1. Introduction

Computed tomography (CT) employs a set of projections through a specimen to reconstruct its three-dimensional interior (e.g. Stock, 2008a). X-radiation and its attenuation are the basis for most CT reconstructions, and use of microCT, CT of micrometre structures within millimetre-sized specimens, is rapidly growing in materials science, biomedicine and other fields (Stock, 2008b, 2010).

Reconstruction can also employ the spatial variation of scattered (including diffracted) X-rays instead of transmitted intensity. The resulting maps are of regions with different scattering characteristics; in the case of polycrystalline solids and diffracted X-rays, the map is of crystallographic phases, possibly reflecting the influence of crystallographic texture. This alternative to absorption CT can be very valuable when the phases in question differ little in their X-ray attenuation characteristics. One example, SiC monofilaments in an Al matrix, is the subject of this report. Invertebrate mineralized tissue containing two forms of calcium carbonate, aragonite and calcite, is a second example where diffraction CT would be valuable.

The literature on X-ray scattering-based CT is not extensive. Reconstructions of a CT phantom (Harding et al., 1985), a lamb chop (Kleuker et al., 1998), a hydroxyapatite bone phantom (Barroso et al., 2001), rabbit bone (Stock et al., 2008), carbon (Bleuet et al., 2008), cement (Artioli et al., 2010), dental prostheses (Korsunsky et al., 2011) and metal (Abbey et al., 2011) have been reported. The last five are microCT studies.

This paper reports high-energy X-ray diffraction microCT of an Al-matrix SiC-monofilament-reinforced composite. The study employs a well characterized batch of materials (via three-dimensional absorption microCT and supporting techniques) (Kinney et al., 1990; Breunig, 1992; Breunig et al., 1993, 2006) to extend diffraction tomography beyond the earlier studies, specifically to establish the accuracy of crystallographic phase mapping and to examine the effects of crystallographic texture.

2. Materials and methods

The Al-matrix SiC-fiber-reinforced composite was fabricated by Lockheed in the 1980s. The unidirectional continuous-fiber SiC/Al laminate consisted of eight plies of SCS-8 SiC fibers (142 µm-outer-diameter SiC sheath surrounding a 32 µm-diameter C core) (Nutt & Wawner, 1985; Ning et al., 1990; Ning & Pirouz, 1991), a 6061-T0 Al matrix and two 1100 Al cover sheets (total panel thickness of 1.5 mm) (Breunig, 1992). A diamond wafering saw was used to cut the 1.5 mm-wide specimen parallel to the axes of the monofilaments from the 1.5 mm-thick sheet. The end of the specimen was trimmed into a pyramid (Fig. 1). A cross section was selected that could be sampled with the desired resolution in the time available for data acquisition. The pyramid shape also simplified matching of the diffraction CT slice with data from synchrotron absorption microCT.

Figure 1 Experimental setup. Note the SiC monofilament direction.

Two-dimensional X-ray diffraction patterns were collected at station 1-ID of the Advanced Photon Source (APS, Argonne National Laboratory) using 65 keV photons and the experimental arrangement shown in Fig. 1. The diffraction patterns were recorded on a General Electric Angio amorphous Si detector, and a PIN diode mounted in the beam stop measured the transmitted beam intensity. Data for the reconstructions were collected in the first-generation geometry (`pinhole' beam, translate-rotate pattern acquisition). Specifically, each projection was sampled by patterns collected at 90 x positions separated by 15 µm, and the slice by 91 projections separated by 2° (rotation about in Fig. 1). Each diffraction pattern was integrated for 1 s with 20 s of detector readout; since these data were collected, tuning of the data collection software and hardware has allowed patterns integrated for 1 s to be recorded every 1.2-1.3 s. The beam dimensions were 15 and 150 µm (horizontal and vertical, respectively), and the 15 µm horizontal beam dimension and 15 µm translation increment were selected to be about one-half of the diameter of the carbon fiber core, i.e. small enough to resolve this feature in the reconstructions. The larger (vertical) beam dimension paralleled the axes of the monofilaments and increased diffracted intensities, i.e. sampled more grains. The resulting anisotropic reconstructed volume elements (voxels) were then 15 × 15 µm in the plane of reconstruction and 150 µm perpendicular to the slice, much like in conventional clinical CT where thick slices preserve in-plane resolution while degrading out-of-plane resolution and minimizing local X-ray dose.

