In situ synchrotron measurements of oxide growth strains Jonathan D. Almer1, Geoffrey A. Swift2, John A. Nychka3, Ersan
Üstündag2 ,and David R. Clarke3
1 Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439; [email protected]
2 Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125 3 Materials Department, University of California, Santa Barbara, CA 93106
Abstract
Synchrotron x-rays are used for in situ determination of oxide strain, during oxide formation on a Kanthal A1 FeCrAlZr substrate at 1160°C. The measurements rely on use of high-energy (~80keV) x-rays and transmission geometry, and the methodology of the strain measurements is presented. Oxide growth strains at elevated temperature, relative to pure alumina, were seen to be small, while temperature excursions induced significant strains. Furthermore, significant strain relaxation was observed during isothermal holds, suggesting oxide creep as a major relaxation mechanism. Upon cooling to room temperature, significant residual strains developed, with a corresponding in-plane residual stress of -3.7 GPa. 1. Introduction
FeCrAl alloys, such as the commercial Kanthal alloys, form a uniform, adherent scale of α-Al2O3 when oxidized [1], characterized by a flat alloy-oxide interface. This has made FeCrAl based alloys a model material for studying stress generation during oxidation. The formation of a thermally grown oxide is also important for thermal barrier coating (TBC) applications, in which zirconia coatings are applied to an alloy substrate, and a bond coat is used between the two materials. The oxidation of this bond coat is often the key to the lifetime of the TBC because the oxide grows in thickness as the bond coat oxidizes and the strains that develop due to this growth can cause failure of the TBC, especially through spalling on cooling. Understanding the oxide formation and the stresses generated consequently are crucial to determining the lifetime of such material systems.
In this investigation, high-energy synchrotron x-rays were used to study the oxidation of kanthal A1 in situ for several reasons. First, the high x-ray brilliance provides a high-flux density on the sample surface where oxidation occurs, yielding a high oxide diffraction signal. Second, the small diffraction angles associated with high x-ray energies, when coupled with large two-dimensional detectors, yields diffraction information from multiple grain orientations and hkl-planes in a single exposure, thus enabling kinetic studies of strain evolution. 2. Experimental Procedure
A 5.15-mm-diameter cylindrical substrate (Kanthal A-1, composition in wt%: Fe-22Cr-5.8Al-0.1Zr-<0.3Ti, height=4.7 mm) was polished on the top surface to 3 µm, in order to provide a flat surface for oxide growth. The sample was held in a 25-mm- diameter polycrystalline Al2O3 holder, into which a sample hole and protruding tab had been machined. A K-type thermocouple was positioned to touch the edge of the sample. The coordinate system used for the experiments is shown in Figure 1, with x1 transverse to the x-ray beam, x2 along the beam and x3 vertical. The polycrystalline alumina tab was aligned to be coincident with the midpoint of the sample along x2 and offset 6mm along x1. Since its position relative to the sample was constant and nothing other than thermal expansion would affect its lattice
Licensed to Ersan Üstündag ([email protected]) - California Institute of Technology - USAAll rights reserved. No part of the contents of this paper may be reproduced or transmitted in any form or by any means without thewritten permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 12.179.2.226-04/02/05,03:57:37)
parameter, it provided a reference signal for calibration of diffraction data from the sample.
X-ray measurements were carried out at sector 6 of the Advanced Photon Source, using an undulator and a mosaic Si monochromator to produce an 83 keV (λ=0.149 Å) x-ray beam. The incident beam was reduced by slits to 300 x 40 µm2 along x1-x3, respectively. The beam illuminated all the sample along the x2 direction. Diffraction images were captured using an area detector [2], placed at L(x2) = 970 mm from the center of the alumina sample holder. The holder was mounted on motorized stages, allowing three translational and two rotational degrees of freedom. The finely polished sample surface was aligned parallel to the x-ray beam (surface normal parallel to x3), and positioned along x3 to intersect the center of the 40 µm x-ray beam along the sample surface. The sample was also centered in x1 over the beam, so that the irradiated volume of the oxide, having thickness t, was 0.3 x 5.15 x t mm3. During heating, the sample was adjusted in x3 such that the beam remained centered on the sample surface. By translating along x1, the Al2O3 tab was brought into the beam for reference diffraction measurements.
