LOW-POROSITY CERAMICS FOR THERMAL BARRIER COATINGS
Following from: Spectral radiative properties of some important materials: Experimental data and theoretical models
Let us consider the radiative properties of zirconia ceramics produced by a plasma-spraying technology. This ceramic is widely used as a thermal barrier coating to provide thermal insulation and to protect metallic turbine-engine components from hot gas streams (Bose, 2007; Markosan et al., 2007; Golosnoy et al., 2009). The low thermal conductivity of the ceramic makes it possible to considerably decrease the temperature at the metal-ceramic interface even in the case of a small coating thickness (~0.1-0.5 mm). There are many other actual and potential industrial applications of yttria-partially-stabilized zirconia ceramics (Liang and Dutta, 2001; Bose, 2007). In many cases, one of the more important properties of this material is a very low thermal conductivity. It is known that zirconia is semitransparent in the near-infrared spectral range. For this reason, the role of thermal radiation in effective thermal conductivity of porous zirconia ceramics is expected to be significant. Note that both absorption and scattering characteristics are important for transient radiative-conductive heat transfer in porous ceramics (Siegel, 1998; Sadooghi and Aghanajafi, 2006).
To the best of our knowledge, there are only very limited experimental data in the literature for absorption and scattering characteristics of porous zirconia ceramics in the near infrared. The theoretical modeling of radiation scattering by pores, grains, and cracks in ceramics is also difficult because of the complex microstructure of the material. In the present section, we consider the results of our paper (Dombrovsky et al., 2007) on complex experimental and theoretical analysis of the near-infrared radiative properties of porous zirconia ceramics.
Following the paper by Dombrovsky et al. (2007), we focus on the main characteristics of the material: the absorption coefficient and transport scattering coefficient which determine the radiation heat transfer in ceramics (see the article Transport approximation). In the experimental part of the work, we used a formal identification procedure based on the measurements of directional-hemispherical reflectance and transmittance for the samples of ceramics in the wavelength range 2.5 < λ < 9 μm and the general model for radiation transfer in a refracting, absorbing, and scattering material. The theoretical analysis is based on a physical model of the radiative properties which treats the scattering-pores structure as polydisperse spherical bubbles. The effect of flat microcracks is also considered. It is important that the scattering of radiation by small pores is insensitive to the weak absorption of zirconia, whereas the absorption does not depend on the shape and size distribution of the micropores. As a result, the theoretical model enables us to predict the absorption coefficient of bulk zirconia and to find approximate analytical dependences for both absorption and scattering characteristics of ceramics.
Consider first the material microstructure. The morphology of thermal barrier coatings (TBCs) of yttria-stabilized zirconia ceramics depends on the plasma-spraying technology. As was noted by Jadhav et al. (2005), the microstructure of air plasma-sprayed (APS) barrier coatings is characterized by 15%-20% porosity and large “splat” boundaries/cracks (~100 μm) that are parallel to the coating surface. Xie et al. (2003) have analyzed the solution-precursor plasma-spray (SPPS) method, which is a potentially low-cost process. In this process, an aqueous chemical precursor feedstock, that results in ZrO_{2}-7 wt % Y_{2}O_{3} ceramic solid solution, is injected into the plasma jet. This is in contrast to the APS process, where ceramic powder is used as the feedstock. The typical microstructure of a SPPS TBC includes through-thickness vertical cracks and lack of large-scale “splat” boundaries that are present in APS TBCs. Air plasma spraying and in situ laser irradiation by diode laser processes were combined by Antou et al. (2005) to modify structural characteristics of TBCs of porosity ~5%-15%. It was shown that laser remelting induces the growth of a vertical columnar dendritic structure with the characteristic dimension of the columnar grains ~0.4 μm and the formation of large horizontal cracks parallel to the coating surface.
In this earlierpaper (Dombrovsky et al., 2007), we investigated the radiative properties of ZrO_{2}-8 mole % Y_{2}O_{3} ceramics produced by APS air plasma spraying. The samples are supplied by the ONERA institution. The surfaces of all the samples were hand polished with different abrasives containing 120-, 400-, 600-, 800-, and 2400-grit silicon carbide paper. Typical pictures of sample cross sections obtained by using scanning electron microscope (SEM) (XL-20 Philips) are presented in Fig. 1. The ceramic microstructure is similar to that described in the literature. One can see irregular isotropic pores, small-scale dendritic structures with very fine vertical pores, and long horizontal cracks. The measurements of ceramic porosity for three samples give the values in the range from 14.6% to 15.5% (see Table 1). The porosity was calculated for the density of dense material, 6006 kg/m^{3}.
