Abstract

An integrated system with a 2 GHz digitizer of 500 MHz analog bandwidth is used to ultrasonically monitor thickness and acoustic velocity with real-time temporal resolution of 0.5 nanoseconds. It is shown that with additional digital signal processing the standard deviation in time-of-flight measurements can be made less than 100 picoseconds, and that sub-micron thickness variations can be monitored. In the case of measuring thickness, the typical constant velocity assumptions necessarily made in the presence of local velocity variations and practical limitations on calibration are discussed. Practical application examples are described for evaluating glass, ceramics, and semiconductor wafers over the range of 20 MHz to 180 MHz. Key ultrasonic considerations that have been shown to impact thickness and acoustic velocity measurements are addressed. Implementation of point and user defined grid measurement modes support both laboratory and production inspection requirements for the integrated system.

Introduction

Research and development efforts on higher frequency ultrasonic thickness and acoustic velocity measurement methods are meeting the requirements for characterization of advanced materials and components. Ultrasonic thickness gages are in common usage for evaluation of material thickness, and typically employ frequencies below 20 MHz (1,2). Herein, complementary methods are described employing broadband ultrasonic transducers with center frequencies up to 180 MHz for practical thickness and material velocity characterization. With the availability of high sampling frequency digitizers and inexpensive robust processors, digital techniques are now replacing primarily analog methods of velocity measurement (3,4) with capabilities as low as 5 ppm.

Applications of monitoring the acoustic velocity of special glasses, high performance ceramics, and sintered metal matrix composites are common. The inhomogeneity of the materials or components is of interest due to non-uniform distribution of doping agents or constituent additives, or other processes that cause anisotropy. Acoustic velocity is also indicative of mechanical behavior of the material via relationships involving elastic properties and their derivatives such as fracture toughness, thermal coefficient of expansion, etc. Elastic properties can be calculated from measured acoustic velocity data (5-7), and references to the use of these properties in NDE (nondestructive evaluation) and materials evaluation are provided in the literature (8,9).

An integrated system with a 2 GHz digitizer of 500 MHz analog bandwidth with real-time temporal resolution of 0.5 nanoseconds is used to monitor acoustic velocity and thickness. Although Fourier domain or resonance methods can be employed with the apparatus described, the basis for thickness measurements discussed herein are time-of-flight measurements of reflected echoes. The echoes monitored can be from the front and back surface of the component or from intermediate layers within the sample under test. Essentially, the time-of-flight between echo peaks within selected gates (time windows) is measured.

In the simplest form of the measurement, the ability to precisely locate the peaks is dependent on the intersample interval of the digitizer, which is the reciprocal of the sampling frequency. The nature of the ultrasonic measurement is that the sound must travel in a “round trip” through the specimen or intermediate layer, yielding an improvement in thickness resolution, as illustrated in Figure 1. A typical material velocity of 6 mm/µs (or 6 µm/ns) is employed in the example.

Fig 1: Simplified Illustration of Temporal and Thickness Resolution.

From the figure, it could be concluded that increasing the sampling frequency would yield an improvement in the time-of-flight and thickness resolution; however, the influence of other phenomena such as noise modulating the peaks, random signal fluctuations, phase distortion, local material velocity variations, and calibration of velocity imposes limitations.

As discussed, advanced materials require measurement of variations less than the 0.5 ns (or 500 picoseconds) threshold. It will be demonstrated that digital signal processing can yield standard deviation in time-of-flight measurements of less than 100 picoseconds. It is this precision along with care in periodically monitoring reference standards that affords the relative measurement of subtle variation in material velocity.

Ultrasonic Time-of-Flight Measurements

A 2 GHz digitizer was employed with a Panametrics Model 5800PR pulser-receiver to first monitor the time-of-flight between the surfaces of glass and ceramic materials under test that were nominally 12.7 mm (0.5 in) in cross-sectional thickness. A 20 MHz non-focused broadband transducer was employed in immersion. In immersion, the sample is placed in a bath below the transducer and water serves as a couplant. Alternatively, a transducer mounted in a water column can be employed in the case of large samples under test. It was observed that much higher frequency transducers could be employed for the thinner samples of the materials under test; however, significant frequency down shifting and phase distortion were apparent in the echoes of interest. Additionally, the technique was ultimately to be employed in production on samples as thick as 200 mm where the higher frequency transducer would not be effective.

