Effect of Porosity on the Infrared Radiative Properties of Plasma

Article pubs.acs.org/JPCC

Effect of Porosity on the Infrared Radiative Properties of PlasmaSprayed Yttria-Stabilized Zirconia Ceramic Thermal Barrier Coatings Leire del Campo,*,† Domingos De Sousa Meneses,† Karine Wittmann-Ténèze,‡ Antoine Bacciochini,§ Alain Denoirjean,§ and Patrick Echegut† †

CNRS, CEMHTI UPR3079, Univ. Orléans, F-45071 Orléans, France CEA DAM Le Ripault, 37260 Monts, France § CNRS, CEC-SPCTS UMR7315, 12 Rue Atlantis, 87060 Limoges, France ‡

ABSTRACT: Far- and mid-infrared spectroscopy is presented as a powerful and nondestructive tool for estimation of the porosity of oxide ceramic films, which are typically employed as part of thermal barrier coatings. A radiative model that takes porosity into account and includes the optical response of thin films has been used. Provided that pore size is small enough as compared to the infrared wavelength, the porosity level can be included as an adjustable parameter of effective medium theories (EMT) such as MaxwellGarnet or Bruggeman. Periodic interferential oscillations are found on radiative properties in spectral ranges where the coatings are semitransparent and do not scatter significantly infrared radiation. This information has been used to retrieve the porosity level of several semitransparent samples. Analysis of plasma-sprayed yttria-stabilized zirconia (YSZ) ceramic coatings shows that the radiative model is relevant, and the comparison between experimental and theoretical porosity values illustrates the level of accuracy of the technique.

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INTRODUCTION Thermal barrier coatings (TBCs) have become a crucial component of structural pieces in applications where extreme temperature and mechanical conditions are combined. In general, the TBC protects a structural superalloy from severe temperature conditions. TBCs are multipart systems composed of a metallic bond coat directly in contact with the superalloy to be protected, a thermally grown oxide (TGO), and a ceramic top coat with low thermal conductivity and improved mechanical properties. Several materials have been proposed as constituents of the top coat, but nowadays yttria-stabilized zirconia (YSZ) remains the most popular ceramic employed for this purpose.1−3 Even so, a large range of deposition techniques such as plasma spraying4 or electron beam-physical vapor deposition (EB-PVD)5 are used, giving rise to a variety of top coats with very dissimilar microstructural architecture; depending on the application a rather columnar or lamellar structure is preferred. For example, turbine blades are generally coated using EB-PVD, which gives rise to a columnar microstructure that considerably enhances the strain resistance. Concerning the combustion chamber, the preferred deposition technique is atmospheric plasma spraying (APS) which produces a rather porous and lamellar structure that minimizes conductive heat transfer. Suspension plasma spraying (SPS) as well as the PROSOL process (the two deposition techniques studied in this paper) result in a more compact and denser coating with smaller porosity level and size. Optimization of the efficiency of the TBCs depends on several factors, such as the top coat thermal conductivity, its © 2014 American Chemical Society

thermal diffusivity, its mechanical toughness, bond coat adherence, lifetime, etc. Most of these parameters depend on the microstructure of the top coat, notably on porosity size, porosity level, and architecture.3 The challenge is to develop a technique that will be able to characterize the microstructure of the top coat of a TBC; this will allow optimizing the process parameters when developing a new TBC or when improving its performance. Furthermore, nondestructive techniques are desirable. In this work, infrared spectroscopy is analyzed as a complementary characterization technique that allows obtaining information about the microstructure of ceramic coatings, notably the porosity. Ceramic YSZ plasma-sprayed films have been prepared and analyzed for studying the relevance of the technique. Infrared (IR) spectroscopy is well known as a characterization technique that allows obtaining the intrinsic optical properties of homogeneous materials.6,7 This is possible due to coupling between the crystalline normal vibrational optical modes and the electric field of electromagnetic radiation. The interaction is governed by the dielectric response of the medium which is directly related to the optical properties of the material. Moreover, infrared spectroscopy also allows obtaining information about the extrinsic optical properties due to the influence of texture (surface roughness, porosity, grain boundaries, etc.). When treating with heterogeneous materials, Received: February 10, 2014 Revised: May 19, 2014 Published: June 2, 2014 13590

