Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part I: C₃S hydration in dilute suspensions

1 Introduction

An appropriate simulation of cement hydration is essential for predicting the various physical and mechanical properties of cement-based materials. The hydration of Portland cement is a complex process and many detailed features are still not clearly understood today. Recent reviews of the numerous mathematical models and simulations developed in the past 40 years show that a complete simulation that can accurately simulate both the hydration kinetics and the microstructure development still does not exist [1, 2]. This study further explores the possible mechanisms of cement hydration and introduces a new and relatively simplified numerical model (with only three independent parameters) to simulate the hydration kinetics.

The complexity of cement hydration process is partly due to the multiphase nature of Portland cement and the impurities present in its various phases and their interactions. As the major component whose hydration kinetics strongly resembles that of Portland cement itself, pure C₃S (cement chemistry notation: C=CaO, S=SiO₂, H=H₂O, A=Al₂O₃, F=Fe₂O₃) or alite (an impure form of C₃S) is often used to study the kinetics of cement hydration. Portland cement and C₃S hydration process is traditionally subdivided into five periods according to the derivative curve of hydration kinetics [3, 4]: (i) initial reaction, (ii) induction (dormant) period, (iii) acceleration period, (iv) deceleration period, and (v) steady state of slow reaction. The initial reaction, which probably depends on a number of factors such as water-to-cement (w/c) ratio and mixing method, occurs within a very short period of time and is difficult to measure accurately.

The early hydration mechanisms (transition from period 1 to period 2) are still not well understood today. At room temperature, the cumulative heat evolution measured during the initial reaction peak of alite is <1% of its total enthalpy of hydration [5]. As the total amount of hydration achieved during the first two periods is very small, cement hydration models are typically developed to simulate the last three periods of hydration only that are often referred to as the main hydration. The main hydration is traditionally believed to be controlled by a mechanism that gradually transforms from nucleation and growth (NG) controlled to diffusion controlled (DC). It is now well established that period 3 is controlled by the NG mechanism [1]. However, many details with regard to the shift of the rate-controlling mechanism are still uncertain and there is no clear separation point between period 4 and period 5. Some recent studies have shown that the NG mechanism can be used to model period 4 but did not rule out an eventual transition to the DC mechanism [1, 3, 6, 7]. The feasibility of using the traditional assumption to model period 4 will be further discussed in Part II.

Cement hydration models developed based on the NG mechanism cannot usually be used to explain hydration at later ages. A diffusion model, which cannot explain hydration at early ages (typically t<10–20 h), has been successfully used to model cement hydration up to 1000 h [8, 9]. Therefore, in order to successfully model the entire hydration process, it is most appropriate to combine a NG mechanism with a DC mechanism. The effectiveness of such a combined model to simulate the hydration behavior of C₃S paste has been demonstrated by many investigators [8–18]. However, test data were traditionally fitted with two completely different models, which often resulted in discontinuities at the transition points [8–18]. In this study, a new type of NG model developed from the particle level is proposed while an existing DC model developed on the same scale is modified such that the two models are compatible with each other and can be continuously connected.

As cement hydration is an extremely complex process, development of the model in Part I starts with a much-simplified system: C₃S hydration in stirred dilute suspensions with constant lime concentrations, where neither inter-particle interaction nor calcium hydroxide (CH) nucleation could occur. The model is fitted with previously published experimental data by Garrault et al. [19–22]. It should be pointed out that Garrault et al. [20, 22] had originally proposed a cluster model to simulate C₃S hydration, where a gigantic square matrix was used to describe the entire initial C₃S grain surface. The original model was only applicable to the NG stage of hydration, but has recently been further developed to simulate the entire hydration process [23]. The advantage of the model presented here over the cluster model is that it is analytical, has smaller number of independent parameters, it is less calculation intensive, and it is easier to use. In addition, the model can easily provide a much better time resolution than the cluster model due to its small calculation requirements. In Part II, the model is expanded to account for the hydration of Portland cement paste.

2 Model formulation

2.2 Modeling the nucleation and growth controlled stage

Hydration of C₃S produces C-S-H gel and CH. Experimental results have shown that C-S-H gel primarily nucleates and grows on particle surfaces while CH typically nucleates and grows in the pore spaces, with most researchers believing the former to be rate controlling [5, 29]. The fact that C₃S hydration in solutions of constant lime concentrations (with no nucleation of CH) exhibits a similar behavior as C₃S paste hydration further confirms this assertion [19–22].

