Temperature-Dependent Optical Reflectivity of Tetragonal-Prime Yttria-Stabilized Zirconia
Descrição do Produto
J. Am. Ceram. Soc., 89 [3] 908–913 (2006) DOI: 10.1111/j.1551-2916.2005.00813.x r 2005 The American Ceramic Society
Journal
Temperature-Dependent Optical Reflectivity of Tetragonal-Prime Yttria-Stabilized Zirconia John A. Nychka,w Michael R. Winter, and David R. Clarke*,** Materials Department, University of California, Santa Barbara, California 913605-5050
Tamaki Naganumaz and Yutaka Kagawa Institute of Industrial Science, The University of Tokyo, Tokyo, Japan
which we present measurements of the reflectance of dense, tetragonal-prime zirconia as a function of temperature. Being a metastable form, no single crystals exist and a significant part of the work reported here is the successful preparation of dense bodies of tetragonal-prime zirconia; TBCs are prepared by highly metastable routes, such as plasma spraying or electron beam evaporation. An additional motivation for our measurements is to provide baseline optical properties of dense t0 YSZ material, with the aim to evaluate the potential of using optical reflectance to monitor the densification and sintering of TBCs non-destructively. A report of initial observations of the reflectance of TBC coatings is presently in preparation.9
The optical reflectance of dense, metastable, tetragonal-prime zirconia plates, made by densifying electron beam physical vapor-deposited powder, is reported as a function of temperature up to 1673 K (14001C) over the range of 400–1500 cm1 (6.67–25 lm). Curve fitting of the reflectance as a function of temperature was performed using two different damped oscillator models, each with three infrared (IR)-active modes. Oscillator parameters were then used to calculate the values of the indices of refraction and absorption as a function of temperature using the classical dispersion theory. The reflectance data of tetragonal-prime yttria-stabilized zirconia at room temperature are qualitatively similar to that reported for the equilibrium tetragonal phase in that it can be fit with three IR-active modes.
II. Experimental Procedure
I. Introduction
C
(1) Preparation of Dense Tetragonal-Prime Zirconia After several attempts to fabricate dense plates of tetragonalprime zirconia from chemically precipitated powders that failed because of partial transformation of the zirconia to monoclinic zirconia, we found that the material scavenged from the walls of the chamber used in the electron-beam deposition of commercial coatings was a suitable starting material. Having been evaporated by the electron beam and then deposited on the cold walls of the chamber, it is likely that this material is as highly metastable as is possible to synthesize. The scavenged material was in an aggregated state so it was first ground in an attrition mill with zirconia-milling media in isopropanol. Then, the powder was consolidated in a uniaxial hot press at 16001C for 1 h at a pressure of approximately 60 MPa in a graphite die under vacuum. Subsequently, the densified material was diced with a low-speed diamond saw into 3 mm 22 mm 22 mm plates. The surfaces and edges were then milled using a surface grinder to final dimensions of 2 mm 20 mm 20 mm, and annealed in air at 12001C for 15 h. After annealing, the samples were determined to be 98% of the theoretical density by the Archimedes technique. Specimens were polycrystalline, with an estimated grain size on the order of 0.5–1.0 mm from atomic force microscopy.