dx.doi.org/10.1021/jp5014362 | J. Phys. Chem. C 2014, 118, 13590−13597

The Journal of Physical Chemistry C

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the composition and crystalline structure of the medium is not enough to entirely describe the whole thermo-radiative response; the texture is also needed. The heterogeneities such as grain boundaries, surface roughness, and pores are likely to scatter the radiation, and an extrinsic response will be added to the intrinsic one. Thus, the radiative properties will change as compared to those of the homogeneous medium. This influence will take place within two levels, depending on the size of the heterogeneities or inclusions. If the ratio of the characteristic size of the heterogeneous entities and the wavelength of the radiation is high enough, the photons will be reflected and refracted at each heterogeneity interface according to the laws of the geometrical optics.8 Light scattering dominates the optical response in this regime. At the extreme opposite, where the size of the inclusions is by a large factor smaller than the wavelength, scattering tends to vanish but the heterogeneities still affect the optical and dielectric properties of the medium. The optical properties of the heterogeneous material will depend on the form and quantity of the heterogeneities, and they can be evaluated using mixing laws known as effective medium theories (EMT).9−12 Some of these effective approximations have already been applied for modeling the infrared reflectance spectra of textured media.13−17 Certain authors combined the effective medium theories together with the optical response of thin films in the visible and near IR spectral ranges to obtain the nanometric porosity and/or thickness of thin films using ellipsometry and/ or IR spectroscopy.18,19 The same idea has already been applied in the mid-infrared for estimation of the porosity of nanometric thin and nonscattering films.20,21 The aim of this work is to prove the viability of using these kinds of approaches in the far-infrared spectral region for characterizing thicker ceramic films with higher porosity and roughness characteristic sizes, as found in thermal barrier coatings. To our knowledge, this is the first time that the semitransparent far-infrared spectral region is used to characterize the porosity of rough ceramic plasma-sprayed coatings, which are some tens of micrometers thick and whose mean pore size is about several hundred nanometers. We will show that the proposed approach is valid even when surface roughness is rather coarse. Infrared spectroscopy has been used to obtain the radiative properties of YSZ plasma-sprayed coatings. In the following, the optical properties of the ceramic matrix together with the effective medium theories and the optical response of thin films have been joined to simulate the experimentally obtained radiative properties of the porous ceramic films. Spectral features in the semitransparent spectral zones of the spectrum allow us to fit the thickness and/or porosity of the films. A sample synthesized by the PROSOL process has been used to study the suitability of the model, and the extracted porosity values are compared to values measured using ultrasmall angle X-ray scattering (USAXS). The porosity of other three samples, prepared by the SPS technique, is estimated using the proposed IR spectroscopic technique.

Figure 1. Schema of ceramic thermal barrier coating deposited on metallic substrate showing multiple reflections within the semitransparent film. p and d are porosity and thickness of the coating, Nef and Ns denote the complex optical index of the coating and the substrate, respectively, and ρ is the reflectance.

