A flow-through method for measuring the dissolution rate of alite and Portland cement clinker

Cement and Concrete Research 51 (2013) 47–56

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A flow-through method for measuring the dissolution rate of alite and Portland cement clinker Jan Bisschop a, b,⁎, Alexey Kurlov a a b

Institute for Building Materials, ETH-Zürich, Schafmattstr. 6, 8093 Zürich, Switzerland TFB AG, Technology and Research for Concrete Structures, Lindenstrasse 10, 5103 Wildegg, Switzerland

a r t i c l e

i n f o

Article history: Received 10 April 2012 Accepted 12 April 2013 Keywords: Hydration (A) Kinetics (A) Image analysis (B) Diffusion (C) Ca3SiO5 (D)

a b s t r a c t A flow-through method for measuring dissolution rates of cement minerals is described. The quantity of dissolved material is measured after the dissolution experiment from SEM-BSE images. This makes it possible to measure dissolution rates of individual phases in multiphase cements. The SEM images also directly show if precipitation (hydration) occurred and how the surface roughness changed during dissolution. Furthermore, the method is designed for the purpose of determining if dissolution rate is reaction- or diffusioncontrolled, by changing water flow rate or by calculating expected diffusion fluxes. Dissolution rates of flat-ground Portland cement clinker and synthesized alite in deionized water were measured to demonstrate the potential of the method. Initial dissolution rates at lower flow rates were transport-controlled as indicated by the flow rate dependency and predicted diffusion fluxes. The highest alite dissolution rate measured in this study was 93 μmol/m 2/s. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction Hydration of Portland cement is a complex chemical process involving dissolution and precipitation reactions [1,2]. An understanding of what the rate-controlling reactions in cement hydration are, will benefit cement hydration modeling and ultimately the development of improved concretes or admixtures to control concrete setting [1,2]. It has been proposed that dissolution is a rate-limiting step in the early hydration of cements containing alite (Ca3SiO5), and that this explains the existence of the induction period in such cements [1–3]. The rate of alite dissolution decreases with increasing Caconcentration of the (pore) fluid [3,4,7], and dissolution therefore is expected to decrease rapidly in the beginning of alite hydration [3,7,8]. Solution controlled dissolution of many minerals can be explained by transition state theory and by the existence of specific dissolution mechanisms, i.e., etch-pit formation and step-retreat, at higher and lower undersaturations, respectively [9]. The recent observations of etch-pits in dissolving alite and the sigmoidal shape of the alite dissolution rate vs. undersaturation curve are in agreement with the dissolution theory proposed by Lasage & Lüttge [3,7]. This dissolution theory applies for minerals that dissolve when the rate of the dissolution surface reaction is lower than the rate of aqueous diffusion of the dissolved ions. Other dissolution theories exist for minerals that dissolve under transport (diffusion) controlled dissolution conditions [10]. Far from equilibrium, alite has a dissolution rate ⁎ Corresponding author at: TFB AG, Technology and Research for Concrete Structures, Lindenstrasse 10, 5103 Wildegg, Switzerland. Tel.: +41 628877227. E-mail address: [email protected] (J. Bisschop). 0008-8846/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cemconres.2013.04.013

that is 10 5 to 10 7 times larger than the corresponding rates for the silicate systems that were used to validate the dissolution theory of Lasage & Lüttge [3,7]. In fact, alite can be placed in the category of moderately soluble salts for which either transport processes or surface kinetics may limit the dissolution rate [11]. The possibility therefore exist that alite dissolution is transport-controlled for certain solvent properties, alite fabrication or powder milling procedures. Alite dissolution rates have been measured in a number of studies (e.g., [4–7]), but it remains unclear under what conditions alite dissolution is reaction- or transport (diffusion) controlled. Knowing the type of dissolution control would enable to more specifically implement the dissolution step in mechanistic cement hydration models. The difference between reaction-controlled and transport-controlled dissolution of a solid is shown in Fig. 1. If aqueous diffusion is ratelimiting then the solute concentration will approximately be saturated at the dissolution front (Fig. 1a). If the rate-controlling step is the reaction at the dissolution front, the concentration in the solution will be uniform (Fig. 1c). For some materials or under certain conditions dissolution may be controlled by a balance of transport and surface reactions (Fig. 1b). There are a number of ways to determine how the dissolution rate is limited [12]: Firstly, the flowing or stirring rate of the solution in a dissolution experiment can be changed. If this has an effect on dissolution rate, the dissolution is likely to be transport- or at least mixed-controlled. Secondly, by using Fick's law the maximum diffusion flux in an experimental system can be predicted and compared to the measured dissolution rate. If the calculated diffusion flux is significantly higher than the measured dissolution rate, dissolution is likely to be reaction-controlled. Finally, the morphology of the dissolution front may give a hint about the type of dissolution control.

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Csat

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(a)

(b)

(c)

Table 1 Composition of synthesized alite and Portland cement clinker samples. Synthesized alite

Cbulk

Distance from dissolution front Fig. 1. Solvent concentration profiles under different modes of dissolution: (a) diffusion rate control; (b) mixed rate control; and (c) reaction rate control.

XRD (batch wt.%)

SEM (vol.%)

Alite (Ca3SiO5) Belite (Ca2SiO4) Ferrite (Ca2(Al,Fe)2O5) Aluminate (Ca3Al2O6) Lime (CaO) Periclase (MgO) Pores

97.5 0.97 – 0.21 0.16 1.12 –

≥94.5 ? – ? ≤2 ? 4.5

Crystal size (sectional)

11.3 ± 6.2 μmx (n = 440)

PC clinker (SEM; vol.%)

84.2 ± 2.0⁎ 5–10 (estimate) 12.2⁎ 2.6⁎ 1.0⁎ – see Fig. 2b: 17% (I) to 48% (II) 23.9 ± 12.6 μm (n = 575)

*For the pore and belite free fractions; xmeasured from etched surfaces.

