma treatment of pre-sintered ZrB2 -SiC samples and the complete immersion of the samples in the slurry was less than 10 s.
The samples coated with the ZrO2 layer were placed in a graphite crucible on a surface coated with inert boron nitride to prevent sticking of the test sample to the substrate, and were then transferred to a vacuum furnace. The time of transfer of the coated samples to the vacuum furnace for sintering was no more than 30 min. The ZrB2-SiC samples coated with ZrO2 were sintered in vacuum at a temperature of 1800 °C without isothermal holding.

Experimental Methods
The ceramics microstructure was studied by scanning electron microscopy (Vega 3 SH, Tescan) with secondary and backscattered electron imaging. The porosity and pore size distribution were measured on the polished cross section of a test sample by applying the point-counting method as well as using the linear intercept method according to ASTM E112.
The phase composition was studied by X-ray diffraction analysis. XRD analysis was carried out on a DRON diffractometer (BOUREVESTNIK, JSC) in the angular range 20-80 • with a step of 0.03 • and an exposure of 3 s using CuKα filtered radiation. XRD patterns were recorded directly from the coating surface, which was polished with 10 to 0.5 µm diamond pastes to remove a 5-µm thick layer in order to improve the quality of the surface microstructure. Further X-ray diffraction analysis was performed after the removal of 25-µm thick surface layers. The obtained XRD patterns were analyzed using Match! Version 3.1 software (Crystal Impact) and cards 00-034-0423 (ZrB 2 ) and 04-011-9021 (ZrO 2 ) of the International Centre for Diffraction Data. The magnitude of the second-order microstresses acting in the ceramics structure was determined from XRD peak broadening as the product of the microstrain value [26] and the Young's modulus of the corresponding phase at room temperature.
The initiation of microcracks and the crack propagation behavior were studied by Vickers indentation along the ZrO 2 -ZrB 2 -SiC interface at a load of 100 N, Duramin-5 (Stuers A/S).

Numerical Methods
In view of the cylindrical symmetry of the samples, the problem can be considered in a two-dimensional axisymmetric formulation. The z symmetry axis is directed perpendicular to the disk plane, and the r axis is directed along the disk radius. All stress-strain parameters along the third θ axis are assumed to be constant because the layers are homogeneous.
The system of equations in the adopted formulation includes equilibrium Equations (1), strain-displacement relations (2), constitutive equations (Duhamel-Neumann relations) (3), and heat conduction Equation (4) [27][28][29]: Here σ ij is the stress tensor component, ε ij is the strain tensor component, u r , u z are the displacement vector components, λ and µ are the Lame parameters, K is the bulk modulus, α is the linear thermal expansion coefficient, T is the current temperature, T 0 is the temperature of the initial state (sintering temperature), c ε is the heat capacity at constant strains, ρ is the density, and λ T is the thermal conductivity. Stresses, strains, and displacements are functions of spatial coordinates. Material parameters (Young's modulus, Poisson's ratio, and linear thermal expansion coefficient) are also functions of coordinates.
For the initial conditions, we assume that there are no initial stresses and strains. Due to symmetry, we consider 1 /4 of the disk cross section. The boundary conditions are set based on the conditions of axial symmetry at r = 0, plane symmetry at z = 2.5 mm, and free boundary conditions on the outer surfaces of the disk (z = 5 mm and r = 15 mm): For the heat conduction equation, Newton's conditions for the heat flux were set on all outer surfaces: and zero heat flux was set on the axes of symmetry: where β is the heat transfer coefficient, and T r is the room temperature. At the interfaces between different layers, the condition of ideal mechanical and thermal contact was assumed to be fulfilled.
The numerical simulation of the stresses and strains during sample cooling was performed by the finite element method in a two-dimensional axisymmetric formulation, implemented in Abaqus/Standart software. The temperature dependences of elastic moduli and linear thermal expansion coefficients were taken into account. A finite element model was developed using a mesh with axisymmetric four-node coupled temperature-displacement elements (CAX4RT) as shown in Figure 3. To obtain favorable and precise simulation results, the mesh contained 1,000,000 elements.
where β is the heat transfer coefficient, and r T is the room temperature.
