ANL-87-52 hnoloqy • Materials ; i
Mater.Ji - .niponenis T(H;.'niv).v>gy Division Matenr!f :^.nd Comoortcrtts n Materials and Components X-Ray Computed Tomography for Technology Division Materials and Components Nondestructive Evaluation of Technology Division Advanced Structural Ceramics Materials and Components Technology Division M^ inU Conipoiiedis lechnology Division by William A. Ellingson and Materials and Comp'^f^*»nts Michael W. Vannier Technology r i Materials and Components Technology r n Materials and Components Technology Division Materials and Components Technology Division Materia Components 1 ecnnology Division Materials and Components Technology Division j-Tf?f*ni Tf> r»"' Materials and Components RET • FILE Technology Division Materials and Components •,•> Technology Division Materials and Components Technology Division
Argonne National Laboratory, Argonne, Illinois 60439 n operated by The University ot Chicago tor the United States Department ot Energy under Contract W-31-109-Eng-38 Materials and Components Technology D -. Materials and Componenis Technology Division Materials and Components Technology Division Materials and Components Technoloav Division Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is owned by the United States govemment, and operated by The University of Chicago under the provisions of a contract with the Department of Energy.
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ANL-87-52
ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue Argonne, Illinois 60439
X-RAY COMPUTED TOMOGRAPHY FOR NONDESTRUCTIVE EVALUATION OF ADVANCED STRUCTURAL CERAMICS
by
Williaffl A. Ellingson and Michael U. Vannier*
Materials and Components Technology Division
September 1988
Prepared for the U.S. Department of Energy, Office of Fossil Energy, Advanced Research and Technology Materials Development Fossil Energy Materials Program (FVP 49640) and the U.S. Department of Energy, Assistant Secretary for Conservation and Renewable Energy, Office of Transportation Systems, as part of the Ceramic Technology for Advanced Heat Engines Project of the Advanced Materials Development Program (Contract ACK-85234).
*Malllnckrodt Institute of Radiology/Washington University, St. Louis, MO.
TABLE OF CONTENTS
Page
ABSTRACT 1
I. INTRODUCTION 1
1.1. System Architecture 2 1.2. Technical Considerations 5 1.2.1. X-Ray-induced Artifacts 5 1.2.2. Mechanical and Thermal Stability of Components 6 1.2.3. Detectors 6
II. CONSIDERATIONS FOR CERAMIC MATERIALS 8
III. CORRECTION FOR BEAM HARDENING 10
IV. EXPERIMENTAL RESULTS 15
4.1. Verification of Optimum Energy 15 4.2. Inclusions 16 4.3. Turbocharger Rotors 29 4.4. Ceramic-Ceramic Composites 31
V. SUMMARY AND CONCLUSIONS 41
ACKNOWLEDGMENTS 41
REFERENCES 42
APPENDIX A: EFFECTIVE ATOMIC NUMBER 45
APPENDIX B: PHOTON SOURCES 48
ill LIST OF FIGURES
No. Title Page
1. Schematic Diagram of X-Ray Computed Tomography System 3
2. Source-Detector Configurations for CT Scanners 4
3. Schematic Diagram of an Ionization Multidetector 7
4. The Basis-Material Plane 12
5. Processing Scheme for Dual-kVp Data Evaluation 13
6. Illustration of the Dual-Energy Principle and Resulting CT Images 14
7. Theoretical Optimum Incident Photon Energy as a Function of Energy for Green and Dense SijN^ Specimens of Various Thicknesses 16
8. Set of Equivalent Monoenergetic-Photon Images of a 105-mm- diam Bottle of Freon TF 17
9. Linear Attenuation Coefficient of Green and Dense SioN/ and a Potential Calibration Fluid, Freon TF 19
10. Experimentally Obtained Optimum Incident Photon Energy for a 51-mm-diam Green-State SioN^ Sample 19
11. Experimentally Obtained Optimum Incident Photon Energy for a 105-mm-diam Freon TF Sample 20
12. Schematic of SijN^ Test Specimen Used in CT Studies 20
13. Schematic Diagram of Array of High-Density Seeded Inclu sions in Green-State Specimen Shown in Fig. 12 20
14. Computed Scan Projection Radiograph of Si^N^ Test Specimen 21
15. Same Image as Fig. 14 but with Window at 350 and Center at -37 HU 22
16. Series of CT Images of Green-State Si3N^ Test Specimen with Seeded High-Density Inclusions 23
17. Series of CT Images of Same Specimen Shown in Fig. 16, with 1-mm Slice Thickness 24
18. CT Image of Same Specimen Shown in Figs. 16 and 17, with 2-mm Slice Thickness 25
IV LIST OF FIGURES (continued) tifi. lilifi Page
19. Densitometer Traces of CT Image at Table Position 42, along Lines through 1000-/im Fe Markers, Fe Test Inclusions, SiC Test Inclusions, and W Test Inclusions 27
20. Densitometer Traces of CT Images at Table Positions 42 and 43; Windows and Center Positions are Different from those of Fig. 19 28
21. Green-State Turbocharger Rotor Used in Experimental Dual- Energy CT Scan Tests 29
22. Close-up Photograph of Turbocharger Rotor, Showing Circum ferential Surface-breaking Crack 29
23. Axial CT Image of Rotor Shown in Fig. 22, Obtained with the Dual-Energy Beam-hardening Correction 30
24. Transaxial CT Image of Same Rotor, Taken Through the Vanes 30
25. Transaxial CT Image of Same Rotor, Taken Upstream of the Vanes 31 26. CT Image of Same Rotor Section Seen in Fig. 25, with Densitometer Trace 31
27. Photograph of Three of the CVI SiC Specimens of Set 2 after Infiltration and Removal from Holder 32
28. Photograph of Two of the CVI SiC Specimens of Set 2, Still in Holders 33
29. Metallographic Polished Section of Plain-Weave Specimen CVI - 57 34
30. CT Images of Specimen CVI-57 35
31. Metallographic Polished Section of Chopped-Fiber Specimen CVI-64 36
32. CT Image of Specimen CVI-64 36
33. Photomicrograph of Satin-Weave Specimen CVI-65 37
34. CT Image of Specimen CVI-65 37
35. Digital Radiographic Image Showing Arrangement of CVI Specimens on CT Scanner Table 38
36. CT Image of Unlnflltrated Plain-Weave Preform in Holder .. 39 LIST OF FIGURES (continued)
No. Title Pass
37. CT Image of Infiltrated Plain-Weave Specimen 130-4 . 39
38. CT Image of More Completely Infiltrated Plain-Weave Specimen 127-1 in Holder 39
39. CT Image of Infiltrated Satin-Weave Specimen 130-2 40
40. CT Image of Chopped-Fiber Specimen 130-3 Taken at the Interface Between the Known Low-Density Region and the Higher Density Region 40
41. CT Image of Specimen Shown in Fig. 36, Obtained with CT Scanner in Dual-Energy Configuration at 85 and 125 kVp Head Voltages 40
42. Portion of CT Image Shown in Fig. 41, Enlarged to Show More Detail of the Composite Structure 41
LIST OF TABLES
I. Common Processing Operations for Advanced Ceramics 9
II. Comparison Between Inclusion and Voxel Volume for Various
Inclusion Sizes 25
III. CVI Specimen Set 1 32
IV. CVI Specimen Set 2 32
VI X-RAY COMPUTED TOMOGRAPHY FOR NONDESTRUCTIVE EVALUATION OF ADVANCED STRUCTURAL CERAMICS
William A. Ellingson and Michael W. Vannier
ABSTRACT
This report characterizes the current status of X-ray computed tomography (CT) as applied to the nondestructive evalua tion of ceramic materials. The principal advantages of X-ray CT scanning are two. The first is the capability to produce high- contrast, geometrically accurate digital pictures (images) of slices through an object with a reasonably high spatial reso lution. The second is that these slice images are not influenced to any significant degree by overlap or by structures outside of the plane of section (the tomographlcally imaged plane). Conven tional radiography offers neither of these advantages.
I. INTRODUCTION
Computed tomography (CT) is a well-established imaging modality used in medical diagnostic radiology. Industrial applications have been described in the nondestructive testing literature for the past 10 years. The tech nology, especially for ceramic materials, is still in its infancy, and CT is thought of primarily as a research technique, but with important potential for future improvements.
CT scanning is, fundamentally, a method for producing spatial maps of the local X-ray attenuation within a slice through an object. Generally speaking, slice imaging is synonymous with tomography. It is possible to form slice images of an object by holding the object stationary and moving a source and detector about a point in the object which lies between them. Part of the object will be in focus on the resulting image and part will be blurred. If one-dimensional detectors are used and sufficient projections are available, the influence of blurring from over- and underlying struc tures may be removed mathematically.
The mathematical basis for CT scanning is reconstruction from pro jections. In much the same fashion that the temperature distribution within a flame or the distribution of stars within a galaxy may be computed from external projections, the spatial distribution of X-ray attenuation within an object may be reconstructed by obtaining samples of line integrals through the object at different source-detector orientations (1-dimensional projections) followed by a suitable computational step.
One of the applications for which X-ray CT imaging holds great promise is materials characterization. Theoretically, CT should be able to provide very accurate information on X-ray absorption at points within an object. These X-ray absorption values should be useful in quantitative characteri zation of inclusions, cracks, short- and long-range density gradients, and other local inhomogeneities. This type of characterization should be possible for internal structures that occupy less than 1 mm^. In addition, when X-ray CT is used for parts with complex shapes, one does not encounter mode conversion problems, as one does with the elastic waves used in ultra sonic NDE.
This potential for detailed materials characterization by CT imaging has been difficult to realize for objects of arbitrary complexity when con ventional X-ray sources are used. Problems occur because the X-ray sources used in CT scanners are polychromatic (i.e., they produce a spectrum of photon energies), and X-ray absorption by materials is energy-dependent. Correction for the polychromaticity of X-ray heads used in CT imaging requires knowledge of the source spectrum and the interaction of X-rays in the relevant energy range with the compounds that make up ceramic materials.
1.1. System Architecture
It is not the intent of this report to give a comprehensive review of X-ray CT, as several excellent references already exist. ' Rather, this report will concentrate on considerations for applying CT to advanced structural ceramic materials and on recent development efforts and results.
Figure 1 shows a schematic diagram of an X-ray CT system. The major components are the X-ray source, the detector, the computer, and the image display system. Each has been thoroughly discussed elsewhere and has been the subject of complete conferences. Therefore, the following discussion will be limited to some features of these components which are important for application to ceramics.
The X-Ray Source. For ceramic materials, high spatial resolution is needed, since it is desirable to be able to accurately determine defect sizes of <100 ;*m. Therefore, the X-ray focal spot should be small to mini mize geometric unfocusing due to divergence between the source and detector.
