###### Abstract  
This paper presents a cement hydration model over time using the cemdata07 thermodynamic database and a series of derived discrete solid phases (DSPs) to represent calcium silicate hydrate (C-S-H) as a binary solid solution with two end-members. C-S-H in cement is amorphous and poorly crystalline with a range of molar Ca/Si ratios from 0.6 to 1.7. It displays strongly incongruent dissolution behaviour, where the release of calcium into solution is several orders of magnitude greater than silicon. It is, therefore, important that any cement hydration model provides a credible account of this behaviour. C-S-H has been described in the cemdata07 thermodynamic database as a number of solid solutions using different end-members with differing levels of complexity. While solid solutions can be included in most modern geochemical software programs, they often lead to a significant increase in computation time. This paper presents how an  
C-S-H in cement is amorphous and poorly crystalline with a range of molar Ca/Si ratios between 0.6 and 1.7. It displays strongly incongruent dissolution behaviour, where the release of calcium into solution is several orders of magnitude greater than that of silicon. It is, therefore, important that any cement hydration model used to predict stable-phase assemblages, pH and pore chemistries over time employs a suitable C-S-H gel solubility model to accurately describe its variable composition and solubility behaviour. An example of this incongruent dissolution behaviour is given in [11]. Solid solutions are homogeneous crystalline structures where one or more component can be partly or wholly substituted on specific lattice sites with moieties of equivalent charge. If the host and substituting moieties are chemically similar, the formation of an ideal solid solution is possible. However, as is often the case, differences are sufficiently large enough to cause the formation of a nonideal solid solution, which can be readily confirmed by the appearance of a miscibility gap [12]. Solid solutions are of great importance in cement chemistry, where they can be used to describe the strongly incongruent dissolution behaviour of calcium silicate hydrate (C-S-H) gel [13; 14], the substitution of SiO\({}_{4}\)\({}^{4-}\) and 4 OH\({}^{-}\) in hydrogarnets [15; 16; 17] and the substitution of cationic Al\({}^{3+}\) and Fe\({}^{3+}\) and anionic 2 OH\({}^{-}\), 2 Cl\({}^{-}\), SO\({}_{4}\)\({}^{2-}\) and CO\({}_{3}\)\({}^{2-}\) components in AFt and AFm minerals [15; 16; 17]. If the thermodynamic properties of the unsubstituted and pure end-members are known, it is possible to calculate a series of DSPs that can be used to provide a credible thermodynamic model of cement hydration. Work by [18] demonstrates that DSPs can be derived for any ideal or nonideal solid solution. For example, [19] developed a DSP C-S-H gel solubility model based on two binary, nonideal, solid solutions that yielded satisfactory predictions of pH, Ca and Si concentrations for molar Ca/Si (C/S) ratios from 0 to 2.7, the occurrence of portlandite at C/S \(>\) 1.65, amorphous silica at C/S \(<\) 0.55 and congruent dissolution at C/S \(=\) 0.85. Previous work employing the density functional theory (DFT) [20; 21] developed thermodynamic predictions for silicate hydrates and other chemical systems and provided accurate predictions of thermochemistry using constitutive models. In the current paper, DSPs are derived for the jennite and tobermorite-II C-S-H gel solubility models in cemdata07 [7] and used to predict ordinary Portland cement (OPC) hydration as a function of time using the geochemical code PHREEQC. The results are compared to the experimentally supported GEM predictions from [22] using cemdata07 to provide comparisons.