thermal barrier coatings (TBCs) are porous yttriastabilized zirconia (YSZ) with a composition 7 m/o YO1.5.1–3 The presence of the porosity serves several crucial functions: it provides strain compliance to accommodate the large thermal expansion mismatch with the superalloy under the coating; it decreases the effective thermal conductivity of the coating; and causes multiple optical scattering to minimize radiative heat transfer through the coating. This last attribute is already important in coatings for combustion chambers and is also likely to become significant in coating blades and vanes as gas turbine temperatures are projected to increase further in future designs.4 Although the role of the porosity in strain compliance and thermal conductivity of TBCs has been the subject of extensive research, there has been little quantification of the effect on optical scattering, in particular in the visible and infrared. The studies that have been performed have been carried out on other crystallographic forms of zirconia, such as tetragonal5–7 and cubic,5,7,8 rather than the metastable tetragonal-prime (t0 ) crystal structure of TBCs.3 Furthermore, while the optical properties of the stable cubic5,7,8 and monoclinic forms of zirconia7 have been well characterized, there are no reports of the optical properties of the metastable form. It remains unclear whether the optical response of the t0 metastable phase should be any different from the tetragonal, monoclinic, or cubic phases of Y31-doped zirconia. Thus, this lack of basic optical data motivates the present contribution in URRENT
(2) Crystallographic Characterization X-ray diffraction was used to establish that the dense plates retained the tetragonal-prime crystal structure. The X-ray diffraction analysis was performed using an automated diffractometer system (X’Pert PRO MRD, PANalytical, Almelo, the Netherlands) with a 3 h scan in the range of 721–761 2y. The X-ray diffraction pattern over 721–761, 2y (the distinctive range for tetragonal-prime YSZ) is shown in Fig. 1. Analysis of this figure indicates that the metastable material had begun to phase separate toward the equilibrium phases (t1c), evidenced by a mixture of two different metastable tetragonal phases with different c/a ratios (1.003 and 1.008 calculated according to Lughi and Clarke10).
R. French—contributing editor
Manuscript No. 20813. Received November 10, 2004; approved October 3, 2005. This work was supported in Japan through the auspices of the Ministry of Education and in Santa Barbara by the Office of Naval Research under grant 844249023118. *Member, American Ceramic Society. **Fellow, American Ceramic Society. w Author to whom all correspondence should be addressed. e-mail: nychka@engr. uky.edu z Present address: National Institute for Materials Science (NIMS), Composites Group, Tsukuba, Japan.
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Fig. 1. X-ray diffraction patterns from as-deposited tetragonal-prime powder (AD), and hot-pressed plate after reflectance measurements (AR). Positions of tetragonal, tetragonal-prime, and cubic peaks are indicated by dashed lines and arrows. Intensity has been adjusted to show equivalent noise and background for both patterns.
(3) Reflectance Spectroscopy The optical reflectance measurements were carried out using a Fourier Transform Infrared (FTIR) system (FT/IR-670 Plus, JASCO Corporation, Tokyo, Japan) modified for high-temperature measurements with a specialized detector, described previously.11 A schematic diagram of the instrument is shown in Fig. 2. The sample was heated in an electric resistance furnace with a Pt–Rh thermocouple approximately 1 cm away from the sample, but touching the sample holder. Measurements were taken at increments of 2001C from room temperature (251C; 298 K) to 14001C (1673 K). The sample was held at each temperature for a minimum of 1 h before reflectance measurements were made. A water-cooled heat shield with a small hole shielded the optics from thermal radiation of the furnace, and special water-cooled copper mirrors were used to reflect the light from the FTIR system into the furnace and the reflected light to the detector. A special feature of the instrument is the sample holder that enables the sample and a polished platinum reference to be alternately slid under the optical beam without changing any of the settings and while maintaining the same temperature. This feature also enables the effects of atmospheric absorption, such as water vapor, nitrogen, and carbon dioxide, in the optical path to be cancelled out. The system enables measurements to be made from 350 to 7800 cm1 (1.28–28.6 mm) with a nominal resolution of o4 cm1 from room temperature up to 15001C. Measurements were made in air and the angles of illumination and reflection were fixed at 81, with a divergence of less than 711. The optical beam size was B10 mm. The measured reflectance was strictly the directional reflectance at 81 from the surface normal and was corrected by the FTIR instrument with reference to the polished platinum plate at the same temperature, assuming that the platinum reflectance was 100%. Over the analyzed measurement range this assumption is accurate; however, at lower wavelengths a correction would need to be performed. Another assumption of the measured reflectance was that there was no internally scattered energy leaving the surface layer. This was based on the large slab thickness of 2 mm, which was assumed to be large enough to allow all the radiation transmitted through the surface layer to be absorbed; thus, no reflections from the back surface could have returned and been
Fig. 2. Schematic of the optical arrangement used in measuring the optical reflectance as a function of temperature. The recorded spectra are compared with the reflectance of a platinum reference that can be slid into the position of the zirconia sample. T 0 CPL denotes the location of the thermocouple relative to the specimen position.