The Detector. Although Fig. 1 shows a one-dimensional detector array, the detector can be film that is subsequently digitized, or a two- dimensional detector array, as used in some recent experiments with a synchrotron as the X-ray source. '
The Computer. In general, the computing elements in a CT system consist of a data acquisition system, a control computer, and an array pro cessor. The control computer maintains the data files, stores and retrieves programs, performs user interface and archival functions as well as net working, and generally acts as the "assistant gatekeeper." The array pro cessor is the site of the computational steps needed to perform the image reconstruction from projections. Generally speaking, these array processors are not general-purpose devices but are optimized to perform the convolution and back-projection (addition) operations that are required for this recon struction. The speed of data acquisition, data "crunching" in the array processor, and production of the final reconstructed image is totally dependent upon the speed and effectiveness of the control computer.
The Display System. High-resolution display systems of up to 1024 X 1024 pixels are now commonly available. This means that over the longest dimension of an object, 1024 segments can be individually displayed. For example, if the detection system can be shown to resolve 25 pm, then a 25- object can be fully displayed at a pixel-to-pixel resolution of 25 /im. kitmu mocfSKM "'*" ^^
City oaruti or caoss SECTION iflSoii'Wvriei' '
Fig. 1. Schematic Diagram of X-Ray Computed Tomography System. DAS - data acquisition system.
The detector-source configurations used in various CT scanners are classified into several so-called "generations," as shown schematically in Fig. 2. Figure 2(A) shows the original "first-generation" system developed by Dr. Geoffrey Hounsfield (who together with Dr. Allan Cormack was awarded the 1979 Nobel Prize in Medicine for the development of the CT scanner) and introduced commercially in 1974 by EMI, Ltd. The system employs a "translate-rotate" motion. The X-ray tube and a single detector traverse the object in a straight line while a pencil beam scans across the object. The source-detector assembly then rotates about the object by a small angular increment and the process is repeated until a rotation of 180* or 360* is completed. Acceptable image quality is obtainable with this basic method as long as the object to be imaged is held fixed for the duration of each complete scan across the object. Very little scattered radiation is present and the source-detector combination can be moved in small steps to yield a very high spatial resolution. The principal drawbacks are long scanning times and low efficiency in terms of source loading and consequent tube heat limitations.
Figure 2(B) shows the second-generation configuration introduced in the late 1970s to speed up data collection without losing the advantages of the first-generation multidetector translate-rotate geometry. In this configu ration, the source-detector system still undergoes translate-rotate motion, but an array of detectors is used. Thus, for each linear scan, data are collected for many sets of parallel rays (typically 20 to 60). The X-ray beam is in a fan configuration, allowing greater source efficiency and faster scanning. Systems of this type offer excellent image quality and spatial resolution, and have significant potential for ceramic applications. (A) (B) (C) (D)
SOURCE •-- SOURCE SOURCE SOURCE TO —
DETECTOR (3 ARRAY \ DETECTOR DETECTOR ARRAY
1st GENERATION 2nd GENERATION 3rd GENERATION 4th GENERATION CT SCANNER CT SCANNER CT SCANNER CT SCANNER
SOURCE AND SOURCE AND SOURCE AND SOURCE ROTATES SINGLE LINEAR FAN BEAM WITH FIXED 360* DETECTOR DETECTOR DETECTOR DETECTOR ARRAY TRANSLATE ARRAY ROTATE AND ROTATE TRANSLATE AND ROTATE
Fig. 2. Source-Detector Configurations for CT Scanners.
Figure 2(C) shows a third-generation configuration, which employs a "fan beam." This architecture involves only one motion (rotation), and it represents the most commonly used geometry for medical scanners. The array of detectors is made large enough to enclose the whole reconstruction area, and the source-multidetector combination rotates around the object. For each CT "slice," the data collection process can be completed in a few seconds. This type of CT is well suited for medical imaging; because data are acquired rapidly and motion effects are minimized, motion artifacts are considerably reduced. However, this architecture requires a very stable detector and data acquisition electronics. Each detector cell images a circular path around the center of the rotation, and a very small difference in response between adjacent cells can generate circular artifacts. Owing to considerable efforts by manufacturers of medical CT systems, stability problems have been largely overcome. Third-generation architecture is now the most widely used because it represents a favorable trade-off between performance, in terms of scanning time (1-2 seconds), and technological complexity (especially the number of detectors, which ranges from 512 to 1024).
Figure 2(D) shows another system architecture, designated fourth- generation geometry. This system employs a stationary circular array of detectors and a rotating X-ray source. It is a suitable architecture for fast data acquisition and reduction of motion artifacts. However, such a system requires a very large nvunber of detectors, significantly more than third-generation designs, and the detectors must be very thin since each cell has to detect X-rays over a wide range of angular directions. In addition, scattered radiation is more of a problem than for third-generation detectors. 1.2. Technical Cvngtdoritigna
For practical reasons, reconstruction from projections for medical imaging is virtually always performed by the filtered back-projection method, although many other algorithms for obtaining two-dimensional tomo graphic images from one-dimensional projections exist. A large number of one-dimensional projections, typically 400 or more, are used to produce an overall average two-dimensional slice image. The data acquisition system and array processor (see Fig. 1) first normalize the detector readings for offset and gain. The corrected data are convolved with a suitable convo lution kernel, interpolated, and averaged to produce the final CT scan images. These images are typically displayed at 512 x 512-pixel resolution on monochrome CRT monitors. The video signals supplied to the monitor can be used to produce hard copies on transparent film via a special recorder or by photographing the screen.
The CT scanner has remarkable dynamic range, and meaningful data can be obtained at a resolution of 12 bits (4096 gray levels). Typically, these values are scaled to Hounsfield units (HU). On the Hounsfield scale, the X-ray attenuation of water is set at 0 HU, air at approximately -1,000 HU, and dense bone at approximately -»-l,000 HU. Since the CT scanner yields digital values of X-ray attenuation, the potential for extracting quanti tative values is obvious. However, the reliability of the X-ray attenuation estimates produced by a CT scanner is affected by several factors, which are discussed below.
1.2.1. X-Ray-induced Artifacts
Beam hardening. Beam hardening (BH) is most responsible for the inaccuracy of X-ray attenuation values obtained with CT. It occurs when a polychromatic X-ray source, such as tungsten, is used. Such a source pro duces X-rays with a spectrum of energies, extending from relatively low values (a few keV) to the accelerating potential of the X-ray tube. The lower energy X-rays contribute little to the formation of images, since they are almost totally absorbed by the materials of interest. In fact, aluminum or copper filters are often placed between the tube and the object to absorb the low-keV X-rays. For the range of energies that do enter the object, X- ray absorption varies with energy in a manner that depends on the object's composition, geometry, and orientation within the scanner. The result is variation in the X-ray energy spectrum from point to point within an object. As a result, even the simplest object will appear to have higher attenuation (as computed by the CT scanner) at its periphery than deeper within. The influence of BH varies considerably with the shape and location of the part of the object being examined. The error due to BH effects may be 10% or more of the overall X-ray attenuation. This error is many times larger than the difference in X-ray attenuation between relatively similar materials. As a result, there is relatively little use of the X-ray attenuation values themselves except under specially controlled measurement circumstances where the reliability can be increased. One such approach is to use test objects or "phantoms" of known composition to calibrate the system. A calibration procedure involving several attenuation phantoms is needed to determine the detector response to a polychromatic X-ray beam over a range of object thicknesses. Scattered Radiation. A variable fraction of the incident X-ray photons on an object is scattered. The scattered radiation can reach the detectors and produce a signal of the same order of magnitude as the desired signal. It is essential therefore to reject scattered radiation by colli mating the beam in front of the detectors. The geometrical accuracy, posi tioning, and stability of such collimators in rotating-motion architectures must meet stringent requirements.
Partial-Volume Effects. If the image reconstruction plane has a pixel size of 100 x 100 fxm, one is tempted to say this is the detection accuracy. However, the "z-axis" slice thickness factor must be taken into account. Each displayed pixel has an attenuation coefficent value obtained by integrating over the z-axis slice thickness, which ranges from 500 /xm to several millimeters. With an 8-mm slice thickness and a 1 x 1-mm pixel, for example, the size of each voxel would be about 1 x 1 x 10 mm. As some structures present complicated shapes with strong density gradients, this means that the measured attenuation is an average. This phenomenon is called the "partial-volume" effect. It can be reduced by X-ray source or detector collimation to control the slice thickness.
1.2.2. Mechanical and Thermal Stability of Components
The physics and mechanics of the CT systems and their associated elec tronics must also be taken into account. The stability of the mechanical components, especially the source-detector assembly, is of major importance in CT imaging because very accurate measurements (with a repeatability of 2-3%) are required for acceptable image quality. Another item of importance is the X-ray tube. For long-term operation, high-current X-ray tubes having a rotating anode with a high heat capacity are necessary. A reliable spot size is also necessary to minimize geometric unsharpness. These two con ditions are very difficult to obtain. Special tubes (such as oil-cooled rotating anodes whose wobble and filament vibrations have been reduced to avoid severe artifacts in the reconstructed image) have been designed for medical CT systems. In addition, the high-voltage power for the X-ray head must be very stable (varying by no more than -10" ).
1.2.3. Detectors
Detectors are a major factor in CT design and performance, and a com- mensurately large amount of effort has been put into their development. The most commonly used types in CT systems are solid-state detector arrays and ionization chambers; these types are described below. A third type, the phototube-based scintillation counter, is used less frequently. Desirable characteristics for detectors include a high stopping power, good linearity over a large dynamic range (-500), negligible crosstalk (caused by scat tering) between adjacent cells, high stability of response, and, for solid- state detectors, high packing fraction and fast response time. Solid-State Detectors. Each cell is made of a scintillator optically coupled to a low-current-leakage photodiode working in photovol taic mode. This arrangement exhibits a good packing fraction and a high stopping power. It is essential to choose a scintillator that does not yield a long-period light emission component in order to avoid pile-up effects between successive measurements. Bismuth germanate and cesium iodide have been employed, but cadmium tungstate is now preferred because it combines three major advantages: (1) the light emission is well suited to the photodiode sensitivity, (2) it is not hygroscopic, and (3) it has no long-period light source. These thin and efficient detectors are well adapted to fourth-generation machines (with a complete ring of stationary detectors) because they can detect over a large range of angular directions. They have also been employed for third-generation machines.
lonitation Chambers. Figure 3 shows a typical arrangement for such a detector. The electrodes, which are focused at the focal spot of the X-ray head, have a triple function: (1) collimation of the scattered radia tion froa the object, (2) collimation of the scattered radiation and fluo rescent X-rays produced inside the detector itself, and (3) collection of the charges created by ionization in the gas. Xenon is the best choice for this application because of its high stopping power. No purification system is required, since the chamber operates in ion collection mode. The time response is compatible with the time sequence of the data. For instance, for a 1-mm interelectrode space, at 30 atm pressure and with a 1-kVp supply, the collection time is about 1.5 ms. This solution offers four major advan tages: good linearity of response over a large dynamic range, very good stability, absence of pile-up effects, and good quantum efficiency. Never theless, extreme care is required in the insulating, positioning, and mechanical holding of the electrodes. Small deviations from the ideal mechanical and electrical conditions generate severe artifacts.
