The first step in generating an original three-dimensional cement particle microstructure is the creation of a three-dimensional image of digitized spheres representing the actual PSD of the cement of interest. Spheres have been chosen for computational simplicity, although digitized ellipsoidal shapes could also be employed. Bonen and Diamond [15] have measured the aspect ratio of cement particles in 2-D SEM images and found values on the order of two, suggesting that the use of spheres is an adequate approximation. For this study, a computational volume 100x100x100 pixels is typically employed. Spherical particles following the measured PSD are placed into this computational volume from largest to smallest in diameter, such that no two particles overlap. Periodic boundaries [3] are used to eliminate edge effects; if a portion of a particle extends beyond one or more faces of the 3-D box, the remainder of its volume is protruded into the opposite face. Particles typically range from 3 to 35 pixels in diameter. Since the scale of the model is such that one pixel is equivalent to 1 µm, the cement particles range from 3 to 35 µm in diameter, which encompasses most of the PSD of a typical cement, although some truncation at both the high and low ends is necessary.
Phase assignment during particle placement is implemented in one of two manners. In the first case, the particles are randomly assigned to be one of the major cement phases to match the volumetric phase fractions computed from the calculated Bogue composition of the cement. In this case, the particles are monophase and no effort is made to utilize the information available from the SEM image analysis of the cement. Thus, the only required inputs are the PSD of the cement and its Bogue potential phase composition. In the second case, during this initial placement, a portion of the particles are assigned to be gypsum, based on the Bogue calculation for the cement, with the remainder being cement. The four major clinker phases are then distributed amongst the pixels assigned to be cement as described in the next section, in order to match the volumetric and surface phase fractions determined from the SEM images.
During particle placement, particles can be optionally flocculated or dispersed [16]. For this study, since no dispersing agents were used in the experimental procedures, the particles were totally flocculated. To do this, each particle centroid is displaced a distance of one pixel in one of six random directions (+ x, + y, + z). If this move causes the current particle to impact another one, the two are flocculated and move as a single unit in all future random displacements. This algorithm is repetitively implemented until the user-selected number of flocs (one single floc in this study) is formed. The use of this algorithm is justified by recent experimental results [17] suggesting that such a flocculated structure will reform even after mixing.