Diffraction patterns from a ceria reference sample (NIST SRM-674a) were used to calibrate the area detector-specimen separation (1 m), beam center and detector tilts (approximately perpendicular to the incident beam). The diffraction patterns were converted from polar coordinates, intensity I(r, ), where r is the radial distance from the pattern center and is the azimuthal angle (see Fig. 1), to Cartesian coordinates I(d, ), where d is the Bragg spacing, using the standard FIT2D (http://www.esrf.eu/computing/scientific/FIT2D/ ) and MATLAB (The MathWorks Inc., Nattick, MA, USA) routines (e.g. Stock et al., 2008). Fig. 2 shows a typical diffraction pattern in Cartesian coordinates; the scalloped edge at lower d (left side of plot) reflects the corners of the square active area of the detector.

Figure 2 (a) Typical diffraction pattern converted to d spacings and Cartesian coordinates: azimuthal angle over the range 1.0 < d < 4.4 Å. Intensities are represented by different colors: from lowest to highest intensity in the linear scale, black (0 counts), blue, green, yellow, orange, brown, red, purple, white (> 240 counts). The peak intensities nearly saturate the detector. (b) Sinogram [intensity (color) as a function of position and rotation angle] of SiC 10.2 diffracted intensity. The color bar inset on the left shows maximum to minimum diffracted intensities in the sinogram. The intensity scale is linear and runs from 0 to 100.

As labeled in Fig. 2(a), each diffraction pattern consisted of up to 11 rings; fewer were present when the SiC monofilaments, for example, were not intercepted by the incident beam for that particular (x, ). Each diffraction pattern was divided into 720 azimuthal bins and one radial bin per pixel; these sectors extended outward from the position of the incident beam. For each peak fit, the azimuthal mean intensity over 20 bins (10°) was computed. For each (x, ), this resulted in an array of 11 peaks × 36 azimuth bins for fitting of parameters such as peak intensity, center and full width at half-maximum intensity (FWHM). Each mean intensity (for the 36 bins of a given reflection) at each (x, ) was the input for reconstruction with filtered back projection, i.e. sinograms like that shown in Fig. 2(b). The transmitted beam intensity, again measured at each (x, ), was also reconstructed.

Synchrotron absorption microCT (full-field imaging) was also performed on the pyramid sample at station 2-BM, APS, to confirm the diffraction tomography results. Projections were recorded every 0.125° over 180° with 25 keV photons, and each (2 K)² slice was reconstructed with isotropic 1.45 µm voxels using a filtered back projection routine.

3. Results

The azimuth versus d spacing plot (Fig. 2a) labels 11 peaks that were complete or nearly complete within the area sampled by the detector. Table 1 gives the d spacing of each of these peaks and, where possible, identifies the crystallographic phase and hkl. Within the analyzed range (4.5 < d < 1.4 Å), there were three strong peaks attributable to Al (PDF card 4-787) and three to SiC (PDF card 29-1131): peaks 6, 9 and 11 and 4, 5 and 10, respectively. The other five peaks were much weaker, and their identification remains obscure. Diffraction rings 6, 9 and 11 (assigned to Al) all consist of a large number of strong discrete spots that uniformly populate the ring, a characteristic of a small number of relatively large grains. Discrete diffraction spots cannot be resolved in rings 4, 5 and 10 (assigned to SiC), but the intensity varied substantially with azimuth for all three rings, indicating the presence of small grains and significant crystallographic texture approaching 5 MRD (multiples of random distribution). No diffraction peaks were observed from C, i.e. the fiber cores or the coating on the monofilaments.

Fig. 2(b) shows a sinogram for the SiC 10.2 reflection, i.e. a plot of this reflection's diffracted intensity (color) as a function of position (horizontal axis) and rotation (vertical axis). The sinusoidal arcs (e.g. that labeled `f', light blue) trace out the paths followed by single fibers. The green areas of the plot are positions where two fibers are in line along the beam path, and orange areas are positions and angles where multiple fibers are intersected by the beam.