TO HIGH-VOLTAGE POWER SUPPLY
OUTPUT
ALUMINUM PLATE HIGH PRESSURE GAS ELECTRODES WITH HIGH X-RAY ATTENUATION.eg XENON ALUMINUM PLATE
INCIDENT PHOTO FLUX
Fig. 3. Schematic Diagram of an Ionization Multidetector. Many of the technological difficulties described in Section 1.2 have been overcome; however, several additional parameters have to be considered in designing a CT system for ceramics, such as calibration method, moni toring of the stability of the X-ray beam, and X-ray energy optimization as a function of the ceramic material to be imaged (i.e., green or densified, monolithic or composite). Some of these will be discussed in later sections of this report.
II. CONSIDERATIONS FOR CERAMIC MATERIALS
The sensitivity of ceramics to flaws necessitates carefully controlled processing and finishing operations (see Table I) to improve reliability. The sizes of individual flaws that affect load-bearing capabilities are dependent upon the stress levels in the part, but are frequently on the order of 10-100 fim. The performance of ceramic parts is also affected by density gradients, binder/plasticizer (B/P) distribution in the green state, and porosity distributions. Since ceramic materials compete with metal materials for many market applications, the need to hold down fabrication costs becomes a driving force for the development of effective NDE methods. Finishing (grinding, machining, etching, etc.) can be a costly step in ceramic processing; therefore, any NDE method that can be used to screen parts prior to densification or final machining may increase yield by allowing final operations to be done only on parts that have a high proba bility of being acceptable (i.e., flaw-free). NDE techniques, therefore, must be developed with the following questions in mind: (a) What is the sensitivity (i.e., minimum detectable flaw size)? (b) What is the cost of the inspection system? (c) How difficult is the systera to implement? (d) What throughput can be handled? Few of these questions can be ade quately answered as yet for X-ray CT methods. However, the technology appears to be very promising. Our X-ray CT efforts have concentrated on characterization after the forming step (see Table I); however, we have also conducted a significant amount of work on densified bodies.
Density gradients are of fundamental importance to ceramic processing. They are responsible for many of the problems with "shrinkage" cracking, warping, and deviations from near-net shape that have traditionally frus trated the ceramic engineer. X-ray CT offers a method of nondestructively mapping density gradients in both green (undensified) and densified ceramic parts within the limits of the contrast of the CT image. "^^
Another factor of importance in characterizing ceramics is the distri bution of the organic B/P. Nuclear magnetic resonance (NMR) may be better suited to detect this distribution. •'•° However, if the density variation is large enough. X-ray CT may also be sensitive to it.
Solid inclusions, voids, and cracks (which can be considered to be a special case of a void) constitute significant defects in ceramics Probably the best description of the severity of inclusions and voids in ceramics was given by Evans et al. Inclusions (Fe, WC, densified ceramic particles, etc.) are introduced into ceramics at various points in the process stream (see Table I), often in the powder preparation step which involves grinding operations and transport of the material. Voids are often produced at the forming step as well as during dewaxing or so-called debinderizing (i.e., removal of the organics). Both inclusions and voids can vary in siza; tha critical size is dependent mainly on the stress level at the location of tha void or inclusion. For ceramics processing that includes a graan-body step, the density difference between a void and the green body is less than that between the void and the final densified body, whereas an inclusion has a higher density difference at the green-body stage. Since X-ray CT measures differences in attenuation coefficients, voids should be easier to detect in dense ceramics and inclusions should be easier in green ceramics.
Table I. Common Processing Operations for Advanced Ceramii:s *
Operation Method Examples
Powder preparation Synthesis SiC Sizing SijN^ Granulating Zr02 Blending Solution chemistry Glasses Forming Slip casting Combustors, stators Dry pressing Cutting tools Extrusion Tubing, honeycomb Injection molding Turbocharger rotors Tape casting Capacitors Melting/casting Glass ceramics Densification Sintering AI2O3 Reaction bonding SijN^ Hot pressing SijN^, SiC, BN Hot isostatic pressing SljN^, SiC
Finishing Mechanical Diamond grinding Chemical Etching Radiation Laser, electron beam Electric Electric discharge
^Adapted from Ref. 11.
Since small density gradients ( CT image (i.e., the inverse of the noise) for fixed scan parameters depends on the value of the absorption coefficient (and therefore the energy spec trum of the source) and the intensity of the radiation transmitted through the object (and therefore the sample thickness). Thus, for industrial CT applications, one would like to both optimize the photon energy and increase the beam intensity (photon flux). Polychromatic X-ray sources are generally considered preferable to isotopic sources because of their greater intensity. The optimum photon energy choice can be estimated by using the rela tionship /i«x = 2, where fi is the attenuation coefficient at a given photon energy and x is the part thickness. This relationship, which comes directly from the mathematical relationships developed to establish CT noise, yields an optimum photon energy of about 1.25 MeV for 10-cm-thick objects of both AI2O2 (p = 3.95 g/cm ) and zirconia (p = 4.65 g/cm ); this value is approximately equal to the photon energy of a Co source. In comparison, the use of a photon energy of 60 keV, which is about the peak effective energy of a 120-kVp X-ray tube, decreases the S/N ratio (for the same scan parameters, source intensity, and scan time) by a factor of 10 in the case of AI2O2, and by -8 orders of magnitude in the case of zirconia. For a 10-cm AI2O2 object, this increase in noise can be compensated for by using a source 100 times as intense, which is possible for an X-ray source relative to an isotopic source. However, for a 10-cm zirconia object, the lowest practical energy is about 150 keV (which corresponds to a tube voltage of -300 kV), and thus the intensity must be greater by a factor of 10*^ compared to an isotopic source. III. CORRECTION FOR BEAM HARDENING The aim of CT is to assign to every point inside an object a number that is specific to the material located at that point. A suitable candi date for this number is the X-ray attenuation coefficient of the material As discussed earlier, a difficulty arises because the X-ray beam typically used in CT consists of photons at different energies (referred to as poly chromatic X-rays). Since the attenuation at a given point is generally greater for photons of lower energy, the energy distribution or spectrum of the X-ray beam changes ("hardens") as it passes through the object A possible solution is to assign to the point the attenuation coefficient of photons at a particular energy. If we used monoenergetic X-rays, beams from different directions should be attenuated in the same way at a given ooint Reconstruction of such attenuation coefficients is a well-defined aim f " CT. Generally, we are given the total attenuation of polychromatic X-ray beams through an object, and we wish to produce estimates of the total attenuation of monoenergetic X-ray beams. The physical processes by which attenuation of the photon beam occurs are photoelectric absorption and Compton scattering. Compton scatter! the dominant process, depends on electron density; photoelectric ab ^^• significant only at low energies or for high-atomic-number materiair'^^^^^'^' as about the fourth power of the atomic number and the cube of the ' ^^^^^^ These processes are also involved in the detection of the transmitt^d^h^^ 11 Beam hardening can be avoided by using radionuclides or isotopes to provide a monoenergetic photon source. However, such scanners have other disadvantages related to source characteristics, such as flux (see Section II) and choice of energies, and to detector limitations.^^ Consequently, several approaches to BH correction have been developed. The most important correction methods are (1) preprocessing (prefiltering, water baths, bone convolution functions, and linearization); (2) postprocessing (second-order correction); and (3) the dual-energy ("material selective" or multicom ponent, energy-independent reconstruction) method. These methods have been discussed in an earlier report, but the dual-energy technique will be reviewed below, since it is used in the analysis presented in Section IV. 1 Q 0/ Dual-energy methods provide an analytically correct solution to the BH problem. In current medical practice, dual-energy methods have been found to be more accurate, reproducible, and reliable for quantifying the mineral content of bone than the use of polychromatic sources operated at single kVp values. The drawbacks are the increased cost and complexity of the instrumentation, larger data sets with associated increased data pro cessing requirements, and noise limitations. A basic assumption underlying dual-energy reconstruction methods is that within the X-ray energy range of interest, the energy-dependent mass attenuation coefficient (/i/p)(E) of materials can be expressed with suf ficient accuracy as a linear combination of the Compton and photoelectric coefficients. The mass attenuation coefficient can be expressed as a sum of two linearly independent basis vectors that span its space: « (/i/p)(E) - S a f (E) (1) i-l Among the pairs of vectors that can be used to span this space are X-ray attenuations for a pair of basis or calibration materials (Fig. 4). Provided that the energy dependence of the coefficients of these materials is known, the X-ray spectra at two different tube energies are known, and the measured attenuation values for the sample object are given at the corresponding energies, it is possible to compute conventional CT values as well as many new equivalent values for each voxel in the reconstructed images. For example, one can compute images at equivalent monochromatic energies (which are relatively immune to BH artifacts), equivalent basis- material composition images, electron density images, and effective-z images. The principal applications of these computed or synthesized images are removal of BH effects and selective display of different material densi ties (Fe, Si, Al, ...). It can be shown that any material's mass attenuation coefficient can be expressed as a linear combination of the coefficients of two so-called basis or calibration materials: (/i/p)(E) - a^.