LASER ULTRASONIC INSPECTION OF COMPOSITIONALLY
GRADED MULLITE COATINGS
T. W. Murray1, O. Balogun1, V.K. Sarin2, and S.N. Basu2
Department of Aerospace and Mechanical Engineering
Boston University, Boston MA 02215
Department of Manufacturing Engineering
Boston University, Boston MA 02215
ABSTRACT. The mechanical properties of mullite (3A12O3 2SiO2) environmental barrier coatings
are determined using a laser-based ultrasonic system. It is shown that the laser source generates the
two lowest order SAW modes in these systems. Experimental waveforms are generated using a
600ps pulsed Nd:YAG microchip laser and detected using a stabilized Michelson interferometer.
The dispersion curves for the generated modes are extracted from the experimental data and the
mechanical properties of the coatings are obtained by minimizing the error between the measured
and calculated velocity values. In addition, laser ultrasonic characterization of compositionally
graded coatings is discussed and preliminary results presented showing the effect of a linear
composition profile on the dispersion behavior.
INTRODUCTION
Mullite (3A12O3 2SiC>2) is an important engineering ceramic exhibiting excellent hightemperature strength, low thermal expansion, and good chemical stability. Mullite is a
candidate material for corrosion resistant coatings on silicon based ceramics (SiC and
SisN4) that are susceptible to hot-corrosion when used in hostile environments [1]. There is
some concern, however, that the silica content within mullite may itself be susceptible to
hot-corrosion during long term exposure to hostile environments. A solution to this
problem is to functionally grade the coatings such that the silica content within the mullite
is gradually decreased from stoichiometric mullite at the interface to essentially silica-free
mullite at the surface. It is expected that such functionally graded coatings will maintain
strong bonding characteristics to silicon based ceramics while showing improved corrosion
resistance over those grown with pure mullite.
Laser based ultrasonic (LBU) techniques for the generation and detection of acoustic
waves have been used for a variety of nondestructive evaluation and materials
characterization applications [2-4] and they have been shown to be particularly well suited
for the inspection of thin films and coatings [5-9]. Our current research effort is focused on
determining the properties of stoichiometric mullite coatings, evaluating the effects of
composition gradation within the coatings, and using LBU to detect disbonding at the
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/$20.00
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coating-substrate interface. The first two topics are briefly addressed in this paper. A
discussion of SAW propagation in graded materials is presented first. It is shown that
introduction of a composition gradation in the coating produces a small change in the
dispersion characteristics, and that it should be possible to obtain information about the
composition or elastic property gradation using laser generated surface acoustic waves.
Next, a laser ultrasonic microscopy system has been used to measure the dispersion
characteristics of surface acoustic waves propagating in stoichiometric mullite coatings on
silicon carbide substrates over a bandwidth of approximately 200 MHz. Multiple surface
acoustic wave modes are generated by a laser source in 11.2 jLim coatings. Using the 2-D
FFT technique [10], the SAW modes, which are overlapping in the time domain, can be
separated and the density, elastic modulus, and Poisson's ratio determined.
THEORY
Consider the case of SAWs propagating on a single or multilayer homogeneous,
isotropic film on a semi-infinite halfspace. SAWs are confined to propagate in the near
surface region and are thus very sensitive to the properties of surface coatings. Unlike
SAWs which propagate on a half-space, SAWs which propagate on a coating/substrate
system are dispersive. The penetration depth of SAWs depends on their wavelength
allowing us to probe the elastic properties as a function of depth. High frequency (short
wavelength) SAWs interact primarily with the near surface region while low frequency
(long wavelength) SAWs penetrate further into the material as illustrated in Figure 1 a. The
SAW velocity depends on the elastic moduli, Poisson's ratios, densities, and thicknesses of
each of the coating layers and the substrate. The dispersion relation can be written
explicitly by solving the equations of motion subject to the appropriate boundary
conditions at the coating surface and coating/substrate interface. The zeros of the
characteristic determinant of this system of equations give the relationship between f and
X [11]. Measurement of the dispersion of SAWs over a wide frequency bandwidth makes it
possible to extract the elastic properties, density, and thickness of single and multilayer
films.
In a compositionally graded coating, the distinctive feature is a variation of the material
properties through the thickness of the coating, and it can be treated as a large number of
layers of varying material properties. It will be assumed that there is a gradual, continuous
gradient in the mechanical properties such that the elastic modulus can be written in the
form of a smooth function. For example, a linear gradient, shown schematically in Fig.lb,
Graded
Coating
D
AVE
Substrate
FIGURE 1. a) Surface acoustic waves propagating on a coating/ substrate system and b) compositionally
graded coating with the elastic modulus increasing linearly from the coating-substrate interface to the
surface.
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can be expressed as:
ES-EO
z,
0)
where E0 is the Young's modulus at the coating-substrate interface, Es is the elastic
modulus at the coating surface, z is the distance from the interface towards the coating
surface, and t is the thickness. In order to calculate the SAW dispersion behavior in a
graded coating, the film is divided into N layers, N is a value chosen such that convergence
of the model to a stable value of velocity (to the desired accuracy) of the SAW mode in the
gradient region is achieved. For large values of N the dispersion curves are found using the
transfer matrix technique [12].