How the nuclei are formed during C₃S or in cement hydration is one of the most controversial issues in developing NG models. Scherer et al. [26] have demonstrated that cement hydration kinetics can be modeled with the boundary nucleation and growth model by assuming either constant nucleation rate or a constant number of initial nuclei (site-saturated nucleation), with the latter providing a better fit to the derivative curve. It has been suggested that the decrease of silicon ion concentration during early hydration (from the peak reached within a few minutes after mixing to the end of the induction period) correlates with the precipitation of C-S-H nuclei from the solution [19–21]. Due to the relatively short duration, this period of hydration may be simplified as an instantaneous nucleation process. The “growth” of these initially formed nuclei then results in the acceleration period of C₃S hydration. Thomas et al. [30] pointed out that the macroscopic growth kinetics is technically a nucleation process in that the formation of new C-S-H particles is caused by stimulation of existing C-S-H particles. The autocatalytic theory is supported by the fact that the hydration of C₃S is greatly accelerated by small additions of C-S-H seeds. Such behavior may imply that nucleation at new sites is less likely to happen during the “growth period” as it seems easier for the ions to attach to C-S-H surfaces than C₃S surfaces. Even if new nucleation does occur, it has been demonstrated that early hydration kinetics is much more sensitive to the amount of instantaneously formed nuclei than the subsequent nucleation rate [31]. The model presented here only investigates the case of site-saturated nucleation.

As many details of the dissolution, nucleation, and growth process are still not known, simplifications and assumptions have to be made to represent this process mathematically. In this study, it is assumed that all nuclei are formed instantaneously on cement particle surfaces at the beginning of hydration. These nuclei are then assumed to grow at two uniform rates: parallel to the particle surface at a rate of g₁ and perpendicular to the particle surface at a rate of g₂. As nuclei growth is confined within the pore-space and accompanied by dissolution of the anhydrous core, the nuclei may not grow into regular shapes. The model presented here will test different growth scenarios to study the effect of the shape of the nuclei on the modeled results. The three simplified growth models include the cone model, the half-ellipsoid model, and the modified cone model. As will be shown later, these different growth scenarios only affect the fitted nuclei growth parameters and have very little effect on the fitting results of the model.

2.2.1 The cone model

In this model, nuclei are assumed to grow into cones due to the anisotropic growth rates. The total volume of the cones (i.e., hydration products) grown on a cement particle can be obtained by integration. As shown in Figure 1, consider a plane parallel to the particle surface at height y above the surface (ignore the curvature effect); the area of the intersection between the plane and the cone can be expressed as

Figure 1

Schematic illustration of nuclei growth on a cement particle (cone model).

(6)πx2=π(g1t-g1g2y)2 (6)

Let A₀ be the original surface area of the cement particle, and n the number of nuclei per unit surface area at the beginning of hydration (nucleation density). The total extended area of hydration product at height y can be obtained as

(7)Ahe(y)=A0nπ(g1t-g1g2y)2 (7)

If we ignore the surface area change of the anhydrous core and the curvature effect (i.e., assume the available area for growth on a cement particle always equals to its original surface area), the total extended area fraction of hydration product at height y becomes

(8)Ye(y)=Ahe(y)A0=nπ(g1t-g1g2y)2 (8)

The above assumption is only valid if the size of the cone is much smaller than that of a cement particle. The effect of such simplification on the modeled results will be further discussed in Section 3. The actual area fraction at height y is (taking into account overlap between different nuclei that are randomly distributed)

(9)Y(y)=1-exp[-Ye(y)]=1-exp[-nπ(g1t-g1g2y)2] (9)

The total volume of hydration product can be obtained by integrating the actual area of hydration product from 0 to the total height of the cones (g₂t). That is,

(10)Vh=∫0g2tA0Y(y)dy=A0g2t-A0g22ng1erf(πng1t) (10)

where erf is the error function. Assume the hydration of 1 unit volume of cement produces volume c of hydration product on the cement particle surface, the degree of hydration of a cement particle can be obtained as

(11)α=VhcV0=3KR0[t-12Serf(πSt)] (11)

At room temperature, the density of C₃S is approximately 3.15 g/cm³ while the density of C-S-H is approximately 1.8 g/cm³ during early age (1 day) [32]. Hence, c may be assumed to be 1.75 for C₃S hydration. A parallel growth rate constant S=ng12 and a perpendicular growth rate constant K=g₂/c are introduced here to couple some of the model parameters, which cannot be determined independently when fitting the proposed model to experimental data. These constants are introduced purely for the purpose of limiting the total number of simulation variables. The parallel growth rate constant may be regarded as a parameter that describes how fast the nuclei are spreading around the surface of the cement particle.