Figure 1. Typical SEM images of the cross section of zirconia ceramics samples.
Table 1. Main parameters of the samples
Sample number | Thickness d, mm | Density ρ, kg/m^{3} | Porosity p, % |
1 | 0.32 | 5126 | 14.7 |
2 | 0.52 | 5074 | 15.5 |
3 | 0.66 | 5130 | 14.6 |
The early measurements of the refractive index of cubic zirconia stabilized with yttria in the range 0.36 < λ < 5.1 μm have been reported by Wood and Nassau (1982). The data for the sample of 12 mole % Y_{2}O_{3} at room temperature were fitted to a three-term Sellmeier equation useful for interpolation at any wavelength. It was shown that the index of refraction increases linearly with temperature, but the temperature coefficient in the interval between 20°C and 130°C appears to be very small: 1.6 · 10^{-5} K^{-1} at λ = 0.36 μm and 0.62 · 10^{-5} K^{-1} at λ = 1.6 μm. More detailed data for n(λ) in the range 0.36 < λ < 5.5 μm at various mole fractions of yttria were reported by Wood et al. (1990). It was shown that the index of refraction decreases monotonically with the yttria stabilizer concentration in the range between 10.9 and 32.4 mole % Y_{2}O_{3}. Some additional data for temperature dependence of refractive index for zirconia with 9.4 and 24 mole % of yttria were reported in an earlier paper by Botha et al. (1993). The measurements at wavelength λ = 0.51 μm showed an increase in refractive index of ~6% in the temperature range 300 < T <1450 K. The experimental data by Ferriere et al. (2000) for plasma-sprayed ZrO_{2}-Y_{2}O_{3} refer mainly to the visible range. The measurements at wavelength λ = 0.65 μm showed a significant increase in spectral absorptivity with temperature from 0.1 below 1000 K to 0.75 at 2300 K. It was also found that the total hemispherical emissivity ε of opaque samples increases from 0.25 at 1500 K up to 0.6 at 2200 K, but they did not discuss the physical mechanism responsible for the darkening of zirconia at high temperatures. Makino et al. (1984) have reported the measurements of reflectance for the samples of zirconia ceramics stabilized by yttria in the temperature range from 290 to 700 K. The porosity of ceramics was not specified in the paper. It was only indicated that the density is high. It was found that, for the wavelength λ < 5 μm, scattering (at grain boundaries, inclusions, or pores) is more significant than absorption and that, above 7 μm, scattering vanishes as the size of the scattering centers decreases relative to λ. The measurements reported showed that the temperature dependence of the ceramic radiative properties in the investigated temperature range is negligibly low. The experimental points demonstrated only a very small increase in the absorption coefficient with temperature at wavelength exceeding 5 μm. The radiative properties of ZrO_{2}-Y_{2}O_{3} crystals in the temperature range from room temperature to 1930 K were studied by Cabannes and Billard (1987). It was found that up to 1600 K, the absorption coefficient of cubic zirconia stabilized with yttria at any wavelength from the 3-6 μm range increases monotonically with temperature, and a much more significant increase in absorption is observed in the temperature interval from 1600 to 1930 K. The radiative properties of ceramic of cubic zirconia stabilized with 8 mol % yttria for the wavelengths at very high temperatures (up to 3200 K) have been also studied by Petrov and Chernyshev (1999) and Akopov et al. (2001). The interest in such high temperatures is explained by the potential use of thick protective layers of zirconia ceramics in ex-vessel catchers of nuclear reactors for retention of core melt in conditions of severe accident. The measurements of the normal-hemispherical reflectance were performed at the wavelengths 0.488, 0.6328, 1.15, and 1.39 μm. It was noted that a significant increase in the emissivity of zirconia ceramics is observed at temperatures >1400 K. A similar conclusion about weak temperature dependence of the emissivity of zirconia ceramics in the temperature range from 867 to 1298 K was made by Pfefferkorn et al. (2003) for the wide spectral range from 1 to 14 μm.
