It is good to remember where CMSC came from, before going on to describing what it is now and what it might be in the future. This description of its development is incomplete, but gives the main intellectual sources, at least for us.
From our point of view, there were really four intellectual sources. First came the work on the structure of amorphous semiconductors like silicon and germanium in the 1960´s and 1970´s (which was the background of one of us, EJG). Here the problem was first really faced of not having a periodic lattice upon which to do calculations of various material properties. Physicists had before developed crystal physics to a high degree, and had even allowed for crystal defects like dislocations. However, the problem of amorphous semiconductors, or of glass, was entirely different. There was no underlying crystal lattice. How was one to do any calculations at all? Analytical approximations were tried, with only a limited degree of success [12, 13]. Then models were built, where several hundred atoms (which pushed the computing power back then to the limit) were linked together randomly. Algorithms were applied to these models to compute properties, which then were compared to experiment in an attempt to explain the experimental results. In essence, these models and their associated computations were the beginning of the computational materials science for amorphous materials, at the atomic level.
Second came two developments in the materials science of concrete community, which appeared to be unrelated to the previous amorphous semiconductor work, but which were similar to it. These were both highly original, highly innovative developments. In 1984-5, Wittmann, Roelfstra, and Sadouki published two important papers on numerically simulating the structure and properties of concrete in 2-D [14, 15]. In these papers, which anticipate all our work at the concrete level, simple models were developed for simulating the shape and arrangement of aggregates in concrete. A finite element array was then applied to these models in order to compute properties like thermal conductivity and elastic moduli.
In the very next year, 1986, Jennings and Johnson published work on a three-dimensional (3-D) model of cement paste microstructure development for C3S pastes [16]. This was the equivalent of the amorphous semiconductor models, but at the cement particle scale, not at the atomic length scale. This effort carried the development of CMSC down to the micrometer scale of cement. Particles of various size, mimicing a cement particle size distribution, were dispersed randomly in 3-D. Various rules were applied to these continuum spherical particles to simulate the dissolution of cement and the growth of hydration products. We have been told that a digitized structure for the model was originally contemplated, but computer power at the time was deemed insufficient [17]. This is an example of the interplay between computer hardware developments and algorithm developments, as was mentioned in the Introduction. The percolation properties of this model were analyzed by Navi et al. [18] in the 1990´s. The further development of this model has been impeded because of the difficulty in carrying out the cement hydration process and subsequent calculation of properties using non-digitized continuum particles.
The fourth development, which completed the preliminary steps that led to our part of the development of CMSC over the last 11 years, was a paper showing how a random walk algorithm could be applied to continuum models to compute electrical and diffusive transport in their pore space [19]. We sought to apply this algorithm to Jennings´ cement paste model, since it was a continuum model. While learning this random walk algorithm, we experimented with digitizing the microstructure of simple models and then using random walks on the digital lattice. The combination of the ideas of random walks, digital images, and a cement paste hydration microstructure development model led directly to the first NIST cement paste hydration model. Fortunately, at the time of its first development, 1989, we had just enough computer power to barely implement a 3-D model of sufficient size (1003 pixels). Three-dimensional models are necessary to accurately compute properties of these highly random materials. Two-dimensional models and real 2-D images are generally insufficient because the percolation properties of these systems are quite different in two and three dimensions.
Once the model was on a digital lattice, a suggestion by Thorpe, one of the leaders in the amorphous semiconductor modelling work, led us to the realization that any finite element or finite difference algorithm will work on a digital lattice. Therefore, almost any physical property could be simulated, thus greatly increasing the ability of the cement paste model to be compared to experimental results. With the development of percolation theory [20] and composite theory [21-23] for digital lattices, all the pieces were in place for the further rapid development of CMSC.