Experience has shown that repeatability of results is improved when the echoes have ideally the same shape or are phase reversed, but necessarily different in amplitude. This is the principal objective of optimizing the analog ultrasonic settings. The energy in the excitation was minimized to a 12.5 µJ setting and damping adjusted to 50 Ohms. The water path was set to less than the natural focal length of the transducers at about a 22.5 µs round trip time. Analog filter settings of the pulser-receiver were left fairly broadband with a low-pass filter of 35 MHz and a high pass filter of 1 MHz. Normalization of the transducer and adjustment of the parameters mentioned influenced the wave shape of the echoes. Of the variables that could change from measurement to measurement, the water path was forgiving due to the non-focused transducer, and the normalization did not vary because the surfaces of the samples were reasonably parallel. Figure 2 shows an image of the real-time scope display.

Fig 2: Scope Display of Ultrasonic Signals.

From left to right in Figure 2, the first echo is the front surface of the specimen, the second is the first back echo, and the third is the second back echo. There is an expected phase reversal between the front surface and first back echo due to high to low acoustic impedance mismatch at the backwall (7). Successive backwall echoes are in phase.

Care must be taken to determine the appropriate phase. Gates can be readily set for the polarity of choice in the digital system employed. It should also be noted that for practical purposes, the number of gates employed is unlimited (32 gates), but often as many as four are used for multi-layer and multi-mode measurements. The measurement of the peak within a gate can also be referenced to any other gate. The most precise measurements have been observed employing thickness gates sensitive to the peak of the signal; however, cross trigger gates can be used in cases where an echo is saturated.

In the present example, the relative measurement of interest could employ either of the echo pairs discussed, and results showed insignificant difference in the standard deviation of the measurements. There was a marginal difference in the absolute time-of-flight. Successive backwall echoes had very much the same wave shape. The first back echo would ideally be a phase-reversed image of the front surface echo. Distortion (ringing) noted in the front echo was minimized with pulser energy reduction and damping adjustment to nominally match the transducer and cable impedance.

It is difficult to draw generalities with regard to transducer selection. The samples evaluated throughout had flat and parallel surfaces. The lower frequency transducer was selected because less frequency downshift (diffraction, frequency dispersion) occurred traversing the specimen. The non-focused element reduced refraction at the front surface, which would otherwise lead to distortion of the waveforms. The beam diameter was necessarily larger, and this could present a problem for thickness measurement of curved surfaces due to refraction and elongated paths to the backwall. The higher frequency transducers discussed later are not always readily available with non-focused elements. The focused elements increase sensitivity to small defects in flaw detection, and focusing allows shorter water paths and higher frequency response, which may be required to achieve echo separation in thickness measurements. More distortion of the waveforms results from refraction, especially in high velocity materials.

For thick or attenuative samples, obtaining multiple back echoes where the leading echo is unsaturated is sometimes more practical than keeping the front echo unsaturated while having enough signal height in the first back echo. Additionally, the phase distortion or downshift in frequency between multiple back echoes is often less, because the high frequency components are preferentially attenuated in the first pass through the sample under test. Of course, where attenuation is extreme or distortion occurs in the waveforms, the measurements must be made from the front surface echo to the first back echo. For brevity in the analysis here, the time-of-flight between the successive back echoes is discussed.

The measurement of successive back echoes was selected for the data presented in the parametric study in Table 1. The standard deviation and total time variation (maximum – minimum) were monitored for 100 measurements for each condition to be described, and these data are displayed in picoseconds.

Sampling Frequency	Digital Low Pass Filter	Advanced Digital Processing	Waveform Averaging	Standard Deviation (picoseconds)	Total Time Variation (picoseconds)
2 GHz	-	-	-	736	3000
2 GHz	Active	-	-	126	250
2 GHz	Active	Active	-	60	236
2 GHz	Active	Active	Active	27	103
500 MHz	-	-	-	885	4000
500 MHz	Active	-	-	504	1000
500 MHz	Active	Active	-	169	745
500 MHz	Active	Active	Active	125	350
Table 1: Parametric Study

Standard deviation was first observed without any digital signal processing, and it was found to be approximately the temporal resolution of the 2 GHz digitizer (500 picoseconds). A low pass digital filter was introduced. The filter was set with a cut off frequency such that the nominal peak amplitudes of the echoes were not reduced, and no phase distortion was introduced. A 20 MHz setting did not reduce the amplitude of the echoes because the high frequency components of the broadband signal had been preferentially attenuated in the water path and initial traverse of the sample. The digital low pass filter reduced noise that could be readily seen in the baseline signal, and also in the random fluctuation of echo peaks. A large reduction in the standard deviation was noted.