Figure 1. Setup for transmission diffraction measurements showing (a) top view and (b) cross-sectional view at the midpoint of the sample, with x-ray beam positioned at the sample surface. All dimensions in mm unless otherwise noted (note dimensions are not to scale).
Two identical infrared heaters consisting of six bulbs apiece [3] were vertically centered on the sample. The heaters were canted to permit exit of (horizontally) diffracted x-rays over 4θ< 20º, corresponding to a minimum achievable d-spacing of dmin=0.85 Å. The sample was heated to 1160°C in air, at a rate of approximately 2.5ºC/min. This temperature was maintained for approximately 12 hours, so as to monitor oxide growth, and then the temperature was rapidly dropped in steps to 1060°C, 840°C, and then room temperature, with isothermal holds of one and five hours at the elevated temperatures, respectively (see Figure 3). The final oxide thickness is calculated to be 4 µm based on the time-temperature profile and reference [1]. Throughout the heating and cooling cycles, diffraction data were
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recorded from both the sample and reference tab, with typical exposure times of 30 sec and collection intervals of 2-5 min. 3. Analysis
3.1. Strain and stress analysis
The diffraction strain analysis method used here has been detailed for bulk systems [4] and applied to coatings [5], so it is only discussed briefly here. A new correction for differential absorption, important for near-surface measurements utilizing this technique, is presented in the next section.
The small 2θ angles associated with high-energy x-rays, coupled with area detectors, allows for probing of multiple sample directions and hkl-planes with a single detector exposure. The detector records the radius (r) and azimuth (η) of diffracted intensity, which are referenced to the direct beam center and calibrated through use of a standard (here the Al2O3 tab). The angle η is nearly identical to the angle ψ used in traditional sin2ψ strain analysis [5]. By using an on-edge transmission geometry (Fig. 1), all diffraction vectors which are oriented in a 2-d plane having principal axes along one in-plane direction (x1, η=[0,180 deg]) and (nearly) along the growth (x3,η=[90, 270 deg]) direction are recorded. Diffraction strain for a given grain orientation η is given by the relative shift in the measured radial position rη, or equivalently d-spacing (dη) from the unstrained value:
( )0
0
o
o
d
dd
r
)rr( −=
−=ε
ηη
η (1)
where r0 and d0 are the unstrained radial position and d-spacing, respectively, obtained from the measurements of the alumina tab. By fitting εη over the entire azimuth (and including the rη absorption correction given below), three strain components can be determined: (1) in-plane: ε11 ; (2) normal: ε33 and shear: ε13 . It is important to note that since diffraction occurs over the entire diameter of the sample along x2, the ε11 value is composed of both radial and tangential components in the sample coordinate system. Here we assume an equi-biaxial strain model, such that the in-plane directions (x1-x2) have the same value, and the normal stress σ33 is zero. These assumptions are typically used for thin film stress analysis [6]. Thus ε11 represents the average in-plane strain in the oxide. By excluding texture (which was negligible for the oxide, see Figure 3), the in-plane stress is related to measured strains εij via:
σ11= Ehkl(ε11- ε33)/(1+νhkl) (2) where E and v are the elastic modulus and Poisson ratio, respectively. For the Al2O3 (116) peak analysed here, these values were calculated, using single-crystal alumina elastic constants at room temperature and the Eshelby-Kroner method [7], to be E116=408 GPa and ν116=0.226. 3.2 Differential absorption correction
With the transmission geometry used here, the degree of absorption of the diffracted x-rays from the growing oxide varies as a function of azimuth. This