(/i/p)^(E) + a2-(/i/p)2(E) . (2) where subscripts 1 and 2 refer to reference material 1 and 2, respectively. Since any two linearly independent sums of two basis functions (the Compton and photoelectric components) span the space, they are also adequate basis functions. It follows then that any material ^ can be expressed as a linear combination of any other two materials, a and fi, which are designated the basis-set materials: 12 Fig. 4 The Basis-Material Plane. Material M is represented by a vector in the two-material basis plane. An and A2 are the equi valent dimensions of materials a and j9, respectively. fi (E) /i (E) M (E) _s „ + ^^ _e— (3) 1 p. 2 p '^ P where N (Z ^-^ - Z ^-^ (4) ^"N (z^-« -z/-«) ga a P N^ rz/-« - Z^3-«) (5) 2~N,(z/-«-Z^-«) g/3 /3 a ' and N is the electron mean density for material x. The two basis or calibration materials should be sufficiently different in their atomic number z to demonstrate measurable differences in their Compton and photo electric attenuation characteristics. In CT imaging, the line integral over the linear attenuation coefficient is determined for each focus position and detector element. This integral can be expressed accordingly as M(r,E)ds = (/i/p)^(E).5^ -1- (.fi/p)2(E)-S^ , (6) where 5. = p^(r)ds 1 (7) The symbol 6^ represents an "area density" in g/cm^, and p.(r) represents the local mass density in g/cra , of basis material i. When materials oth than the basis materials are present, the densities are rpfci-i-o^ <-„ , . . , , . . - . , J-ej.errea to as equi valent basis-material densities, a linear combination of which refle ^ i^Vi physical density of the attenuating material. 13 The equivalent "area densities" 61 and 62 of the two basis materials have to be determined for each ray path. By measuring the attenuation with two different spectra, we obtain two nonlinear equations for each ray path: -(fi/p)^(E)'6^ dE (8) •I ^oh(^> exp (M/P)2(E)-62 •-II^^(E)'ex p -(M/p)i(E).fi^ (/i/p)2(E)-«2 dE (9) where I and I^ are the attenuated and primary intensities and the subscripts h and i refer to the high- and low-kVp X-ray head voltages, respectively. Equations (7) and (8) can be solved for the equivalent "area densities" S-i and $2, characterizing the unknown material. The basis-material decomposition is thus accomplished by calculating the 6-1 and $2 values from the measured projection values. Materials with an atomic number z different from those of the two basis materials will contri bute to both 6-1 and $2 in a specific fashion. The values 6^ can be interpreted as components in a two-dimensional vector space with the basis materials defining the basis vectors. The dual-energy correction is usually implemented by use of table look up procedures. Figure 5 summarizes the basic procedure for the rapid kVp- switching method, which we have chosen for our application. Profiles of attenuation measurements made along the X-ray beam path demonstrate sig nificant BH in Freon TF on medical CT scanners operated in this energy range. This effect is virtually completely removed by dual-energy mono chromatic-equivalent reconstruction using rapid kVp-switching, as will be shown in a later section. SCAN OAIA OUM. ENKROT D«U HS Fig. 5. Processing Scheme for Dual-kVp Data Evaluation. Data DATA PBOCC SSIMO and images obtained from one scan using rapid kVp-switching. (Adapted from Ref. 26). EFFECTIVE ATOMIC NUMBER IMAGE ftlNOlC hVp SAStC UATCR MAT HIOM MAT-LOW kav 14 We have applied dual-energy CT scanning to demonstrate its potential for reducing BH artifacts in images of ceramic materials. Using calcium and water as the basis materials, we computed equivalent monochromatic images as illustrated in Fig. 6. The initial test object, a container filled with Freon TF fluid, was scanned at room temperature at 85 and 125 kVp. RAPID kVp SWITCHING X-RAY HEAD TURBOCHARGER ROTOR HIGH-z BASIS MATERIAL (CROSS SECTION OF SHAFT SHOWN) BASIS MATERIAL DECOMPOSITION ) DETECTOR ARRAY ^ LOW-z BASIS MATERIAL (CROSS SECTION OF SHAFT SHOWN) w z LU I I. LOW kVp -HIGH kVp < • z X-RAY HEAD SPECTRUM Fig. 6. Illustration of the Dual-Energy Principle and Resulting CT Images. The low-density ceramic matrix is significantly different from the high-density inclusions with regard to attenuation properties at the two X-ray energies, owing to differences in the energy depen dence of X-ray attenuation in the two materials. The basis- material decomposition process (see text) makes use of this infor mation to calculate material density images. As mentioned earlier, dual-energy CT scanning techniques are not with out drawbacks. Additional X-ray accelerating potential, rapid switch' hardware, and specialized reconstruction software are required to nr 'H reconstructed results in a timely fashion. The comolexitv ^.^^ t-v,„ J ... . , . J , , I'.LCJAxuy OL cne data pro cessing is certainly increased, and the success of the method is b accurate knowledge of the original X-ray tube spectra, their resce f accelerating potentials, and the attenuation characteristics of th h 15 materials. With dual-energy scanning, BH effects are suppressed, but not completely eliminated. It is often assumed that all the density errors near the borders of scanned objects are due to BH, but this is not the case in practice. Most investigators have neglected the contributions of partial- volume effects, specimen inhomogeneity, and off-focal radiation (scatter). Dose-related noise is a limitation in dual-energy methods, especially at the lower kVp setting. The spectral separation obtained in practice by switching the X-ray source from 85 to 125 kVp is not ideal for all situ ations. The decomposition table that is used to perform the dual-energy X-ray computations can be inaccurate owing to variations of the X-ray spectra and incorrect assumptions regarding the basis materials and the energy dependence of their X-ray attenuations. IV. EXPERIMENTAL RESULTS In this section, results are presented for four CT applications: (1) verification of optimum energy; (2) green-state ceramics with well- defined inclusions; (3) turbocharger rotors; and (4) disk specimens of ceramic-ceramic composites. A Siemens Somatom Model DR-H CT scanner, located at the Mallinckrodt Institute of Radiology, was used for these studies. This polychromatic-source scanner is in everyday use for medical examinations, and no special modifications were made for the work described here. 4.1. Verification of Optimum Energy It was noted earlier that dual-energy software could be used to obtain quasi-monochromatic image data sets. Optimum energies can be determined from these data sets through statistical analysis of noise in the resulting images. We applied dual-energy BH correction methods to sets of densified and green-state SioN^ specimens made especially for us by the Norton Ad vanced Ceramics Company. In addition, we experimented with Freon TF as a calibration fluid. The green-state, cold-pressed cylinders had diameters of 64, 51, 38, 26, and 13 mm, and heights of 46, 37, 28, 20, and 9 mm, respectively; the densified specimens were of the same sizes. Theoretical optimum-energy calculations • have shown that for a 50-mm-dlam green-state Si^N^ specimen, the optimum incident photon energy for maximum sensitivity to thickness change should be near 55 keV, as shown in Fig. 7. Figure 8 shows a set of equivalent 50- to 125-keV monoenergetic-photon images of a 105-mm-diam polyethylene bottle filled with Freon TF. Previous work had established that Freon TF had a mass attenuation coefficient close to that of green-state SijN^, as shown in Fig. 9. A region within each of the images in Fig. 8 was analyzed statistically for noise. Thus, a statis tical noise level as a function of equivalent photon energy could be ob tained. Figure 10 shows such a plot for the 51-mm-diam Si^N^ test cylinder and Fig. 11 shows the data for the 105-mm-diam Freon TF test specimen. The theoretical optimum energy is about 55 keV for the Si-jN^ (see Fig. 7) and about 70 keV for 105 mm of Freon TF. The experimental data show values of about 75 and 80 keV, respectively. This level of agreement (within about 16 20 keV for the SijN^ and 10 keV for the Freon TF) clearly shows the poten tial of the dual-energy approach for quantitative densitometry studies and significant reduction of BH. OPTIMUM PHOTON ENERGY FOR Si3N4 (GREEN,G; DENSE,D) AS A FUNCTION OF THICKNESS o THICKNESS z I mm (g) cr < UJ occ tr oc UJ > UJ CE PHOTON ENERGY.keV Fig. 7. Theoretical Optimum Incident Photon Energy as a Function of Energy for Green and Dense SIONA Specimens of Various Thicknesses. 4.2. Inclusions Green-state Si^N^ specimens with intentional inclusions were studied in order to get some idea of detection capabililty. The test object studied (see Fig. 12) was a green, cold-pressed Si^N^ specimen measuring -5.1 cm x 5.1 cm X 5 mm. Inside this specimen, at the midsection, was placed a thin plastic sheet which held a rectangular array of high-density inclusions. The array consisted of several sizes of Fe, densified SiC, and W inclusions as shown in Fig. 13. The 1000-/im Fe inclusions served as markers- the smaller ones were designated "test" inclusions, since the capability of the system to detect them was not known in advance. 17 H«l r KkUN T^ Ha 11-NOV-a« I a* rmtOH rr FKONT 1 a*i I I-MOV-*« H %l a« «-• aa M • •« ••• •• OU4 aic 0U4 eii k • CAM 1 k • CAM I • t r T T 9 © 99>tv a x«3 • »•) Tl •» Tl ' 4a »vi«9 as w 4ai •Vl»9 •^ f-ee MS ei C l«9< MS ai SL ^ HB FaCON TF H« FaCON TF FVONT 1 ••! 11-Hov-a* I 8*1 11-Nov-ac H^BI e« «"• •» M'Sl •« 2- aa 0U4 a I) OU4 eia • CAN I L SCKH 1 • rT 9 Cl ^ cencv CSkCV a xe3 • X23 Tl - Tl •• W 4* trVI25 a^ y 4ai »vi«9 a* c i3ai AS 81 c 14a AS S3 • L 2 SL ^ CT a FaCOH TF F»CON Tr FaONT FaOHT I a«i I I-MOv-a« •N!^ 11-MOv-a« H «f a< 2-- •• •« 2- aa OU4 ai? 0U4 ai4 SCAN I c SCHN I w T -•»• BV •••»SV a X23 a X2 3 T I •• M Tl •" w 4a> •V129 as lrVI29 a* c I ta) AS a3 C 14 AS ai • L t «L e CT a CT a_ FaCOM TF F"PEON "TF I a«i I ati 11-Hov-a« FPOHT 11-NOV-a* FaONT H SI ac f •• M'»» a« 2-' •» DU4 aic OU4 ai"" I. I. SCAN I • CAM I • c F F T T (CV • 9KCV a XC9 • X23 Tl 7 Tl •• 4 at KVIC9'a» 4 at »rvi«9 a* est •• a I AS a3 •L « • L t CT a CT a Tr -S« Tl» -•»« Fig. 8. Set of Equivalent Monoenergetic-Photon Images of a 105-mm-diam Bottle of Freon TF. The same dual-energy raw data set was reconstructed at 5-keV increments from 50 to 125 keV. 18 MB FREON TF MSI FPEON TF 1 e*i J I -NOV-8e. FPOMT 1 e*i Ii-Mov-ae ee £"• 08 H -Si »« 27 ee D U 4 O 1 8 DU4 019 L L SCAM I SCMt 1 e E F F T T 5 C 5 O 95KeV tt y.