At the interfaces between different layers, the condition of ideal mechanical and thermal contact was assumed to be fulfilled.
The numerical simulation of the stresses and strains during sample cooling was performed by the finite element method in a two-dimensional axisymmetric formulation, implemented in Abaqus/Standart software. The temperature dependences of elastic moduli and linear thermal expansion coefficients were taken into account. A finite element model was developed using a mesh with axisymmetric four-node coupled temperature-displacement elements (CAX4RT) as shown in Figure 3. To obtain favorable and precise simulation results, the mesh contained 1,000,000 elements.

Experiments
The plasma treatment method used in this work is characterized by a low temperature relative to the ZrB2 crystallization temperature, which prevents structural changes in the ceramic surface. It is known, however, that plasma treatment in an air atmosphere

Experiments
The plasma treatment method used in this work is characterized by a low temperature relative to the ZrB 2 crystallization temperature, which prevents structural changes in the ceramic surface. It is known, however, that plasma treatment in an air atmosphere can lead to the precipitation of hydrophilic functional groups on the surface of ceramics [14] and therefore increase the wettability of the ZrB 2 surface, including inside open subsurface pores. An attempt to deposit a ZrO 2 coating on an untreated ZrB 2 -SiC substrate with reduced wettability led to the formation of cracks at the coating-substrate interface. The coating adhesion to the substrate turned out to be extremely weak or even absent in some regions, so that the coating detached from the sample after removal from the vacuum furnace. A similar result was reported in a study where a composite based on ceramics with different thermal expansion coefficients was fabricated by methods without pressure sintering, such as hot pressing or spark plasma sintering [30].
The microstructural study of the polished cross-sectional surface showed that the thickness of the formed ZrO 2 layer was about 50 µm. The coating porosity was about 5%. The residual porosity of ZrB 2 -SiC after sintering was less than 10%. Pores in the ZrO 2 layer were characterized by a much lower density but a larger size as compared to ZrB 2 . The nanostructured ZrO 2 powder obtained by plasma chemical synthesis had a high packing density, which prevented cracking of the structure during shrinkage. However, the presence of voids in hollow spherical powder particles and between large spheroidized agglomerates resulted in the formation of micro-(<500 nm) and macropores (>10 µm) after sintering. Macropores could also be due to the high sintering temperature, relative to the homologous temperature of ZrO 2 , and a long time of thermal treatment sufficient for the micropores to coalesce [31].
The phase composition of the coating surface is represented by cubic ZrO 2 and lowintensity reflections of the monoclinic modification (Figure 4). At a distance of 25 µm from the surface, the phase composition consists mainly of ZrB 2 and cubic ZrO 2 (32%). At a dis-tance of 50 and 75 µm from the surface, the ZrO 2 reflections become barely distinguishable. The gradient phase composition in the interfacial region between the ZrO 2 coating and ZrB 2 -SiC substrate was determined by open subsurface pores in the pre-sintered ZrB 2 -SiC sample, where the pores and pore channels were large enough for the ZrO 2 -based slurry to penetrate. Furthermore, the high diffusivity of oxygen and boron contributes to the redistribution of these elements in the contact region at high sintering temperatures, resulting in a strong mechanical bond, a smeared interface, and a small amount of interfacial defects [32,33].
the presence of voids in hollow spherical powder particles and between large spheroidized agglomerates resulted in the formation of micro-(<500 nm) and macropores (>10 μm) after sintering. Macropores could also be due to the high sintering temperature, relative to the homologous temperature of ZrO2, and a long time of thermal treatment sufficient for the micropores to coalesce [31].