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differential absorption causes the effective position of the diffracted x-rays along the beam direction, x2, to vary versus η, which will in turn lead to a η-dependent radial peak shift. We calculate this effect with reference to Figure 2. The absorption-averaged position of diffracted x-rays at a given (2θ, η) position is given by:
∫ ∫=d d
ave dxxTdxxxTx0 0
22222,2 ),,2(/),,2( ηθηθ (3)
where T is the sample transmission and d is the sample diameter. Considering only absorption in the substrate (a good assumption since absorption from the thin oxide and air are negligible by comparison), the transmission for a diffracted x-ray arising from the oxide is given by T=1 for η<= π and:
T = 1- exp(-µl)= 1- exp(-µx2/cos2θ) (η> π) (4)
Where µ is the substrate linear absorption coefficient and l is the path length through the substrate. Using µ=2.1 mm-1 and 2θ=5 (for Al2O3 (116)), we calculate a shift of δx2=1 mm, which is appreciable and can be compared to the maximum possible value of d/2=2.58 mm. We corrected for this effect by modifying measured radii rη (η> π ) by:
rη’= rη-δz*tan(2θ) (η> π) (5) The resulting profile is shown in Figure 3(b). It is clear that the corrected data (open circles) are symmetrical over η=+-π, which was not the case without the applied correction (crosses).
Figure 2. X-rays diffracted from the oxide layer (shaded) are more attenuated going into the Kanthal FeCrAlZr substrate (η>π), due to its higher absorption coefficient. Since diffraction occurs over the entire sample diameter d, this causes the weighted diffraction position x2,ave to move upstream of the incident beam (closer to the detector). 4. Results and Discussion
Prior to heating, smooth BCC diffraction peaks were observed from the alloy, which were attributed to surface deformation from polishing. When heating above ~700ºC these alloy lines disappeared, and the rings became very spotty with diffuse streaks, as expected from the large-grained alloy substrate. Upon reaching 1160ºC, oxide rings identified as α-Al2O3 (corundum) appeared, and a typical pattern at this temperature is given in Figure 3. These rings are seen to be continuous, indicating
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small (nm-sized) domains [8], with constant intensity versus azimuth, indicating negligible texture.
Figure 3. (a) Diffraction image at 1160ºC, showing fine-grained α-Al2O3 Debye cones and spots, with diffuse streaks, from large-grained alloy substrate, with the position of the (116) reflection indicated. Note intensity variation about η=nπ. (b) Diffraction strain εη after cooling to room temperature. To account for differential absorption, an offset of δx2= 1 mm was applied to the raw data (crosses) for η>π, leading to a symmetrical strain profile about η = π., (open circles), with biaxial fit shown (line). Data error bars calculated from peak fitting statistics.
Figure 4 shows the biaxial strains (for clarity, only ∆ε=ε11- ε33 and ε13 are
plotted) derived from the Al2O3 (116) reflection as a function of time and temperature. It is clear that the strains are small at 1160ºC, both in the early stages of oxide formation and up to 12 hours later, with both components near the experimental error bars of ~500 µε. The shear component ε13 remained negligible for all subsequent thermal cycling. Upon cooling to 1060ºC, however, |∆ε| increased to -1200 µε, indicating compressive in-plane strain as expected from the lower CTE of the oxide (~8.6x10-6 ºC -1) compared to the substrate (~14.4x10-6 ºC -1) [1]. During an isothermal hold at this temperature |∆ε| relaxed to -800 µε after 1 hour, which is indicative of creep in the oxide. Such creep has been cited as a significant relaxation
r(x1)
η
r(x3)
Al2O3
(116)
(a)
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process in the formation of such an oxide scale on fecralloy [1]. Upon further cooling to 840ºC, |∆ε| again increased, to -4000 µε, with subsequent decrease to -3600 µε during an isothermal hold for 5 hours. The decrease in the rate of strain relaxation at lower temperature is further indication of thermally-activated creep.
