3.2 Assignment of Phases to 3-D Cement Particles

In version 2.0 of the CEMHYD3D programs, an extensive series of steps was necessary to properly distribute the four major cement clinker phases (C₃S, C₂S, C₃A, and C₄AF) amongst the cement particles (or more specifically the voxels comprising the cement particles in the three-dimensional microstructure). The goal of this phase distribution process is to generate a three-dimensional starting cement microstructure that matches the two-dimensional SEM/X-ray images of the real cement powder in terms of its particle size distribution (completed via genpartnew), phase volume (area in 2-D) fractions, and phase surface area (perimeter in 2-D) fractions. Matching of the latter two of these characteristics is achieved using the program distrib3d in version 3.0 of CEMHYD3D. This program accepts as input the starting microstructure consisting of cement (including calcium sulfate, limestone, etc.) particles, and the measured two-dimensional correlation files for various phase combinations (typically silicates, C₃S, and either C₃A or C₄AF) [2]. It then distributes the four major cement clinker phases amongst all of the particles labeled as cement, to achieve the user-requested volume and surface area fractions for each of these phases. The measured correlation files for the cements available in the cement images database are typically available at the ftp site, as outlined in section 2. These (three) correlation files must be downloaded to the directory where the distrib3d program is being executed, prior to its execution. The files typically all have the same root name (e.g., cement152), with the extensions sil, c3s, c3a, and c4f indicating the correlation files for the silicates, C₃S, C₃A, and C₄AF, respectively.

An example annotated datafile for using distrib3d is as follows:

-99                               random number seed
cem152w04floc.img                 filename of original microstructure image
cement152                         file root name for correlation filters (sil, c3s, c3a, etc.)
cement152w04flocf.img             filename under which to save final microstructure
0.7344                            volume fraction of C3S in microstructure to be created
0.6869                            surface area fraction of C3S in microstructure to be created
0.0938                            volume fraction of C2S in microstructure to be created
0.1337                            surface area fraction of C2S in microstructure to be created
0.1311                            volume fraction of C3A in microstructure to be created
0.1386                            surface area fraction of C3A in microstructure to be created
0.0407                            volume fraction of C4AF in microstructure to be created
0.0408                            surface area fraction of C4AF in microstructure to be created

The output created by executing the program distrib3d with the above input datafile (using a command such as distrib3d <distrib3d.dat >distrib3d.out at the command line prompt of a Linux or UNIX-based system) is as follows:

Enter random number seed (negative integer) 
-99
Enter name of cement microstructure image file
cem152w04floc.img
Enter root name of cement correlation files
cement152
Enter name of new cement microstructure image file
cem152w04flocf.img
0.734400
0.686900
0.093800
0.133700
0.131100
0.138600
0.040700
0.040800
Number of points in correlation file is 60 
Critical volume fraction is 3.194648
Phase    Volume      Surface     Volume    Surface 
 ID      count        count      fraction  fraction 
  0      627570            0  
  1      290463       267309     0.83004   0.83543
  2           0            	0       0.00000   0.00000
  3       59477        52656     0.16996   0.16457
  4           0            	0       0.00000   0.00000
Total    349940       319965
  5       10662        19661
  6       11581        14196
  7         247          634
  8           0            0
  9           0            0
  10           0            0
  11           0            0
 20           0            0
 24           0            0
 25           0            0
 26           0            0
 27           0            0
 28           0            0
nsph is 179 
Phase area count is 290463 
Phase surface count is 267309 
Hydraulic radius is 1.629928 
Now: 1.629928  Target: 1.659389 
Cycle: 1 
ntot is 400 
Ave. solid curvature: 59.118914 
Ave. air curvature: 112.222842 
Phase area count is 290463 
Phase surface count is 266566 
Hydraulic radius is 1.634471 
Now: 1.634471  Target: 1.659389 
Cycle: 2 
ntot is 400 
Ave. solid curvature: 59.017920 
Ave. air curvature: 112.716058 
Phase area count is 290463 
Phase surface count is 265868 
Hydraulic radius is 1.638762 
Now: 1.638762  Target: 1.659389 
Cycle: 3 
ntot is 400 
Ave. solid curvature: 58.920623 
Ave. air curvature: 113.191217 
Phase area count is 290463 
Phase surface count is 265161 
Hydraulic radius is 1.643132 
Now: 1.643132  Target: 1.659389 
Cycle: 4 
ntot is 400 
Ave. solid curvature: 58.825730 
Ave. air curvature: 113.654640 
Phase area count is 290463 
Phase surface count is 264478 
Hydraulic radius is 1.647375 
Now: 1.647375  Target: 1.659389 
Cycle: 5 
ntot is 400 
Ave. solid curvature: 58.732592 
Ave. air curvature: 114.109488 
Phase area count is 290463 
Phase surface count is 263750 
Hydraulic radius is 1.651922 
Now: 1.651922  Target: 1.659389 
Cycle: 6 
ntot is 400 
Ave. solid curvature: 58.641355 
Ave. air curvature: 114.555055 
Phase area count is 290463 
Phase surface count is 263055 
Hydraulic radius is 1.656287 
Now: 1.656287  Target: 1.659389 
Cycle: 7 
ntot is 400 
Ave. solid curvature: 58.551970 
Ave. air curvature: 114.991577 
Phase area count is 290463 
Phase surface count is 262474 
Hydraulic radius is 1.659953 
Number of points in correlation file is 60 
Critical volume fraction is 3.287097
Phase    Volume      Surface     Volume    Surface 
 ID      count        count      fraction  fraction 
  0      627570            0  
  1      257658       232284     0.73629   0.72597
  2       32805        30190     0.09374   0.09435
  3       59477        57491     0.16996   0.17968
  4           0            	0     0.00000   0.00000
Total    349940       319965
  5       10662        19661
  6       11581        14196
  7         247          634
  8           0            0
  9           0            0
  10           0            0
  11           0            0
 20           0            0
 24           0            0
 25           0            0
 26           0            0
 27           0            0
 28           0            0
nsph is 179 
Phase area count is 257658 
Phase surface count is 232284 
Hydraulic radius is 1.663855 
Now: 1.663855  Target: 1.759084 
Cycle: 1 
ntot is 400 
Ave. solid curvature: 58.195903 
Ave. air curvature: 95.943789 
Phase area count is 257658 
Phase surface count is 231676 
Hydraulic radius is 1.668222 
Now: 1.668222  Target: 1.759084 
Cycle: 2 
ntot is 400 
Ave. solid curvature: 58.082707 
Ave. air curvature: 96.832861 
Phase area count is 257658 
Phase surface count is 231100 
Hydraulic radius is 1.672380 
Now: 1.672380  Target: 1.759084 
Cycle: 3 
ntot is 400 
Ave. solid curvature: 57.971901 
Ave. air curvature: 97.703155 
Phase area count is 257658 
Phase surface count is 230527 
Hydraulic radius is 1.676537 
Now: 1.676537  Target: 1.759084 
Cycle: 4 
ntot is 400 
Ave. solid curvature: 57.863501 
Ave. air curvature: 98.554550 
Phase area count is 257658 
Phase surface count is 229905 
Hydraulic radius is 1.681073 
Now: 1.681073  Target: 1.759084 
Cycle: 5 
ntot is 400 
Ave. solid curvature: 57.757291 
Ave. air curvature: 99.388752 
Phase area count is 257658 
Phase surface count is 229289 
Hydraulic radius is 1.685589 
Now: 1.685589  Target: 1.759084 
Cycle: 6 
ntot is 400 
Ave. solid curvature: 57.653141 
Ave. air curvature: 100.206767 