Reaction-controlled dissolution may lead to the formation of crystallographically shaped features (sharp edges; etch-pitch), whereas transport-control generally leads to rounded dissolution features. In the paper we propose an alternative method to measure dissolution rates of cements. The method has a number of advantages over existing techniques that are based on measuring ion concentrations in (diluted) suspension systems. In this study dissolution rates were measured directly from SEM images after a dissolution experiment. This allows to measure dissolution rates of individual phases in multiphase cements. The SEM images also directly show if precipitation (hydration) occurred in a dissolution experiment. The surface area of the dissolution front can also be directly measured from the SEM images, and this is an advantage when dissolution rate per surface area is to be determined. The accuracy of the dissolution rate value (per m 2) measured from suspension systems, largely depends on the accuracy of the surface area measurement of the tested cement powder. Finally, the flow through cell can potentially be designed in a way to obtain specific hydrodynamic conditions for which the diffusion flux can be accurately predicted. This, in addition to the possibility to change flow rate, would help to determine if dissolution is transport- or reaction controlled under certain conditions. The capabilities of the method are shown in this paper by experiments carried out on synthesized alite and Portland cement clinker samples in deionized water. 2. Methods 2.1. Materials The synthesized alite (polymorph MIII) had a molar ratio of CaO = 2.92; SiO2 = 0.97; Al2O3 = 0.02; and MgO = 0.11 and was prepared according to the protocol in reference [13]. Samples were compacted before burning in order to produce dense alite pellets. The average mineralogical composition of the alite batch, from which the samples were prepared, was measured with x-ray powder diffraction and the Rietveld method (Table 1). The 30 dissolution samples were prepared from two alite pellets with a diameter of 4 cm and a thickness of 8 mm. Most of them contained 1–2 vol.% CaO inclusions as determined from SEM-BSE images. The significantly higher CaO content of the dissolution samples compared to the average one of the alite batch, was possibly a result of mixture nonuniformities. The SEM-BSE images show the presence of small dark inclusions in the alite samples (~ 0.1 vol.%) that, considering the XRD results, probably consisted of periclase or tricalcium aluminate. The clinker samples were prepared from one batch of Portland cement clinker. The average volume fraction of alite in the clinker given in Table 1 was measured from many SEM-BSE images in 10 dissolution samples using image analysis. The volume fractions of calcium aluminoferrite, tricalcium aluminate and lime were also measured from BSE images in three randomly chosen samples. The image analysis consisted of manual tracing of the phase of interest,

convertion of the traced image into a binary image, and pixel counting in Matlab. The belite in the clinker occurred in localized crystal clusters that could be easily distinguished from alite in BSE images on basis of crystal shape and gray value (Fig. 5). The amount of belite in the clinker was estimated (from low magnification images in five different samples) to be 5–10% of the solid clinker volume. 2.2. Sample preparation In this project a simple flow-through dissolution experiment was developed utilizing a laboratory deionized water tap. The sample type used in this study was a half cylinder of epoxy resin containing an embedded piece of an alite pellet or raw clinker grain (Fig. 2a). This half cylinder was pushed into a rubber tube connected to the deionized water tap. The flow chamber above the sample was kept small by using a half cylinder having a diameter larger than the one of the tube, producing a flow chamber shape as shown in Fig. 2b. In order to obtain a good reproducible flow chamber size, the half cylinders needed to be of constant dimensions. Moreover, the final sample surface needed to be flat in order to obtain accurate dissolution rates. These requirements were achieved by the sample preparation procedure summarized below. A fragment (around 5 × 5 × 5 mm) of a crushed alite pellet or raw clinker grain was flat-ground on one side and embedded in epoxy resin mixed with coarse sand in a 2.5 cm diameter holder. The purpose of adding coarse sand around the alite/clinker fragment was to avoid grinding-induced rounding of the sample that would produce a slightly curved dissolution front. The hardened embedded sample was flat-ground to a thickness of 4 mm. Next, the sample

alite/clinker sample

(a) 9.5 mm

(b) flow area

I

II

1 mm Fig. 2. (a) Sample type used in this study; (b) cross-section view of sample in tube showing the size of the flow chamber and the variation in porosity of a clinker sample (see Table 1).

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glass plate

glue

Fig. 3. Cross-section view of dissolved synthesized alite sample with reference surface. Image is compressed in horizontal direction by a factor 30.

was laterally reduced in size by grinding to produce a rough half cylinder. It was then placed in a piece of rubber tube with a diameter of 8 mm. The rubber tube piece was squeezed between two glass plates to obtain an ovally shaped sample holder with the largest diameter being 9.5 mm and the shortest 6 mm. The tube was filled with epoxy resin to embed the sample for a second time. The excess hardened epoxy layer of 2 mm on top of the sample was ground away to obtain the sample dimensions as shown in Fig. 2a. The sample surface was finished using water on grit 1000p grinding paper, producing an initial surface roughness (Ra) of 0.6 μm. It was then dried and ultrasonically cleaned in isopropanol for 5 min, followed by drying in an oven at 70 °C for 1 h. The reference surface for the dissolution experiments was obtained by gluing two pieces of a microscope cover glass on both sides of a 5 mm wide strip of sticky tape glued over the sample surface center. Just before the dissolution the tape was removed from the sample surface experiment and the surface was cleaned with ethanol. 2.3. Dissolution experiments The flow-through dissolution experiment was created by pushing the half cylinder sample into the end of a long rubber tube with a diameter of 6 mm. This tube was connected to a flow meter (Vögtlin) which in turn was connected to a laboratory deionized water tap. The