Fig. 3 shows slices reconstructed from the intensity diffracted by the three Al and the three SiC reflections identified in Fig. 2 and Table 1. The slices of Figs. 3(a)-3(g), 3(k) and 3(l) are scaled to the maximum diffracted intensity in each slice, and the color bar superimposed on an area of Fig. 3(l) (where no contrast was present) shows the linear scale of intensities. The number in the lower-right corner of each Al, SiC or identified reconstruction gives the intensity of the maximum in each slice relative to the maximum in the Al 111 map (Fig. 3a). Figs. 3(a)-3(c) present the three Al reconstructions, and Fig. 3(d) sums these three intensity reconstructions using the numerical values, not the individually rescaled maps. Figs. 3(e)-3(g) show the three SiC reconstructions, and Figs. 3(k) and 3(l) reconstructions with the unidentified reflections (d = 2.3 and 4.15 Å, respectively). Fig. 3(h) compares the Al and SiC reconstructions: the map of Fig. 3(d) (sum of three Al intensity maps) is shown in green, SiC 11.0 (Fig. 3f) in blue and SiC 10.2 (Fig. 3g) in red. The absorption contrast reconstruction from the transmitted beam in the diffraction experiments appears in Fig. 3(i) and a slice from the full-field synchrotron microCT data set in Fig. 3(j). The full-field slice is from a slightly different position from the slice in Fig. 3(i).

Figure 3 Reconstructions of the Al/SiC composite specimen. The area is 62 × 62 voxels (15 µm in-plane dimensions). Except as noted otherwise, the linear color table runs from lower to higher `intensity' using dark blue, light blue, yellow, red and dark brown; the relative `intensities' of the different reconstructions are given by the number in the lower-right corner of the panels [except (h)-(j)]; for reference, the `intensities' in panel (g) run from 250 to 0. Reconstruction with (a) Al 111; (b) Al 200; (c) Al 220. (d) Sum of the Al reconstructed slices shown in (a)-(c). Reconstruction with (e) SiC 10.1; (f) SiC 11.0; (g) SiC 10.2. (h) Sum of the three Al reconstructions (green) and of the SiC 11.0 reconstruction (blue) and SiC 10.2 reconstruction (red). (i) Reconstruction from transmitted-intensity data. (j) 2BM, APS, reconstruction of a slice near to the sampling plane in (a)-(i), recorded at 25 keV and reconstructed with 1.45 µm voxels. The reconstruction in (j) is scaled to match those in (a)-(i). In (i) and (j), black indicates the highest values of linear attenuation coefficient and white the lowest. (k) Reconstruction with diffracted intensity from the peak with d = 2.3 Å (the reconstruction with the d = 3.65 Å peak differs little and is not shown). (l) Reconstruction with d = 4.15 Å.

All of the reconstructions showed the same pattern of SiC fibers in the Al matrix. In the case of the Al reconstructions, the fiber positions were within the circular minima of Al intensity (see Fig. 3h). Three columns of fibers (three of the eight plies in this specimen) were present in this portion of the pyramidal sample. There were four complete and one partial fiber in ply 1 (p1, Fig. 3i), three complete and one partial fiber in ply 2 (p2), and four partial fibers in ply 3 (p3). Plies 1 and 2 contained regularly spaced fibers, but ply 3 had a significant gap. Between the top two SiC fibers in ply 1 (Figs. 3i and 3j), there was a large pore visible in both the transmitted-intensity and the full-field reconstructions, and this pore extended through many slices in the full-field data set.

The reconstructions with the Al diffraction peaks contained highly variable intensities. The lowest peak intensity was seen for the Al 220 reconstruction (Fig. 3c), which was nearly twice that of the strongest SiC reflection, 11.0 (Fig. 3f). The Al 111 reconstruction [positions above and below `#' in Fig. 3(a)] appears to show that most of the cover sheet was missing or was a different phase with similar absorption characteristics [see position `#' in the transmitted-intensity reconstruction of Fig. 3(i)], but the Al 220 reconstruction showed intensities within most of the cover sheet (Fig. 3c). The sum of Al reconstructions in Fig. 3(d) showed at least some Al intensity at all of the positions where Al is expected from the absorption reconstructions (Figs. 3i and 3j). The non-uniform intensity in the sum of Al reconstructions is consistent with the spotty diffraction rings (Fig. 2a) and with large grain size. The uniform distribution of Al diffraction spots within all of these Debye rings indicates that preferred orientation is not present.