Consider a semitransparent film that has been deposited on a metallic substrate. Thin film theory22 evaluates the reflectance ρ of such a system given as a function of the thickness of the semitransparent film (d) and the complex optical indices of both the film (Nef = nef + ikef) and the substrate (Ns = ns + iks). If the film is porous (considering the size of pores being largely smaller than the wavelength of the electromagnetic radiation analyzed by infrared spectroscopy), its complex dielectric index can be calculated by applying effective medium theories which take into account the porosity value (p) as well as the dielectric functions of both the matrix (ε) and the pores (εp). The dielectric function of pores is supposed to be that of air, that is, εp = 1. The dielectric function of the matrix is obtained from infrared spectroscopy measurements performed on a homogeneous sample of the same composition and applying a model of the dielectric function, such as the semiquantum (SQ) model.7 When treating with submicrometric porous films, the conditions for applying the effective medium theories are accomplished in the mid- and far-infrared. Nevertheless, surface roughness, which also contributes to texture, may have a higher characteristic size than bulk porosity. In this case, it can induce surface scattering and the extrinsic radiative response due to surface roughness should be considered separately from porosity. Monte Carlo ray tracing techniques, which take account of the geometrical optics laws, may be used to include surface roughness. In this work, surface roughness has not been taken into account, and as explained further, in the frame of study presented here it is not needed for obtaining information about bulk properties. Thus, imagine that inclusions whose dielectric constant is εp are put in a medium of dielectric constant ε. Using effective medium approximations an effective dielectric constant εef can be calculated, which is given as a function of εp and ε, and the fraction p of inclusions. Several effective medium theories can be used. In this work, the Maxwell−Garnett theory9 (which is supposed to be a good approximation when inclusions do not interact between them) and the Bruggeman EMT10 (which is obtained assuming a rather important interaction between inclusions) have been applied and results compared. The Maxwell−Garnett (eq 1) and Bruggeman (eq 2) EMTs allow approximating the dielectric response using an effective permittivity calculated by εp − ε εef − ε =p ε + A(εef − ε) ε + A(εp − ε) (1)

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THEORETICAL METHODS The existing relation between radiative and optical properties of homogeneous materials, effective medium theories, and theory of thin films is put together to reproduce the radiative properties (reflectance and emittance) of porous semitransparent ceramic films deposited on metallic substrates. The schema of the ceramic film is shown in Figure 1.

p

εp − εef ε − εef =0 + (1 − p) εef + A(ε − εef ) εef + A(εp − εef ) (2)

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In the equations, A is the form factor of the heterogeneities, which have been considered spherical (A = 1/3). In the case of pores, the dielectric function of the inclusions is the air’s dielectric function (εp = 1). As seen, the Bruggeman EMT gives rise to a relation that is symmetric concerning matrix and inclusions. The whole model is constructed following these steps: A model of the dielectric function is first used to retrieve the intrinsic optical properties of a homogeneous sample whose radiative properties have been obtained by infrared spectroscopy. The calculated dielectric function will be the dielectric function of the ceramic coating matrix (ε). Using effective medium theories the dielectric function of the ceramic matrix (ε calculated in step 1), the dielectric function of inclusions (εp = 1), and the porosity p of the ceramic films are combined to evaluate an effective dielectric function (εef) that will satisfactorily describe the dielectric response of the ceramic film. The effective dielectric function directly gives the complex optical index of the film (nef and kef). The complex optical indices of the metallic substrate (ns and ks) and ceramic film (nef and kef calculated in step 2) together with film thickness (d) are then combined within the theory of radiative effect of thin films to obtain the spectral reflectance of porous ceramic film deposited on a metallic substrate. The FOCUS software, which has been developed at the CEMHTI laboratory and is freely accessible,23 has been used as a modeling tool. Libraries for modeling the radiative properties (emittance, reflectance, and transmittance) of ceramic coatings deposited on metallic substrate have been created following the described protocol.

Figure 2. ESEM fractograph of plasma-sprayed yttria-stabilized zirconia ceramic coatings deposited on metallic substrate (a)YSZ1, (b)YSZ2, (c)YSZ3, and (d)YSZ4.