Advanced processing was next implemented in the measurement system to further reduce the standard deviation. The actual digital processing algorithms are necessarily proprietary, but it can be readily appreciated that the high density of points obtained with a 2 GHz sampling rate of a 20 MHz bandwidth limited signal would lend itself to further processing. Standard deviation in measurements was minimized using the greatest height in the signals processed. In some applications, the DC offset voltage of the digitizer is adjusted to allow more full screen amplitude in the echoes of interest with increased gain. This again suggests employing echoes that are in phase where possible. Advanced digital processing yielded a measurement standard deviation of less than 100 picoseconds.

Waveform averaging was employed as a part of the study to further reduce the standard deviation. Results shown are for averaging 20 waveforms prior to digital filtering and advanced processing. The reduction in standard deviation is accomplished with lag introduced in measurement update rates. The digital filter and advanced processing function in near-real time. Waveform averaging can also lead to peak broadening if successive signals are not coherent beyond the significance of the picosecond measurements. Because digital filtering and advanced processing satisfy present requirements and waveform averaging raises some concerns, the remaining discussion does not employ the averaging utility. The digital signal processing functions are readily activated in the graphical user interface depending on the application requirements.

The measurements were repeated with a lower sampling rate digitizer, as displayed in Table 1. These digitizers are more economical. Additionally, it was originally expected that due to the bandwidth limit of the ultrasonic signal, the 500 MHz digitizer would minimize the standard deviation of the measurement. With the degraded temporal resolution and the reduced density of points available for digital filtering and processing, the standard deviation in the measurement increased. There are many applications that would be satisfied with the lower sampling rate digitizer.

For completeness with regard to time-of-flight measurements, a 200 mm thick sample of the same material used in the study was monitored using the 2 GHz digitizer with digital filtering and advanced processing active. The measurement between successive backwall echoes was still possible even with the greatly increased attenuation. The standard deviation in the measurement of successive backwall echoes was again monitored for 100 measurements yielding 100 picoseconds and a total time variation of 400 picoseconds.

Taking the now conservative estimate of the standard deviation of 100 picoseconds, for a significant number of measurements, a time variation of 100 picoseconds should be discriminated. With reference to Figure 1, this corresponds to a 50 picosecond one-way time-of-flight. This standard deviation has been monitored for glass and ceramic samples of nominally 12.7 mm. Interestingly, acoustic velocity does not vary over a wide range. Polymers are typically about 2 mm/µs, metals and glass about 6 mm/µs, and ceramics about 7 mm/µs-12 mm/µs. Employing the nominal mid range, a glass or metal sample of 12.7 mm would have a one-way time-of-flight of about 2.1 µs. A 50 picosecond one-way time-of-flight difference discriminated in a 2.1 µs total time-of-flight would yield about a 20 ppm measurement. Discriminating a 50 picosecond (or 0.05 ns) thickness of material in the range of 6 mm/µs (or 6 µm/ns) would yield a 0.3 µm measurement. Actual measurement of thickness to this precision in samples where the velocity is locally varying and calibration is limited to mechanical means is difficult.

The most straightforward measurements appear to be relative time-of-flight observations that with carefully measured thickness can be related to acoustic velocity variations. Reference standards of similar thickness and nominally the same acoustic properties are employed. The data provided are at constant temperature (about room temperature) but constant temperature baths are sometimes necessary even for relative velocity monitoring. Actual measurements are somewhat operator dependent and clearly material or component specific; consequently, measurement capability studies must be the user’s responsibility.

Illustrative Examples of Ultrasonic Thickness Measurements

High precision and very high frequency capabilities are now applied to ultrasonic thickness measurement of a variety of materials and components.

Glass Thickness Measurements
A non-proprietary glass step wedge sample with three nominal thickness cross-sections was prepared. Calibration was performed using the graphical user interface. In this user interface, known mechanical thickness values are entered and corresponding time-of-flight measurements are made in the same locations on the sample. In this simple example, only a three-step calibration was performed, although any number of steps can be used. The velocity is determined from a linear regression of the points. A zero offset is also determined, and the user is given the option of employing the offset. Experience with immersion indicates minimal zero offset is typically calculated. Again, these measurements are based on either the time-of-flight between first surface echo and first back surface echo (referred to as a Mode 2 measurement) or subsequent back echoes (referred to as a Mode 3 measurement). For contact transducers, where measurements are take from the “main bang” or transducer excitation to the first back surface echo (referred to as a Mode 1 measurement), the offset accounts for delays due to coupling capacitance in the probe, cables, and couplant.