Before comparing the different SiC reconstructions, it is useful to describe the reconstruction from transmitted intensity (Fig. 3i). The reconstruction showed clear C cores with diameters of about 3 voxels (45 µm). Barely enough absorption contrast existed to differentiate between Al and SiC (SiC was slightly more attenuating than the surrounding Al matrix), but SiC fiber diameters could be measured and were 10 or 11 voxels across (150-165 µm). The full-field reconstruction (Fig. 3j) showed the same features but with higher resolution.

In the 10.2 SiC reconstruction, the fibers appeared to have a core producing no diffracted intensity at this d spacing (Fig. 3g). The fibers have an outer diameter of between 9 and 10 voxels (135-150 µm) and an inner diameter of about 4 voxels (60 µm). The inner diameter is significantly greater than the core diameter, as seen in the transmitted-intensity reconstruction.

One would expect open areas in the center of all reconstructions of the SiC fibers [e.g. in Figs. 3(e) and 3(f) as well as in Fig. 3(g)]. Such open areas were not seen in the 10.1 and 11.0 SiC reconstructions, and the peak intensities in these two reconstructions are at matching positions. One difference between the 10.1 and 11.0 SiC reconstructions is that the latter has a weak halo surrounding the peak intensities for each fiber whereas the former does not. The diameter of the peak regions is about 4 voxels (60 µm) in the 10.1 SiC reflection and is slightly larger in the 11.0 SiC reflection, as a result of the halo (see Fig. 4c below). The fact that Fig. 3(h) shows discrete blue and red regions within the SiC fibers means that the SiC 11.0 and 10.2 intensities, respectively, come from different volumes within the specimen, specifically 10.2 is from the outer portion and 11.0 from the inner portion of the SiC fiber sheath. The positions of the peaks in the 10.1 and 11.0 SiC reconstructions match the C core positions in the transmitted beam reconstruction (Fig. 3i), which is physically unreasonable, and the reason for this apparent discrepancy is examined in the Discussion.

Figure 4 (a) Enlarged area around the two fibers indicated by red arrows in Fig. 3(j). (b) Area at the edge of the specimen, just above `#' in Fig. 3(i). In (a)-(b), the horizontal field is 100 voxels. White represents high and black low attenuation, and a small number (<5 vol.%) of high-attenuation impurity particles are scattered throughout. (c) Profiles through the center of the fibers shown in (a) for the 220 Al and 11.0, 10.1 and 10.2 SiC reconstructions.

Fig. 3(h) shows that there is almost no overlap between the Al and SiC reconstructions.

Fig. 4(a) shows an enlargement of an area of the full-field reconstruction containing the two fibers across which the line profile in Fig. 4(c) was measured, and Fig. 4(b) shows part of the surface area and cover sheet. Two zones of contrast in the SiC sheath are visible in Fig. 4(a), and high-absorption small-diameter particles are present in the Al phase, both between the fibers and in the cover sheet. From the full-field reconstruction, the fiber diameter was 142 µm, the C core diameter was 36 µm, the thickness of the outer SiC zone was about 42 µm and the inner SiC zone was 10-11 µm wide. Fig. 4(c) compares intensity profiles across two adjacent fibers for Al and SiC reconstructions; the red arrowheads in Fig. 3(j) show the positions between which the plots were obtained.