2.2.2 The half-ellipsoid model

This model is similar to the cone model except that nuclei are assumed to grow into half-ellipsoids instead of cones. Again, consider a plane parallel to the particle surface at height y above the surface (Figure 2), the area of the intersection between the plane and the half-spheroid can be expressed as

Figure 2

Schematic illustration of nuclei growth on a cement particle (half-ellipsoid model).

(12)πx2=π[(g1t)2-(g1g2y)2] (12)

Using a similar derivation process as the cone model, one can obtain the degree of hydration of a cement particle as follows:

(13)α=VhcV0=3KR0[t-12Sexp(-πSt2)erfi(πSt)]=3KR0[t-1πSD+(πSt)] (13)

where erfi is the imaginary error function, while D₊ is the Dawson function.

2.2.3 The modified cone model

In both the cone model and the half-spheroid model, the actual total area of hydration product at the surface of the anhydrous core (i.e., at y=0) is assumed to be

(14)Ah=A0Y=A0(1-exp(-πSt2)) (14)

which means that complete coverage (Y=1) is approached asymptotically when the curvature effect is ignored. A finite transition time between the NG and DC stages can only be obtained if the surface area decrease of the anhydrous core due to dissolution is taken into account. The modified cone model is developed to resolve such inconsistency by introducing a growth scenario that takes into account the surface area decrease of the anhydrous core during hydration (i.e., calculating the available area for growth incrementally). It should be pointed out that the modified cone model presented here is not necessarily more accurate than the first two models as the surface area increase with increasing distance from the anhydrous core is still ignored in all three models. The modified cone model may be considered as a lower bound solution for the cone growth scenario as it assumes the most severe impingement condition possible.

In this model, nuclei are still assumed to grow into cones. However, calculation of the total volume of the cones grown on a cement particle is performed in two steps here. The first step calculates the lateral growth of the total base area of the cones (i.e., total area of hydration product at the surface of the anhydrous core); the second step calculates the total volume growth by assuming that the cones grow a layer of their base area during a small time interval. The total extended base area of the cones at time t is

(15)Ahe=A0n·π(g1t)2=πA0St2 (15)

The increase of the extended area during each time increment is

(16)dAhe=2πA0Stdt (16)

As the distribution of nuclei is random, the fraction of the extended area that forms during each time increment that is real will be proportional to the area fraction of the uncovered particle surface, that is,

(17)dAh=dAhe(A-AhA)=2πA0St(1-AhA)dt (17)

where A_h is the actual base area of the cones while A is the total surface area of the anhydrous core. Apparently, the primary distinction of the modified cone model is that A is assumed to decrease with time due to dissolution, which renders Eq. (17) not integrable analytically. After substituting A₀ and A, Eq. (17) becomes

(18)dAh=2πSt(4πR02-Ah(1−α)2/3)dt (18)

During each time increment, the covered surface would grow a thickness of g₂dt, hence the incremental change of the total volume of hydration product can be expressed as

(19)dVh=Ahg2dt (19)

therefore,

(20)dα=Ahg2cV0dt=AhKV0dt (20)

The degree of hydration as a function of t can be obtained by numerically integrating Eqs. (18) and (20). When the curvature effect is ignored (i.e., assume A_h=A₀*Y), the integration gives the same results as the cone model,

(21)α=∫0tA0YKV0dt=3KR0[t-12Serf(πSt)] (21)

