Figure 2 shows the BE image and the four X-ray images for an ASTM Type I portland cement. In these images, each pixel is about 0.5 µm on a side, which is near the resolution limit for X-ray images. For the iron, aluminum, and sulfur X-ray images, the threshold levels used to produce binary images were determined by finding a local minimum in the greylevel histogram for each image. For calcium, the X-ray image is segmented into four levels, indicating high, medium, low, and no calcium content, depending on the local (pixel) intensity of the X-ray signal. By combining these four X-ray images with the BE image, each of the four main clinker phases of a portland cement along with gypsum may be distinguished. For instance, the presence of iron in the X-ray image indicates the tetracalcium aluminoferrite phase while the presence of aluminum but not iron indicates the tricalcium aluminate phase. Similarly, gypsum is indicated by the presence of sulfur. Here, we should note that all sulfates, including the sodium and potassium sulfates, are assigned to be gypsum, since the microstructure model described later assumes all sulfates will react with aluminates to form ettringite and monosulfoaluminate. If further segmentation were required, however, the X-ray images for sodium and potassium could be used to distinguish the various alkali sulfates from gypsum. Finally, the tricalcium and dicalcium silicate are identified based on the intensity of the BE and calcium X-ray images, where the brighter areas in these images correspond to the tricalcium silicate phases. If the calcium X-ray and BE images are insufficient to separate the silicate phases, an X-ray image for silicon is collected to process along with these two images. Here, segmentation can be based on the calcium/silicon ratio, which should be higher for C3S than for C2 S.
The segmented image produced in this fashion still contains noise and some pixels which are not porosity but which have not been assigned to one of the solid phases. To sharpen the phase distinction and eliminate the noise, the image is filtered using a median filter. Here, each "solid" pixel in the image is reassigned to be the phase occupied by the majority of its neighbors, excluding (resin-filled) porosity, if this majority exceeds a preset limit. Applying these processing steps to the images in Figure 2 results in the final image shown in Figure 3. The complexity of both shape and phase distribution for the cement particles shown in Figure 3 suggests that the artificial computer generation of such particles would be a formidable task, reinforcing the importance of the experimental technique described herein.
Images like those shown in Figure 3 can be further processed in a number of ways. The shapes and phase distributions of the individual cement particles can be stored in a database using a line segment encoding technique [6] and used to create computer-assembled images representing a given cement at a variety of water-to-cement (w/c) ratios, where the porosity is now assumed to be filled with water. The areas of the individual cement particles also can be assessed, although converting this two-dimensional size distribution to a true three-dimensional particle size distribution is possible only when assumptions concerning particle geometry (such as assuming spherical particles) are made [7]. The bulk area fractions, which should correspond to volume fractions [7], can be computed by simply counting the number of pixels assigned to each phase. These fractions can then be compared to those computed on a volume basis by applying the Bogue calculation to the oxide composition of the cement. Since cement hydration is critically dependent on the contact surface between water and the cement particles, the perimeter or surface fraction of each of the phases is also a quantity of interest. This measure can be determined by counting those pixel edges separating porosity and solid pixels for each solid phase.
Figure 2. Backscattered electron (top and X-ray images (bottom) for a real Type I portland cement.
Figure 3. Final 256*199 µm (512*398 pixel) image of real cement particle microstructure (w/c=0.36) for images shown in Figure 2. Phase colors are as indicated in color bars at the bottom of the image.