(a)

49

flow rate was controlled manually by tightening or opening the tap and usually remained constant for long periods. The displayed flow rate was regularly checked by measuring the amount of water coming out of the tube over a given time interval. Dissolution experiments were carried out under a flow rate of 0.1, 1, or 3 l/min and dissolution times were 1, 3, and 6 h. One series of experiments was carried out under stagnant conditions in a 60 l container filled with deionized water. Each flow and stagnant experiment was repeated at least 3, respectively, 2 times on new samples. After the experiments, the samples were quickly dried, placed in isopropanol for 10 min and dried at 70 °C for 1 h, followed by epoxy impregnation and preparation for SEM-BSE analyses. The flow area above the sample was determined from sample cross-section images such as in Fig. 2b and was 3.7 ± 0.3 mm 2 in average for 10 samples. This chamber size resulted in average flow rates past the samples of 27.3 ± 2.2, 273 ± 22 ml/mm 2/min, and 819 ± 67 ml/mm 2/min for the 0.1, 1 and 3 l/min flow rates, corresponding to mean water velocities of 0.45, 4.55, and 13.64 m/s, respectively. The variation in flow area caused an uncertainty in flow rate of about 8%. The temperature of the deionized tap water changed over time spans of weeks and months. Experiments were carried out at temperatures ranging between 18.0 and 22.6 °C. The average temperature and standard deviation of all 60 experiments was 20.8 ± 1.0 °C. During a single experiment the temperature variation stayed below 0.5 °C in most experiments; a maximum temperature drop of 2 °C was recorded during two 6 h experiments. No trends were found by plotting dissolution rate versus actual temperature or actual flow rate for repeat experiments.

2.4. SEM image analysis One or two cross-sections of each impregnated sample were recorded using the BSE-detector in the low-vacuum mode of an ESEM (FEI Quanta 600), with the purpose to determine the amount of dissolved alite. Of each sample a total of 20 images were taken at 250× magnification and stitched together to cover the dissolved sample surface with a width of 5 mm in between the glass plate markers (see Figs. 2b, 3). Scanning direction was perpendicular to the dissolution front to avoid possible sample drift effects on the dissolved thickness. In both, the synthesized alite and clinker samples, the dissolution fronts were traced manually in Photoshop. Existing automated image processing algorithms for separating phases in hydrated PC paste could in principle also be used for this purpose.

(b) IV II

I

dissolved area III

porous area excluded from the analysis

Fig. 4. SEM-BSE image analysis examples for (a) a synthesized alite sample, and (b) clinker samples after 6 h of dissolution in high flow experiments. I = hydrated alite; II = hydrated CaO inclusion; III = CaO inclusion; and IV = sand grains, added to epoxy to reduce grinding damage of the dissolution front.

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Fig. 5. Partly dissolved/hydrated belite and alite crystal clusters in a high flow experiment after 6 h dissolution. Top of image represents the sample surface before dissolution.

The amount of dissolved material in the synthesized alite samples was measured by tracing the dissolved sample surface of 5 mm length. The original starting surface was obtained by connecting the points under the glue with a straight line (Fig. 3). The total area below the reference surface to the traced dissolution front was taken as the dissolved material, including the up to 2% CaO that the samples contained, but excluding the average porosity of 4.5% in the material (Fig. 4a). The size of the dissolved area as well as the depth profile and roughness (Ra) of the dissolution front were measured in Matlab. The dissolved area is converted into the dissolved volume per sample area based on the stereological principle [14]. The dissolved volume is divided by the molar volume of alite (70 cm3/mol) to obtain dissolution rates in μmol/m 2/s. The dissolution front is defined as the depth level at which 50% of the alite is dissolved. In clinker samples the amount of dissolved alite was determined as follows. First the original starting surface (with a length of 5 mm) was traced by using the two reference points under the glass markers and clusters of non-dissolved ferrite outlining the original surface (see Fig. 4b). Subsequently, all porous areas were excluded from the analyses (see Fig. 4b), which resulted in analyzed sample surface lengths ranging between 1.6 and 3.2 mm. In a few samples, belite crystal clusters were cut by the sample surface (see Fig. 5) and these