The phase composition of the coating surface is represented by cubic ZrO2 and low-intensity reflections of the monoclinic modification (Figure 4). At a distance of 25 m from the surface, the phase composition consists mainly of ZrB2 and cubic ZrO2 (32%). At a distance of 50 and 75 μm from the surface, the ZrO2 reflections become barely distinguishable. The gradient phase composition in the interfacial region between the ZrO2 coating and ZrB2-SiC substrate was determined by open subsurface pores in the pre-sintered ZrB2-SiC sample, where the pores and pore channels were large enough for the ZrO2-based slurry to penetrate. Furthermore, the high diffusivity of oxygen and boron contributes to the redistribution of these elements in the contact region at high sintering temperatures, resulting in a strong mechanical bond, a smeared interface, and a small amount of interfacial defects [32,33].   Vickers indentation along the ZrO 2 -ZrB 2 -SiC interface led to the formation of microcracks in cubic ZrO 2 , which has lower fracture toughness than ZrB 2 , and no interfacial cracks were observed ( Figure 5). A similar result was obtained in three-point bending of the graded ceramic composite: when a crack reached cubic zirconia, it bifurcated, but the formed microcracks were directed parallel to or slightly deviated from the applied load axis, and therefore the zirconia surface layer did not detach ( Figure 6).
The result obtained can be explained by the generation of second-order elastic microstress fields in the ZrO 2 -ZrB 2 gradient layer, which is due to the different thermal expansion coefficients of the components. Since the ZrO 2 reflection intensity at high diffraction angles of the XRD pattern is insufficient, it is impossible to empirically estimate the stresses arising in the oxide. The dependence of the microstress values in ZrB 2 on the distance from the surface of the test sample is shown in Figure 7. According to the numerical simulation shown below, the decrease in microstresses in ZrB 2 with increasing ZrO 2 content may be caused by a change in the sign of stresses.
The literature contains many studies on the generation and evaluation of residual stresses in composite ceramics due to different CTEs of the components. Some authors used the effect of the CTE difference to increase the impact strength of brittle ceramics. This effect was achieved by increasing the work of a propagating crack in the region of compressive stresses. In other cases, the difference in the CTEs between the matrix and the inclusion can lead to multiple microcracking but without sample failure [34][35][36]. At the same time, a multiple increase in the surface area also increases the required energy of the main macrocrack to propagate through the stressed region [37,38].
Vickers indentation along the ZrO2-ZrB2-SiC interface led to the formation of microcracks in cubic ZrO2, which has lower fracture toughness than ZrB2, and no interfacial cracks were observed ( Figure 5). A similar result was obtained in three-point bending of the graded ceramic composite: when a crack reached cubic zirconia, it bifurcated, but the formed microcracks were directed parallel to or slightly deviated from the applied load axis, and therefore the zirconia surface layer did not detach ( Figure 6).  The result obtained can be explained by the generation of second-order elastic microstress fields in the ZrO2-ZrB2 gradient layer, which is due to the different thermal expansion coefficients of the components. Since the ZrO2 reflection intensity at high diffraction angles of the XRD pattern is insufficient, it is impossible to empirically estimate the stresses arising in the oxide. The dependence of the microstress values in ZrB2 on the distance from the surface of the test sample is shown in Figure 7. According to the nu- Vickers indentation along the ZrO2-ZrB2-SiC interface led to the formation of microcracks in cubic ZrO2, which has lower fracture toughness than ZrB2, and no interfacial cracks were observed ( Figure 5). A similar result was obtained in three-point bending of the graded ceramic composite: when a crack reached cubic zirconia, it bifurcated, but the formed microcracks were directed parallel to or slightly deviated from the applied load axis, and therefore the zirconia surface layer did not detach ( Figure 6).  The result obtained can be explained by the generation of second-order elastic microstress fields in the ZrO2-ZrB2 gradient layer, which is due to the different thermal expansion coefficients of the components. Since the ZrO2 reflection intensity at high diffraction angles of the XRD pattern is insufficient, it is impossible to empirically estimate the stresses arising in the oxide. The dependence of the microstress values in ZrB2 on the distance from the surface of the test sample is shown in Figure 7. According to the nu-  The literature contains many studies on the generation and evaluation of residual stresses in composite ceramics due to different CTEs of the components. Some authors used the effect of the CTE difference to increase the impact strength of brittle ceramics. This effect was achieved by increasing the work of a propagating crack in the region of Presumably, the observed pattern of different-sign elastic stresses at the coatingsubstrate interface can have a favorable effect on the impact strength of the composite as a whole. Multiple bifurcation of a crack propagating in the coating should undoubtedly result in the partitioning and dissipation of its energy and, with a high probability, crack arrest.