As in the paper by Dombrovsky et al. (2007), we will focus on near-infrared scattering and absorption characteristics of zirconia ceramics used in TBCs. Our measurements have been done at room temperature. In the analysis of experimental data, we used a three-term Sellmeier equation with coefficients suggested by Wood and Nassau (1982). This relation was used in the wavelength range up to λ = 9 μm. The calculated dependence n(λ) is shown in Fig. 2. It is known from our experience (one can see the article Semitransparent media containing bubbles) that identification of absorption and scattering characteristics of the material are not sensitive to small uncertainties in the index of refraction.
Figure 2. Spectral dependence of the refractive index of zirconia.
The samples of zirconia ceramics were illuminated by a normally incident collimated beam (the cone angle is 2.23°). The experimental setup consisted of two main parts: a BIO-RAD FTS 60A FTIR spectrometer with a ceramic source heated up to 1300°C and a KBr beam splitter, and a gold-coated integrating sphere CSTM RSA-DI-40D which collects hemispherically the radiation crossing, or reflected by, the sample onto a detector placed on the wall of the sphere. The FTIR spectrometer can be used for the measurements for the wavelengths from 2.5 to 25μm. In our case, the upper boundary of the spectral interval was limited to the wavelength of ~9 μm because of the opacity of the samples in the long-wave range. The latter limitation is not important for high-temperature applications of the ceramics. At the same time, it would be interesting to complete our data by the measurements at the wavelength <2.5 μm by using another experimental technique. The measurements have been done five times for each sample and the standard absolute deviation is <5% for both transmittance and reflectance in the wavelength range from 2.5 to 9 μm. We ignored the points with the erroneous negative and unreliable, very small values of transmittance. These points appear only for thicker samples, 2 and 3. The data for sample 1 seems to be more accurate. The results of directional-hemispherical measurements at normal incidence are presented in Fig. 3. The large values of reflectance in the wide range 2.5 < λ < 7 μm show that zirconia ceramics is a highly scattering material. It is clear that absorption is especially small in the wavelength ranges λ < 2.7μm and 4 < λ < 5.5 μm. The long-wavelength range λ > 7 μm is characterized by low transmittance and reflectance. It means that the ceramic is highly absorbing in this range. The detailed information on absorption and scattering characteristics of the ceramics can be obtained by using the identification procedure. This procedure should be based on an adequate theoretical model for radiative transfer in porous ceramics.
Figure 3. The measured directional-hemispherical reflectance and transmittance: 1, 2, 3 are the sample numbers (see Table 1).
We consider two alternative models for radiation transfer in an absorbing, refracting, and scattering medium. The general model is based on numerical solution of integro-differential radiative transfer equation (RTE) by use of the discrete ordinates method (DOM) (Modest, 2003). The simplified model is based on a modified two-flux approximation for the radiation transfer in homogeneous isotropic medium (see the article Hemispherical transmittance and reflectance at normal incidence). It was shown that the modified two-flux approximation gives rather accurate results for the directional-hemispherical characteristics in the case of small and moderate optical thickness of the sample of a not-strongly-refracting medium (n<1.5). We will consider the error of this approach for optically thick samples of strongly refracting and scattering zirconia ceramics.
In the identification procedure, we assume the index of refraction n(λ) and the sample thickness d to be known. The absorption coefficient α(λ) and the transport scattering coefficient σ_{tr}(λ) of porous ceramics are determined from the spectral data for directional-hemispherical reflectance and transmittance. The results obtained for various samples by use of a modified two-flux approximation are presented in Fig. 4. Note that the analytical solution presented in the article Hemispherical transmittance and reflectance at normal incidence makes the calculations very simple and there is no need in a specific procedure for the inverse problem solution. One can see in Fig. 4 that measurements for all the samples give practically the same values of spectral characteristics of zirconia ceramics. Two spectral regions are clearly observed: the range of semitransparency, λ < 7 μm and the opacity range, λ > 7 μm. In the first range, the ceramic is a strongly scattering material with albedo ω_{tr} > 0.7. The especially high values of albedo take place at λ < 2.7 μm and in the range of 4 < λ < 5.5 μm where the absorption coefficient is very low. In the opacity range, the absorption predominates the scattering and albedo decreases monotonically with the wavelength.