regions were also excluded from the analysis. Near the starting surface, alite dissolved with relatively minor precipitation in the flow experiments, but at depth the alite was usually replaced by hydrates (see Fig. 4b). The hydrated phase contained inclusions with the same brightness as the clinker and inclusions that are much darker in BSE-images. Large bright inclusions are considered to be non-dissolved clinker inclusions (Fig. 5) and were excluded from the traced area. Darker inclusions are trapped silica-rich sand grains from the grinding paper (Figs. 5,6) and these were ignored (i.e., included in the traced area). For the clinker samples, the dissolution front is defined as the depth level at which 50% of the alite dissolved. This requires knowing the volume fraction of alite in the (pore- and belite-free) clinker (Table 1). The definition is based on the assumption that ferrite does not dissolve in the experiments, and includes most of the aluminate. All dark inclusions within ferrite clusters are considered to be original or former (dissolved or hydrated) aluminate. Near the original sample surface some of the ferrite was flushed away, because it was encapsulated by dissolving alite. The material that disappeared from the original sample surface therefore was not only alite, but also consisted of ferrite and aluminate. The lowest depth level at which all of the original ferrite was still present (i.e., the 100% level in Fig. 9d–f) was assumed to be the level at which the volume fraction of disappeared clinker equals the average volume fraction of alite in the solid clinker. 3. Observations 3.1. Morphology of the synthesized alite dissolution front In the synthesized alite dissolution experiments, the degree of precipitation varied from almost none to minor under flow conditions. Two types of precipitates were observed. Relatively dense precipitates occurred in surface depressions protected from flowing water (Fig. 4a). These precipitates were uncommon and did not accumulate because they were washed away when the underlying alite dissolved. Precipitates that were more commonly observed occurred as thin sheets with a high angle to the original surface (Fig. 7b). These precipitates are believed to form on crack or grain boundary surfaces by water penetrating into the material, and remained connected to the surface after the adjacent alite dissolved. The degree of precipitation generally seemed to decrease with increasing flow rate, but clear exceptions to this trend exist. No trends were found between the final degree of precipitation and the dissolution rate for a given flow rate, suggesting that the limited precipitation in the synthesized alite experiments did not affect the dissolution rate. For the experiments carried out in stagnant water this was probably not true, because the alite dissolution front became covered with a dense uninterrupted and accumulating layer of cement hydrates. The overall morphology of the dissolution front is given by the roughness (Ra) of the surface profile traced from the SEM images. Ra is defined as the arithmetic average of the absolute values of the vertical deviations of the roughness profile from the mean line. This parameter increases with dissolution front depth and is also affected by flow rate (Fig. 8). The roughness development is related to the crystal size distribution; a crystallographic orientation dependent dissolution rate; and preferred dissolution starting from grain boundary and intracrystalline fracture surfaces. 3.2. Dissolution rate of the synthesized alite

Fig. 6. EDX element map showing clinker composition in a high flow experiment after 6 h dissolution. Top of images represents the surface before dissolution. Bright grains in Si map are trapped sand grains from the grinding paper.

The depth profiles of the alite dissolution front in experiments under three different flow rates and after 3 different dissolution times are given in Fig. 9a–c. There generally is a good reproducibility of dissolution front profiles despite the temperature variations and the uncertainty in flow rate mentioned in Section 2.3. At the highest

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(a)

(b)

(c)

(d)

(e)

(f)

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20 µm Fig. 7. Variation in degree of precipitation among synthesized alite (a–c) and clinker (d–f) samples after 1 h of dissolution at flow rates of 0.45 (a,d), 4.55 m/s (b,e) and 13.64 m/s (c,f). Dissolution rates of the shown samples were for (a) 36.8; (b) 54.8; (c) 93.3; (d) 45.5; (e) 59.5; (f) 57.1 μmol/m2/s.

velocity of 13.6 m/s the reproducibility was relatively poor. The dissolution front depth is defined as the depth level where 50% of the alite dissolved. Dissolution front depth versus time for all alite experiments including the stagnant experiments, are plotted in Fig. 10a. The first clear trend is that the dissolution rate increased with flow rate (Figs. 10,11). Secondly, it can be observed that dissolution rate went down with increasing dissolution time in flow experiments. For the stagnant experiments it is observed that the dissolution rate was decreasing in the first 3 h, but increased again from 3 to 6 h (Fig. 10a). The dissolution rates in Fig. 11 are calculated on the basis of either the initial or final surface area of the dissolution front. These values represent the upper and lower bounds for the average first hour dissolution rate. The true average dissolution rates would fall in between these limiting values.

3.3. Clinker dissolution and hydration The presence of non-dissolving ferrite crystal clusters had a strong effect on the morphology of the dissolution front in clinker samples. These clusters created regions in the dissolution front that were protected from the bulk water flow and where, as a result, precipitation of hydrates was not hindered. The larger the dissolution front depth, the more and denser precipitates were observed (Figs. 4b, 5, 7d–f). As for the case of synthesized alite, the degree of precipitation generally seemed to decrease with increasing flow rate in the first hour, but clear exceptions to this trend exist. There were no

indications that precipitation had a significant slowing down effect on the dissolution rate during the first hour. The chemical and structural nature of the hydration products that formed in this system has not been determined, but appears to be like C-S-H-gel. The high water content of the gel is suggested by the oxygen enrichment at the hydrated locations (Fig. 6). Moreover, the gel had high absorbed water content as indicated by the presence of shrinkage cracks in the dried gel (Figs. 4b, 5, 7d–e). Calcium hydroxide crystals have not been observed as a hydration product. Clusters of belite crystals were occasionally exposed at the sample surface. The ratio in dissolution front depth of belite over alite was around 0.5 at these locations (Fig. 5). The morphology and evolution of a polished clinker dissolution front in a precipitation-free region is shown in Fig. 12. Alite crystals showed many intracrystalline (cleavage) cracks that formed by thermal contraction gradients upon quenching after high temperature clinkering, or by the grinding of stressed crystals. The cracks were sites of accelerated dissolution and formed the tapered ‘pits’ that are visible on sample cross-sections. Crystal and inclusion boundaries were also sites of accelerated dissolution (Fig. 12). No obvious dislocation-induced etch-pits were observed in these experiments, meaning that they either were not present or too small to be observed in SEM images. Smaller or larger rounded dissolution pits were sometimes observed, but these were probably caused by dissolution starting from void- or solid inclusions that occurred commonly in alite crystals (Fig. 12a). 3.4. Dissolution rate of alite in clinker

Roughness Ra (µm)

4

3

2

0.45 m/s 4.55 m/s 13.64 m/s (high) 13.64 m/s (low)

1

0 0

2

4

6

Dissolution time (hours) Fig. 8. Roughness (Ra) development of the dissolution front in synthesized alite samples. The data points for 13.6 m/s are the averages of the three high, resp. two low dissolution rate points in Fig. 11.