Numerical Simulation
The residual macrostresses arising in the studied samples were evaluated in a numerical study of a porous ZrB 2 -30 vol % SiC ceramic disk with a multilayer oxide coating with different ZrO 2 contents, cooled from sintering temperature to room temperature. A schematic illustration of the composite sample structure is presented in Figure 8. For residual stress analysis, we calculated the elastic moduli (Young's modulu Poisson's ratio), thermal expansion coefficients, coefficients of thermal conductivity an heat capacity, and densities of the composite components, taking into account the tem perature variation of these physical and mechanical properties. The elastic and thermo physical characteristics of ZrO2 and ZrB2-SiC were determined based on the temperatur dependences taken from Refs. [39,40]. The effective properties of the intermediate laye of the composite were determined by the mixture rule.
It was also necessary to account for the effect of the porosity of the layers on the e fective mechanical and thermal characteristics of the material. The effect of porosity o Young's modulus value (E eff ) was described using the exponential relationship propose in Ref. [41]: Here, E M is the Young's modulus of the matrix (pore-free ceramics), and θ is th porosity.
The effective value of Poisson's ratio of porous ceramics was determined using th following relationship [42,43]: where  M is the Poisson's ratio of the matrix. Analysis of the literature [44][45][46] revealed that porosity does not affect the linea thermal expansion coefficient of most materials. Therefore, we assumed here that α eff independent of porosity in the gradient ceramic composite under study. Table 1 gives the values of the physical and mechanical properties of the composi layers at the sintering temperature (T0 = 1800 °C) used in the calculations.  In accordance with the experimental data, we study a disk-shaped composite sample of thickness 5 mm and diameter 30 mm consisting of five layers of different composition. All the layers are assumed to be homogeneous. Due to symmetry, we consider 1 /4 of the disk cross section (region Γ in Figure 8a). The geometric model of the composite used in the numerical simulation is presented in Figure 8b. The thickness of the layers is specified from the experimental data: the thickness of layers I to IV is 0.025 mm, and that of layer V is 2.4 mm. The porosity of layers I to IV is taken to be 5%, and that of ZrB 2 -SiC layer V is 11%.
For residual stress analysis, we calculated the elastic moduli (Young's modulus, Poisson's ratio), thermal expansion coefficients, coefficients of thermal conductivity and heat capacity, and densities of the composite components, taking into account the temperature variation of these physical and mechanical properties. The elastic and thermophysical characteristics of ZrO 2 and ZrB 2 -SiC were determined based on the temperature dependences taken from Refs. [39,40]. The effective properties of the intermediate layers of the composite were determined by the mixture rule.
It was also necessary to account for the effect of the porosity of the layers on the effective mechanical and thermal characteristics of the material. The effect of porosity on Young's modulus value (E eff ) was described using the exponential relationship proposed in Ref. [41]: Here, E M is the Young's modulus of the matrix (pore-free ceramics), and θ is the porosity. The effective value of Poisson's ratio of porous ceramics was determined using the following relationship [42,43]: where ν M is the Poisson's ratio of the matrix.
Analysis of the literature [44][45][46] revealed that porosity does not affect the linear thermal expansion coefficient of most materials. Therefore, we assumed here that α eff is independent of porosity in the gradient ceramic composite under study. Table 1 gives the values of the physical and mechanical properties of the composite layers at the sintering temperature (T 0 = 1800 • C) used in the calculations. Figures 9 and 10 present the numerical simulation results for the stress state of the studied composite during cooling. The curve of radial stress distribution through the disk thickness in Figure 9 is discontinuous, where the discontinuities are indicated by dotted vertical lines. It can be seen that the thermal residual stresses in the ZrB 2 -SiC layer are compressive and their value does not exceed 43 MPa. In all other layers of the composite, the residual stresses are tensile. Their values increase as they get closer to the outer ZrO 2 layer and reach 1525 MPa.
