Effects of Splat Interfaces, Monoclinic Phase and Grain Boundaries on the Thermal Conductivity of Plasma Sprayed Yttria-Stabilized Zirconia Coatings

: Microstructure has a signiﬁcant inﬂuence on the thermal conductivity of thermal barrier coating (TBC) systems. In this work, the microstructures including splat interface, monoclinic phase and grain boundaries in the YSZ air plasma spraying (APS) TBC systems are investigated. A ﬁnite element simulation model based on electron backscatter diffraction (EBSD) images is established. It is found that the simulation results of thermal conductivity are in good agreement with the experimental results. Using this model, the effect coefﬁcient of splat interface, monoclinic phase and grain boundaries on thermal conductivity are calculated. Results show that the splat interface inﬂuences the thermal conductivity of the TBCs. Those results provide important guidance for reducing the thermal conductivity of thermal barrier coatings.


Introduction
Thermal barrier coatings (TBCs), an oxide ceramic layer for the protection of a substrate material, are widely used for the thermal, oxidation and hot corrosion protection of high-temperature components in gas turbines [1]. The coatings provide insulation to metallic structures, thus, delaying the thermally-induced failure that governs the component durability and life [2,3]. However, as the thrust-weight ratio of engines become higher, the temperature of gas turbines for military aircraft engines has reached 1700 • C. The operating temperature of traditional YSZ coatings is generally lower than 1200 • C, which cannot meet the requirements of future military aircraft engines [4,5]. Therefore, the method to reduce the thermal conductivity of YSZ coatings became a hot topic in recent years. The thermal conductivity of YSZ coatings is closely related to the microstructure; therefore, it is necessary to study the microstructure of the TBCs in order to reduce its thermal conductivity.
Numerous works have investigated the relationship between the microstructures and thermal conductivity. Pores and cracks are the most important factors affecting the thermal conductivity. Moreover, there have been many studies on the effect of pores and cracks that focus on thermal conductivity. Chi and coworkers used image analysis (IA) data to simulate the effect of porosity on the thermal diffusivity; it turns out a very fast increase in the thermal diffusivity within the first 15 h of service. It might be due to the crack-like pores that filled with air through this process and to the thermal diffusivity of air (2.2 × 10 −5 m 2 ·s −1 ) which is roughly two orders of magnitude higher than the air thermal diffusivity of typical YSZ porous TBCs (3-5 × 10 −7 m 2 ·s −1 ) [6]. Chi et al. [7] compared coatings with different microstructures prepared with different feedstocks and different Microstructure of the YSZ coating is characterized by SEM (Magellan 400, FEI, Hillsboro, OR, USA) equipped with an EBSD detector. EBSD provides the conditions for the analysis of crystal microdomain orientation and crystal structure while preserving the conventional features of SEM. Through EBSD image analysis of a certain sample area, the size, distribution, orientation and grain boundary distribution of the crystal grains and the phase contained in the area can be obtained.
In this study, 25 EBSD images were selected for each YSZ coating, and an FE mesh model that is consistent with the true microstructure is generated. The FE meshes of the M 1 , M 2 and M 3 coatings with microstructures are illustrated in next part. The thermal conductivities of the YSZ coatings are obtained through a steady-state heat transfer analysis, while the thermal conductivity of ceramics in the direction of the temperature gradient can be computed with Fourier's equation: where h is the thickness of ceramic, l is the width, λ m represents the thermal conductivity for the bulk material, Γ is the integral path of the heat flux density and ∇T is the temperature gradient. The thermal conductivity of the tetragonal phase, the grain boundaries and the splat interface are 2.65, 1.54 and 0.03 W/m·K, respectively [14]. Rhagavan et al. revealed that the thermal conductivity of pure monoclinic zirconia with 98% density was 3.6 W/m·K [15]. Thus, the thermal conductivity of monoclinic phase in our model is also set to be 3.6 W/m·K. The thermal conductivity of each content is shown in Table 2.