3 Model verification: the effects of particle size distribution

Garrault et al. studied the effect of particle size on hydration kinetics of C₃S in stirred saturated lime solutions with a liquid-to-solid ratio of 50:1 [22]. The lime content in the solution was kept constant to avoid dependence of hydration rate on lime concentration. Five samples with median diameters of 7, 10, 11, 12.5, and 14 μm, designated as sample 1, 2, 3, 4, and 5 respectively, were obtained by sedimentation of a C₃S suspension in ethanol. The particle size distributions of the samples were measured in about 10–15 gradations in the original experiment and re-digitized to more than 50 gradations. The total amount of hydration product (C-S-H) produced was measured for a period of 20 h for each sample. The data were re-digitized and converted to degree of hydration assuming the hydration of 1 mol of C₃S produces 1 mol of C_1.7SH₄ [33]. All three models developed in this study were fitted with the experimental data. Figure 3 shows the fitted results of the modified cone model as an example. The best-fit curves obtained with the various models are almost identical. Hence, the assumed growth scenario and impingement severity on a single particle (the modified cone model assumes more severe impingement than the cone model) has relatively small effect on the overall quality of the model and an excellent fit can always be obtained even though the assumed growth mechanism is not strictly accurate. The obtained model parameters are listed in Table 1. The higher specific surface area calculated in this study compared to the originally reported values is likely due to the larger number of gradation used during re-digitization of the PSD graph. The fitted diffusion constants remain invariant among different models, which are identical during the DC stage, while the fitted growth parameters (S and K) vary systematically with the assumed growth scenarios. The ratios of the growth parameters obtained from different models remain relatively constant for different samples. Further examination of the results shows that the transition time between the NG and DC stages predicted by these different models are nearly the same for particles of the same size. In other words, the growth parameters of different models are mainly adjusted to give the “correct” transition time that matches the experimental data. The more accurate the assumed growth scenario, the more accurate the fitted growth parameter becomes.

Figure 3

Experimental [22] and modeled hydration kinetics of samples with different particle size distributions.

The parallel growth rate constant (S=ng12) was found to increase slightly with particle size. As the parallel growth rate (g₁) is not likely to be dependent on particle size, the result suggests that the nucleation density (n) increases slightly with particle size. A more accurate relationship between nucleation density and particle size would have to be established by further experimental work. The slightly random variations of K with respect to particle size may be attributed to experimental errors, especially in particle size distribution measurements. For example, samples 2 and 3 had very similar particle size distributions [22], but their degree of hydration curves were quite different (Figure 3). The authors [22] also pointed out that “each size distribution curve is wide and can be indicative of the presence of agglomerates formed by elementary particles.” Despite all possible experimental errors, the variations in the fitted growth parameter (S and K) of all samples are within ±25% from their medians. As will be shown in Section 4, the fitted results seem to be more sensitive to K than S. Hence, similar values of K would be obtained if S was held constant for all samples.

The nuclei growth rates on a polished C₃S (sintered pellet) surface has been estimated experimentally using atomic force microscope without lime concentration control [21]. The estimated results were 4.1×10^-11 m/s (0.148 μm/h) for parallel growth rate (g₁) and 1.8×10^-11 m/s (0.065 μm/h) for perpendicular growth rate (g₂). Substituting the estimated value of g₁ into the fitted values of S in Table 1, the nucleation density was estimated to range from 0.3 to 0.8 μm^-2 for all different samples and growth scenarios, which is in good agreement with a range of 0.1–0.6 μm^-2 obtained by applying the BNG model (assuming a fixed number of nuclei) to the calorimetric data of C₃S paste hydration [26]. Bullard (personal communication) also estimated a value of 1.42 μm^-2 using the kinetic cellular automaton model [34, 35]. Substituting a value of 1.75 for c into the fitted values of K in Table 1, the perpendicular growth rate was estimated to range from 0.088 to 0.13 μm/h, also in reasonable agreement with the experimental observation (0.065 μm/h). In particular, the half-ellipsoid model seems to give the best fit of perpendicular growth rate (from 0.061 to 0.091 μm/h for different samples).

The traditional nucleation and growth mechanism cannot explain the deceleration of C₃S hydration rate in dilute suspensions, unless one assumes that nucleation and growth only occurs within a limited “reaction zone” close to the C₃S particle surface [36]. If diffusion is the controlling mechanism here, the obtained diffusion constant should be directly related to the property of the diffusion barrier (i.e., the inner C-S-H hydration product in this case), as all C₃S particles are completely surrounded by water all the time. As shown in Table 1, the fitted diffusion constant does not vary with the growth scenario and is largely independent of C₃S particle size. The slightly higher value obtained for sample 1 could be due to experimental difficulties of accurately measuring the sizes of fine particles or due to the limited applicability of the model when applied to very fine particles as it assumes the size of a nucleus is much smaller than that of a cement particle.