transmitted through the front surface layer. For the minimum wavelength of 6.67 mm reported herein, this assumption is valid, but at shorter wavelengths more attention to the back surface reflections would need to be addressed. Unfortunately, transmission measurements could not be made to verify this assumption as a function of temperature in the current experimental setup. Although measurements were taken over the entire equipment range, the range discussed herein is mainly 350–1500 cm1 (6.67–28.6 mm). Excessive noise was present above 3000 cm1 (o3.33 mm), especially at high temperatures, making curve fitting unreliable. Unfortunately, reflectance data above 1500 cm1 (o6.67 mm), although of considerable interest to radiative heat transfer in TBC materials, could not be curve fit to determine the optical properties because of the noise, and difficulty in modeling back surface reflections at short wavelengths. This is not to say that curve fitting the region 46.67 mm to determine optical properties is minor, because the largest changes in index of refraction and absorption occur in the longer wavelength regions of the electromagnetic spectrum; thus, accurate modeling in this regime is critical in establishing relationships to predict behavior in different wavelength regimes. As mentioned above, a report on manufactured TBC materials is in preparation, with particular attention devoted to this shorter wavelength regime, and comparison of the dense t0 YSZ produced in this work with as-deposited and heat-treated structures.9 Because the samples had 98% theoretical density, some porosity was surely present. The possible effects of scattering from the small amount of porosity were deemed negligible because of the fact that the pore size was likely much smaller than the size at which there would be a high enough scattering cross-section to interfere with the measurements 46.67 mm.
III. Observations and Analysis The reflectance recorded from one of the 7YSZ plates from room temperature up to 1673 K (14001C) is shown in Fig. 3. These data are averaged from three separate measurement runs
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Journal of the American Ceramic Society—Nychka et al. eðoÞ ¼ e1
N o2 o2 ig o Y Lj Lj j¼1
o2Tj o2 igTj o
(1)
where oLj and oTj are the longitudinal and transverse frequencies of the jth vibrational mode, respectively, and the coefficients, g are the corresponding damping factors, eo being the high-frequency dielectric constant. The transverse oscillator strength, Dej, of any j term was determined by Q 2 2 e1 k oLk oTj Dej ¼ 2 Q oTj k6¼1 o2Tk o2Tj
(2)
The second model, a series sum model, was the usual classical oscillator dispersion equation (CODE): eðoÞ ¼ e1 þ
N X
o2 j¼1 j
Sj o2j o2 iogj
(3)
in which Sj is the dimensionless mode strength (where all modes are of the transverse type). For both the product (LST) and sum models (CODE), the reflectance is, in turn, related to the dielectric constant through the standard relationship: pffiffiffiffiffiffiffiffiffi eðoÞ 12 RðoÞ ¼ pffiffiffiffiffiffiffiffiffi eðoÞ þ 1
Fig. 3. Average optical reflectance as a function of wavelength and temperatures of 295, 673, 1273, and 1673 K. (a) Raw data for chosen temperatures, and (b) smoothed data used for curve fitting. Average of three separate measurements per temperature. A zoomed region of the higher energy portion of the curves is given in the inset. Every fifth data point is show for clarity in the main scale, and every 20th data point in the zoomed region.