The same configuration, ultrasonic settings, and digital signal processing described above were employed in measuring the step wedge. The expectations for the results were not great (relative to the potential of 0.3 µm discussed) given that the mechanical measurements were performed with a micrometer with a 1 µm readout resolution and there was a known velocity gradient in the sample. It was also known that steps of great change in thickness would contribute to measurement errors due to the change in the ultrasonic signal propagation. Nonetheless, these variations were typical of real world measurement situations, and the data were illustrative. The averages of three mechanical and three ultrasonic thickness measurements for each step are provided in Table 2. The ultrasonic thickness measurements were obtained with separate calibrations for Mode 2 and Mode 3, and these data were acquired simultaneously with multiple gates. The data in Table 2 indicate an agreement of 5 µm (0.0002 in).

Mechanical (mm)	Mode 2 Ultrasonic (mm)	Mode 3 Ultrasonic (mm)
19.058	19.05311	19.05403
22.226	22.22864	22.22844
25.382	25.38491	25.38392
Table 2: Comparison of Thickness Measurements of a Glass Step Wedge.

Only a baseline capability is implied by the data shown since the velocity is assumed to be relatively constant about the material measurement range and the calibration is using the same thickness steps to be measured. Material and acoustic factors typically limit even relative thickness measurement capabilities. Blessing et al. analyzed the material and sensor factors in a successful effort to achieve ±2.5 µm (±0.0001 in) thickness measurements in stainless steel components, showing material factors (grain size) affecting velocity were dominant. In cases where lesser precision is needed, a two step calibration is typical, where points of minimum thickness and maximum thickness are employed for a constant velocity determination.

Aluminum Oxide Ceramic Thickness Measurement
An aluminium oxide ceramic block with varying cross-sectional thickness was employed for a comparison of mechanical and ultrasonic thickness measurements. Ten points were measured about the block. The rough ground block was about 100 mm x 300 mm and nominally 12.7 mm (0.500 in) thick. The same ultrasonic and digital signal processing conditions previously described with the 20 MHz transducer were employed. Exceptions to the previous ultrasonic conditions are exhibited with the aid of Figure 3.

Fig 3: Scope Display of Ultrasonic Signals of Ceramic Specimen.

As shown in Figure 3, due to the more highly attenuating nature of the alumina block, the first echo from the front surface of the specimen is saturated when the first back echo and second back echo are adjusted to reasonable signal heights. Only a Mode 3 measurement is employed, and the echoes used are quite similar in shape. Calibration of the velocity yielded a value of 10.574 mm/µs. Note that the calibration was performed using ten ultrasonic and mechanical measurements taken at various locations on the sample. Data reported in Table 3 were taken as a later series of ultrasonic measurements obtained at approximately the same locations as the calibration data, which was necessitated by the limited number of available samples.

Again, the mechanical measurements were performed with a micrometer with a 1 µm readout resolution and there was a velocity gradient (probably due to a density gradient) observed about the long isopressed and sintered alumina sample. The sample was also only rough ground. The averages of three mechanical measurements and a single ultrasonic thickness measurement are provided in Table 3. The data in Table 3 again indicated an agreement of 5 µm (0.0002 in).

Mechanical Thickness (mm)	Mode 3 Ultrasonic Thickness (mm)
12.675	12.678
12.679	12.682
12.680	12.681
12.681	12.676
12.681	12.684
12.682	12.677
12.691	12.689
12.692	12.687
12.698	12.699
12.698	12.696
Table 3: Alumina Block Thickness Measurement.

In many applications, the measurement capability indicated would be adequate. More demanding thickness gage applications at higher frequencies are now addressed.

High-Frequency Ultrasonic Thickness Measurement of Semiconductor Wafers
Two examples comparing ultrasonic and micrometer measurements of germanium wafers will be described in brief, and then an example of measurement of silicon wafers in comparison to a more exact capacitance thickness gage will be detailed.

