We have also developed a more sophisticated means of creating 3D images which produces more realistic initial particle shapes. The algorithm is derived from previous work concerned with the development of synthetic 3D models of porous carbonate rocks in which both the solid matrix and pore space are percolating over a wide range of porosities (Schwartz et al 1991). It was found that a 3D image of striking visual resemblance and similar statistical properties to real carbonate rocks could be generated by thresholding suitable Gaussian convolutions of 3D random white noise images. By raising the threshold level, we can generate non−percolated data sets of irregularly shaped particles. In order to obtain the desired water−cement ratio, the algorithm is repeatedly invoked to generate new particles which are accumulated into one 3D image if they do not intersect any existing particles. The algorithm used is sketched in Figure 10. The output of this algorithm is shown in the 3D visualization of Figure 11. A partially hydrated data set with irregular particles composed of two phases, C3S and C3A, using the simple method of marking the nth plane is shown in Figure 12. In both figures, the visual appearance of these grains is quite like that of real cement particles. Intuitively, this is not an unreasonable result, since cement grains are produced by the essentially random process of smashing large lumps of clinker after they emerge from the kiln. It would be perfectly possible to perform a statistical analysis of the particle size distribution and attempt to adjust the parameters within the algorithm to ensure close agreement with corresponding experimental data; we have not, however, done this in the present work. This flexible algorithm for generating random particle shapes and size distributions may be of potentially wider significance in computational materials science than solely for describing cement grains.
To obtain more realistic multi−phase particles, such as those in the real 2D images, the process of accumulating particles can be modified so that when intersecting particles are detected, the overlap could be assigned to one of the other phases. This would produce irregularly shaped particles composed of irregularly shaped phases. 2D sections of 3D images produced in this way could then be cross−checked with the 2D images obtained from the BE/x−ray method described earlier. Such comparison would be necessary to determine the combination of convolution/thresholding needed to produce multi−phase particles with the correct morphological features.
Figure 12. 3D particles generated from smoothed white noise - multi-phase (size 128 x 128 x 64) (red = C3S, purple = C3A, Green = GYP).