The fitted diffusion constant D (1.8–3×10^-15 m²/h) is in good agreement with previously obtained values for C₃S paste hydration using similar models, which are typically of the order of 10^-16–10^-15 m²/h [8–18]. Somewhat higher diffusion constants were obtained by Bishnoi and Scrivener (10^-15–10^-14 m²/h) [5] as well as by Xie and Bienacki (1.1×10^-13 m²/h) [2] when other diffusion models were applied. All these values are significantly lower than that suggested by Bullard who reports the diffusivity of H₂SiO₄^2- ion to be in the range of 10^-8–10^-7 m²/h [34]. For comparison, the effective diffusion constant for water into silica glass is estimated to be around 1.1×10^-16 m²/h at 25°C if we extrapolate the test data obtained in the temperature range of 200–550°C to room temperature [37]. As the porosity of the C-S-H (i.e., the diffusion barrier for cement hydration) is believed to be much higher than that of a dense solid, such as silica glass [2], the extremely low values of diffusion constants are sometimes used as evidence that the DC mechanism cannot be used to explain cement hydration kinetics [2, 6]. However, it should be noted that many details about the diffusion mechanism, as well as the property of the inner C-S-H, are still not well understood today. For example, as the space inside the diffusion barrier is not enough to accommodate all hydration products, diffusion could occur simultaneously in opposite directions. Namely, while water needs to diffuse inward to the anhydrous core certain dissolved ions also have to diffuse outward to the pore spaces. Additionally, the ion concentrations at both sides of the diffusion barrier are also not known [2].

The diffusion equation used in this study was developed assuming a hydrating cement particle is fully surrounded by water, which is only true in dilute suspensions or during the early stage of cement paste hydration. With the progress of hydration, the depletion of water and the bridging among different cement particles in a paste may reduce the area fraction of the particle surface exposed to water and hence result in lower apparent diffusion constant over time. Such phenomenon would apparently be more pronounced at lower w/c ratios. Previous studies have reported that the apparent diffusion constant decreases with decreasing w/c ratio [8, 38]. Interestingly, as will be shown in Part II of this study, such dependency of diffusion constant on w/c ratio seems to disappear when inter-cement-particle impingements are taken into account in the model [39]. The diffusion constants obtained for Portland cement paste hydration are about two orders of magnitude higher than those obtained here [39]. This is probably due to the presence of other hydration products in the diffusion barrier, which increases its permeability.

4 Influence factors of the proposed model

By changing the value of each parameter of the model individually, their effects on the total hydration kinetics can be observed. The effects of different model parameters on the obtained hydration kinetics curves of sample 3 are shown in Figure 4. It appears that the parallel growth rate constant S mainly controls the time at which hydration rate peaks (i.e., the duration of the NG stage) and, to a lesser extent, the degree of hydration achieved during the NG stage. The perpendicular growth rate constant K mainly controls the magnitude of the peak hydration rate and the degree of hydration achieved during NG stage. The diffusion constant D only controls the rate of reaction during the DC stage. An important implicit influence factor of the model is the particle size distribution. Figure 5 shows the effect of initial particle size on hydration kinetics (integral curves) of different particles. The transition point from the NG to the DC stage was found to occur earlier for smaller particles than for larger ones with the degree of hydration achieved at the transition point decreasing significantly with increasing particle size. Therefore, for a sample with multiple particle sizes, the transition of the rate-controlling mechanism occurs through a period of time instead of a single point. The transition period of a multiple-particle model is assumed to start when the first particles enter the DC stage and end when all particles have entered the DC stage.

Figure 4

Effect of different model parameters on total hydration kinetics curves (the units of S, K, and D are h^-2, μm/h, and μm²/h, respectively).

Figure 5

Effect of initial particle size on hydration kinetics of the particles (R₀ is the initial particle radius in μm; ♦ indicates the transition point between nucleation and growth and diffusion controlled stages).