on the same sample. As can be seen in Fig. 3(a), the noise in the reflectance curves increases with temperature. Some spikes in the data, presumed to be noise from the electronics, were removed, and the data used for curve fitting are shown in Fig. 3(b). Nearly identical spectra were recorded from the other plates. The reflectance spectra observed in this study are similar, in broad features, to those presented in the literature for both yttria-stabilized tetragonal and cubic zirconia5,7,12 and yttriastabilized cubic hafnia.13 The principal features are the low broadband reflectance over the short wavelength region (o12 mm; 4833 cm1), a minimum reflectance at B12 mm (B833 cm1), followed by the steep increase in reflectance to another, higher, broadband reflectance at long wavelengths (412 mm; o 833 cm1). The primary difference lies in the large wavelength region, specifically at wavelengths greater than the minimum reflectance at B12 mm (B833 cm1). To express the reflectance data in terms of classical optical harmonic oscillators, we have attempted to fit the spectra with a calculation of the reflectance based on two different models. The first model, a series product model, was the standard Lyddane– Sachs–Teller (LST) relation
(4)
To use Eq. (4) to fit the measured reflectance data, a non-linear least-squares curve-fitting algorithm, coded in MATLABt (v.6.1, TheMathWorks Inc, Natick, MA), was developed. This program used Eqs. (1) and (3) for expressing e(o) in the curvefitting algorithm to determine the oscillator parameters for both models over the range 0–1500 cm1 (46.67 mm). In both cases, three oscillators were sufficient to obtain excellent fits. These oscillators corresponded to the three predicted IR-active modes in tetragonal zirconia: two Eu modes (one low and one high frequency) and an A2u mode.5 Initial values for the oscillator parameters in the product model were chosen based on values given for the first three oscillators for tetragonal zirconia from Pecharroma´n et al.5 In both the series and product models, the oscillator parameter values were first determined by fitting the room-temperature data. Then, successive temperature data were fit using the values determined from the optimization procedure for the previous temperature as the initial values. The optimization routine for the sum model was not as sensitive to the initial values of the parameters as was the product model. The oscillator parameters determined from the best fit of both models to the measured reflectance data are listed in Table I. The location of the oscillators below 400 cm1 (425 mm) is considered to be of limited value, as no data were collected below 350 cm1. Nonetheless, prediction of the reflectance as a function of frequency for the material at room temperature qualitatively matches the results found for tetragonal zirconia powder and the pellets reported in Pecharroma´n et al.5 There is found to be a good agreement in transverse oscillator frequency between the two models (recall that the sum model only assumes transverse modes). Neglecting the lowest frequency mode from each model because of lack of data in that frequency range, comparison shows that there are systematic temperature dependencies of the mode position and damping coefficients. For example, the positions of the highest frequency transverse (product and sum model) modes and longitudinal (product model only) modes all decrease with increasing temperature, while the damping coefficients of the modes increase. The fits between the experimental data and both the series sum and product models were generally excellent, as shown in
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Table I. Curve Fitting Parameters for the Triple-Damped Oscillator Models Product model (LST) 1
1
Sum model (CODE)
T (K)
j
oT i (cm )
oL j (cm )
gT i
gL j
Dej
295
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
86 535 426 131 566 430 39 543 420 43 536 419 47 532 428 42 526 419 85 506 446
276 521 716 226 560 714 329 534 709 361 528 705 398 524 700 358 517 693 328 479 678
50 160 61 70 122 46 115 149 85 126 143 93 139 150 103 153 155 92 121 169 143
175 140 72 81 123 75 171 143 87 155 141 96 139 150 104 125 156 112 162 118 119
104.8 0.34 0.67 22.2 0.09 5.28 791.5 0.16 2.70 790.2 0.13 1.77 743.6 0.10 0.85 687.0 0.14 1.57 91.5 0.71 1.03
473 673 873 1073 1273 1673
eN
4.1 3.9 4.1 4.1 4.0 3.7 3.1
1
oj (cm )
gj
Sj
143 569 432 141 565 432 145 557 428 147 547 424 163 545 416 201 510 423 244 514 430
300 40 36 300 50 47 300 59 58 300 63 69 300 100 92 153 137 80 50 187 100
17.0 0.027 6.0 19.0 0.03 5.8 16.0 0.03 5.7 15.0 0.04 5.6 5.0 0.18 6.1 16.3 0.25 2.8 10.0 0.88 0.59
eN
4.1 4.0 3.9 3.8 3.6 3.4 3.0
LST, Lyddane–Sachs–Teller; CODE, classical oscillator dispersion model.