Germanium Wafer with Comparison to Micrometer Measurements
In one application example, nominally 180 µm germanium wafers were evaluated with a broadband 180 MHz ultrasonic transducer in a similar ultrasonic configuration as previously described. A Panametrics Model 5910PR pulser-receiver with 400 MHz RF bandwidth was used. The higher frequency was needed to enable separation of the front surface and first back echoes or multiple back echoes in the very thin component. Both Mode 2 and Mode 3 measurements were employed. A mechanical micrometer was again used for comparison, and agreement in the ultrasonic and mechanical thickness readings of approximately 1.5 µm were observed without employing digital signal processing. As for the previous samples, the calibration data and the subsequent series of ultrasonic measurements were recorded at approximately the same physical locations. The calibrated velocity for the material was approximately 5.06 mm/µs, and referring to Figure 1, the 1.5 µm level would be about the thickness resolution limit imposed by the digitizer.

In a more recent evaluation of the germanium wafer, digital filtering and advanced processing were employed, and again a comparison to a mechanical micrometer measurement was conducted. A 110 MHz transducer with an 8 mm focal length in water was employed because there was adequate separation of the echoes, and less down shift and phase distortion in the echoes were noted compared to the 180 MHz transducer. A Panametrics Model 5900PR pulser-receiver with 200 MHz RF bandwidth was used.

The mean values of mechanical and ultrasonic thickness measurements for each of ten points about the wafer are provided in Table 4. The ultrasonic thickness measurements were obtained with separate calibrations for Mode 2 and Mode 3, and these multi-mode data were acquired simultaneously using multiple gates. The data in Table 4 indicate an agreement of about 1 µm (0.000039 in), which is at the limit of the mechanical measurement precision.

Mechanical Thickness (µm)	Ultrasonic Mode 2 (µm)	Ultrasonic Mode 3 (µm)
178	178	179
179	178	178
180	180	180
182	183	183
182	181	181
183	183	183
183	183	183
184	183	183
185	185	184
186	186	186
Table 4: Comparison of Measurements of a Germanium Wafer.

Silicon Wafer with Comparison to Capacitive Thickness Gage Measurements
Silicon wafers are typically measured employing non-contact capacitive thickness gages. Common devices have somewhat limited resolution specifications. Typically, the wafers must be removed from polishing equipment and dried prior to measurement. Drying the wafer can cause water spots. Also, the resistivity of the wafer affects the measurement with greater difficulty in obtaining precise measurements with increased resistivity. The introduction of new oxide layers in the silicon-on-insulator processes under development in wafer fabrication can adversely impact the measurement capability of capacitive thickness gages. Advantages of ultrasonic thickness measurements are the ability to provide precise data, in-situ measurement possibilities, the wafer is kept wetted by water or immersed, and experience has shown relative insensitivity to resistivity and oxide layers; however, additional investigation is needed in this area. Herein, the baseline ultrasonic measurements are of interest.

A silicon wafer was measured employing a similar configuration to that described for the germanium case. Given the focused transducer and the increased velocity of the material (8.72 mm/µs for silicon versus 5.06 mm/µs for germanium), distortion of the second back echo occurs, so only a Mode 2 measurement was employed. It appears that enough pressure is available at angles necessary to partially mode convert the longitudinal wave to a shear wave. Because the velocity of the shear wave is about 50% of the longitudinal wave, the first back echo of the shear wave is nearly coincident with the second back echo of the longitudinal wave, and this circumstance causes constructive interference. This distortion could potentially be overcome with the use of a non-focused transducer, but would require further investigation. As will be shown, the Mode 2 measurement provides excellent results. A composite image of the data is shown in Figure 4.

Fig 4: Composite Image of Silicon Wafer Measurement.

As shown in Figure 4, the first back echo is nearly identical in shape to the front surface echo but is phase-reversed by 180°. The second back echo is distorted as noted previously. Ultrasonic thickness data were obtained as previously described for ten points about the wafer. Velocity calibration yielded a value of 8.720 mm/µs. For this case, the mean values of 25 rapid measurements were employed for the measured time-of-flight in the calibration, as this option of selecting the number of raw readings from the thickness gate to average was recently added to the graphical user interface used for calibration. As for the previous samples, the calibration data and the subsequent series of ultrasonic measurements were recorded at approximately the same physical locations.

The capacitive thickness gage employs a single point calibration based on a mechanical measurement traceable to an NIST standard. The particular lot of wafers is calibrated once at a single point on a representative wafer because the mechanical device can damage the wafer surface, which is why a non-contact method is required. The capacitance thickness gage display is balanced to the absolute value of the mechanical measurement, and wafer thickness and total thickness variation about the wafer are then measured relative to that value. Data are provided in Table 5 for each of ten points on the silicon wafer.

