At the National Institute of Standards and Technology (NIST), images such as the one in Figure 3 have been used extensively as input to a digital-image-based cement hydration microstructure model. The goal of the model is to simulate the microstructure of cement paste as it hydrates. Hydrated microstructures are then numerically evaluated to compute physical properties such as ionic diffusivity or elastic modulus, to quantitatively relate microstructure to properties and design improved materials [4]. Initially, the microstructure model was based solely on the hydration of C3 S, the major component of portland cement, but it recently has been extended to include hydration reactions for all of the major phases [8].
The model is based on a cyclic process of dissolution, diffusion, and reaction, and is similar to a cellular automaton [8 ]. Basically, material dissolves in pixel-sized units from the cement particle surfaces, diffuses within the water-filled pore space, and reacts to form hydration products. The silicate phases form calcium silicate hydrate (C-S-H) gel and calcium hydroxide (CH) while the interstitial (aluminate and ferrite) phases form a variety of products (hydrogarnet-C3 AH6, ettringite- AFt, and a monosulfoaluminate phase- AFm) depending on the amount of gypsum present in the system. Both surface- precipitated products such as the C-S-H gel and crystalline products such as CH are included in the rules representing the physical mechanisms of cement hydration. Both the chemical (molar) stoichiometry of the reactions that occur during hydration and the molar volumes of the products and reactants determine the volume (pixel) stoichiometry implemented within the digital-image-based computer model. For example, for each pixel of C3S which dissolves, 1.75 pixels of C-S-H gel and 0.61 pixels of CH will be formed. Since the hydration products occupy a larger volume than the solid reactants, the cement paste ultimately converts from a viscous suspension into a rigid solid material.
It is well known that the various phases of cement react at different rates in a cement paste. Within the model, probabilities can be assigned to the dissolution processes so that the rank order of these phase reactivities can be maintained (e. g. C3A > C 3S > C2 S, C4AF). The mobility of various diffusing species may be controlled by choosing the location of a diffusing species relative to the location of the dissolution source. Silicate and iron diffusing species are located near the dissolution source to simulate their low mobility, while calcium, sulfate, and aluminate species are located at random throughout the microstructure, representing a uniform dispersion of these species. By monitoring the reactions occurring in a given cycle of hydration, the heat of hydration as a function of the number of cycles or the degree of hydration may be obtained. For this calculation, either the heats of formation of the cement compounds or tabulated values of the heats of hydration of the four main cement phases may be used [ 9, 10].
Once cement particles have been stored in a database, they may be utilized to study the formation of interfacial zone microstructure. Interfacial zones in concrete have been shown to exhibit different microstructural characteristics than bulk cement paste both for cement paste-aggregate [11, 12] and cement paste-steel rebar [13] interface. A simpler version of the NIST microstructure model has been successfully applied to simulating interracial zone microstructure as a function of mineral admixture characteristics and aggregate absorptivity and reactivity [ 14]. For this model, a simple two-dimensional rectangular aggregate is first placed into the microstructure image and then the stored cement particles are added at random locations in the microstructure to obtain a representation of the desired global WIC ratio. The cement particles are not allowed to overlap any previously placed particle or any portion of the aggregate and are added in order of largest to smallest. The interracial zone microstructure may be quantified by measuring the phase fractions as a function of distance from the aggregate surface both before and after hydration. These measurements may then be compared to those obtained from SEM images of real concrete specimens [14].