total porosity level was determined precisely by “ultrasmall angle X-ray scattering” (USAXS) at the Argonne National Laboratory.24,25 The obtained value was 14 ± 1% with a pore size distribution below 50 nm. The second set of YSZ films (YSZ2, YSZ3, and YSZ4) has been prepared by thermal deposition using the technique of suspension plasma spraying (SPS).26 Films were deposited on polished stainless steel cylinders. Nanometric (∼50 nm) YSZ (ZrO2−8% mol Y2O3) powder dispensed in ethanol has been plasma sprayed on preheated (523 K) substrates. YSZ films ∼50 μm thick have been obtained. Two plasma mixtures have been used, namely, Ar−He (40−20 L/min) and Ar−H2 (55−5 L/min), and the distance from the torch to the sample has been settled on 30 or 50 mm. Combining these spraying conditions three samples have been prepared: YSZ2, YSZ3, and YSZ4. The main difference between films obtained with dissimilar spraying conditions is the porosity, which varies from 8% to 16%. The thickness of the films has been obtained using the same ESEM, and d = 63 ± 1, 34 ± 1, and 41 ± 1 μm has been measured for YSZ2, YSZ3, and YSZ4, respectively. Figure 2b, 2c, and 2d shows fractrographs of the samples with some measured thickness values. The porosity size of the films is bigger than that for YSZ1, but it remains submicrometric (50 nm to 1 μm). As reference, for characterization of the intrinsic optical properties of the films the optical properties of a polished homogeneous monocrystalline YSZ sample has also been measured. The sample has the same percentage of yttria (8% mol) as the ceramic films. The sample was a 1 cm × 1 cm parallel face blade, 0.5 mm thick. Infrared Spectroscopy. A homemade infrared spectrometer that combines two Fourier transform infrared (FT-IR) spectrometers (Bruker V70 and Bruker V80v) was used to obtain the radiative properties of the samples. Using this experimental device the normal emittance (E), the near-normal specular reflectance (ρspec) and transmittance (τspec), and the near-normal diffuse reflectance (ρdif, which also takes account of the specular feature) can be measured. Specular reflectance and transmittance at room temperature were measured for the homogeneous sample. Using these spectra and taking into

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EXPERIMENTAL METHODS Sample Preparation. Two sets of samples have been prepared. The first set consists of a single YSZ coating (YSZ1) prepared at the CEA laboratory in Le Ripault (France). This sample has been used for testing the usefulness of the technique. The second set consists of other three YSZ ceramic films (YSZ 2−4) prepared at the SPCTS laboratory in Limoges (France). The porosity of these ceramic films has been estimated by the proposed technique. Sample YSZ1 was prepared by thermal deposition using the PROSOL process. An aqueous zirconia sol used as precursor was prepared by urea neutralization of zirconium oxychloride in an aqueous medium followed by hydrothermal crystallization. The YSZ (ZrO2−8% mol Y2O3) nanoparticles (about 20 nm) were suspended in water due to addition of hydrochloric acid (pH 3) under vigorous stirring and ultrasonic assistance. The resulting sol, containing 10 wt % of zirconia nanoparticles, had the same viscosity as water and was absolutely stable (no sedimentation, even after many months). The sol was introduced with an adapted liquid injector in an Ar−He (50−50 L/min) plasma mixing generated by a F4 plasma torch (from Sulzer Metco) working under air at low pressure (200 mbar = 20 200 Pa). In the plasma medium, the water of the sol was vaporized and the YSZ nanoparticles accelerated onto a polished stainless steel substrate located at 40 mm as the standoff distance. A cryogenic cooling system allowed maintaining the substrate temperature at quite low temperature, below 550 K, during the spraying stage. The resulting coating (Figure 2a) observed using an environmental scanning electronic microscope (ESEM) had a thickness of 32 ± 1 μm and showed a compact and homogeneous microstructure. Such a tool was not adapted to observe the nanometric porosity. The 13592