£7 • X23 TI ^ TI 7 ,1 40 KV12^ - 8^ 40« ; 80 (»S 83 75 FREOM TF He; FREON TF He) 1 1-NOV-86 1 8«f 11-NOV-86 FRONT 1 s«i 06 27 08 H^SI 06 27 08 H^S» 0U4 eae 0U4 02J SCftM 1 L SCAN J I. E E F F T T t00KEV 105KEV # X23 • : X23 TI 7 TI 7 KVjas-'SS 40( KVI25''85 401 AS 63 70« AS 83 6SI SU 2 SL 2 GT e GT 0 FREON TF HB FPEON TF He; 11-HOV-S6 1 8* 1l-HOV-86 1 8«l 0€ 2"' 08 H'-S e« 27 08 H-'SI DU4 022 0U4 023 SCHH 1 L SCAN 1 I. E E F F T T t 10KEV 1JSKEV • X23 • X23 Tl -• Tl 7 Kvi 2-. a's 401 KV t 25--85 601 AS S3 SL 2 SL 2 GT 0 GT a TP -5(5 TP -SS 50M«T0M DR »»ACLI»«C»tROOT INST RAO S Cl 12SKEV 1 .;• • X23 Fig. 8 (continued) 19 10 100 1000 K/* PHOTON ENERCY. E (MVI Fig. 9. Linear Attenuation Coefficient of Green and Dense SinN/ and a Potential Calibration Fluid, Freon TF. > UJ o o o< z < (0 Fig. 10. Experimentally Obtained Optimum Incident Photon Energy for a 51-mm-diam Green-State SijN^ Sample. 20 80 FREON TF 60 > LU Q Fig. 11 a 40 cc < Experimentally Obtained Optimum ^ Incident Photon Energy for a z 20- 105-mm-diam Freon TF Sample. < (0 > I —I ' I— I 40 60 80 100 120 140 keV Fig. 12 Schematic of Si^N^ Test Specimen Useci in CT Studies. a a a a 500 200 100 50 ^m •Fe Fig. 13 »SiC Schematic Diagram of Array of High-Density Seeded CT CT Studies Inclusions in Green- State Specimen Shown in *~ 1000/im -dia Fe PARTICLES Fig. 12. 21 The seeded green Si-jN^ ceramic test specimen was placed on the CT scan ner table and a computed scan projection radiograph (topogram*) was obtained (see Figs. IA and 15). In these "frontal projection images," which show the test specimen as seen from above, the specimen occupies only a small portion of the scan field even with the topogram obtained in the "head" mode (25 x 25-cm field of view). The pixel size is 0.5 x 0.5 mm. At this resolution and with a window (optical contrast) width setting of 175 to 350 HU, we are not able to see any of the inclusions. SOHATOn MALLINCKRODT INST RAD 9 cs 174 -J3 Fig. 14. Computed Scan Projection Radiograph (Topogram) of Si^N^ Test Specimen. Contrast of image was set with window at 176 and center at -37 HU. •Topogram (or scanogram) is a designation used by Siemens for a projection- type radiographic image obtained with the CT scanner head in a fixed position. Computed radiography can be performed with CT scanners by disabling the rotatory motion of the X-ray source and detector and fixing their orientation. The table on which the object lies is motorized and can be moved past the source and detector under computer control. If the source is beneath the patient, who is lying supine on the table, while the detectors are above and in front of the patient, the motion of the table with incremental sampling of the detector outputs will create a digital radiograph. These digital radiographs can be viewed on the TV monitor and used for determining the location and orientation of slices in a sequence of scans. 22 NORTON GREEN SI3-N4 2S-MAR 19 11 = DUI 00 SCAN Fig. 15. Same Image as Fig. 14 but with Window at 350 and Center at -37 HU. In order to test the effect of changing the specimen orientation, we obtained a second topogram after attaching the ceramic sample to a rec tangular object consisting of foam rubber coated with hard plastic, and positioning it such that its narrowest dimension (the 5-mm dimension) lay along the direction of the table motion. Again, it was not possible to see the intentional defects in the topogram image. However, with this configu ration, it was easy to align the CT scanner cut plane with the principal plane of the test object. Once these planes were aligned, we obtained several CT test sections. For the CT images, the CT scanner was initially adjusted to provide a slice thickness of 2 mm, and later 1 mm. The zoom or magnification factor used was 10.0, so that the pixel edge length in the plane of section was 100 fim. Ordinary single-energy CT scans were obtained with 125 kVp X-rays (nominal maximum photon flux at -60 keV) at 4100 mA»s. Five-second scans were obtained and resulting projection data were recon structed with a standard head mode convolution kernel available on the Siemens Somatom DR-H CT scanner. The table positioning accuracy of the scanner is ±1 mm. In order to study partial volume effects, scans were obtained through the test object from front to back and back to front at 1-mm intervals, with l-mm slice thickness. The test specimen required a minimum of 4 contiguous 1-mm slices to encompass all of the intentional defects within the CT scanner field of view. This is because the seeded inclusions do not lie in a single plane within the test object. It should be noted that even if all defects did lie in a single plane, it might be impossible to align the CT scanner plane of section with a specific plane internal to the test object by means of manual positioning. Results of scanning front to back and back to front are shown in Figs. 16 and 17, respectively. In the first series (Fig. 16), the outline of the plastic insert is only seen in the image for table position (TP") 42. A comparison of the images at TP 41 (or 43) in Figs. 16 and 17 clearly shows the consequences of the effect of volume averaging and the table hysteresis. 23 ATOM OR H MALLINCKRODT INST R.HTOM MHLLINCKRODT INST RAD SEEDED IN H R I C H T VMMM 1 E I- E^L I ((GrOM HUL ATOM OR H MMLLINC>ROOT INST HHTOM OP' H MMLLlm:hPODT IW^.T PwD TON GREEN SI3-N4 66-1 SEEDED >TON GREEr< ;.I3-M4 86-1 SEEDED -MMRi 42 I 02\ .ir4 1 ar, 1 o VANHIER ELLINGSON HML 44 VntlH I EF ELL HNL Fig. 16. Series of CT Images of Green-State Si3N^ Test Specimen with Seeded High-Density Inclusions. Slice thickness is 1 mm. The scan was made from front to back (table position 41-»44) , with 1-mm steps. 24 SOMATOM D R H M A L L I N C K P. O D T INST RAD y NORTON GREEN I 3-N 4 8 6-1 SEEDED HBl £ S-MAR 1H13 19^43^ D U1 ^63 S C A r-4 1 R I G H T cr TI 7 KV 1 £5 35G AS . 5 5 957 SL 1 GT 0 TP 4 1 V A H N I E R Fig. 17. Series of CT images of Same Specimen Shown in Fig. 16, with 1-mm Slice Thickness. The scan was from back to front (table position 44->-41) , with 1-mm steps. In addition to this series of tests, we conducted an initial study on the effects of a larger slice thickness. Figure 18 shows a 2-mm slice at TP 43. What is significant in this image is the identification of an additional inclusion (near upper edge of figure), which lies outside but in close proximity to the inclusion matrix. The results of these tests show that the 1000-pm orientation markers placed in a rectangular array about the other inclusions in the green Si^N, test object were visualized with 100% success. However, since the markers were not coplanar in their internal orientation, visualization of all of them required more than one slice. In addition, the plastic sheet used to 25 hold the defects has a much lower X-ray attenuation value than green Si-jN^, and thus the CT scan images show more contrast near these inclusions than might be expected had a plastic holder not been used. Fig. 18 CT Image of Same Specimen Shown in Figs. 16 and 17, with 2-mm Slice Thickness. Note detec tion of additional inclusion. ANL The detectability of inclusions is influenced by the discrepancy be tween inclusion size and CT slice thickness. In our case, there is a large discrepancy for many of the inclusions. With a slice thickness of 1 mm, each voxel (or volume element) can be assumed to be 100 x 100 x 1000 fim or 10 fim in size. The largest test inclusion is 500 ^m long; the smallest only 50 fim. Only the largest test inclusion, with a volume of 500 x 500 x 500 fim or 1.25 x 10 fim (assuming that the inclusions are roughly cubic), will occupy more than one voxel, as shown in Table II. Table II. Comparison Between Inclusion and Voxel Volume for Various Inclusion Sizes^ Inclusion Si ze Inclusion Number of (fim) Volume (fim ) Voxels/Indus ion 500 1.25 X 10^ 12.5 200 8 X 10^ 0.8 100 1 X 10^ 0.1 50 1.25 X 10^ 0.0125 a 7 3 Cubic inclusions and a voxel volume of 10 fim are assumed. To be detectable by the human eye, gray-scale changes in the CT images must have a signal-to-noise (S/N) ratio greater than 1. To determine whether more information was available in the images shown in Figs. 16 and 17, and keeping in mind that the voxel volume argument does not directly take into account attenuation differences, we made densitometer traces of 26 representative images. Figure 19 shows a series of densitometer traces from an image at TP 42. In each panel, a diagonal line indicates the set of pixels that was traced. (Note that in each case, the total width of the densitometer trace is much greater than the x-axis projection of the diagonal line.) Figure 19b, a densitometer trace along the Fe test inclusions, clearly shows the 200-Atm inclusion, but the background noise obscures any existing indi cations of the 100- and 50-fim inclusions. This problem is worse for the SiC inclusions (Fig. 19c), among which only the 500-^m inclusion is obvious. In the case of tungsten (Fig. 19d) , the 100-fim inclusion is obvious, as might be expected from the higher atomic number of this element. In order to better establish the ability to detect the inclusion, densitometer traces were made of another series of tomographic images at TPs 42 and 43, as shown in Fig. 20. In the case of Fe (Fig. 20a), it is not clear if we are detecting anything smaller than 200 fim. In the case of SiC (Fig. 20b), we now detect the lOO-^tm inclusion, but the 50-;um inclusion is still not apparent. The signals in the profile plots show a S/N ratio ranging from infinity to a minimum of 1.09 [-35 HU of noise on a baseline of 800 HU, with a signal of 35 HU above the noise; S/N = (35 + 800)/800 - 35)]. It is to be noted that low-contrast inclusions (inclusions with low attenuation compared to the matrix) that fill only slightly greater than 1% of a voxel are not likely to be detected in CT scans unless much smaller slice thicknesses are implemented. The "high-resolution" head-scan mode of the DR-H scanner was used for all the images presented here. These selec tions limit the field of view in the scanner to -25 cm diam, and utilize only the more densely packed central portion of the CT scanner X-ray de tector array. A high-resolution convolution kernel was used in the recon struction from projections to provide edge enhancment and better high- or intermediate-contrast detail at the sacrifice of increased image noise. The observed increased noise is due to sampling and detector variations, and cannot be removed by simply increasing the X-ray tube operating factors. With these CT scanner conditions, we have shown that it is possible to detect all of the 500-, 200-, and 100-fim inclusions in 1-mm slices. However, the 50-fim inclusions cannot be confidently separated from the background by visual inspection, and it is not altogether clear whether it is possible to detect them in profile densitometer tracings obtained with the CT scanner. It is very difficult to reach any conclusion regarding the 50-fim inclusions, since they were not definitely seen in the original X-ray radiograph obtained under laboratory conditions with static small-focal-spot settings such as are used for industrial applications. We know from other research that the 50-fim inclusions were not in line with the other defects. 