Several diffraction lines remain unidentified, but their reconstructions revealed different spatial distributions. The maximum intensity in the 4.15 Å reconstruction (Fig. 3l) equaled the maximum of the weakest SiC reflection (10.1, Fig. 3e), 4% of the largest maximum in an Al reconstruction. The only intensities were within a thin layer, and the position of this layer in the 4.15 Å reconstruction matched the outer surface of the cover sheet in the simultaneously collected, transmitted-intensity reconstruction. The order-of-magnitude higher resolution reconstruction (full-field, Fig. 4b) revealed a thin layer slightly separated from the Al cover sheet. The 2.3 Å reconstruction (Fig. 3k) is typical of the other three minor phases (not shown) and differed from the 4.15 Å reconstruction in two ways: its peak intensity is one-fourth that of the higher d spacing reflection and its intensities are colocalized with Al. It is interesting to note that the small-diameter high-absorption particles appear throughout the Al phase (Figs. 4a and 4b).

The fiber positions in the full-field reconstruction were compared numerically with those in the diffraction-based reconstructions using the fiber-fiber separations in each. The center of the holes in the 10.2 SiC diffracted intensity and the center of the C cores in the full-field reconstruction were used to measure the fiber separations, and Fig. 5 plots the fiber separations in the 10.2 SiC reconstruction (Fig. 3g) versus the corresponding separations in the full-field reconstruction (Fig. 3j). The regression line fit to the data shows excellent agreement between the two reconstructions: the slope equals one and R² > 0.99.

Figure 5 Separation between fiber centers in the 10.2 SiC reconstruction (Fig. 3g) versus the distance between fiber centers in the full-field reconstruction (Fig. 3j).

4. Discussion

Table 1 shows that all of the expected Al reflections were observed within the analyzed range of 4.5 < d < 1.4 Å. All of the SiC (PDF card 29-1131) reflections were observed within this d-spacing range if their powder intensities were greater than 20% of the maximum diffraction line. Much longer counting times would be required to detect the low-intensity SiC reflections (10.3, 10.4, 10.9).

No diffraction peaks from C were observed in diffraction patterns of any position or rotation angle, and this is not surprising. First, the atomic scattering factor of carbon is quite low at this high energy. Second, the transmission geometry superimposes scattering from C onto background and diffraction rings from several hundreds of micrometres of SiC or Al, so any signal from C would be very difficult to detect. Electron diffraction of these C fibers showed a turbostratic structure, not one with single- or polycrystalline material (Ning et al., 1990), and such structures produce very broad and relatively weak peaks. Extreme C texture (00.l parallel to the C core axes, i.e. consistent with turbostratic deposition) would not go undetected: specimen rotation over 180°, the very small diffraction angles, the range of C `crystallite' orientations within one fiber and the spread of fiber axis orientations combine to cover the entire pole figure.

4.3. Silicon carbon fibers

Fig. 2(a) shows strong minima in the SiC 10.2 diffraction rings at = 90 and 270°, i.e. along the fiber axes, and indicates that the 10.2 normals are concentrated orthogonal to the fiber axes. Fig. 2(a) also shows maxima in the 10.1 and 11.0 rings at  = 90 and 270°. Both observations are consistent with earlier work that found {111} of cubic -SiC strongly oriented parallel to the surface of the carbon fiber substrate (Nutt & Wawner, 1985); note that the cubic {111} planes correspond to the 10.2 planes indexed in the hexagonal system (Table 1).

Earlier microCT investigations showed that the fibers in this batch of composite material are close to parallel (Breunig, 1992; Breunig et al., 1993, 2006). In the full-field data set, the centers of three fibers were measured over 300 slices, and the fiber centers translated by an average of 17.5 voxels, with the range of values less than one-half of a voxel (thus consistent with the fibers being parallel). The displacements correspond to a 3.3° tilt of the fibers with respect to the tomography rotation axis. The slope of the fiber separation comparison for the full-field and SiC 10.2 reconstructions (Fig. 5) is one: thus, the sample orientation did not change significantly between the full-field and diffraction reconstructions, and the slight displacement of the full-field slice (Fig. 3j) from the transmitted/diffracted intensity reconstruction plane (Fig. 3k) did not affect the comparison.