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account that no diffusion takes place (smooth surface), emittance was determined as E = 1 − ρspec − τspec. The room-temperature specular and diffuse reflectances as well as the normal emittance at low temperature were determined for the YSZ ceramic coatings. Assuming that the sample is opaque (metallic substrate prevents radiation passing through the sample) the emittance should equal 1 − ρdif. The emittance measurement set up and technique are thoroughly described in ref 27. As explained, the two FT-IR spectrometers are placed face to face at both sides of the sample chamber box, where a sample whose emittance will be measured and a reference black body (Pyrox PY8) are positioned. Samples are usually heated by a CO2 laser (Coherent K500), but for studying the YSZ thermal barrier coatings a resistive heater in contact with the back surface of the samples has been used. Sample and a black body furnace are placed on a revolving plate which serves to place both sources in front of each spectrometer and interchanges their position automatically. Several detectors can be combined, and as long as there is enough signal, the emittance can be obtained for wavenumbers (σ) between 40 and 18 000 cm−1 (wavelength λ = 0.5−250 μm). The so-called Christiansen point (spectral point at which the emittance is one) is used to determine the sample temperature.28 A specular reflectance accessory (Bruker Optics) can be placed in one of both FT-IR spectrometers (V80v), which allows obtaining the near-normal (11°) specular reflectance at room temperature, for the same spectral range (40 and 18 000 cm−1). An integrating sphere (Infrared Associates Inc.) can also be placed in the other FT-IR spectrometer (V70) to perform nearnormal diffuse reflectance measurements. The infrared beam coming from the source enters the integrating sphere and reaches the sample or reference placed on the surface of the sphere with a nearly normal incident angle, and the integrating sphere allows recovering all the reflected radiation onto a nitrogen-cooled HgCdTe detector (Infrared Associates Inc.). The relation between the sample and the reference signals provides the diffuse reflectance.

Figure 3. Experimental reflectance (dotted line), transmittance (dash−dotted line), and emittance (solid line) of 8% mol YSZ homogeneous sample at room temperature. Modeled emittance spectra (dashed line) using the semiquantum (SQ) model of the dielectric function is also shown.

to correctly model the infrared spectrum. Identification of the absorption bands indicates that the sample is not entirely stabilized in the cubic form, as normal modes related to the tetragonal and monoclinic phases of the zirconia have been identified (see Figure 3). Effectively, as proposed by Pecharroman et al.,29 the large absorption band (σTO ≈ 330 cm−1) and the small band vibrating inside it (σTO ≈ 600 cm−1) could be related to the cubic phase, the second mode being a secondary oscillator resulting from an interaction between an optical and an acoustic phonon. Conversely, the band in the far-infrared (σTO ≈ 200 cm−1) and the second band vibration inside the large cubic band (σTO ≈ 400 cm−1) would be due to traces of tetragonal YSZ. Finally, a monoclinic absorption band is also perceptible at σTO ≈ 700 cm−1. The simulation of the experimentally obtained emittance spectrum leads to the complex dielectric function for the 8% mol YSZ at room temperature. Figure 4 represents the real (ε′) and imaginary (ε′′) parts of the calculated dielectric function.

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RESULTS AND DISCUSSION Homogeneous Sample. First, the intrinsic radiative response has been studied. To do so, a homogeneous monocrystalline YSZ sample has been used. Its radiative properties at room temperature have been measured. In Figure 3, the measured specular reflectance and transmittance (together with the calculated emittance (E = 1 − ρspec − τspec) are shown. The Christiansen point where the reflectance and transmittance are zero (thus, emittance equal to 1) is found at σ = 790 cm−1. The sample is opaque in the spectral region where phonon absorptions take place; this region is spread between ∼50 and ∼1100 cm−1 at room temperature and becomes larger at higher temperatures. The opacity zone will also depend on the thickness of the sample; thinner samples will have a narrower opacity spectral region. At both sides of the opaque zone, within the so-called transmission fronts, the emittance drops abruptly; the sample is said to be semitransparent in these spectral regions. After the transmission fronts (σ < 50 cm−1 in the far-infrared and σ > 2200 cm−1 in the mid-infrared) the sample becomes transparent. The emittance spectrum has been fitted using the semiquantum (SQ) model of the dielectric function7 (dashed curve in Figure 3). Five infrared active normal modes have been used

Figure 4. Real (ε′) and imaginary (ε′′) part of the dielectric function of 8% mol YSZ at room temperature.