27 SOMATOM Oft M MALLIHCKBOOT IN»T RAI^ QR N MALLINCKRODT INST MOHTON GRKKN •I3-N4 •«-! •tl^OBO CRCEN SI3-N4 •«-! •••DID ^•-MAK 1»'30 out •< •CAN ANL (a) (b) SOMATOM OR H MALLINCKRODT IN8T RAC^ DP H MALLINCKRODT INST RAD NORTON GRCCN SI3-N4 8C-1 8CCDCD GREEN SI3-H4 &6-1 DEEDED CR-MARf 19 3R OUI 021 SCAN ANL (c) (d) Fig. 19. Densitometer Traces of CT Image at Table Position 42, along Lines through (a) 1000-/im Fe Markers, (b) Fe Test Inclusions, (c) SiC Test Inclusions, and (d) W Test Inclusions. Peaks corresponding to known inclusions are labeled with the inclusion size in fim, or "M" for marker. 28 28- MAR 19 = 43 = 3U1 = 031 5CAN 1 (a) ri 7 ^s 1- 1 5L ST 0 gs--MAR 13 42 = DUI I ••02 ^^%«^ Wf Pf (b) TI KV AS GT Tl* 43 ^Hl, Fig. 20. Densitometer Traces of CT Images at Table Positions 42 and 43- Windows and Center Positions are Different from Those of Fig. 19. (a) Fe, (b) SiC. Peaks are labeled as in Fig 19 29 4.3. Turbocharger Rotors The dual-energy software package was Implemented on the Somatom DR-H to image both liquid Freon TF and a green-state injection-molded Si-jN^ turbo charger rotor (see Fig. 21). The particular turbocharger rotor selected for testing had at least one known defect, a circumferential crack, which is visible in Fig. 22. An axial CT section of the entire rotor was taken, with a slice thick ness of 2 mm and the dual-energy BH correction. Figure 23 shows the image produced from the "Hi-kV" image reconstruction data file. The crack is detected at "A" in the figure. The streak labeled "B" in Fig. 23 may be a second crack, or an artifact in the image. We plan to cut the rotor open to establish the nature of this feature. Fig. 21 Green-State Turbocharger Rotor Used in Experimental Dual- Energy CT Scan Tests. Fig. 22 Close-up Photograph of Turbocharger Rotor, Showing Circumferential Surface-breaking Crack. 30 TURBINE. GRRRETT/GREEN.^ SI3N4 HB j 19_HnV-S€. FRONT 1 85E 1 9 : 3 5 £• 8 H/SF DU7 035 L S HI N S C E F T Cl D IJ A L " E B TI 7 K V 1 £ 5 ; y £ £ 9 < A '=. S 3 C £ £ 0: c- t '-• .». l_ t— W M E L. L I N U S 0 N GT 0 ARGONNE NATIONAL LAB T P "3 6 Fig. 23. Axial CT Image of Rotor Shown in Fig. 22, Obtained with the Dual-Energy Beam-hardening Correction. Transaxial CT sections were also obtained. Figure 24, a section through the vanes, shows edge artifacts (the star pattern in the hub) but also shows an apparent low-density region near the core of the shaft. In order to obtain better information on the shaft, we obtained transaxial sections just upstream of the vanes, as shown in Fig. 25. Again, the "Hi- kV" reconstruction data were used to reconstruct the image. Figure 25 clearly shows regions of high and low density. A densitometer trace through these regions (Fig. 26) reveals the wide variation in density across the two regions. Fig. 24 Transaxial CT Image of Same Rotor, Taken Through the Vanes. 31 Fig. 25 Transaxial CT Image of Same Rotor, Taken Upstream of the Vanes. 24 5 Fig. 26 CT Image of Same Rotor Section Seen in Fig. 25, with Densi tometer Trace. 1 Ul I c 4.4. Ceramic-Ceramic Composites In order to further explore the application of CT to ceramics, we have conducted a preliminary test on chemical vapor infiltrated (CVI) ceramics Two types of specimens, " both made by Oak Ridge National Laboratory, were used for this preliminary evaluation. Set 1 (Table III) consisted of SiC/SiC specimens produced in early stages of the CVI process development; the actual composite regions were very thin. Set 2 (Table IV) consisted of SiC/SiC specimens made with improved CVI technology relative to set 1, along with one unlnflltrated specimen. Photographs of the test specimens of set 2 are shown in Figs. 27 and 28. Figure 27 shows three specimens which have been infiltrated and removed from the graphite holders. The differences in appearance between plain, satin, and chopped fiber configurations are obvious. Figure 28 shows the two remaining specimens of set 2, still in their graphite holders. The single gas inlet hole of one holder and the multiple gas exit holes of the other are visible. All dual-energy data were obtained with 125- and 85-kVp settings 1^ The results obtained for set 1 and set 2 are presented separately. 32 Table III. CVI Specimen Set 1 Specimen Fiber Fiber Loading Density Achieved after Identification Configuration (vol. %) Infiltration (% TD) CVI-65 satin weave 37 80 CVI-57 plain weave 42 82 CVI-94 triple plain weave 40 80 CVI-63 plain weave 39 82 CVI-88 unidirectional 53 74 CVI-64 random chopped 26 75 Table IV. CVI Specimen Set 2 Specimen Fiber Fiber Loading Density Achieved after Identification Configuration (vol. %) Infiltration g/cm- % TD reinfiltrat ion plain weave 40 127-1 plain weave 40 unknown'' 130-2 satin weave 40 2.54 130-3 random chopped 10 1.70 130-4 plain weave 40 2.31 80 Not removed frora holder. ""Average over whole specimen. CVD SiC/SiC Composites Fig. 27. Photograph of Three of the CVI SiC Specimens of Set 2 after Infiltration and Removal from Holder. From left to right are specimens 130-4 (plain weave), 130-2 (satin weave), and 130-3 (chopped fibers). 33 CVD SiC/SiC Comoositcs Fig. 28. Photograph of Two of the CVI SiC Specimens of Set 2, Still in Holders. On the left is specimen 127-1 (plain weave); the gas inlet aperture can be seen. On the right, the unlnflltrated plain-weave specimen is visible through the gas flow orifices on the hot face of the specimen holder. Set 1. The CT images obtained from set 1 were evaluated primarily to determine what void sizes could be discriminated as well as to ascertain the ability to detect an axial density gradient through the thickness of the specimens. Such density gradients could develop because of the way the zone of rapid SiC deposition moves from the top of the preform toward the bottom. The specimens of set 1 were sectioned by making parallel axial cuts on either side of a diametral line. The resulting "slices" (45 x 12 x 1-3 mm) were then placed in round molds for metallographic polishing. Figure 29 shows a metallographic section of the axial cross section of specimen CVI-57. This is a plain-weave specimen with 42 vol.% fiber, which was infiltrated to 82% of theoretical density or 2.31 g/cm . In this image, voids are dark and high-density regions are light. The density tends to be higher near the hot face because of the increased temperature and free gas flow. The CT results for specimen CVI-57 are shown in Fig. 30. As in Fig. 29, the lower density regions are dark and the higher density regions are light. Because the specimen was very thin, a 1-mm CT slice was imaged. The image was obtained without use of a dual-energy BH correction because the epoxy disk acted as a pre-beam hardener. (The epoxy disk is not visible in Fig. 30 because of the contrast conditions selected for display of these images.) Figure 30 shows that with current technology (a medical CT scanner), voids 50-200 fim in size cannot be individually detected. The gradient in density from hot face (2.5 g/cm^) to cold face (2.2 g/cm"^) is clearly detected, but not quantifiable without additional analysis. 34 0«NL-PMOTO 2599-8t COMPOSITES WITH DENSITIES EXCEEDING 80% HAVE BEEN PRODUCED BY INFILTRATING CLOTH-REINFORCED PREFORMS HOT FACE •'•%.' •- .- -. ' •• • : , • _ -*• *: «t- "JL?-"» • ••»'-«- - '- * COLD FACE Fig. 29. Metallographic Polished Section of Plain-Weave Specimen CVI-57 (42 vol. % Fiber, 82% TD). The gray regions are the individual Nicalon fibers, the white area around each gray fiber is the CVI SiC, and black regions are voids. Figure 31 shows a metallographic axial cross section of the right half of specimen CVI-64. This specimen was made with 26 vol.% random-length chopped fibers. Although high fiber loadings are difficult to obtain with chopped-fiber preforms, the porosity is finer and more uniformly distributed than the porosity present in cloth layup-type preforms. Figure 32 shows a CT image of specimen CVI-64. Since the CT data for a 1-mm-thick CT slice were quite noisy, a 2-mm-thick slice was used. However, 2 mm was the total specimen thickness, so image degradation due to partial- volume averaging with air could easily occur. To avoid this, two specimens were placed face to face and oriented nominally 90° from each other. The horizontal streaks in the image of Fig. 32 result from the placement of a second specimen against specimen CVI-64. Again, individual voids (<50 fim) are not detectable with the DR-H system as operated. However, density gradients are clearly detected. For example, the material near the circum ference of the composite (far right side of Fig. 31; top and bottom of Fig. 32) is more dense than material near the center of the composite. Figure 33 shows the right half of specimen CVI-65, a satin-weave specimen with 37 vol.% fiber and a density of 80% TD (2.31 g/cm"^) . A comparison of Fig. 29 with Fig. 33 clearly shows the difference in weave structure between plain and satin-weave preforms. Figure 34 shows a CT image of specimen CVI-65. Again, individual voids are not detectable. However, macroscopic density variations are detected to the -1-mm level. A comparison with the CT image of the plain-weave specimen CVI-57 (Fig. 30) shows a clear difference in overall texture, but the features are not sufficiently distinctive to allow one to identify an unknown preform. In general, it is quite clear from the results for set 1 that CT imaging with a BH correction (prehardening filter or equivalent) will allow gross density variations to be detected, but that small (50-200 pm) individual voids will not be detected with a medical scanner. 35 • MMPLE .. CVDR5- HE: I - 1 -FEB-86 FRONT ISlcl xe £1 £rs '1 • •r.F -> i o OO- (a) T I - Ul Jit.e^ -•'-• 59 C 2110 L 1 .T O (b) Fig. 30. CT Images of Specimen CVI-57. Black regions correspond to voids (low-density areas), as in Fig. 29. (a) Lower contrast, (b) higher contrast. 36 . ^ , t - Fig. 31. Metallographic Polished Section of Chopped-Fiber Specimen CVI-64 (26 vol. % Fiber, 75% TD). The black regions are voids; the white region (clearly seen at the hot face) is the infiltrated SiC; the gray regions are the random-length chopped fibers. Fig. 32. CT Image of Specimen CVI-64. White regions correspond to higher density regions. 