Next: Data and techniques Up: Main Previous: Main
Once an adequate resolution 3-D image of a particle has been obtained, a recent paper has demonstrated how to use mathematical techniques to analyze the image using the coefficients of the spherical harmonic series [1]. Using these coefficients, an accurate image of the particle can be visualized, rotated, translated, and shrunk/expanded [2]. "Adequate resolution" means that there should be at least about 5 voxels to 10 voxels per unit length in all three particle dimensions. A voxel is a small cube that forms the basic element of a 3-D digital image, in the same way that a square pixel is the basic element of a 2-D digital image.
If the approximate particle size in any one dimension is x, then the voxel size should be about 0.1x. A mid-range fine aggregate is about 1 mm in size, so that an adequate resolution for it would be 100 µm/voxel, which is an easily obtainable figure for most X-ray computed tomography scanners. However, for portland cement, with a mean size of about 15 µm, an adequate resolution is then in the range of 1.5 µmm/voxel. This resolution can only be obtained by the best X-ray microtomography synchrotron sources.
Recently, a paper and companion web site has appeared entitled the "Visible Cement Database" [3], which presents the results of an X-ray microtomographic study of cement paste. The X-ray microtomography beam line at the ESRF facility in Grenoble, France was used to gather 3-D images at a resolution of 0.95 µm/voxel (cubic voxels) of a standard reference cement, CCRL-133 from the Cement and Concrete Reference Laboratory [4]. The cement had a Blaine fineness of about 350 m2/kg. Images were taken of the cement paste microstructure at various ages to compare with the output of the CEMHYD3D cement hydration model [5], which is usually run at nearly the same resolution, 1 µm/voxel. Image acquisition of the unhydrated cement particles was attempted, but because of motions of the cement particles in the water, clear images were only able to be obtained after 3 h of hydration. At this point, only a few percent by volume of the cement had hydrated, just enough to cause set [6]. These images could be analyzed, and the hydration products identified and removed. What was left after this process was the cement particles (except possibly the very finest particles having diameters on the order of a micrometer or less), which are very close to their original shape. It is this image that has been analyzed to numerically acquire cement particle shapes, quantitatively analyze the shapes, and visualize the shapes in 3-D. Thus for the first time, individual cement particle shapes can be seen in 3-D. Some surface modification might have taken place due to surface hydration, even for the larger particles, but the scale of the image, 0.95 µm/voxel, probably would not have picked up this small change.