The experimental set-up produced a reasonable reproducibility of the alite dissolution front depth profiles in clinker (Fig. 9d–f). The profiles are vertically stretched to compensate for the loss of ferrite and aluminate from the clinker surface during the dissolution experiments as explained in Section 2.4. The maximum amount of ferrite and aluminate loss was limited by their combined volume fractions in the clinker, meaning that the total loss of material from the top surface was at most 119% of the alite content in the clinker (Fig. 9d–f). The alite dissolution front is defined as the depth level where 50% of the alite is dissolved. It can be seen that the dissolution rate decreased with flow rate and dissolution time in the flow experiments (Fig. 10b). The depth versus t 1/2, given in the inset of Fig. 10b, is approximately a straight line, meaning that the dissolution front migration was slowing down as fast as expected for a diffusion limited migration process. For the stagnant experiments it can be seen that dissolution rate was going down in the first 3 h, but remained more or less constant after 3 h (Fig. 10b). The dissolution front depth of alite in clinker after one hour of dissolution was similar to the one in synthesized alite (Fig. 10b). In

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Dissolved alite fraction (%)

100

(a)

(b)

(c)

80 60 40 20 0 0

10

20

30

40

50

60 0

10

20

Depth (µm)

30

40

50

60

70 0

Depth (µm)

10

20

30

40

Depth (µm)

Dissolved alite fraction (%)

120 100

(d)

(e)

0.45 m/s

4.5 m/s

(f) 13.6 m/s

80 60 40 20 0 0

10

20

30

40

50

60 0

10

20

Depth (µm)

30

40

50

60

70 0

Depth (µm)

10

20

30

40

Depth (µm)

Fig. 9. Dissolution front profiles of synthesized alite (a,b,c) and alite in clinker (d,e,f) after 1 h (blue), 3 h (red), and 6 h (black) for flow rates of 0.45, 4.55, and 13.64 m/s.

to sample did not correspond to variations in the observed degree of precipitation. Moreover, the clinker samples showed much higher degrees of precipitation than synthesized alite samples (Fig. 7), but the dissolution rates of the former were generally higher at velocities up to 4.55 m/s (Fig. 11). After one hour dissolution time, dissolution of synthesized alite became increasingly faster than the dissolution of alite in clinker. This can be explained by the increasing thickness and densification of the layer consisting of the non-dissolving clinker phases intermixed with precipitates that slowed down diffusion processes in the

Dissolution front depth (µm)

terms of total amount of dissolved material the initial dissolution rate of alite in clinker was slightly larger (Fig. 11). Note that the excess material loss above the 100% level shown in Fig. 9 is excluded in the dissolution rate calculation. Also note that the dissolution rate is only calculated on the basis of the initial surface area of the dissolution front. The final surface area of the alite dissolution front in clinker can in principle be measured, but this requires many higher magnification images to be taken. Precipitation did not seem to have slowed down the dissolution rate of alite in clinker in the first hour. This is because variation in the dissolution rate from sample

(a)

50

(b)

40 30 0

1

syn. alite: stagnant syn. alite: 0.45 m/s syn. alite 4.55 m/s PC-alite: 0.45 m/s PC-alite: 4.55 m/s

2

20 10

0

1

2

PC-alite: stagnant PC-alite: 0.45 m/s PC-alite: 4.55 m/s

0 0

1

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Dissolution time (hours)

5

6

0

1

2

3

4

5

6

Dissolution time (hours)

Fig. 10. Effect of dissolution time and flow rate on dissolution front depth in synthesized alite (a) and alite in clinker (b). Insets show depth plotted versus t1/2. Error bars indicate maximum and minimum values of three samples.

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Dissolution rate (µmol/m2/sec)

100 alite in PC-clinker synthesized alite syn. alite (final Ra corr.) calcite (first 3 hours)

80

60

40

20

DBL-model

0 0

2

4

6

8

10

12

14

Mean water velocity (m/s) Fig. 11. Effect of flow rate on average first hour dissolution rate. Dashed lines show the trends suggested by the average value of the 5 alite measurements at 13.6 m/s. Also plotted is the measured dissolution rate of a calcite (Iceland spar) sample with a flat-ground miscut of 15°, under the same experimental conditions. The DBL model predicts aqueous ion diffusion rates as function of flow rate in μmol/m2/s (see Appendix A). The dissolution rates from the stagnant experiments are not included, because dissolution may have been limited by precipitation or by diffusion through hydration products in these experiments.

clinker experiments. After 6 h, the dissolution front in the synthesized alite had migrated to a 1.3 times larger average depth compared to the alite in clinker. 4. Discussion