The Microstructure of YSZ Coatings
The EBSD images of the polished cross-sections of the YSZ thermal barrier coatings and the cross-section backscattered image of M 3 are shown in Figure 1. The phase composition of each sample and the content of each phase, the distribution of cracks, the pores and the grain boundaries can be observed from the EBSD images. Different colors indicate different compositions. Red represents the monoclinic phase, green represents tetragonal phase, black represents grain boundaries and white represents cracks and pores. In the process of APS, the spraying powers for the coatings of M 1 and M 3 were lower than that of coating M 2 . This caused the lower temperatures of in-flight particles in as-sprayed M 1 and M 3 coatings and then led to worse melting state. Therefore, the porosities of coatings M 1 and M 3 were higher compared with that of coating M 2 . Furthermore, the larger raw spraying powders for coating M 3 also contributed to the relatively worse melting of in-flight particles, which resulted in more pores in the coating M 3 . The content of monoclinic phase, tetragonal phase, cracks and pores can be obtained from the data measured by EBSD; all are listed in Table 3. M3 were lower than that of coating M2. This caused the lower temperatures of in-flight particles in assprayed M1 and M3 coatings and then led to worse melting state. Therefore, the porosities of coatings M1 and M3 were higher compared with that of coating M2. Furthermore, the larger raw spraying powders for coating M3 also contributed to the relatively worse melting of in-flight particles, which resulted in more pores in the coating M3. The content of monoclinic phase, tetragonal phase, cracks and pores can be obtained from the data measured by EBSD; all are listed in Table 3.

Simulation of Thermal Conductivity
The  Table 4.

Simulation of Thermal Conductivity
The FE meshes of the M1, M2 and M3 coatings with varied microstructures are illustrated in Figure 2a-c, respectively. The thermal conductivity of the coating along the spray direction is calculated. The distributions of the thermal gradient along the spray direction under steady-state conditions are shown in Figure 3a-c, and the thermal fluxes are shown in Figure 3d-f, pertaining to coatings M1, M2 and M3, respectively. The simulation results λs and experimental results λ0 of thermal conductivity are listed in Table 4.

Simulation of Thermal Conductivity
The FE meshes of the M1, M2 and M3 coatings with varied microstructures are illustrated in Figure 2a-c, respectively. The thermal conductivity of the coating along the spray direction is calculated. The distributions of the thermal gradient along the spray direction under steady-state conditions are shown in Figure 3a-c, and the thermal fluxes are shown in Figure 3d-f, pertaining to coatings M1, M2 and M3, respectively. The simulation results λs and experimental results λ0 of thermal conductivity are listed in Table 4.     Comparisons show that the calculation error is very large because the splat interfaces cannot be seen in the EBSD image. However, the splat interfaces have a significant influence on the thermal conductivity of YSZ coatings [11]. This influence will be discussed later in detail.

The Effect of Splat Interface on the Thermal Conductivity
To analyze the effect of the splat interfaces on thermal conductivity, an idealized model was introduced. In a study by Shen et al. [13], an artificial image with dimensions of 25 µm × 25 µm was created, and all the splat interfaces were represented as rectangular elements having a size of 3.25 µm × 0.125 µm, as indicated in Figure 4. The thermal conductivity of splat interfaces is obtained through iterative computation and was set to 0.03 W/m·K, which made the simulated thermal conductivities map well with the experimental thermal conductivities of as-sprayed coatings [16]. The distribution of the thermal flux about the coating is shown in Figure 5. Using Equation (1), the thermal conductivities of the coatings were calculated. The simulation results (λ c ) and the experimental findings (λ 0 ) are listed in Table 5. Comparisons show that the calculation error is very large because the splat interfaces cannot be seen in the EBSD image. However, the splat interfaces have a significant influence on the thermal conductivity of YSZ coatings [11]. This influence will be discussed later in detail.