Upon further cooling the strain incrementally increases in magnitude, reaching a final value of -11500 µε at room temperature. Using equation 2, this corresponds to an in-plane stress value of σ11= -3.7 GPa. Thus, a significant residual stress develops in the oxide, which primarily originates from thermal mismatch stress, rather than growth stress at elevated temperatures. It is clear that creep processes play a significant role in reducing stresses at elevated temperatures, even down to 820ºC. Further quantification of the microstructure and creep behavior are planned to investigate these processes in more detail [8].
-0.014
-0.012
-0.01
-0.008
-0.006
-0.004
-0.002
0
0.002
0 5 10 15 20
Time (hr)
Stra
in
0
200
400
600
800
1000
1200
Tem
pera
ture
(C
)e11-e33
e13
Temperature
Figure 4. Al2O3 (116) diffraction strain and sample temperature versus time for oxide grown on a Kanthal A1 substrate. Note the significant increase in ∆ε= ε11- ε33 upon cooling, with strain relaxation during isothermal holds at elevated temperatures. 5. Conclusions
Diffraction strains in an Al2O3 oxide growing on a thick Kanthal A1 alloy substrate have been measured in-situ using a high-energy synchrotron diffraction. Through use of a large 2D detector, this diffraction technique is capable of resolving the relevant strain directions (in-plane and out-of-plane) rapidly and without sample movement. A correction for data taken with this method, due to differential absorption of diffracted x-rays, is shown to increase data integrity. This correction should be applicable for any transmission strain measurements in the presence of interfaces with different electron densities (i.e. x-ray absorption coefficients).
α-Al2O3 (116) diffraction strains acquired at 1160°C were found to be small compared to pure alumina once the oxide is converted to alpha-alumina and subsequent growth (to ~ 4µm thickness) over 12 hours. Sudden cooling, however, induced large strains which partially relaxed due to creep at 1050°C and 840°C. Cooling to room temperature induced large strains in the oxide layer, with a resulting in-plane stress of -3.7 GPa, pointing to thermal mismatch as the primary stress generation mechanism. These results illustrate the promise of this technique to study
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the interplay between strain/stress generation and relaxation in situ during formation and growth of oxides, as well as in other gradient systems. Acknowledgments The authors would like to thank the personnel of Sector 6, MU-CAT, APS, for their assistance with setup and data acquisition. The work at Caltech was supported by NASA Glenn Research Center (grant no. NAG3-2686). Use of the APS was supported by the U.S Department of Energy, Office of Science, Office of Basic Energy Science, under contract number W-31-109-Eng38. References 1. Tolpygo, V.K. and D.R. Clarke, Determination of the growth stress and strain
in a-Al2O3 scales during the oxidation of Fe-22Cr-4.8Al0.3Y alloy. Acta Materialia, 1998. 46(3): p. 927-937.
2. Mar345 on-line image plate detector, see www.mar-usa.com. 3. Control IR furnace model 5075, see www.researchinc.com. 4. Wanner, A. and D. Dunand, Synchrotron x-ray study of bulk lattice strains in
externally loaded Cu-Mo composites. Metallurgical and Materials Transactions A, 2000. 31A: p. 2949-2962.
5. Almer, J., U. Lienert, R.L. Peng, C. Schlauer, and M. Oden, Strain and texture
analysis of coatings using high-energy X-rays. Journal of Applied Physics, 2003. 94(1): p. 697-702.
6. Leoni, M., U. Welzel, P. Lampater, E.J. Mittemeijer, and J.-D. Kamminga, Diffraction analysis of internal strain-stress fields in textured, transversely
isotropic thin films: theoretical basis and simulation. Philosophical Magazine A, 2001. 81(3): p. 597-623.
7. Gnaupel-Herold, T., Hauk.exe, available from author upon request. 8. Almer, J., E. Ustundag, G.A. Swift, J.A. Nycha, C.C. Aydiner, and D.R.
