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It has been shown previously that a cellular automaton model, based on digital images of continuum surfaces, can reproduce real sintering situations, using only local pixel-counting and random selection rules, where curvature differences are the driving force for mass transport and surface rearrangement [15]. This algorithm has now been successfully extended to 3-D. Realistic images can be produced in 3-D of simple sintered powder compacts, and preliminary investigations have been made, in qualitative agreement with experiment, of the percolation properties of the pore space. It is interesting to note that the percolation thresholds in Ref. [22] were determined by noting where the fluid permeability vanished. In the near future, we will be able to carry out 3-D fluid flow computations for 1003 pixel models like that discussed above. The capability already exists for 10002 pixel models in two dimensions [26].
Other physical features can also be built into the model. Grain boundary energies can be handled by checking whether a given pixel is at a boundary or not [13,14]. When measuring the curvature at such a pixel, a mis-match term can be put into the curvature box to bring in a grain boundary energy. It is important eventually to be able to build in elastic forces, so that stresses are taken into account as sintering proceeds, since grain boundary and lattice diffusion are driven by elastic stresses due to applied forces and surface tension. Simple methods for computing the elastic properties of digital images of model materials have been developed [27], and should be applicable after some further development to the 3-D sintering problem.