Figure 4. The transport scattering coefficient (a), absorption coefficient (b), and transport albedo (c) of zirconia ceramics: 1, 2, 3 are the sample numbers.
It is interesting that transport scattering coefficient strongly decreases with the wavelength over the spectrum. Such behavior is typical for radiation scattering by particles of a size less than the wavelength. It means that scattering properties of zirconia ceramics are determined by pores of characteristic size <~2 μm. We use this observation by constructing the physical model of radiation scattering in ceramics.
The error of the modified two-flux approximation in the specific range of parameters of zirconia ceramics is estimated by comparison with an exact numerical solution by high-order DOM including the results for alternative approximation for the scattering function. In Fig. 5, the approximate calculations for sample 1 are compared with the results of numerical identification procedure. One can see the great underestimation of short-wave transport scattering coefficient in approximate solution [Fig. 5(a)], whereas the results for absorption coefficient are in very good agreement with the exact calculations over the spectrum [Fig. 5(b)]. This result is explained by a good approximation of absorbance and significant relative error in transmittance in the approximate solution for optically thick weakly absorbing media. It is important that the exact solution is insensitive to the type of scattering function and the simplest transport approximation is sufficiently accurate in the problem considered.
Figure 5. The transport scattering coefficient (a), absorption coefficient (b), and transport albedo (c) of zirconia ceramics obtained for sample 1 by using the different models for radiation transfer: (1) modified two-flux approximation, (2), (3) high-order discrete ordinate model [(2) transport scattering function, (3) Henyey-Greenstein scattering function for asymmetry factor μ = 0.5].
Because of the low porosity of zirconia ceramics, it seems natural to model the scattering characteristics of this material as a result of independent scattering by single pores. It means that each pore scatters infrared radiation in exactly the same manner as if all the other pores did not exist. It is known that this occurs when the pores are separated by distances exceeding their characteristic size and the wavelength (Baillis and Sacadura, 2000).
The model suggested by Dombrovsky et al. (2007) is based on the following additional assumptions: (1) The absorption coefficient of ceramics in the semitransparency range is proportional to the volume fraction of bulk zirconia (1 - p) and does not depend on the pore structure; (2) the scattering is insensitive to the weak absorption and can be determined by calculations for nonabsorbing medium; and (3) the scattering is determined by isotropic pores which can be treated as polydisperse spherical bubbles. The first two assumptions are justified by the rigorous calculations for single pores in a weakly absorbing medium. Note that similar results were obtained for water with steam bubbles and fused quartz containing gas bubbles (see the article Semitransparent media containing bubbles). The last assumption is similar to that suggested by Manara et al. (1999) for dense alumina ceramics of porosity <5%. It was shown that experimental results on directional-hemispherical transmittance in the range 0.7 < λ < 2.5 μm are explained by the scattering of radiation by small pores which can be considered as polydisperse spherical bubbles of diameter <1 μm. In further analysis, the short cracks are also considered as isotropic pores whereas the specific solution is derived to take into account the effect of long cracks.
According to the suggested model, the absorption and transport scattering coefficients of porous ceramics can be calculated as follows:
(1) |
(2) |
where α_{0} is the absorption coefficient of bulk zirconia, Q_{s}^{tr} is the transport efficiency factor of scattering for a single spherical pore, and F(a) is the size distribution of the pores. We will use Eq. (1) not only in the range 2.5 < λ < 7 μm but also for 7 < λ < 9 μm. One should remember that the error of this approach may be considerable in the last range. As for Eq. (2), one needs to specify the size distribution of pores. The great number of very small pores makes reasonable the model exponential distribution:
(3) |
It is difficult to measure the size distribution of pores and find a function describing the distribution of equivalent spherical pores, but our experience shows that effect of the distribution shape is usually insignificant in comparison with the effect of average size of pores or particles (see the article Radiative properties of polydisperse systems of independent particles). It is convenient to introduce the specific transport scattering coefficient (per unit volume fraction of pores): S_{tr} = σ_{tr}/ p. For monodisperse pores, this value is expressed as follows:
(4) |
The dependences S_{tr}(a) shown in Fig. 6(a) illustrate the negligible contribution of very small and large pores to the scattering by porous ceramics. Note that one can use the monodisperse approximation with average radius a_{32} = 3a_{0} instead of calculations for polydisperse pores.