YSZ1, Evaluation. The normal spectral emittance of YSZ1 sample has been measured at 380 K. The obtained emittance spectrum together with the emittance spectrum of the homogeneous YSZ sample at room temperature is shown in Figure 5. As observed, the Christiansen point is found for both samples at σ = 790 cm−1. Absorption bands appear in the 13593



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Figure 6. Diffuse reflectance (solid black line) and specular reflectance (solid gray line) spectra measured on YSZ1 at room temperature. One minus emittance (dashed line) at 380 K is also shown for comparison.

Figure 5. Normal spectral emittance of YSZ1 measured at 380 K (solid line). Spectral emittance of homogeneous YSZ at room temperature (dashed line) is also shown for comparison.

very close to one; thus, there is no sufficient index contrast between the air and the oxide to induce scattering. As explained in the Introduction, infrared spectroscopy allows obtaining information about the extrinsic contribution to the optical properties due to texture. Analysis of the diffusion profile in the opaque spectral region can give us information about surface texture, and studying the radiative response of the sample in the semitransparent spectral regions can give access to volumetric texture characteristics. In this work, we just studied the semitransparent regions in order to obtain information about the bulk of the samples. As already pointed out, in the spectral regions where the absorption coefficient is small enough to make the ceramic film semitransparent (σ < 150 cm−1 and σ > 825 cm−1) oscillations of a certain periodicity are observed (see Figures 5−7). The

emittance spectra of the ceramic coating within the spectral range from 1400 to 1600 cm−1, indicating that the ceramic coating is rich in H2O molecules. As the thickness of the YSZ ceramic film is smaller than the thickness of the homogeneous sample, the spectral region where the film is opaque is reduced; the ceramic film is opaque between ∼150 and ∼825 cm−1. As seen, in the far-infrared semitransparent zone, oscillations are seen in the emittance spectrum of the ceramic coating. These oscillations are due to an interference phenomenon taking place between consecutive reflections within the film, pointing out that the film is semitransparent. On the opposite side of the spectrum, in the mid-infrared semitransparent zone, the transmission front of the ceramic film, which reveals the opacity limit, is displaced through smaller frequencies as compared to the homogeneous sample. Much softer oscillations are also observed near the Christiansen point. Additionally, substrate contribution in the mid-infrared is remarkable, and the emittance value in this region is directly related to the emittance of the substrate. Finally, the difference in the emittance level of the homogeneous sample and the coating within the opaque zone is too elevated to be only due to the porosity of the film. Thus, surface roughness is thought to be large enough to add a non-negligible contribution to the radiative response of the ceramic coating. In Figure 6 results obtained by specular and diffuse reflectance (ρspec and ρdif, respectively) at room temperature are plotted together with the emittance (1 − E) at near room temperature (T = 380 K). As expected, the results from diffuse reflectance and emittance coincide, that is, 1 − E is equivalent to ρdif, which corresponds to the directional−hemispherical reflectance. Figure 6 also confirms the existence of considerable diffusion due to surface roughness since the specular reflectance does not match the diffuse reflectance. Additionally, for wave numbers smaller than 250 cm−1 and between the Christiansen point and 900 cm−1, scattering becomes negligible while ρspec, ρdif, and 1 − E turn into the same intensity. In the far-infrared, as we approach 250 cm−1 from high frequencies, diffusion becomes less important while the characteristic size of roughness becomes negligible as compared to the wavelength, that is, diffusion due to surface roughness vanishes for high enough wavelengths. In the vicinity of the Christiansen wavenumber diffusion also disappears but due to other reasons. In this spectral region the refractive index of the YSZ matrix is