An example of the dispersion characteristics in a coating-substrate system with a linear
variation in elastic modulus in the coating is given in Figure 2. The coating is 20|o,m thick
with the elastic modulus equal to the nominal value for stoichiometric mullite in the center
of the coating (Eave in Figure Ib), increasing linearly from the center of the coating to the
surface by 10%, and decreasing linearly 10% from the center to the coating/substrate
interface. The substrate is silicon carbide. Dispersion curves are given for the first and
second SAW modes in Figure 2a and 2b, respectively. In each plot, dispersion curves are
given for films divided into 1, 2, and 8 layers with 1 layer representing a homogeneous film
with elastic modulus Eave. The 2 and 8 layer coatings have linear elastic modulus variations
but maintain the same average modulus as the single layer case. The first mode shows
maximum velocity differences between the graded coating (8 layers) and the homogeneous
coating (single layer) of about 1% in the first mode and 4% in the second mode. The
frequency range is chosen to match the range that we have achieved experimentally in
homogeneous mullite coatings. These initial results suggest that it may be possible to
experimentally measure elastic property gradations within coatings using SAWs, especially
in cases where the functional form of the gradation is known. Future work in this area will
focus on developing the inverse problem for determining composition or property variation
as a function of depth in FGMs.
b)
a)5.50
1st mode
8.0-
5.45-
I
5.405.35.2 5.30S
5.255.20
140
"0 7.6
7.4
160
180
200
220
240
260
280
140
160
180
200
Frequency (MHz)
Frequency (MHz)
FIGURE 2. Dispersion curves for a compositionally graded mullite coating on a SiC substrate showing the
result of splitting the coating into 1,2,and 8 layers with the average E remaining constant for a) the first SAW
mode and b) the second SAW mode.
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EXPERIMENTAL SETUP
The mullite coatings were tested using the laser acoustic microscopy system illustrated
in Figure 3. The system has three optical paths that lead to the sample surface through the
same long working distance objective (Numerical Aperture = 0.4). The first path leads to a
CCD camera and allows for optical imaging of the sample surface as well as sample
alignment. In the second path, the detection laser light enters the microscope from a single
mode optical fiber, is collimated, and directed to a beamsplitter where it is divided into
reference and signal beams. The reference beam reflects off of a mirror mounted on an
actuator (used for stabilization) and is sent to a photodiode with a 1 GHz bandwidth. The
signal beam is sent to the specimen surface and, upon reflection, returns back to the
beamsplitter and interferes with the reference beam at the photodetector. The detection
system thus forms a standard Michelson interferometer. Additionally, polarization optics
(not shown in the figure) are used to control the amount of light sent into the reference and
signal beams. The detection laser is a 200mW frequency doubled Nd:YAG (A,=532nm).
The generation laser is collimated, directed to a mirror on a gimbal mount, sent though
a relay lens system, and on to the specimen. The gimbal mount allows for precise control of
the generation point within the field of view (1.25 mm) of the microscope and allows the
C1M
BCM
FIGURE 3. Laser acoustic microscopy setup for coating inspection. Figure is labeled as follows: CGB
(collimated generation beam), GM (gimbal mount), DCM (dichroic mirror), BS (beamsplitter), RM
(reference mirror), SMF (single mode fiber), CL (collimating lens), DL (detection laser), PD
(photodetector), RBS (removable beamsplitter), IFL (image forming lens), LWDO (long working
distance objective).
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source-to-receiver distance to be controlled by adjusting the angle at which the beam enters
the objective. The source-to-receiver distance can be controlled with greater than 500nm
resolution. The generation laser is a 600 ps. Nd:YAG microchip laser with a pulse energy
of lOjjJ which is used at the fundamental frequency (1064nm). The generation laser energy
was attenuated to below 1 juJ to avoid damage to the coating surface. To determine the
ablation threshold, the specimen surface was observed under the optical microscope as the
generation laser was increased. The ablation threshold was taken as the point where a slight
discoloration of the sample surface was observed.
The laser ultrasonic system is well suited for the local inspection of materials
properties. The source and receiver probe the sample through a single microscope objective
and experiments are typically performed with a maximum source-to-receiver distance of
500-600jim. The use of a diffraction limited detection beam (spot size ~ 665 nm) allows us
to work on specimens which are unpolished and optically rough but have localized
optically flat regions where high modulation depth can be obtained using standard
Michelson interferometer. The precision of our velocity measurements is ultimately limited
by the resolution of the source-to-receiver measurement (less than 500nm) and the sample
rate of the digitizer (4Gs/s).