Figure 6. Specific transport scattering coefficient for monodisperse spherical pores (a) and for flat cracks at normal (b) and oblique (c) incidence.
The SEM pictures of the sample cross section showed that a considerable volume of ceramic pores is presented by large cracks oriented along the sample surface (see Fig. 1). The scattering characteristics of these cracks can be estimated on the basis of the known solution for reflection from a thin plate (Born and Wolf, 1999). This solution was used by Dombrovsky (2004) in the analysis of scattering characteristics of hollow-microsphere ceramics. The coefficient of reflection of unpolarized radiation from a flat crack of thickness δ can be expressed as follows:
(5) |
The equations (5) can be used when sinθ < 1/ n. For larger angles the total reflection takes place and the following expressions should be used instead of Eq. (5):
(6) |
Because the angle between the directions of incident and reflected radiation is π - 2θ, the transport factor of scattering is calculated by the obvious relation:
(7) |
The transport scattering coefficient of polydisperse flat cracks can be expressed as follows:
(8) |
where f_{v}^{cr} is the volume fraction of the cracks. Obviously, the value of the transport scattering coefficient is different for normal illumination by the collimated radiation and for diffuse illumination by the scattered radiation. As for spherical pores, we introduce the specific coefficient S_{tr}(θ) = σ_{tr}(θ)/ f_{v}^{cr}. For monodisperse cracks, one can write:
(9) |
One can see in Fig. 6(b) that the cracks of thickness 0.1 < δ < 1 μm give the main contribution to the scattering at λ = 3 μm and likewise the cracks of thickness 0.2 < δ < 2 μm at the wavelength λ = 6 μm. This result is similar to that for spherical pores. Moreover, the average values of S_{tr}(θ) in the angular range from θ = 0° to 60° are close to S_{tr}(0) [see Fig. 6(c)]. Therefore, the cracks parallel to the sample surface are not considered as a separate component of the physical model.
A comparison of the model calculations with experimental data for transport scattering coefficient is presented in Fig. 7. One can see a good qualitative agreement of the spherical pore model with average radius a_{32} between 0.3 and 0.7 μm with the experimental results. The above range of average pore size corresponds to the results of calculations shown in Fig. 6. An overestimating of σ_{tr}(θ) in an approximate theoretical model can be explained by the role of longitude pores and cracks which give a relatively small contribution to scattering in the case of a large angle of radiation incidence.
Figure 7. Comparison of calculations with experimental data for transport scattering coefficient: (1) experimental data for sample 1, (2)-(4) calculations [(2) a_{32} = 0.3 μm, (3) 0.5μm, (4) 0.7μm].
The absorption coefficient and index of absorption of bulk zirconia can be determined from Eq. (1) and the results of identification procedure based on an analytical solution in a modified two-flux approximation. One can see in Fig. 8 that this procedure gives practically the same spectral dependences of the absorption characteristics for all the samples.
Figure 8. Absorption coefficient (a) and index of absorption (b) of bulk zirconia determined from measurements for three samples (1, 2, 3 are the sample numbers).
For a reader interested in wide-range spectral radiative properties of yttria-stabilized zirconia, one can also recommend recent papers by Eldridge and Spuckler (2008) and Eldridge et al. (2009). In the latter paper, the radiative properties of this material at elevated temperatures up to 1360°C were determined.
REFERENCES
Akopov, F. A., Val’ano, G. E., Vorob’ev, A.Y u., Mineev, V. N., Petrov, V. A., Chernyshev, A. P., and Chernyshev, G. P., Thermal radiative properties of ceramic of cubic ZrO_{2} stabilized with Y_{2}O_{3} at high temperatures, High Temp., vol. 39, no. 2, pp. 244-254, 2001.
Antou, G., Montavon, G., Hlawka, F., Cornet, A., and Coddet, C., Microstructures of partially stabilized zirconia manufactured via hybrid plasma spray process, Ceram. Int., vol. 31, no. 4, pp. 611-619, 2005.
