Variable Forms of Calcium Sulfate

The initial version of the cement hydration model was developed to only consider the dihydrate form (gypsum) of calcium sulfate. To increase the utility of the computer codes for studying the influence of PSDs and sulfate forms on cement hydration and microstructure development, version 2.0 of the model also includes reactions between the two other major forms of calcium sulfate (hemihydrate and anhydrite) and the cement clinker phases. All three forms of sulfate participate in similar reactions, but their dissolution rates are generally different. Based on data provided in Uchikawa et al. [19], the dissolution probability for hemihydrate has been set at a value three times that used for dihydrate, while the anhydrite has been assigned a dissolution probablity that is 80 % of the base value for the dihydrate. The cement hydration model allows for the conversion (hydration) of the anhydrite and hemihydrate forms of calcium sulfate to the dihydrate form during the hydration process; these two phases can also directly react with the aluminate phases present in the cement to form ettringite, etc.

Regarding ettringite formation, based on the experimental results of Odler and Abdul-Maula [20], the ettringite that forms in the model as a result of the reaction between C₄AF and sulfate is stable and does not convert to the monosulfoaluminate phase (Afm), regardless of the sulfate concentration remaining in the system. Ettringite formed from C₃A is only stable when sufficient unreacted sulfate is present in the system and the temperature is less than 70 ºC, possibly converting to the Afm phase when these conditions are no longer met. To implement this change in the new version of the hydration model, the diffusing aluminate species created from C₄AF are given a different phase ID (designated diffusing C₄A - DIFFC4A) than those created from the C₃A (in the original version of the codes, both these phases created similar diffusing C₃A species- DIFFC3A).

An example of the ability of the new version of the model to predict the influence of hemihydrate additions on the hydration of portland cement [21] is provided in Figs. 12 to 14. In this case, the particle size distributions of both the cement and hemihydrate were known, along with the detailed phase composition of the cement (one of the Dyckerhoff cements ¹ found in the cement images database described previously). The consumption of C₃S and C₃A and the production of ettringite were assessed using quantitative x-ray diffraction analysis [21]. While not a perfect fit, the model definitely captures the quantitative trends in the experimental results. Improving the model's ability to predict the effects of sulfate form and concentration on cement hydration is a subject of current collaborative research between NIST and Dyckerhoff Zement.

**Figure 12:** Experimentally measured (data points) and model predictions (lines) for C₃S consumption vs. time for different hemihydrate addition rates.
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**Figure 13:** Experimentally measured (data points) and model predictions (lines) for C₃A consumption vs. time for different hemihydrate addition rates.
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**Figure 14:** Experimentally measured (data points) and model predictions (lines) for ettringite formation vs. time for different hemihydrate addition rates.
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