The much higher resolution full-field reconstruction agreed with the transmitted-intensity reconstruction in terms of the fiber positions, but the latter's microstructural dimensions were larger. The transmitted-intensity reconstruction showed C core diameters of about 3 voxels (45 µm) and SiC fiber diameters of 10 or 11 voxels (150-165 µm), but, given the low contrast between Al and SiC, the latter figure should be viewed with some caution. The full-field reconstruction provided the following dimensions: C core diameter of 36 µm, inner SiC width of 10-11 µm and outer SiC thickness of about 140 µm, somewhat smaller than indicated by the transmitted-intensity reconstruction even allowing for its larger in-plane voxel dimensions. The full-field reconstruction also shows a low-attenuation layer coating the SiC fibers (Figs. 4a and 4b). The dimensions from the full-field reconstruction were consistent with dimensions from microscopy of the same type of fibers: C core and pyrolytic C coating, 36 µm diameter; SiC zones 1 and 2, 10.5 µm thick; SiC zones 3 and 4, 39.5 µm thick; outer coating, 3 µm thick (Ning & Pirouz, 1991).

The in-plane beam dimension and translation increment (15 µm) were both slightly less than one-half of the C core diameter, which is not optimum for precise metrology and contributed to the larger dimension of the fiber core seen in the transmitted-intensity compared to the full-field reconstruction. Low contrast is a second factor contributing to the larger than expected SiC fiber diameter seen in the transmitted-intensity reconstruction.

The 10.1 and 11.0 SiC diffraction reconstructions differed from the 10.2 SiC reconstruction. The diameter of 10.1 and 11.0 SiC regions of these reconstructions (Figs. 3e and 3f) was about four voxels (60 µm) with no open region visible at the fiber center. The fibers in the 10.2 SiC reconstruction (Fig. 3g), however, had open areas with (inner) diameters of four voxels (60 µm) and outer diameters of between 9 and 10 voxels (135-150 µm). Thus, the 10.1/11.0 diffracting region of the fiber fit snuggly within the 10.2 reconstruction, and the 10.1 and 11.0 reconstructions are from the inner SiC microstructural zone and the 10.2 reconstruction from the outer SiC zone.

The absence of open areas within the 10.1 and 11.0 SiC reconstructions is due to a combination of microstructural dimension (inner SiC fiber zone) and in-plane beam size. In the plane orthogonal to the fiber axis, the beam through the center of the C core passes through a significant volume of SiC of the inner zone (Fig. 6, left); simple geometry shows that this volume does not differ appreciably from that traversed by the beam passing tangentially through the inner SiC zone, given that the beam width in this plane is 50% wider than the inner SiC zone. If the SiC zone were thicker than the beam width, then the tangential path would intercept more material, diffracting more intensely, than the central path; this is the situation for the outer SiC zone (SiC 10.2, Fig. 3g), whose reconstructions show an open central area. Therefore, without a difference in signal for the tangential versus central paths, the SiC-free C core cannot be detected and the reconstruction algorithm will show solid 11.0 and 10.1 SiC reconstructions. Perhaps a better choice of in-plane beam dimension would have been 10 µm or less instead of 15 µm, but this would significantly decrease the diffracted intensities and the number of grains sampled.

Figure 6 Schematic to scale of one SiC fiber and the X-ray microbeam. (Left) Section perpendicular to the fiber axis showing the beam passing through the center of the C fiber core. (Right) Section parallel to the fiber axis and through the middle of the fiber. The fiber is tilted 3.3° relative to the long dimension of the beam. In situation 1, the beam (solid black rectangle) intercepts only the C core, but slight translations would produce diffraction of the inner SiC zone. In 2 (white rectangle outlined in black), half of the beam area is on SiC and half on C.

The 3.3° fiber tilt (relative to the reconstruction plane) and the out-of-plane beam dimension (150 µm) do not affect the above conclusion about the open area in the 11.0 and 10.1 SiC reconstructions. The longitudinal section through the tilted fiber (Fig. 6, right) shows that the relative volumes of inner SiC zone intercepted are nearly the same for central versus tangential paths. Beam position 1 (top) shows that the beam can barely avoid hitting the thickest portions of the inner SiC zone, so this will be a rare occurrence as the specimen is rotated. In positions 2, one half of the beam's cross-sectional area remains within the C core and the other half is within SiC. If the 15 µm beam dimension were decreased to 10 µm or less, then the fiber tilt would have a significant effect on whether or not the C cores could be detected in reconstructions with 11.0 and 10.1 SiC reflections.