Figure 7. Experimental specular reflectance spectrum of YSZ1 compared with simulated curves using the indicated thickness and porosity in the frame of Maxwell-Garnet (MG) and Bruggeman (Brug) EMT in the mid- (a) and far- (b) infrared spectral regions. 13594



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existence of these oscillations proves that the film is semitransparent and homogeneous as seen by the infrared radiation. Coherence between consecutive reflectance is needed for interferences to take place, and if bulk scattering did exist it would be lost. This justifies the application of effective medium theories to homogenize the optical properties of our porous ceramic coatings. Hence, as anticipated, pore size is small enough as compared to the wavelength in the mid- and farinfrared, at least for σ < 1500 cm−1. It is important to remark that despite the exact reflectance level in the semitransparent spectral region depends on the substrate radiative properties and roughness, the periodicity of the interferences within the ceramic film will be independent of these features and directly related to the optical thickness of the film. The optical thickness is defined as the film thickness times its effective refractive index, which will directly depend on the porosity. The previously described model has been used to reproduce the periodicity of the specular reflectance spectrum. As the porosity of the coating is rather small, pores are thought to be independent and should not interact between them, so the use of the Maxwell−Garnett EMT seems consistent. Thus, the intrinsic dielectric function shown in Figure 4 is combined with the dielectric function of the pores within the Maxwell−Garnett (MG) EMT taking into account the measured porosity rate (14%) and thickness of the film (32 μm). Figure 7 shows the experimentally measured (solid black line) and theoretically modeled (dashed line) reflectance between 800 and 1100 cm−1 (Figure 7a) and in the farinfrared (Figure 7b), and as seen, the real and modeled periodicities do not completely match. Therefore, the porosity and thickness of the film are adjusted to better reproduce the periodicity in both spectral ranges, and p = 16 ± 1% and d = 31.7 ± 0.2 μm are found as the best-fitting values (solid blue line in Figure 7). The comparison of the two modeled curves using the Maxwell−Garnett EMT in Figure 7 (dashed and solid blue curves) gives an idea of the sensitivity of the technique. Small changes in porosity and thickness give rise to considerable changes in the periodicity of the oscillations, which allows a very precise estimation of fitted variables. In order to test the validity of the chosen effective medium theory, Figure 7 also shows the modeled reflectance curve by using the Bruggeman (Brug) effective medium theory (dotdashed line). As seen, in spite of the very dissimilar validity conditions of both approximations, the use of one or other gives nearly identical results. The model can also be used in an inverse way as a technique for determining the optical properties of the ceramic matrix. If the thickness and porosity of the coating are well known, the dielectric function of the matrix can be adjusted to reproduce the periodicity of the interferences. It is also interesting to determine the limits of validity of this technique. On one hand, the film has to be semitransparent (to allow multiple reflections within the coating) in a spectral region for which the wavelength is high enough as compared to pore size (for the effective medium theories to be applicable). Spectral ranges where scattering due to surface roughness is negligible are also desirable; if not, reflected signals would be too small to obtain treatable information. Additionally, the existence of two spectral ranges for which these hypotheses were valid allowed us to adjust both thickness and porosity at the same time. Often only the far-infrared spectral range will be accessible. This will be the case for thicker films, particularly for coatings with higher pore size and more significant surface

roughness. In this situation, for determining the porosity, the film thickness has to be precisely known. YSZ2−YSZ4, Application. The second set of samples has been used to show an example of application of the proposed technique. As coatings were thicker and rougher, interferences were only found for all samples in the far-infrared specular reflectance. Figure 8 shows the oscillations found for the three samples.

Figure 8. Experimental (solid lines) and simulated (dashed lines) specular reflectance spectra in the far-infrared for YSZ2, YSZ3, and YSZ4 samples. The thickness and porosity used in the model is indicated for each sample.