Fig. 4. On closer inspection, the highest temperature investigated had a high scatter in the data, and Fig. 4 shows a rather large deviation in the fit of the 1673 K data for the product and sum models, with the sum model approximating the experimental results more accurately. The sum model also more accurately modeled the changes in curvature in the region around 600 cm1 (16.7 mm); thus, the sum model was used for calculating the dielectric functions and indices described below.
IV. Discussion The data presented in this study indicate that there are no abrupt changes in reflectance with temperature up to 14001C (1673 K) but rather a smooth decrease in reflectance at all wave-
Fig. 4. Comparison between the reflectance spectrum and the fitted curve for three harmonic oscillators showing that an excellent fit can be obtained. For clarity, only 5% of the measured data are shown.
lengths other than the wavelength of the minimum reflectance. Not surprisingly, considering that the local atomic arrangement in the tetragonal-prime zirconia is similar to that of zirconia in its equilibrium tetragonal crystal structure, the reflectance spectra are also rather similar. The spectra for both forms of zirconia can be fit on the basis that the reflectance is governed by the properties of three harmonic oscillators. Although the mathematical fitting of reflectance data using model oscillators can be quite difficult, and so the actual values of the oscillator properties derived by fitting vary from one set of investigators to another, it is clear that the oscillators correspond to the three infrared-active vibrational modes of the tetragonal structure (2Eu, A2u). Although the infrared vibrational modes could not be measured directly, it should be noted that the Raman spectra of the tetragonal and the tetragonal-prime phases are indistinguishable.10 It is expected that the real value of the reflectance spectra presented here will be in modeling the radiative heat transfer in TBCs above 1250 cm1 (o8 mm), where the majority of the radiative energy exists at the high temperatures applicable for TBCs (410001C). For this application there are two features of interest. The first is the temperature dependence of the reflectance and the second is the variation of the index of refraction and absorption coefficient with wavelength. These latter parameters are key to understanding the role of porosity in the reflectance of monitoring microstructural evolution. The temperature dependence of the reflectance at a number of selected wavenumbers is shown in Fig. 5. At each wave number selected, the reflectance decreases approximately linearly with temperature, with the highest changes of magnitude occurring in the low–wave number region (long-wavelength regime). This result demonstrates that changes of the reflectance of dense metastable t0 YSZ in the short-wavelength regime (o12 mm) are of a lesser magnitude than in the long-wavelength regime. By design, TBCs contain extensive small (nano) and intermediate (micron)-sized porosity in order to decrease their thermal conductivity and to impart strain compliance. At high temperatures, during operation, the distribution of porosity evolves with time as the internal porosity coarsens and as sintering of the coating occurs. As porosity causes scattering of light, it is possible that one application of reflectance measurements is to monitor changes in porosity in coatings. To assess the effect of
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Journal of the American Ceramic Society—Nychka et al.
Fig. 5. Temperature dependence of the reflectance at different wavelengths.
porosity, the distance at which light of different frequencies can propagate into dense metastable zirconia is needed. For this reason, we have used the oscillator parameters from the curve fitting to calculate the dielectric constant as a function of wavenumber using Eqs. (1) and (3), assuming a value of e(0) 5 27 (the models were not sensitive to this value). From the real and imaginary parts of the dielectric function, the values for the index of refraction, n, and absorption coefficient, k, were derived according to the relations: 2 n¼4
e0 r þ
2 k¼4
qffiffiffiffiffiffiffiffiffiffiffiffi31=2 e0 2r e00 2r 5 2
e0 r þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi31=2 e00 2r þ e00 2r 5 2
(5)
(6)
The variation of the values derived for the indices of refraction and absorption as a function of wavenumber for two different temperatures (295 and 1273 K) is illustrated in Fig. 6. It
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Fig. 7. Optical constants, n and k, derived from the fit of the measured reflectance data using the sum model at temperatures of 295 and 1273 K extrapolated over an extended wavenumber region: 400–8000 cm1 (1.25—25 mm). A feature of classical dispersion theory, asymptotic behavior is observed for both optical constants; k asymptotes to 0 at B6 mm for both temperatures, and n asymptotes to 2.02 and 1.86 at 298 and 1273 K, respectively, at 1.25 mm, with little change below B4 mm.