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SEM images. Smaller or larger rounded pits can sometimes be observed (Fig. 12c), but these were probably related to dissolution starting from small void or solid inclusions that are common in the alite crystals (Fig. 12a). Under diffusion-controlled dissolution no etch-pit formation is expected. This is because the dissolution conditions at the dissolution front are close to equilibrium (see Fig. 1a). At such low degrees of undersaturation, dissolution proceeds through a relatively slow mechanism of step-retreat starting at crystal edges. This dissolution mechanism generally leads to the formation of smooth surfaces and rounded edges [12,15]. The apparent absence of etch-pits in our study is in accordance with the other types of evidence that show that dissolution was transport-controlled (see Sections 4.2 and 4.3). Since the saturation state is near equilibrium near the dissolution front under transport limited conditions (Fig. 1a), we expect precipitation of hydrates (i.e., C-S-H gel) to occur. Since the solubility of alite is higher than the one of C-S-H gel [7], the chance of precipitation under transport-controlled conditions is much higher for alite than for other minerals with a reversible dissolution reaction. The precipitated hydrates that formed in our experiment did not seem to have a significant effect on the first hour dissolution rate (Section 3.4). This observation suggests that the precipitated hydrates did not initially have a large affect on the diffusion coefficient of the dissolved species. The density of the hydrates that formed in our system may initially have been low and thus not hinder ion diffusion much. Moreover, large parts of the surfaces remained uncovered with hydrates, especially in the synthesized alite experiments. It should be mentioned that precipitation is expected to have a negative effect on the driving force of the diffusion process. In the theoretical absence of precipitation under diffusion-limited dissolution conditions, the ion concentrations at the dissolution front would be higher. That means that the concentration gradient between the dissolution front and the bulk fluid would be higher, and this would then lead to a higher diffusion-limited dissolution rate.

4.1. Interpretation of dissolution front morphology 4.2. Time-dependence of dissolution rate The morphological evolution of a mineral dissolution front may indicate the type of dissolution control (i.e., reaction or transport controlled) if dissolution occurred in a layer-by-layer mode. In the case of reaction-controlled dissolution at high degrees of undersaturation, dissolution from crystal defects (dislocations) is initiated, leading to the formation of etch-pits [9,15–17]. The presence of etch-pits is thus generally an indicator for surface reaction controlled dissolution [12,15]. Etch-pits of dissolving alite surfaces have been observed in a number of studies (e.g., [3,7]). In our study no well-defined crystallographically-shaped etch-pits were observed (Fig. 12), meaning that they were not present or beyond the resolution of the taken

(a)

(b)

In this study the dissolution rates of both alite sample types decreased with time (Fig. 10). For the synthesized alite samples the depth versus t 1/2, is not linear (Fig. 10a), meaning that the decreasing dissolution rate is not simply related to a diffusion process. A significant increase in diffusion distance or resistance due to precipitation is not expected (see Section 3.4). Also a change of the hydrodynamics of the fluid due to roughness development is not believed to have caused the decrease in dissolution rate. The decreasing dissolution rate in synthesized alite may therefore be related to the high initial reactivity of flat-ground crystal surfaces. For single crystal calcite it

(c)

I

II Fig. 12. Morphological evolution of flat-ground clinker surface in high flow deionized water after (a) 0 min; (b) 10 min; and (c) 100 min. I = solid inclusion; II = void inclusion. SEM-BSE image width is 90 μm.

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is well known that polished surfaces have a higher dissolution rate than cleaved or grown (singular) surfaces [18]. Polishing or flatgrinding leads to the creation of miscut (i.e., non-singular) surfaces. The higher the miscut angle, the higher the number of elementary steps on the surface and the higher the dissolution rate is when dissolution occurs in a layer-by-layer mode [19]. In our experiments, the top layer of sectioned crystals was removed from the synthesized alite samples in the first hour of dissolution, since the average crystal size of the alite was 11 μm (Table 1) and the depth of the dissolution front 10–16 μm (Fig. 10a). After 6 h the dissolution front reached a depth of around 4 times the average crystal size. Below the top layer with sectioned crystals, the dissolution front consisted of grown crystal surfaces that probably had a lower dissolution reactivity than the ground ones. The decreasing dissolution rate of the synthesized alite may thus be related to a gradual transition from more to less reactive mineral surfaces. Higher reactivity of ground surfaces will lead to higher dissolution rates under surface reaction rate control, but also under transport-controlled conditions. This is because the higher surface energy of ground (miscut) surfaces increases the equilibrium concentration at the dissolution front and thus the driving force (i.e., concentration gradient) of the diffusion process [20]. For the clinker samples, a grinding-induced high initial reactivity, as in the synthesized alite, is also expected. However, the dissolution rate of alite in clinker samples decreased significantly more after 6 h of dissolution (Fig. 10), and the dissolution front depth was a linear function of t 1/2. This suggests that a diffusion process played an additional role in the decreasing dissolution rate of alite in clinker. The reason is probably that the layer consisting of non-dissolving clinker minerals intermixed with precipitates, separating the dissolution front from the flowing water, gradually increased. This increased the diffusion distance of the dissolution products from the dissolution front to the flowing water. Additionally, the accumulating and densifying layer of precipitates may gradually have decreased the diffusion coefficient. Both effects led to a decreasing dissolution rate under transport-limited dissolution As mentioned before, there were no indications that precipitation slowed down the dissolution in the first hour (see Section 3.4). From 1 to 3 h dissolution, the depth versus time curves for the synthesized alite and clinker started to diverge. It thus seems that during the first hour, the maximum practical dissolution rate in clinker was achieved for a given flow rate in our set-up, and was limited by the diffusion rate of dissolution products in water. After 1–3 h of dissolution, the maximum dissolution rate of alite in the clinker was no longer achieved. This is because the dissolution front was no longer in direct contact with the flowing water (i.e., increasing diffusion distance), and/or because diffusion through a layer of precipitates started to become slower than diffusion through water (i.e., a lower diffusion coefficient). 4.3. Flow rate dependence of dissolution rate The observation that the initial dissolution rate of both alite sample types increased with flow rate is strong evidence that at low flow rates (b4.55 m/s) the initial dissolution rate was transport-controlled. Since the degree of precipitation in the first hour did not seem to have a significant effect the dissolution rate, diffusion of ions in water probably was the main factor limiting dissolution rate, and not diffusion through precipitated hydrates. At water velocities > 4.55 m/s the initial dissolution rate of alite in clinker was no longer flow rate dependent, which could indicate that dissolution rate became surface reaction-limited. For synthesized alite the average dissolution rate continuously increased with flow rate up to velocities of 13.6 m/s. However, the reproducibility of the measurements at the highest velocity was poor (Fig. 11) and uncertainty therefore remains about the type of dissolution control for synthesized alite