Phase area count is 257658 
Phase surface count is 228660 
Hydraulic radius is 1.690226 
Now: 1.690226  Target: 1.759084 
Cycle: 7 
ntot is 400 
Ave. solid curvature: 57.550843 
Ave. air curvature: 101.010242 
Phase area count is 257658 
Phase surface count is 228086 
Hydraulic radius is 1.694479 
Now: 1.694479  Target: 1.759084 
Cycle: 8 
ntot is 400 
Ave. solid curvature: 57.450454 
Ave. air curvature: 101.798720 
Phase area count is 257658 
Phase surface count is 227451 
Hydraulic radius is 1.699210 
Now: 1.699210  Target: 1.759084 
Cycle: 9 
ntot is 400 
Ave. solid curvature: 57.351901 
Ave. air curvature: 102.572779 
Phase area count is 257658 
Phase surface count is 226840 
Hydraulic radius is 1.703787 
Now: 1.703787  Target: 1.759084 
Cycle: 10 
ntot is 400 
Ave. solid curvature: 57.255082 
Ave. air curvature: 103.333211 
Phase area count is 257658 
Phase surface count is 226297 
Hydraulic radius is 1.707875 
Now: 1.707875  Target: 1.759084 
Cycle: 11 
ntot is 400 
Ave. solid curvature: 57.160092 
Ave. air curvature: 104.079287 
Phase area count is 257658 
Phase surface count is 225773 
Hydraulic radius is 1.711839 
Now: 1.711839  Target: 1.759084 
Cycle: 12 
ntot is 400 
Ave. solid curvature: 57.066433 
Ave. air curvature: 104.814906 
Phase area count is 257658 
Phase surface count is 225188 
Hydraulic radius is 1.716286 
Now: 1.716286  Target: 1.759084 
Cycle: 13 
ntot is 400 
Ave. solid curvature: 56.974470 
Ave. air curvature: 105.537205 
Phase area count is 257658 
Phase surface count is 224642 
Hydraulic radius is 1.720457 
Now: 1.720457  Target: 1.759084 
Cycle: 14 
ntot is 400 
Ave. solid curvature: 56.883893 
Ave. air curvature: 106.248621 
Phase area count is 257658 
Phase surface count is 224060 
Hydraulic radius is 1.724926 
Now: 1.724926  Target: 1.759084 
Cycle: 15 
ntot is 400 
Ave. solid curvature: 56.794332 
Ave. air curvature: 106.952050 
Phase area count is 257658 
Phase surface count is 223511 
Hydraulic radius is 1.729163 
Now: 1.729163  Target: 1.759084 
Cycle: 16 
ntot is 400 
Ave. solid curvature: 56.706394 
Ave. air curvature: 107.642737 
Phase area count is 257658 
Phase surface count is 222932 
Hydraulic radius is 1.733654 
Now: 1.733654  Target: 1.759084 
Cycle: 17 
ntot is 400 
Ave. solid curvature: 56.620039 
Ave. air curvature: 108.320988 
Phase area count is 257658 
Phase surface count is 222344 
Hydraulic radius is 1.738239 
Now: 1.738239  Target: 1.759084 
Cycle: 18 
ntot is 400 
Ave. solid curvature: 56.534926 
Ave. air curvature: 108.989483 
Phase area count is 257658 
Phase surface count is 221765 
Hydraulic radius is 1.742777 
Now: 1.742777  Target: 1.759084 
Cycle: 19 
ntot is 400 
Ave. solid curvature: 56.451195 
Ave. air curvature: 109.647127 
Phase area count is 257658 
Phase surface count is 221258 
Hydraulic radius is 1.746771 
Now: 1.746771  Target: 1.759084 
Cycle: 20 
ntot is 400 
Ave. solid curvature: 56.368861 
Ave. air curvature: 110.293797 
Phase area count is 257658 
Phase surface count is 220684 
Hydraulic radius is 1.751314 
Now: 1.751314  Target: 1.759084 
Cycle: 21 
ntot is 400 
Ave. solid curvature: 56.287602 
Ave. air curvature: 110.932023 
Phase area count is 257658 
Phase surface count is 220117 
Hydraulic radius is 1.755825 
Now: 1.755825  Target: 1.759084 
Cycle: 22 
ntot is 400 
Ave. solid curvature: 56.207942 
Ave. air curvature: 111.557689 
Phase area count is 257658 
Phase surface count is 219538 
Hydraulic radius is 1.760456 
Number of points in correlation file is 60 
Critical volume fraction is 1.328790
Phase    Volume      Surface     Volume    Surface 
 ID      count        count      fraction  fraction 
  0      627570            0  
  1      257658       219538     0.73629   0.68613
  2       32805        42936     0.09374   0.13419
  3       45335        43659     0.12955   0.13645
  4       14142        13832     0.04041   0.04323
Total    349940       319965
  5       10662        19661
  6       11581        14196
  7         247          634
  8           0            0
  9           0            0
  10           0            0
  11           0            0
 20           0            0
 24           0            0
 25           0            0
 26           0            0
 27           0            0
 28           0            0
nsph is 179 
Phase area count is 14142 
Phase surface count is 13832 
Hydraulic radius is 1.533618 
Now: 1.533618  Target: 1.622425 
Cycle: 1 
ntot is 400 
Ave. solid curvature: 58.462594 
Ave. air curvature: 104.723878 
Phase area count is 14142 
Phase surface count is 13119 
Hydraulic radius is 1.616968 
Now: 1.616968  Target: 1.622425 
Cycle: 2 
ntot is 400 
Ave. solid curvature: 56.526800 
Ave. air curvature: 105.327738 
Phase area count is 14142 
Phase surface count is 12439 
Hydraulic radius is 1.705362