can be seen from Fig. 6 that there is little change in n or k above 833 cm1 (o12 mm) for the dense material, whereas below 833 cm1 (412 mm), there is noticeable change of the indices with temperature. As mentioned, the region o8 mm is of greatest interest for high-temperature applications, but limitations in the data and fitting did not allow the full wavelength region of interest to be modeled in this work. Nonetheless, because the optical properties exhibited the highest temperature dependence at long wavelengths (exhibited in the reflectance data that were modeled) extrapolation of the classical dispersion model to shorter wavelengths was performed, and n and k data from Fig. 6 down to 1.25 mm are shown in Fig. 7. Figure 7 demonstrates the small differences in n and k with decreasing wavelength over the region where radiative heat transfer would be most important (i.e., o8 mm). Both constants exhibit asymptotic behavior, with the absorption coefficient, k, approaching zero for both temperatures shown at a value of B1670 cm1 (B6 mm) and the refractive index, n, approaching 2.02 and 1.86 at 298 and 1273 K, respectively, at B2500 cm1 (B4 mm).
V. Conclusions
Fig. 6. Optical constants, n and k, derived from the fit of the measured reflectance data using the sum model at temperatures of 295 and 1273 K.
The reflectance of fully dense, polycrystalline 7YSZ zirconia having a metastable tetragonal crystal structure has been measured and analyzed over the range of 6.67–25.0 mm and from room temperature up to 1673 K (14001C). The reflectance spectra of densified t0 YSZ are indistinguishable, within experimental limitations, from those reported for other crystallographic forms of zirconia, such as tetragonal and cubic zirconia. The wavelength of minimum reflectivity occurs at B833 cm1 (B12 mm) and has virtually no temperature dependence. The measured reflectance data as a function of temperature were curve fit by two damped oscillator models, in which the series sum model reproduced the reflectance data more accurately. The real and imaginary parts of the complex dielectric constant were modeled as a function of temperature, and the classical dispersion theory was utilized to calculate the index of refraction (n) and the absorption coefficient (k). Large changes in n and k were observed as a function of temperature below 833 cm1 (412 mm), whereas very small changes in n and k were found above 833 cm1 (o12 mm).
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Acknowledgments The authors are grateful to Dr. Ken Murphy of Howmet Research Corporation for providing the 7YSZ powders from his electron beam deposition system, and to Dr. Samuel Margueron for developing the curve-fitting programs as well as for invaluable discussions.
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NRC report, Coatings for High Temperature Structural Materials. Trends and Opportunities. National Academy of Sciences, Washington, DC, 1996. 2 S. M. Meier and D. K. Gupta, ‘‘Evolution of Thermal Barrier Coatings in Gas Turbine Applications,’’ Trans ASME, 116, 250–7 (1994). 3 D. R. Clarke and C. Levi, ‘‘Materials Design for the Next Generation Thermal Barrier Coatings,’’ Ann. Rev. Mater. Res., 33, 383–417 (2003). 4 R. Siegel and C. M. Spuckler, ‘‘Analysis of Thermal Radiation Effects on Temperatures in Turbine Engine Thermal Barrier Coatings,’’ Mater. Sci. Eng., A245 [2] 150–9 (1998). 5 C. Pecharroma´n, M. Ocan˜a, and C. J. Serna, ‘‘Optical Constants of Tetragonal and Cubic Zirconias in the Infrared,’’ J. Appl. Phys., 80 [6] 3479–83 (1996).
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