It should be noted that the stress distribution curve will not be stepwise, as in Figure 9, but smooth, in accordance with the given law of ZrO 2 content variation, if the concentration of zirconium dioxide in the surface layer changes smoothly from a specified value (30%) on the surface to zero at a depth of approximately 100 mm.
Two-dimensional distributions of the normal stress components are shown in Figure 10. One can see that the residual stresses differ in different layers. They are both negative (compressive) and positive (tensile). The stresses in the disk layers (sections) remain unchanged up to a region at the upper edge of the disk. Figures 9 and 10 present the numerical simulation results for the stress state of the studied composite during cooling. The curve of radial stress distribution through the disk thickness in Figure 9 is discontinuous, where the discontinuities are indicated by dotted vertical lines. It can be seen that the thermal residual stresses in the ZrB2-SiC layer are compressive and their value does not exceed 43 MPa. In all other layers of the composite, the residual stresses are tensile. Their values increase as they get closer to the outer ZrO2 layer and reach 1525 MPa.
It should be noted that the stress distribution curve will not be stepwise, as in Figure  9, but smooth, in accordance with the given law of ZrO2 content variation, if the concentration of zirconium dioxide in the surface layer changes smoothly from a specified value (30%) on the surface to zero at a depth of approximately 100 mm. Two-dimensional distributions of the normal stress components are shown in Figure  10. One can see that the residual stresses differ in different layers. They are both negative (compressive) and positive (tensile). The stresses in the disk layers (sections) remain unchanged up to a region at the upper edge of the disk.  The maximum positive stresses are observed in the upper layer of the modeled ZrO2 coating. As in the experiment, the residual stresses change sign from compressive stresses in the substrate (in the bulk of the ZrB2-SiC disk) to tensile stresses closer to the surface of the composite sample. This confirms the conclusions about the presence of tensile residual stresses in the coating, made in the experimental part of the work when observing the crack growth in the surface layers during indentation.

Conclusions
This proof-of-concept study demonstrated the possibility of applying thick coatings and fabricating graded ceramic/ceramic composites with significantly different thermal expansion coefficients of the substrate and coating materials. The proposed approach was validated on a composite sample consisting of a ZrB2-SiC substrate and ZrO2 coating. It was shown that a gradient coating on a porous substrate can be formed by immersion in a slurry of fine-grained powders and using cold plasma treatment that increases the wettability but does not change the structure and phase composition of the surface, which was confirmed by X-ray diffraction analysis.
The residual stresses in the graded ceramic/ceramic composite were evaluated numerically. Thermal residual stresses in the ZrB2-SiC substrate are compressive, whereas they are tensile in the ZrO2 coating and transition layers, according to simulations. This is corroborated by the experimental data, which showed that growing cracks bifurcate upon reaching the oxide layer of the composite.  The maximum positive stresses are observed in the upper layer of the modeled ZrO 2 coating. As in the experiment, the residual stresses change sign from compressive stresses in the substrate (in the bulk of the ZrB 2 -SiC disk) to tensile stresses closer to the surface of the composite sample. This confirms the conclusions about the presence of tensile residual stresses in the coating, made in the experimental part of the work when observing the crack growth in the surface layers during indentation.

Conclusions
This proof-of-concept study demonstrated the possibility of applying thick coatings and fabricating graded ceramic/ceramic composites with significantly different thermal expansion coefficients of the substrate and coating materials. The proposed approach was validated on a composite sample consisting of a ZrB 2 -SiC substrate and ZrO 2 coating. It was shown that a gradient coating on a porous substrate can be formed by immersion in a slurry of fine-grained powders and using cold plasma treatment that increases the wettability but does not change the structure and phase composition of the surface, which was confirmed by X-ray diffraction analysis.
The residual stresses in the graded ceramic/ceramic composite were evaluated numerically. Thermal residual stresses in the ZrB 2 -SiC substrate are compressive, whereas they are tensile in the ZrO 2 coating and transition layers, according to simulations. This is corroborated by the experimental data, which showed that growing cracks bifurcate upon reaching the oxide layer of the composite.