Baillis, D. and Sacadura, J.-F., Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization, J. Quant. Spectrosc. Radiat. Transfer, vol. 67, no. 5, pp. 327-363, 2000.
Born, M. and Wolf, E., Principles of Optics, 7th (expanded) ed., New York: Cambridge University Press, 1999.
Bose, S., High Temperature Coatings, Amsterdam: Elsevier Butterworth-Heinemann, 2007.
Botha, P. J., Chiang, J. C. H., Comis, J. D., Mjwara, P. M., and Ngoepe, P. E., Behavior of elastic constants, refractive index, and lattice parameter of cubic zirconia at high temperature, J. Appl. Phys., vol. 73, no. 11, pp. 7268-7274, 1993.
Cabannes, R. and Billard, D., Measurement of infrared absorption of some oxides in connection with the radiative transfer in porous and fibrous materials, Int. J. Thermophys., vol. 8, no. 1, pp. 97-118, 1987.
Dombrovsky, L.A., Approximate models of radiation scattering in hollow-microsphere ceramics, High Temp., vol. 42, no. 5, pp. 772-779, 2004.
Dombrovsky, L. A., Tagne, H. K., Baillis, D., and Gremillard, L., Near-infrared radiative properties of porous zirconia ceramics, Infrared Phys. Tech., vol. 51, no. 1, pp. 44-53, 2007.
Eldridge, J. I. and Spuckler, C. M., Determination of scattering and absorption coefficients for plasma-sprayed yttria-stabilized zirconia thermal barrier coatings, J. Am. Ceramic Soc., vol. 91, no. 5, pp. 1603-1611, 2008.
Eldridge, J. I., Spuckler, C. M., and Markham, J. R., Determination of scattering and absorption coefficients for plasma-sprayed yttria-stabilized zirconia thermal barrier coatings at elevated temperatures, J. Am. Ceramic Soc., vol. 92, no. 10, pp. 2276-2285, 2009.
Ferriere, A., Lestrade, L., and Robert, J.-F., Optical properties of plasma-sprayed ZrO_{2}-Y_{2}O_{3} at high temperature for solar applications, J. Solar Energy Eng., vol. 122, no. 1, pp. 9-13, 2000.
Golosnoy, I. O., Cipitra, A., and Clyne, T. W., Heat transfer through plasma sprayed thermal barrier coatings in gas turbines--A review of recent work, J. Therm. Spray Technol., vol. 18, no. 5-6, pp. 809-821, 2009.
Jadhav, A., Padture, N. P., Wu, F., Jordan, E. H., and Gell, M., Thick ceramic barrier coatings with high durability deposited using solution-precursor plasma spray, Mater. Sci. Eng. A, vol. 405, no. 1-2, pp. 313-320, 2005.
Liang, Y. and Dutta, S. P., Application trend in advanced ceramic technologies, Technovation, vol. 21, no. 1, pp. 61-65, 2001.
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Manara, J., Caps, R., Raether, F., and Fricke, J., Characterization of the pore structure of alumina ceramics by diffuse radiation propagation in the near infrared, Opt. Commun., vol. 168, no. 1-4, pp. 237-250, 1999.
Markosan, N., Nylén, P., Wigren, J., and Li, X.-H., Low thermal conductivity coatings for gas turbine applications, J. Therm. Spray Technol., vol. 16, no. 4, pp. 498-505, 2007.
Modest, M.F., Radiative Heat Transfer, 2nd ed., New York: Academic Press, 2003.
Petrov, V. A. and Chernyshev, A. P., Thermal-radiation properties of zirconia when heated by laser radiation up to temperature of high-rate vaporization, High Temp., vol. 37, no. 1, pp. 58-66, 1999.
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Xie, L., Ma, X., Jordan, E. H., Padture, N. P., Xiao, D. T., and Gell, M., Identification of coating deposition mechanisms in the solution-precursor plasma-spray process using model spray experiments, Mater. Sci. Eng.A, vol. 362, no. 1-2, pp. 204-212, 2003.
参考文献
- Akopov, F. A., Val’ano, G. E., Vorob’ev, A.Y u., Mineev, V. N., Petrov, V. A., Chernyshev, A. P., and Chernyshev, G. P., Thermal radiative properties of ceramic of cubic ZrO_{2} stabilized with Y_{2}O_{3} at high temperatures, High Temp., vol. 39, no. 2, pp. 244-254, 2001.