The Effect of Splat Interface on the Thermal Conductivity
To analyze the effect of the splat interfaces on thermal conductivity, an idealized model was introduced. In a study by Shen et al. [13], an artificial image with dimensions of 25 μm × 25 μm was created, and all the splat interfaces were represented as rectangular elements having a size of 3.25 μm × 0.125 μm, as indicated in Figure 4. The thermal conductivity of splat interfaces is obtained through iterative computation and was set to 0.03 W/m·K, which made the simulated thermal conductivities map well with the experimental thermal conductivities of as-sprayed coatings [16]. The distribution of the thermal flux about the coating is shown in Figure 5. Using Equation (1), the thermal conductivities of the coatings were calculated. The simulation results (λc) and the experimental findings (λ0) are listed in Table 5.   The phase composition and content of grain boundaries were easily obtained through the EBSD image as shown in Figure 1. Furthermore, when the ideal splat interface model was introduced, the simulated thermal conductivity and experimental thermal conductivity can be matched well. Therefore, it is more accurate to use this model to figure out the influence coefficient of thermal  Comparisons show that the calculation error is very large because the splat interfaces cannot be seen in the EBSD image. However, the splat interfaces have a significant influence on the thermal conductivity of YSZ coatings [11]. This influence will be discussed later in detail.

The Effect of Splat Interface on the Thermal Conductivity
To analyze the effect of the splat interfaces on thermal conductivity, an idealized model was introduced. In a study by Shen et al. [13], an artificial image with dimensions of 25 μm × 25 μm was created, and all the splat interfaces were represented as rectangular elements having a size of 3.25 μm × 0.125 μm, as indicated in Figure 4. The thermal conductivity of splat interfaces is obtained through iterative computation and was set to 0.03 W/m·K, which made the simulated thermal conductivities map well with the experimental thermal conductivities of as-sprayed coatings [16]. The distribution of the thermal flux about the coating is shown in Figure 5. Using Equation (1), the thermal conductivities of the coatings were calculated. The simulation results (λc) and the experimental findings (λ0) are listed in Table 5.   The phase composition and content of grain boundaries were easily obtained through the EBSD image as shown in Figure 1. Furthermore, when the ideal splat interface model was introduced, the simulated thermal conductivity and experimental thermal conductivity can be matched well. Therefore, it is more accurate to use this model to figure out the influence coefficient of thermal  The phase composition and content of grain boundaries were easily obtained through the EBSD image as shown in Figure 1. Furthermore, when the ideal splat interface model was introduced, the simulated thermal conductivity and experimental thermal conductivity can be matched well. Therefore, it is more accurate to use this model to figure out the influence coefficient of thermal conductivity for the splat interface, grain boundaries and monoclinic phase. The thermal conductivity of pores and cracks, tetragonal phase, monoclinic phase, grain boundaries and splat interface were placed in the simulation model. The thermal fluxes of coatings without splat interface is obtained based on the finite element mesh in Figure 2 and is represented in Figure 6. The distribution of the thermal gradient and thermal flux under steady-state conditions can be estimated through the FE grid and are shown in Figure 7. By combining the results with Equation (1) and (2), the thermal conductivity λ 1 of the coating with splat interface and λ 2 without splat interface, the change in the thermal conductivity (∆λ 1 ) under the influence of the splat interface and the effect coefficient R 2 obtained are therefore listed in Table 6.