37 Fig. 33. Photomicrograph of Satin-Weave Specimen CVI-65 (37 vol.% Fiber, 80% TD). Hot face is at top. Fig. 34 CT Image of Specimen CVI-65. CT slice thickness is 2 mm. Set 2. The CT imaging tests on set 2 had two objectives: (1) an initial determination of the effect of the graphite holder on image degra dation, as a step toward the use of CT imaging for on-line process control; and (2) a preliminary evaluation of the usefulness of the dual-energy image reconstruction software package for CVI ceramic specimens. The test specimens from set 2 were placed in the CT scanner in such a way that full plane-view cross sections would be obtained. Figure 35 is a digital radiographic image (topogram) showing all the specimens of set 2 as arranged on the CT table prior to tomographic imaging. This topogram reveals several interesting details. First, in the image of the uninfil- 38 trated specimen (top of Fig. 35), one can clearly see the single inlet hole in the graphite holder as well as the hot-face hole pattern. Second, the much higher density, infiltrated CVI specimen 127-1 (second from top) is clearly seen within its holder. Third, specimen 130-3 (fourth from top) clearly shows a density variation along the axial direction. (During pro cessing of specimen 130-3, water had contaminated the process gas partway through the run.) ^^^HP SOMHTOn 1 DP H MHLL I ML t PLiDT itrz-i f TH 0 H Ll 11"^" IV 125 ^^A ^1Iw i 1 <- • HmPHr oj-M ^^^1 r - •-' 4 HS £•£• ^^H Lf --^ S L 2 GT 0 • -- --• ^^^-11 .1^n-t^. . l.^W-3.. 1^0-4 1 The first set of CT image comparisons involved the three plain-weave specimens of set 2, which had been subjected to different process condi tions. Figures 36-38 show, respectively, CT images of the unlnflltrated specimen in the graphite holder; infiltrated specimen 130-4 (80% TD) after removal from the graphite holder; and the more completely infiltrated speci- raen 127-1, still in the graphite holder. The CT data were obtained with a standard water BH correction. In all these images, darker regions corre spond to lower density. The apparent hexagonal pattern seen in Fig. 36 results from the fact that the preform was made from a layup of plain-weave layers, with a 30° rotation between successive layers. Since the individual layers are less than 1 mm thick, the 2-mm-thick CT slice contains data from several layers. Figure 37 also shows the hexagonal pattern, even after infiltration to 80% TD. This is because the Nicalon fibers have a lower density (2.55 g/cm"^) than the CVI SiC (p = 3.2 g/cm"^) . However, Fig. 38, because of the contrast window settings selected, does not show the fiber. Instead, a radial density distribution is apparent. This is probably not caused by BH because this specimen was still in the graphite holder. Figures 39 and 40 show CT images of the satin-weave specimen 130-2 and the chopped-fiber specimen 130-3, respectively. Figure 40 was taken at the high-density/low-density interface of specimen 130-3 seen in the topographic image of Fig. 35. The CT images of Figs. 37-40 show significant characteris tic differences among plain-weave, satin-weave, and chopped-fiber specimens. 39 Fig. 36 CT Image of Unlnflltrated Plain-Weave Preform (40 vol.% Fiber) in Holder. Preform had been laid up with 30° angles between successive layers. CT slice thickness is 2 mm. Dark regions correspond to Ic^wor density regions. Fig. 37 CT Image of Infiltrated Plain- Weave Specimen 130-4 (40 vol.% Fiber, 80% TD). Preform was identical to that of Fig. 36. Fig. 38 CT Image of More Completely Infiltrated Plain-Weave Specimen 127-1 (40 vol.% Fiber) in Holder. Preform was identi cal to that of Fig. 36. 40 Fig. 39 CT Image of Infiltrated Satin- Weave Specimen 130-2 (40 vol.% Fiber, 88% TD). CT slice thickness is 2 mm. Fig. 40 CT Image of Chopped-Fiber Specimen 130-3 (10 vol.% Fiber, Average Density 55% TD) Taken at the Interface Between the Known Low-Density Region and the Higher Density Region. Figures 41 and 42 are dual-energy CT scans of the unlnflltrated plain- weave specimen of Fig. 36. Figure 36 (which incorporates a water BH cor rection) represents some improvement over Fig. 41. A large improvement in image quality may not be noticeable because the graphite holder provides some prehardening correction for the Nicalon material, which is reasonably low in density in the preform state. Fig. 41 CT Image of Specimen Shown in Fig. 36, Obtained with CT Scanner in Dual-Energy Con figuration at 85 and 125 kVp Head Voltages. 41 fjB^Bm*uvn:U'4'y.\i*ntiMJ^i^^MSl3i P» F iP ^^kSB^^^m • L Fig. 42 Portion of CT Image Shown in Fig. 41, Enlarged to Show More Detail of the Composite Structure. PLrtIN MEAVE V. SUMMARY AND CONCLUSIONS We have established that the BH problem must be solved when applying polychromatic X-ray CT to advanced ceramics. The most promising solution appears to be the use of dual-energy approaches with careful attention to the two energies selected for calibration. Medical CT scanners have tremen dous potential for application to ceramics. The main difficulties are related to the need for access to proprietary software and the limitation in spatial resolution caused by focal-spot size and slice thickness. Green- state parts up to 6 in. in size can be handled with existing 125-kVp X-ray heads. However, dense pieces of the same size cannot be examined at low energies with desirable S/N ratios. We have conducted many experiments with ceramic test pieces of various types, sizes, and shapes. Some problems still exist with so-called "streaming" or edge artifacts, even with dual energy. It is also quite apparent that calibration fluids will be necessary. Freon TF (z " 14, p - 1.8) may be a suitable calibration fluid for green ceramics and metholyzed iodide (p - 3.39 g/cra ) may be suitable for densified ceramics that are close to it in density. ACKNOWLEDGMENTS The authors would like to acknowledge the contributions of several individuals who have been instrumental in this work. Mr. Bob Knapp and Ms. Carolyn Offutt of the Mallinckrodt Institute of Radiology helped acquire the CT data. Dr. Kamal Amln of the Norton High Performance Ceramic Company, Northboro, MA, supplied many of the test samples used in this work, and Dr. Harry Yeh of the Garrett Ceramic Components Division of the Allied- Signal Aerospace Company, Torrance, CA, provided ceramic test parts. 42 REFERENCES 1. Brooks, R. A., DiChiro, G. , "Principles of Computer Assisted Tomography (CAT) in Radiographic and Radioisotopic Imaging," Phys. Med. Biol. 21, 689-732 (1976). 2. Brooks, R. A., DiChiro, G., "Theory of Image Reconstruction in Computed Tomography," Radiology 117, 561-572 (1975). 3. Reimers, P., Gilboy, W. B., Goebbels, J., "Recent Developments in the Industrial Application of Computerized Tomography with Ionizing Radiation," NDT Intl. 17, 197-207 (1984). 4. Reimers, P., Goebbels, J., "New Possibilities of Nondestructive Evaluation by X-Ray Computed Tomography", Mater. Eval. 41, 732-737 (1983). 5. Persson, S., Ostman, E., The Use of Computed Tomography in Nondestructive Testing of Polymeric Materials. Aluminum and Concrete, SKEGA AB, Ersmark, Sweden, 1985. 6. Segal, E., Notea, A., Segal, Y., "Dimensional Information Through Industrial Computerized Tomography," Mater. Eval. 40, 1268-1279 (1982). 7. Gilboy, W. B., Foster, J., "Industrial Applications of Computerized Tomography with X- and Gamma-Radiation," in Research Techniques in Nondestructive Testing, ed. R. S. Sharpe, Vol. 6, Academic Press, New York, 1982, pp. 255-287. 8. Flannery, B. P., Deckman, H. W., Roberge, W. G., D'Amico, K. L. , "Three-dimensional Microtomography," Science 232, 1389-1544 (1987). 9. Kinney, J. H. , Johnson, Q. C. , Bunse, V., Nichols, M. C. , Saroyan, R. A. Nusshart, R., Paul, R., Brase, J. M., "Three-dimensional X-Ray Computed Tomography in Materials Science," Mater. Res. Soc. Bull. XIIKl). 13-17 (1988). 10. Hounsfield, G. N. , "Computerized Transverse Axial Scanning (Tomography): Part I, Description of System," Br. J. Radiol. 46, 1016-1022 (1973). 11. U.S. Congress, Office of Technology Assessment, New Structural Materials Technologies: Opportunities for the Use of Advanced Ceramics and Composites - A Technical Memorandum. OTA-TM-E-32, U.S. Government Printing Office, Washington, DC, September 1986. 12. Allemand, R., "Basic Technological Aspects and Optimization Problems in X-Ray Computed Tomography," in International Advanced Course on Physics and Engineering of Medical Imaging. Maratea, Italy, 1984, p. 11. 43 13. Segal, E., Ellingson, U. A., Segal, Y., Zmora, I., "A Linearization Beam-Hardening Correction Method for X-Ray Computed Tomographic Imaging of Structural Ceramics," in Review of Progress in Quantitative NDE (Proc. Conf., Univ. of California, San Diego, August 3-8, 1986), ed. D. 0. Thonpson and D. E. (^imentl. Vol. 6A, Plenum Press, New York, 1987, pp. 411-417. 14. Segal, E., Ellingson, U. A., "Beam-Hardening Correction Methods for Polychromatic X-Ray CT Scanners Used to Characterize Structural Cerafflics." in Nondestructive Characterization of Materials II (Proc. 2nd Intl. Synp., Montreal, Canada, July 21-23. 1986), ed. J. F. Busslere et al.. Plenum Press, New York, 1987, pp. 169-178. 15. Sawicka, B. D., Ellingson, W. A., Photon CT Scanning of Advanced Ceramic Materials. Atomic Energy of Canada, Ltd., Chalk River Nuclear Laboratory, Report AECL-9384, 1987. 16. Ellingson, W. A., Segal, E., Vannier, M. W. , X-Rav Computed Tomography for Structural Ceramic Applications: Beam Hardening Corrections. Argonne National Laboratory Report ANL-87-24, May 1987. 17. Alvarez, R. E., Macovski, A., "Energy-Selective Reconstructions in X-Ray Computerized Tomography," Phys. Med. Biol. 21, 733-744 (1976). 18. Alvarez, R. E., Marshall, U. H., Lewis, R., "Tissue Characterization Using Energy-Selective Computed Tomography," Appl. Opt. Instrxim. Med., SPIE Proc. 221, 301-307 (1981). 19. Dual Energy Package -- Operating Instructions for Pandoros CT3 Generator on Somatom DR CT Scanner. Siemens Medical Systems, Inc., Iselin, NJ, 1986. 20. Talbert, A. J., Brooks, R. A., Morgenthaler, D. G., "Optimum Energies for Dual-Energy Computed Tomography," Phys. Med. Biol. 21, 261-269 (1980). 21. Fenster, A., Drost, D., Rutt, B., "Correction of Spectral Artifacts and Determination of Electron Density and Atomic Number from Computed Tomographic (CT) Scans," Appl. Opt. Instrum. Med. VII. SPIE Proc. 121, 333-341 (1979). 22. Genant, H. K. , Boyd, D., "(Quantitative Bone Mineral Analysis Using Dual Energy Computed Tomography." Invest. Radiol. 12, 545-551 (1977). 