at velocities > 4.55 m/s. A speculation is that at a water velocity 13.6 m/s mechanical abrasion of the surface by the flowing water started to play a role and caused the poor reproducibility of the synthesized samples at this flow rate. For flow-through dissolution experiments, ion diffusion fluxes can potentially be predicted, and compared to the dissolution rates in order to elucidate if dissolution is transport- or mixed controlled (see Fig. 1). Diffusion fluxes can be predicted if the hydrodynamics of the flow-cell and the chemistry of the dissolution reaction are well known. The geometry of the flow-cell and the flow rate will determine if the flow is laminar or turbulent. Diffusion flux predictions under laminar flow conditions are less complicated than those for turbulent conditions and therefore a flow cell should be designed with this in mind. For the geometry of our flow cell we calculate the Reynolds number for flow in a pipe according to Re = (Q · Dh)/(ν · A), where Q is the volumetric flow rate (m3/s); Dh the hydraulic diameter of the pipe (m); ν the kinematic viscosity of water (1 · 10−6 m 2/s); and A is the pipe cross-sectional area (m2). Dh is calculated for a rectangular duct and is given by Dh = 2LW/(L + W). This gives Reynolds numbers of 493, 4927, and 14778 for water velocities of 0.45, 4.55 and 13.64 m/s, respectively. The laminar to turbulent flow transition often occurs between Reynolds numbers of 2000 to 4000 [21], meaning that we expect laminar flow in the low velocity experiments, and turbulent flow at the two highest velocities. Diffusion fluxes for dissolution in the laminar regime (v b 1.7 m/s in our set-up) are predicted as explained in the Appendix A. The predicted diffusion fluxes are of the same order of magnitude, but lower than the measured dissolution rates (Fig. 11). The latter can obviously not be the case, and an improvement of the DBL model or input parameters is therefore needed. The diffusion boundary layer (DBL) model is for laminar flow across a smooth plate and this may be a crude approximation for our set-up of flow in a rectangular duct with roughness development. For ion diffusion in water at room temperature the DBL is about 10% of the hydrodynamic boundary layer [22]. At 0.45 m/s the calculated hydrodynamic boundary layer is thus about as thick as the chamber height in our setup. A more elaborate model for the hydrodynamics in our set-up could increase the reliability of the DBL predictions for our set-up. The diffusion flux was calculated using a Si concentration of 1 mol/m 3 at the dissolution front (see Appendix A). This approximately is the saturation concentration with respect to C-S-H [5]. In the theoretical absence of C-S-H precipitation under diffusionlimited conditions, the Si concentration at the dissolution front would be much higher, namely the saturation Si concentration with respect to alite. This Si concentration is not known, but is at least several times higher than 1 mol/m 3 based on a recent estimation of the alite solubility product [7]. The measured dissolution rates are higher than the diffusion fluxes calculated using a Si-concentration of 1 mol/m 3 (Fig. 11). We therefore could argue, under the assumption that the DBL-model is correct, that the actual Si concentration at the dissolution front in our experiments was significantly higher than 1 mol/m 3, i.e., was supersaturated with respect to C-S-H. A higher Si concentration at the dissolution front would increase the concentration gradient with the bulk fluid, and thus the diffusion flux. 4.4. Applications of method The technique described in this paper provides an alternative method for measuring dissolution rates of single and multiphase cements. The maximum dissolution rates measured this study were 93 and 59 μmol/m 2/s for flat-ground synthetic alite and alite in clinker, respectively, in deionized water with a flow velocity of up to 13.6 m/s. These values are based on the assumption that the highest dissolution rate of our samples occurred at the start of dissolution, and thus calculated on basis of the initial sample surface area. These

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dissolution rates are of the same order of magnitude as those reported by others for alite in deionized water. Damidot et al. [5] measured a rate of 10.9 μmol/m2/s for pure alite and Nicoleau and Nonat [7] give values in between 74 to 127 μmol/m 2/s depending on alite type. Apart from material and other experimental differences, disagreements in dissolution rates obtained with different techniques may come from inaccurate measurements of the surface area of alite powders. Moreover, the ratio of the reactive surface area over total surface area may differ between studies depending on material and sample preparation method. In our study, the macroscopic surface roughness (Ra) increased from 0.6 to 3.6 μm for alite in the 6 h experiments (Fig. 8). This corresponds to an increase in dissolution front surface area of around 30%. However, the dissolution rate went down during these 6 h (Fig. 10a). It is expected for diffusion-controlled dissolution that the dissolution rate is independent of macroscopic surface roughness. In addition to measuring dissolution rates, the technique described in this paper can be used to determine if dissolution is reactionor diffusion-limited. In this study, diffusion-limited dissolution of alite in deionized water (with zero or low flow rate) was indicated by: (i) the flow-rate depended dissolution rate; (ii) the calculated diffusion flux being of the same order of magnitude as the dissolution rate; (iii) the apparent absence of etch-pit formation; and (iv) the roughness independent dissolution rate. The results of this study are only relevant for the very onset of cement hydration, when cement powder is mixed with water that initially is highly undersatured. A next step is to measure dissolution rate as function of flow rate at solution concentrations that approach that of pore solutions during cement hydration. It has been shown in a number of studies that the dissolution rate of alite decreases with the Ca concentration of the solvent [4,5,7]. The type of dissolution control (i.e., transport- or reaction) may change with the degree of undersaturation or other solvent properties. For our experimental set-up this practically means that a circulating water systems has to be developed that allows for maintaining a constant Ca concentration of the solution. Moreover, since the dissolution rates for alite drop significantly with Ca concentration, dissolution times need to be increased in order to be able to measure a change of the dissolution front depth with scanning electron microscopy.