EXPERIMENTAL RESULTS
Figure 5 shows representative waveforms detected in an 11.2jnm mullite film at several
propagation distances. The waveforms were averaged 1000 times to improve the signal-tonoise ratio. Multiple modes are observed experimentally and these modes are overlapping
in time for the source to receiver distances shown. The mechanical properties of the
coatings are found by first using the experimental data to determine the dispersion curves
and subsequently minimizing the mean squared error between the experimental and
theoretical dispersion curves using the simplex optimization routine [13]. Using relatively
small source to receiver distances allows for high signal-to-noise ratio
330 urn
50
100
150
time (ns)
FIGURE 4. a) Surface acoustic waves detected at several source to receiver distances in a mullite coating
on a SiC substrate.
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measurements over a broad frequency bandwidth and minimizes the effects of high
frequency signal loss due to scattering and attenuation, but at the propagation distances
shown in Figure 4 the generated modes are not clearly separated in time and thus the
dispersion curves can not be obtained by measuring the displacement at two distances and
using a simple phase unwrapping scheme.
The dispersion curves are found using the 2D FFT technique [10]. A set of 81
waveforms is collected at evenly spaced source-to-receiver intervals of 6jo,m. A 2D FFT
(with respect to space and time) is then taken of the waveforms resulting in the plot shown
in Figure 5a. The waveforms are now in the spatial and temporal frequency domain. The
peaks (bright regions) in the 2D FFT correspond to SAW modes and the two modes are
clearly separated over a large frequency band. While the first mode has significantly higher
amplitude than the second mode, the second mode is still clearly visible below the first
mode in the figure. A vertical slice of Figure 5a at 120 MHz is shown in figure 5b and two
peaks in spatial frequency are clearly observed with the larger peak corresponding to the
first mode and the smaller to the second. The dispersion curve for each of the modes was
found by searching for the peaks in the 2D FFT.
The dotted lines in Figure 6 a,b show the measured dispersion curve for the first two
modes found using this technique. The noise on the second mode is due to the small
amplitude of this mode and poorer signal-to-noise ratio (SNR) with respect to the first
mode. The useful frequency range of the first mode, where the highest SNR is obtained, is
from 80-230 MHz. The simplex search algorithm was used to determine the mechanical
properties of the coatings by minimizing the mean squared error between the measured and
calculated dispersion curves. Only the first mode was used for the optimization routine due
to the low SNR of the second mode. The optimization routine was used to determine the
elastic modulus, Poisson's ratio, and density of the coating. The results from three
independent experiments over separate regions of an 11.2|Lim thick mullite coating on SiC
are given in Table 1. The theoretical dispersion curves agree very well with the
experimental curves and are over-plotted in Figure 6a,b (solid lines). The experiments from
b)
Wave Spectra at 120Mhz
CD
OH
2-
120
40
60
80
100
120
140
160
180
0
Frequency (Mhz)
10
20
30
40
50
60
70
Spatial Frequency ( 1/MM)
FIGURE 5. a) 2D FFT of 81 waveforms collected at 6|um intervals and b) a vertical slice through the 2DFFT at 120 MHz showing two peaks corresponding to two SAW modes.
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a)
6.6 y
b)
6.4• «i
6.26.05.8-
E,
5.6-
•5
5.45.25.04.8-80
100
120
140
160
180
200
220
120
Frequency (MHz)
140
160
Frequency (MHz)
FIGURE 6. Experimental (dotted lines) and theoretical dispersion curves showing a) the first SAW mode
and b) the second SAW mode.
different regions of the sample give consistent results. The simplex algorithm converged to
the same solution with various initial guesses indicating that it had reached a global minima
and that three properties can be reliably obtained for these coatings.
CONCLUSIONS
A laser based ultrasonic system has been used to determine the mechanical properties
of ceramic coatings. The experimental waveforms show the lowest order SAW mode as
well as one higher order mode. The acoustic microscopy system presented allows for the
determination of materials properties over length scales on the order of 500|um. The 2D
FFT technique is used to separate the modes in the spatial frequency- temporal frequency
domain and to map out the dispersion curves of each of the modes. The mechanical
properties of the coating (density, elastic modulus, Poisson's ratio) are subsequently found
by minimizing the mean squared error between the measured and calculated dispersion
curves.
Dispersion curves are also presented for functionally graded coatings which exhibit a
variation in elastic modulus in the through thickness direction. Initial theoretical results
indicate that LBU is a promising technique for the noncontact, nondestructive
characterization of functionally graded materials. Future experimental and theoretical work
will explore laser ultrasonic characterization of FGMs in detail. This technique may also
provide an effective means of monitoring mullite coating degradation during thermal
TABLE 1. Mechanical properties of mullite coating obtained using simplex optimization routine on three
different regions of sample.
data set
p (kg/m3)
E(GPa)
1
188.9
.22
3022
2
190.6
.21
3043
3
188.32
.22
3086
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cycling. It is well known that the elastic modulus is influenced by micro-structural
parameters such as micro-crack density, porosity, bonding condition within the material,
and stoichiometry. Changes in Young's modulus after thermal cycling can be monitored
using laser based ultrasound. Finally, the high spatial resolution of laser-based systems can
be exploited in the future to scan coating materials for crack formation prior to spallation
and failure.
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