Coatings 2018, 8, x FOR PEER REVIEW 6 of 10 grid and are shown in Figure 7. By combining the results with Equation (1) and (2), the thermal conductivity λ1 of the coating with splat interface and λ2 without splat interface, the change in the thermal conductivity (Δλ1) under the influence of the splat interface and the effect coefficient R2 obtained are therefore listed in Table 6.   It can be concluded that the splat interfaces have a significant influence on the decrease of thermal conductivity of YSZ TBCs, and the effect coefficient can reach 50%. The reason is that the splat interface can cause phonon scattering and reduce the phonon mean free path. Furthermore, the lamellar spaces are similar to the pores parallel to the interface, and the pores will cause further phonon scattering, making great reduction of the heat transfer ability of the coatings.
On the basis of Tables 5, 6 and 7, it could be found that the order of experimental thermal conductivity is M1 < M3 < M2. However, the order of simulated thermal conductivity is different, in which the M3 shows the maximum thermal conductivity. It is probably attributed to the fact that the same idealized splat interface models were introduced in all three coatings. In fact, the splat interfaces should also be different from each other due to the differences of the microstructures for the three coatings, as shown in EBSD and SEM images. Therefore, it inevitably leads to different deviation   Figure 7. By combining the results with Equation (1) and (2), the thermal conductivity λ1 of the coating with splat interface and λ2 without splat interface, the change in the thermal conductivity (Δλ1) under the influence of the splat interface and the effect coefficient R2 obtained are therefore listed in Table 6.   It can be concluded that the splat interfaces have a significant influence on the decrease of thermal conductivity of YSZ TBCs, and the effect coefficient can reach 50%. The reason is that the splat interface can cause phonon scattering and reduce the phonon mean free path. Furthermore, the lamellar spaces are similar to the pores parallel to the interface, and the pores will cause further phonon scattering, making great reduction of the heat transfer ability of the coatings.
On the basis of Tables 5, 6 and 7, it could be found that the order of experimental thermal conductivity is M1 < M3 < M2. However, the order of simulated thermal conductivity is different, in which the M3 shows the maximum thermal conductivity. It is probably attributed to the fact that the same idealized splat interface models were introduced in all three coatings. In fact, the splat interfaces should also be different from each other due to the differences of the microstructures for the three coatings, as shown in EBSD and SEM images. Therefore, it inevitably leads to different deviation  It can be concluded that the splat interfaces have a significant influence on the decrease of thermal conductivity of YSZ TBCs, and the effect coefficient can reach 50%. The reason is that the splat interface can cause phonon scattering and reduce the phonon mean free path. Furthermore, the lamellar spaces are similar to the pores parallel to the interface, and the pores will cause further phonon scattering, making great reduction of the heat transfer ability of the coatings.
On the basis of Tables 5-7, it could be found that the order of experimental thermal conductivity is M 1 < M 3 < M 2 . However, the order of simulated thermal conductivity is different, in which the M 3 shows the maximum thermal conductivity. It is probably attributed to the fact that the same idealized splat interface models were introduced in all three coatings. In fact, the splat interfaces should also be different from each other due to the differences of the microstructures for the three coatings, as shown in EBSD and SEM images. Therefore, it inevitably leads to different deviation levels in the as-simulated thermal conductivity and finally results in the different trends of simulated and experimental thermal conductivities. It might be one of the major limitations of this model.