Applying the infrared model (Maxwell−Garnett EMT has been employed) and using the thickness obtained by ESEM (d = 63, 34 , and 41 μm for YSZ2, YSZ3, and YSZ4, respectively), the porosity of each ceramic film has been adjusted. The estimated values are p = 8 ± 2%, 13 ± 2%, and 16 ± 2% for samples YSZ2, YSZ3, and YSZ4, respectively. Figure 8 also shows the simulated specular reflectance for these parameters. Remark that only the periodicity of oscillations has been fitted by adjusting the porosity level. The porosity of the samples studied here has not been measured using other techniques. Nevertheless, similar samples prepared in the same conditions (same original powder, suspension, plasma gas, and distance) have been sent to the Argonne National Laboratory for obtaining the total porosity level using the USAXS technique.24,25 p = 9 ± 1%, 13 ± 1%, and 14 ± 1% were obtained for samples analogous to YSZ2, YSZ3, and YSZ4, respectively. Even though values are not exactly the same for equivalent samples, the trend of porosity level is correctly reproduced.

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CONCLUSIONS A radiative model to simulate the optical properties of porous ceramic films has been developed. The model takes account of the dielectric function of the matrix and uses the porosity of the 13595



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coating to retrieve the effective optical properties of the ceramic film by applying effective medium theories. The effective refractive index is then used together with the thickness of the coating in the frame of the optical response of thin films which determines the periodicity of the interferential oscillations due to consecutive reflections within the film. The model allows fitting the porosity and/or thickness of the ceramic coating to theoretically simulate the measured periodicity, which permits a rather precise determination of p and/or d. The model has been tested with a plasma-sprayed yttriastabilized zirconia ceramic coating (YSZ1). The size of pores (nanometer sized) and existence of interferential oscillations in the semitransparent spectral range justify the use of effective medium approximations. The adjustment of the theoretical periodicity allowed us to determine the porosity and thickness of the film. The values of porosity obtained by USAXS (p = 14 ± 1%) and evaluated by infrared spectroscopy (p = 16 ± 1%) are within uncertainty limits, which confirms the applicability of the model. The periodicity of the interferences is completely independent of the radiative response of the substrate, and it remains unchanged regardless of surface roughness. Thus, it is a nondestructive and rather simple and accessible technique for determination of the submicrometric porosity of ceramic films. It has also been demonstrated that the results are nearly independent of the used EMT since Maxwell−Garnett and Bruggeman approximations lead to very close porosity and thickness values. The technique has been applied for estimation of the porosity of three YSZ suspension plasma-sprayed ceramic films. Only the far-infrared spectral range was accessible in this case, so the film thicknesses measured by ESEM have been introduced as known parameters for modeling the radiative properties. The comparison between the porosity values estimated by the technique presented in this paper (pYSZ2 = 8 ± 2%, pYSZ3 = 13 ± 2%, and pYSZ4 = 16 ± 2%) and values measured by USAXS for analogous samples (p = 9 ± 1%, 13 ± 1%, and 14 ± 1%, respectively) confirms the validity of the technique. The radiative model analyzed in this paper can be used as a technique for the porosity estimation of, for example, newly designed top coats for thermal barrier coatings. Use of this technique would help for a rapid and efficient adjustment of parameters for the deposition technique being studied.

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AUTHOR INFORMATION

Corresponding Author

*Phone:+33238255534. Fax:+33238638103. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge E. Veron for ESEM micrographs and J. Ilavsky for USAXS measurements. REFERENCES

(1) Clarke, D. R.; Levi, C. G. Materials Design for the Next Generation Thermal Barrier Coatings. Annu. Rev. Mater. Res. 2003, 33, 383−417. (2) Padture, N. P.; Gell, M.; Jordan, E. H. Thermal Barrier Coatings for Gas-Turbine Engine Applications. Science 2002, 296, 280−284. (3) Chen, L. B. Yttria-Stabilized Zirconia Thermal Barrier Coatings  a Review. Surf. Rev. Lett. 2006, 13, 535−544. 13596



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Effect of Porosity on the Infrared Radiative Properties of Plasma

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