The fact that C₃S hydration during the DC stage has been successfully modeled with a single particle size in previous studies [8–18] suggests that every sample has a characteristic particle size that can be used to approximately model its total hydration kinetics. The characteristic sizes for the five samples were found by manual fitting to be 3.18, 4.3, 4.5, 5.1, and 6.5 μm, respectively, which are very close to the reciprocals of the weighted mean inverse radius from the PSD data (3.0, 4.1, 4.2, 4.9, and 6.2 μm, respectively). The results modeled with the characteristic particle sizes were compared with those modeled with multiple sizes (the entire particle population of the samples) in Figure 6. The curves obtained with these two different approaches only deviated slightly from each other during the NG stage and were almost identical during the DC stage.

Figure 6

Comparison between model curves obtained with single particle size versus multiple particle sizes (♦ indicate transition points for single-particle model while · indicate the transition period for multiple-particle model).

5 Model verification: the effect of the number of initial nuclei

Garrault [20] has found that the quantity of C-S-H nuclei precipitated on a C₃S sample varied with the lime concentration of the solution in which the sample was suspended. Specifically, the total quantity (N) of precipitated C-S-H for 20 g of C₃S was found to be 50 μmol in a solution with a constant lime concentration of 11 mmol/l and 23 μmol in a saturated lime solution (22 mmol/l), resulting in a ratio of 2.17 for the initial nucleation density. Samples pretreated for 30 min at these two different lime concentrations (presumably wearing different amounts of initial nuclei) were further hydrated in saturated lime solutions to study the effect of initial nuclei on hydration kinetics. The modified cone model was fitted to experimental data by assuming only the number of initial C-S-H nuclei per unit surface area (which is proportional to S) was different for the two samples. As the particle size distribution data of the C₃S sample was not published, a characteristic particle size had to be assumed. It turned out that there existed one set of best-fit model parameters for each assumed representative particle size. This is again due to the fact that the modeled results are primarily controlled by the transition time between the NG and DC stages and the diffusion constant, the latter of which cannot be independently determined from the representative particle size. The growth parameters also need to be adjusted to give the “correct” transition time for different particle sizes. Experimental and fitted results (performed with two different representative particle sizes) are presented in Figure 7, where experimental curves were offset 30 min to the right to take into account the pretreatment time. As shown in the figure, nearly identical modeled curves can be obtained by changing particle size and model parameters simultaneously. The values of the model parameters obtained for different characteristic particle sizes are presented in Table 2. The modeled ratio of n, which is equivalent to the ratio of S, for the two samples (assuming g₁ is invariant) remains constant at 2, in reasonable agreement with the experimental result of 2.17. These results further confirm the validity of the model.

Figure 7

Experimental [20] and fitted hydration kinetics of C₃S in saturated lime solution with different quantities of calcium-silicate-hydrate nuclei.

6 Conclusions

A new type of particle-based model for C₃S hydration is proposed in this study. The model successfully combines the NG mechanism and the DC mechanism of cement hydration, both of which have been widely acknowledged. It takes cement particle size distribution as input and produces hydration kinetics as output. The model assumes that a constant number of nuclei are precipitated on the surface of C₃S particles at the beginning of hydration and that these nuclei grow parallel and perpendicular to the particle surface at two constant but different rates. Hydration of a C₃S particle is assumed to enter the diffusion controlled stage as soon as the anhydrous core is completely covered by hydration products. For the NG stage, three different models were developed based on different growth scenarios using the same growth parameters (a parallel growth rate constant and a perpendicular growth rate constant). These different models are then individually connected with the same DC model, which only involves one additional parameter (the diffusion constant). Fitting these models to experimental data suggest that the modeled results primarily depend on the transition time between the NG and DC stages and the diffusion constant. The growth parameter of different models may be adjusted by a constant factor to generate nearly identical fits to experimental data. Therefore, even though the actual dissolution and growth process is very complicated, all of the models presented in this study are adequate in simulating the overall hydration kinetics and explaining the different influencing factors of C₃S hydration. A more accurate NG model is only necessary if more accurate growth parameters need to be obtained.

In Part I of the study, the model is fitted with experimental data of C₃S hydration in dilute suspensions with excellent agreement. The nucleation density and the nuclei growth rate estimated by the model presented in this study are in good agreement with C₃S paste hydration studies [21, 26]. The diffusion constant is found to be largely independent of C₃S particle size and in reasonable agreement with C₃S paste hydration studies [8–18]. These results suggest that C₃S hydration in dilute suspensions has a very similar mechanism as C₃S paste hydration.