- Antou, G., Montavon, G., Hlawka, F., Cornet, A., and Coddet, C., Microstructures of partially stabilized zirconia manufactured via hybrid plasma spray process, Ceram. Int., vol. 31, no. 4, pp. 611-619, 2005.
- Baillis, D. and Sacadura, J.-F., Thermal radiation properties of dispersed media: theoretical prediction and experimental characterization, J. Quant. Spectrosc. Radiat. Transfer, vol. 67, no. 5, pp. 327-363, 2000.
- Born, M. and Wolf, E., Principles of Optics, 7th (expanded) ed., New York: Cambridge University Press, 1999.
- Bose, S., High Temperature Coatings, Amsterdam: Elsevier Butterworth-Heinemann, 2007.
- Botha, P. J., Chiang, J. C. H., Comis, J. D., Mjwara, P. M., and Ngoepe, P. E., Behavior of elastic constants, refractive index, and lattice parameter of cubic zirconia at high temperature, J. Appl. Phys., vol. 73, no. 11, pp. 7268-7274, 1993.
- Cabannes, R. and Billard, D., Measurement of infrared absorption of some oxides in connection with the radiative transfer in porous and fibrous materials, Int. J. Thermophys., vol. 8, no. 1, pp. 97-118, 1987.
- Dombrovsky, L.A., Approximate models of radiation scattering in hollow-microsphere ceramics, High Temp., vol. 42, no. 5, pp. 772-779, 2004.
- Dombrovsky, L. A., Tagne, H. K., Baillis, D., and Gremillard, L., Near-infrared radiative properties of porous zirconia ceramics, Infrared Phys. Tech., vol. 51, no. 1, pp. 44-53, 2007.
- Eldridge, J. I. and Spuckler, C. M., Determination of scattering and absorption coefficients for plasma-sprayed yttria-stabilized zirconia thermal barrier coatings, J. Am. Ceramic Soc., vol. 91, no. 5, pp. 1603-1611, 2008.
- Eldridge, J. I., Spuckler, C. M., and Markham, J. R., Determination of scattering and absorption coefficients for plasma-sprayed yttria-stabilized zirconia thermal barrier coatings at elevated temperatures, J. Am. Ceramic Soc., vol. 92, no. 10, pp. 2276-2285, 2009.
- Ferriere, A., Lestrade, L., and Robert, J.-F., Optical properties of plasma-sprayed ZrO_{2}-Y_{2}O_{3} at high temperature for solar applications, J. Solar Energy Eng., vol. 122, no. 1, pp. 9-13, 2000.
- Golosnoy, I. O., Cipitra, A., and Clyne, T. W., Heat transfer through plasma sprayed thermal barrier coatings in gas turbines--A review of recent work, J. Therm. Spray Technol., vol. 18, no. 5-6, pp. 809-821, 2009.
- Jadhav, A., Padture, N. P., Wu, F., Jordan, E. H., and Gell, M., Thick ceramic barrier coatings with high durability deposited using solution-precursor plasma spray, Mater. Sci. Eng. A, vol. 405, no. 1-2, pp. 313-320, 2005.
- Liang, Y. and Dutta, S. P., Application trend in advanced ceramic technologies, Technovation, vol. 21, no. 1, pp. 61-65, 2001.
- Makino, T., Kunitomo, T., Sakai, I., and Kinoshita, H., Thermal radiation properties of ceramic materials, Heat Transfer--Japan. Res., vol. 13, no. 4, pp. 33-50, 1984.
- Manara, J., Caps, R., Raether, F., and Fricke, J., Characterization of the pore structure of alumina ceramics by diffuse radiation propagation in the near infrared, Opt. Commun., vol. 168, no. 1-4, pp. 237-250, 1999.
- Markosan, N., Nylén, P., Wigren, J., and Li, X.-H., Low thermal conductivity coatings for gas turbine applications, J. Therm. Spray Technol., vol. 16, no. 4, pp. 498-505, 2007.
- Modest, M.F., Radiative Heat Transfer, 2nd ed., New York: Academic Press, 2003.
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