Capacitive (mm)	Ultrasonic (mm)	Difference (mm)
0.523400	0.523367	-0.000033
0.523460	0.523339	-0.000121
0.523757	0.523784	0.000027
0.524217	0.524117	-0.000100
0.524757	0.525033	0.000276
0.525323	0.525395	0.000072
0.525753	0.525559	-0.000194
0.525890	0.525635	-0.000255
0.526247	0.526159	-0.000088
0.526400	0.526274	-0.000126
Table 5: Comparison of Measurements of a Germanium Wafer.

The data in Table 5 indicate an agreement of about 0.276 µm (0.00001 in), which is better than would be expected with a nominal standard deviation of 50 picoseconds at the velocity of silicon. The wafer by nature minimizes material and acoustic factors affecting velocity because it is highly polished with parallel surfaces, it is a single crystal, and its thickness variation is insignificant relative to the sound propagation. The ppm levels needed are less demanding because the wafer is thin. The velocity of the semiconductor materials does vary with composition, and large changes are expected with crystal orientation variance. A single point calibration for a lot of wafers and relative measurement to the mechanical value may be acceptable, as is the case for the capacitance thickness measurement. Further measurement capability assessment is needed in practice.

It should be mentioned that the velocity is entered for the thickness gate or gates. The graphical user interface also readily accumulates the TTV (total thickness variation or maximum minus minimum) as the sample is moved under the transducer. The TTV for the specimen evaluated was 4.4 µm. The mean value and running statistics of standard deviation, TTV, maximum, and minimum are continuously updated with no lag in the display even when digital signal processing is employed. Data can be logged to a data table compatible with Microsoft Access. The acquisition can be based on elapsed time. Also, point measurements of the waveforms can be obtained.

A user-defined grid can be constructed in advance of the data acquisition, as shown in Figure 5. The data are acquired at each grid point by moving the sample to the location of interest and initiating a measurement with a function key. The grid and the accompanying three-dimensional plot perhaps show a trend in the polishing process of the wafer.

Summary

An integrated system was implemented in which time-of-flight measurements can be made with standard deviation less than 100 picoseconds employing digital signal processing techniques. Relative time-of-flight observations with carefully measured thickness can be related to acoustic velocity variations in straightforward inspections. These techniques are readily extended to high ultrasonic frequencies. Material and acoustic factors that affect velocity typically limit even relative thickness measurement capabilities. Nonetheless, micron and sub-micron thickness variations can be monitored in some applications.

References

1. An Introduction to Ultrasonic Thickness Measurements, www.panametrics-ndt.com [Internet Web Site, February 2002].
2. Standard Practice for Measuring Thickness by Manual Ultrasonic Pulse-Echo Contact Method, ASTM Document E797–95, ASTM, February 1996.
3. Standard Practice for Measuring Ultrasonic Velocity in Materials, ASTM Document E494-95, ASTM, March 1995.
4. Papadakis, E. P., “Ultrasonic Phase Velocity by the Pulse-Echo-Overlap Method Incorporating Diffraction Phase Corrections,” Journal of Acoustical Society of America, Vol. 42, pp 1045- 1051, 1967.
5. Lynnworth, L. C., E. P. Papadakis, and K. A. Fowler, “Ultrasound Propagation Measurements and Applications,” International Advances in Nondestructive Testing, 1977, Vol. 5, pp. 71-115.
6. McMaster, R. C., Nondestructive Testing Handbook, New York, Ronald Press 1959, Section 43-10.
7. Krautkramer, J. and H. Krautkramer, Ultrasonic Testing of Materials, Berlin, Heidelberg, New York, 1983.
8. Cotter, D. J., W. D. Koenigsberg, A. E. Pasto, and L. J. Bowen, “Improving the Reliability of High Performance Ceramics Using Nondestructive Evaluation”; presented at the 12^th Conference on Composites and Advanced Ceramics at Cocoa Beach, FL, Jan 1988.
9. Richerdson, D. W., Modern Ceramic Engineering, Marcel and Decker, Inc. (1982).
10. Blessing, G. V.; Donmez, M. A.; Eitzen, D. G., and Kodama, R. H., “In-Process Ultrasonic Thickness Metrology Applied to Steel Parts of Rotation”, Rev. Prog. Quant. Nondestr, Eval, Vol.10B, pp. 2149-56, 1991.

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