23. Adams, J. E., Chen, S. Z., Adams, P. H., Isherwood, I., "Measurement of Trabecular Bone Mineral by Dual Energy Computed Tomography," J. Comput. Assist. Tonogr. ^, 601-607 (1982). 24. Akutagawa, W. M., Huth, G. C., Levis, N. P., Drianis, G. C., Davis, R. L., "Increased Tissue Differentiation Using Color Display of Multiple- Energy CT Scans," Radiology Uh., 739-756 (1980). 44 25. Kalender, W. A., E. Klotz, Suess, C., "An Integral Approach to Vertebral Bone Mineral Analysis by X-Ray Computed Tomography," presented at the 71st Radiological Society of North America Meeting, Chicago, IL, November 17-22, 1985, Paper No. 375 and Scientific Exhibit No. 230. 26. Kalender, W. A., Perman, W. H. , Vetter, J. R. , Klotz, E. , "Evaluation of a Prototype Dual-Energy Computed Tomographic Apparatus: I. Phantom Studies," Med. Phys. 13, 334-339 (1986). 27. Lehmann, L. A., Alvarez, R. E., Macovski, A., Brody, W. R., Pelc, N. J., Riederer, S. J., Hall, A. L., "Generalized Image Combination in Dual kVp Digital Radiography," Med. Phys. 8, 659-667 (1981). 28. Hentea, T. I., Ellingson, W. A., Kriz, R. J., "Application of Magni fication Xeroradiography to Advanced Ceramics," to be published in the Proceedings of the American Ceramic Society Conference on Composites and Advanced Ceramic Materials, Cocoa Beach, FL, January 17-20, 1988. 29. Theis, J. D., Jr., "The Process Development and Mechanical Testing of a Carbon/Carbon Composite Fabricated by Chemical Vapor Infiltration of a Filament-Wound Substrate," in Proceedings of Third International Conference on Chemical Vapor Deposition, ed. F. A. Glaski, Am. Nucl. Soc, Hinsdale, IL, 1972, pp. 561-573. 30. Pfeifer, W. H., et al., "Consolidation of Composite Structures by CVI," in Proceedings of Second International Conference on Chemical Vapor Deposition, ed. J. M. Blocher, Jr., and J. C. Withers, Electrochem. Soc, New York, 1970, pp. 463-483. 31. Withers, J. C., "Chemical Vapor Deposition of Ceramic Composites Containing Whisker and Fiber Reinforcements," Ibid.. pp. 507-519. 32. Fitzer, E., Hagen, D., Strohmeier, H., "Chemical Vapor Deposition of Silicon Carbide and Silicon Nitride and Its Application for Preparation of Improved Silicon Ceramics," in Proceedings of Seventh International Conference on Chemical Vapor Deposition, ed. T. D. Sedwick and H. Lydtin, Electrochem. Soc, Princeton, NJ, 1979, pp. 525-535. 33. Stinton, D. P., Caputo, A. J., Lowden, R. A., "Synthesis of Fiber- reinforced SiC Composites by Chemical Vapor Infiltration," Am. Ceram Soc. Bull. 65(2), 326-335 (1986). 34. Ellingson, W. A., Vannier, M. W. , Stinton, D. P., "Application of X-Ray Computed Tomography to Ceramic/Ceramic Composites," to be published in the Proceedings of the 20th Annual Meeting of the International Metallographic Society, Monterey, CA, July 27-28, 1987. 45 APPENDIX A: EFFECTIVE ATOMIC NUMBER In CT work, it is necessary to compute a quantitative estimate of the X- or gajBua-ray energy absorption in heterogeneous media. The X-ray energy absorption in a given medium can be determined by means of well-established formulas if certain constants are known. These necessary constants are the effective atomic number, Z-^j or z, and electron density, »>o, of the medium. Theoretical considerations of energy absorption, based on calcu lated values of the effective atomic number of typical carbohydrates, fats, and proteins have been published by Mayneord. Actual measurements of effective atomic number in excised body tissues were reported first by Spiers, together with calculations of linear absorption coefficients and of real energy absorption per roentgen. The determination of effective atomic number is usually attributed to Mayneord. In fact, this procedure is based on the work of Walter. An expression for effective atomic number, z, as described by Mayneord is given here, along with the derivation of the equation. The Cheoretical basis of the method for computing z is the expression given by Walter for the photoelectric coefficient of an element, r - kZ- ,94,3 (Al) We can write the following expression for the mass absorption coefficient of any mixttire or compound (referred to as the total mass absorption coefficient): H| - ,^-1.,'-!... (A2) I''tota l ^ "l 2 Pj F^N ,, 3.94,3 P.N + . . le 1 (A3) In this model, we assvune that Rayleigh (coherent) scatter is negligible and mass attenuation coefficient - photoelectric effect + Compton scatter; ?-x linear absorption or attenuation coefficient, cm' , P physical density, g/cm , P weight fraction of element in compound or mixture (in %), A atomic weight, Z atomic number, N Avogadro's number, Compton scatter-absorption coefficient per electron, eo - and k 2.64 x 10"^^ (constant from Walter^). 46 Rearranging, ^2^2 ^ 2 94 2.94 ^-N W a + k a^Z^^- + «2Z2 + • P 2 t 2 94 2 94 ,3 CT -I- k (A5) °lV -^"2V ^ where rf - number of electrons per gram in the compound !i!i^!2!2^ = NS and a-1 = fractional electron content of element Z^ in the compound NP^ " ^"0 ' aj, a-i, ... are defined similarly. The often-quoted formula for effective atomic number "z is then defined as z = ^-^^ I 2.94 ^ ^ _ 2.94 (A6) With these definitions for effective atomic number (z) and electron density of the meditun (»?_) , the following expression for the total mass attenuation coefficient (fi/p) holds for any compound: -2 94 3 = n CT -I- kZ A P o According to this equation, (M/P)'7O should be a linear function of "z for a given wavelength. This has been tested with known elements and compounds, and the calibration obtained has been applied to determine ¥ experimentally for an unknown substance by using the measured value for (fi/p). To use this formula, TJ^ must be known. These values are usually obtained by 7-ray absorption measurements. REFERENCES Mayneord, W. V., "The Significance of the Roentgen," Acta lUCC 2 271-281 (1937). Spiers, F. W., "Effective Atomic Number and Energy Absorption in Tissues," Br. J. Radiol. 19, 52-63 (1946). 47 3. Walter, B., "Uber die beaten formeln zur berechnung der absorption der Roentgenstrahlan in einem beliebigen stoff," Fortschr. Geb. Roent- genstr. ^. 929-947 (1927). 4. Jones, D. E. A., "The Calculation of the Effective Atomic Number, Z," Br. J. Radiol. 52. 330 (1979). 5. Phelps, M. E., Gado, M. H., Hoffman, E. J., "Correlation of Effective Atomic Number and Electron Density with Attenuation Coefficients Measured with Polychromatic X-rays," Radiology HZ, 585-588 (1975). 6. Latchaw, R. E., Payne, J. T., Gold, L. H. A., "Effective Atomic Number and Electron Density Measured with a Computed Tomography Scanner," J. Comput. Assist. Tomogr. 2. 199-208 (1978). 7. Weber, J., van den Berge, D. J., "The Effective Atomic Number and the Calculation of the Composition of Phantom Materials," Br. J. Radiol. tiZ. 378-383 (1969). 8. White, D. R., "An Analysis of the Z-Dependence of Photon and Electron Interactions," Phys. Med. Biol. 22. 219-228 (1977). 9. Cunningham. J. R.. Library on Photon Interaction Coefficients and Electron Stopping Powers. Physics Division of the Ontario Cancer Institute. Toronto. Ontario. 1980. 10. Segal. Y. E.. unpublished information. 11. Hubbell. J. H. . Gerstenberg. H. M. , Saloman, E. B. , Bibliography of Photon Total Cross Section (Attenuation Coefficient) Measurements 10 eV to 13.5 GeV. U.S. Dept. of Commerce Report NBSIR 86-3461. 1986. 12. Hubbell. J. H. . Photon Cross Sections. Attenuation Coefficients and Energy Absorption Coefficients from 10 keV to 100 GeV. U.S. Dept. of Commerce. National Bureau of Standards. Report NSRDS-NBS 29. 1969. 13. Hubbell, J. H., "Photon Mass Attenuation and Energy-Absorption Coefficients from 1 keV to 20 MeV," Int. J. Appl. Radiat. Isot. 21, 1269-1290 (1982). 14. Jackson. D. P., Hawkes, D. J., "Energy Dependence in the Spectral Factor Approach to Computed Tomography," Phys. Med. Biol. 28, 289-293 (1983). 15. Jackson, D. P., Hawkes, D. J., "X-Ray Attenuation Coefficients of Elements and Mixtures," Phys. Rep. 22. 169-233 (1981). 16. Johns, H. E., Cunningham, J. R., The Phvsics of Radiology. 4th Ed., C. C. Thomas, Springfield, IL, 1983. 48 APPENDIX B: PHOTON SOURCES In medical CT scanners, polychromatic X-ray tubes are used as photon sources, along with a voltage/filter combination that typically yields a spectrum with an average photon energy ranging from 60 to 100 keV. These energies give usable transmission through objects of limited size and low-Z composition. Three isotopes are potentially useful for CT inspection of high-density materials: Ir, 'Cs, and °^Co. Each, due to its energy charac teristics, has advantages and disadvantages, and each has use in certain applications. The Cs source has a 30.2-year half-life, and when new emits about 1010 photons/second per cubic millimeter of material, providing a monoenergetic 662-keV photon. The specific activities of Co (half-life of 5.3 years) and Ir (half-life of 74 days) are higher by factors of 70 and 1560, respectively, and are more appropriate when scanning larger objects at higher speeds. The average photon energies of Co and Ir are 1250 and 390 keV, respectively. Isotopic sources are cheap and portable, and may be incorporated in CT scanners for field use, but they require special handling procedures and trained personnel for safety reasons. Industrial tomography with radioisotope photon sources can require unacceptably long measurement times unless high photon utilization is achieved. In transmission CT, fan beam geometry with a multiple beam detection system is generally used. For precise quantitative imaging, gamma-ray sources are superior to X-ray tubes in almost all respects apart from source brightness. The X-ray tube in a medical CT scanner has an equivalent source strength of 15,000 Ci distributed over a few square millimeters, several orders of magnitude brighter than practicable gamma sources. 49 Distribution for ANL-87-52 Internal: H. Drucker R. Massow J.J. Vaitekunas W.A. Ellingson (15) J.A. Morman R.W. Weeks D.C. Fee M.V. Nevitt H. Wiedersich F.Y. Fradin R.B. Poeppel ANL Patent Dept. S. Gopalsami A.C.Raptis ANL Contract Copy E.L. Hartig R.A. Roberts ANL Libraries T.I. Hentea J.P.Singh TIS Files (3) L.R Johnson E.M. Stefanski D.J. Lam J. Taylor R.L. Larsen CE. Till External: DOE-TIC, for distribution per UC-111 and UC-115 (47) D.T. Goldman, DOE-CH; F. Herbaty, DOE-CH ACUSTICA E SONICA S/CA. P-0. Box 12.946, Sao Paulo, Brazil Professor L.X. Nepomuceno ADVANCED MATERIALS & PROCESSES, Rt. 87, Metals Park, OH 44073 Laurel M. Sheppard AFWAL/MLLP, Wright-Patterson AFB. OH 45433-6533 Allan Katz Joseph Moyzis Robert Ruh Dale E. Chimenti AFSOR/NE. 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Maintenance & Repair Applications Division, EPRI NDE Center. P.O. Box 217097, Charlotte, NC 28221 UtaauHlIMP NMONALJJjfl WESJ "