5. Conclusions • A method has been developed to measure dissolution rates of single or multiphase cements from SEM images after a dissolution experiment. The measured dissolution rates of the synthesized alite and alite in clinker had reasonable to good reproducibility at water velocities up to 4.55 and 13.6 m/s, respectively. The measured dissolution rates in deionized water are of the same order of magnitude as those measured in other studies. • The dissolution rates of alite in deionized water depended on flow rate, indicating that at water velocities b 4.55 m/s the dissolution rate was transport-controlled. The type of dissolution control at water velocities > 4.55 m/s was not established with certainty in this study. • An advantage of the method is the possibility to predict diffusion fluxes if the flow cell is hydrodynamically well designed and the chemistry of the dissolution reaction is known. The preliminary predictions made in this study, illustrate the principle of calculating diffusion fluxes across a diffusion boundary layer as function of water flow rate. • Precipitation of hydrates occurred during dissolution of the synthesized and clinkered alite samples. Precipitation is an expected phenomenon associated with diffusion-limited dissolution, that did not seem to significantly affect the initial dissolution rate under flowing water conditions.

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Acknowledgments We thank Patrick Juilland for providing us with the synthesized alite sample and the XRD analyses, and Asel Maria Aguilar Sanchez for her help with the SEM work. We thank Patrick Juilland, Robert Flatt, and Luc Nicoleau for the discussions from which this study greatly benefited. The anonymous reviewers are acknowledged for their valuable comments to improve the paper. Appendix A When a fluid is flowing past a solid surface it develops a hydrodynamic boundary layer near the solid due to the existence of drag forces. In this layer the fluid velocity grows from zero near the surface to its maximum velocity unaffected by boundary effects [22]. The hydrodynamic boundary layer produces a diffusion boundary layer (DBL) in which, if the solid is dissolving, the solute concentration gradually decreases from the surface concentration to the concentration of the inlet fluid [22]. For convective diffusion, Fick's first law can be written as [10]: j ¼ D  ðcs −cÞ=δ

ð1Þ

with j being the diffusion flux (mol/m 2∙s); D the diffusion coefficient (m 2/s); cs the saturation concentration of dissolved ions in solution (mol/m 3); and c the concentration of the bulk solvent (mol/m 3). δ is the diffusion boundary layer thickness (m) for laminar flow past a plate and is given by [19]: 1=3

δD ¼ 3ðD=ν Þ

1=2

 ðνx=U Þ

ð2Þ

with D being the diffusion coefficient; ν the kinematic viscosity of water (1 · 10 −6 m 2/s); U the mean velocity of the water; and x the distance from the leading edge of the plate. Since the drag force increases with distance x, the boundary layer thickness (δ) increases with x according to δ ~ x 1/2 [22]. In our experiment x = 1 cm, the distance from the embedded sample front (Fig. 2a) where the section was made for SEM imaging. For example, the calculated DBL thickness at this location is 45 μm at a velocity of 0.45 m/s. In order to predict the maximum diffusion flux in our system we have to know the relevant diffusion coefficient and the concentration gradient across the diffusion boundary layer. The dissolution of alite is generally believed to be congruent [1,7,23], meaning that Ca and Si go into solution in a constant ratio of 3:1. The diffusion coefficients of Ca and Si are both close to 1 · 10 −9 m 2/s [24,25]. However, since the Si concentration near the surface is three times lower than the Ca concentration, the concentration gradient across the DBL is expected to be three times lower for the former. Diffusion of Si will therefore limit the dissolution rate if the dissolution is diffusioncontrolled. For the near surface (saturated) concentration of Si we use the empirical value of 1 mol/m 3, which appears to be the maximum measured Si concentration in alite–water mixtures [5,23]. The Si concentration of the inlet deionized water is assumed to be zero. References [1] J.W. Bullard, H.M. Jennings, R.A. Livingston, A. Nonat, G.W. Scherer, J.S. Schweitzer, K.L. Scrivener, J.J. Thomas, Mechanism of cement hydration, Cem. Concr. Res. 41 (12) (2011) 1208–1223. [2] J.J. Thomas, J.J. Biernacki, J.W. Bullard, S. Bishnoi, J.S. Dolado, G.W. Scherer, A. Luttge, Modeling and simulation of cement hydration kinetics and microstructure development, Cem. Concr. Res. 41 (12) (2011) 1257–1278. [3] P. Juilland, E. Gallucci, R. Flatt, K. Scrivener, Dissolution theory applied to the induction period in alite hydration, Cem. Concr. Res. 40 (6) (2010) 831–844. [4] L. Nicoleau, Interactions physico-chimiques entre latex et les phases minérales constituant le ciment au cours de l'hydratation, Université de Bourgogne, 2004. (Ph. D. Thesis). [5] D. Damidot, F. Bellman, T. Sowoidnich, B. Möser, Measurement and simulation of the dissolution rate at room temperature in conditions close to a cement

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