The Effect of Monoclinic Phase on the Thermal Conductivity
To elucidate the effect of the monoclinic phase on the thermal conductivity, the thermal conductivity (λ 3 ) of the coating with monoclinic phase, tetragonal phase, grain boundaries and splat interface are compared with the thermal conductivity (λ m ) of a coating that contains tetragonal phase, grain boundaries and splat interface. According to the idealized FE model, the pores, cracks and monoclinic phase are regarded as the tetragonal phase. Thus, the distributions of the thermal gradient and thermal flux under steady-state condition of the TBCs without monoclinic phase can be obtained, as listed in Figure 8. Similarly, when only cracks and pores are regarded as the tetragonal phase, the distributions of the thermal gradient and thermal flux under steady-state condition of the TBCs with monoclinic phase can be obtained, and it was indicated in Figure 9. Using Equation (1) along with these results, λ m and λ 3 can be calculated, as listed in Table 6. The effect coefficient of the monoclinic phase R 2 on the thermal conductivity of the coating and the change in thermal conductivity ∆λ 2 can be evaluated according to Equation (3).

The Effect of Monoclinic Phase on the Thermal Conductivity
To elucidate the effect of the monoclinic phase on the thermal conductivity, the thermal conductivity (λ3) of the coating with monoclinic phase, tetragonal phase, grain boundaries and splat interface are compared with the thermal conductivity (λm) of a coating that contains tetragonal phase, grain boundaries and splat interface. According to the idealized FE model, the pores, cracks and monoclinic phase are regarded as the tetragonal phase. Thus, the distributions of the thermal gradient and thermal flux under steady-state condition of the TBCs without monoclinic phase can be obtained, as listed in Figure 8. Similarly, when only cracks and pores are regarded as the tetragonal phase, the distributions of the thermal gradient and thermal flux under steady-state condition of the TBCs with monoclinic phase can be obtained, and it was indicated in Figure 9. Using Equation (1) along with these results, λm and λ3 can be calculated, as listed in Table 6. The effect coefficient of the monoclinic phase R2 on the thermal conductivity of the coating and the change in thermal conductivity Δλ2 can be evaluated according to Equation (3).  The amount of monoclinic phase in each coating is listed in Table 3. The monoclinic phase has a   The amount of monoclinic phase in each coating is listed in Table 3. The monoclinic phase has a very small concentration of 2% in coatings M1 and M2, and the thermal conductivity of the coating is increased by 0.1 W/m·K correspondingly according to Table 7. Furthermore, comparing M2 with M3 when the concentration of the monoclinic phase is increased by 6%, the value of the thermal conductivity with monoclinic phase increased by 0.28 W/m·K. Thus, it can be concluded that the monoclinic phase can increase the thermal conductivity of the coatings. The reason is that the content The amount of monoclinic phase in each coating is listed in Table 3. The monoclinic phase has a very small concentration of 2% in coatings M 1 and M 2 , and the thermal conductivity of the coating is increased by 0.1 W/m·K correspondingly according to Table 7. Furthermore, comparing M 2 with M 3 when the concentration of the monoclinic phase is increased by 6%, the value of the thermal conductivity with monoclinic phase increased by 0.28 W/m·K. Thus, it can be concluded that the monoclinic phase can increase the thermal conductivity of the coatings. The reason is that the content of Y 3+ in the monoclinic YSZ decreased, leading to the reduction of point defects and lattice distortions. As a result, the scattering ability of the microstructure for phonons decreases, resulting in an increase in the phonon mean free path. In order to get a coating with a very low thermal conductivity, the content of the monoclinic phase should be kept at minimum.
In our study, the simulation results indicate that thermal conductivity of as-sprayed YSZ coatings at room temperature reduces with the decrease in the content of monoclinic phase. Therefore, the monoclinic phase should be avoided during practical spraying processes to reduce the thermal conductivity of YSZ coatings, which is consistent with the previous researches [17] and common practices. After thermal cycles, the content of monoclinic phase does increase because YSZ coatings would undergo a martensitic phase transformation from tetragonal zirconia to monoclinic zirconia at temperatures above 1200 • C. To avoid the increase of the content of monoclinic phase after thermal cycles, which would result in the increase of thermal conductivity at service temperature, the common practice solution is to improve the thermal stability of YSZ coatings. For example, the thermal stability of YSZ coatings could be improved, and the monoclinic phase was suppressed during thermal cycles by fabricating coatings of Al 2 O 3 doped YSZ materials [18].

Effects of Grain Boundaries on the Thermal Conductivity
The thermal conductivity of the coatings λ m that contain the tetragonal phase and grain boundaries can be seen in Table 6. The simulation results of the coatings for λ m are compared with the thermal conductivity of the tetragonal phase, λ T . The effect coefficient, R 3 , of the grain boundaries on the thermal conductivity of the thermal spray coating can be obtained using Equation (4). Namely, the magnitude of the change in the thermal conductivity of the coatings via the grain boundary can also be calculated. The effect coefficient of the grain boundaries R 3 and the amount of change ∆λ 3 are listed in Table 8. 2.65 −0.14 11.02 M 1 and M 2 are nanocoatings which were sprayed with nanopowders, while M 3 was sprayed with a micropowder. Thus, the different coatings have various grain sizes. Normally, when the grain size is reduced, the concentration of grain boundaries will be increased. The grain boundaries have the characteristic of phonon scattering and can reduce the phonon mean free path, leading to a reduction in the thermal conductivity of the coating. The effect coefficient of the grain boundaries is about 20% for each nanocoating. The grain boundaries play a vital role in the total reduction of the thermal conductivity.

Conclusions
The FE model was established based on EBSD analysis, which could offer more microstructure information. At the same time, an ideal interface model was introduced. The computational results are in agreement with the experimental findings, and the calculation error is lower than 10%. Using this model can simulate the effect of each microstructure on thermal conductivity more accurately.
The splat interface and grain boundaries play a critical role in the reduction of thermal conductivity, and the influence coefficient of the interface on thermal conductivity is much larger than that of the grain boundary. Therefore, it is necessary to take the splat interface into consideration when simulating the influence of microstructures on thermal conductivity. Moreover, when studying methods for reducing the thermal conductivity of coatings, the introduction of splat interfaces is a worthwhile consideration.