3.1. Testing the Carbonation Products Formed in the Pastes
The XRD analyses were conducted on the samples extracted from the colorless and purple regions of the pastes.
Figure 3a,b at 24 h and 72 h and
Figure 4a,b at 24 h and 72 h, respectively, show the XRD results for the non-carbonated (purple) inner regions and the carbonated (colorless) outer side regions of the blocks. For the sample with no γ-C
2S supplementation, C
2S0, the principal phase reacting in the carbonation of the pastes was portlandite (Ca(OH)
2) and, to a lesser extent, alite (C
3S) and belite (C
2S). The presence of portlandite (Ca(OH)
2) in all the paste blocks was mainly indicated by the characteristic XRD 2-theta-degrees peaks at 2θ = 18.09°, 28.76°, 32.2°, 47.23°, 50.89°, 54.45°, and 71.93° [
5]. From
Figure 3a at 24 h and
Figure 3b at 72 h, 3 out of the 6 possible (because the 2θ reading stopped at 60°) peaks at 2θ = 18.09°, 28.76°, and 47.23° were clearly visible, thereby representing the Ca(OH)
2 content inside the paste blocks. The presence of CaCO
3 in the paste blocks in
Figure 3a,b was indicated by the characteristic peaks of calcite (CaCO
3) at 2θ = 23.08°, 29.39°, 36.04°, 39.46°, 42.23°, 47.42°, 48.5°, 57.51°, 60.76°, and 64.8° [
9,
10]. However, despite the range of 2θ having stopped at 60 ° and excluding 1 peak, only 2 peaks were visible out of the possible 6 peaks, at 2θ = 23.08° and 48.5°. Notably, the XRD intensities for both Ca(OH)
2 and CaCO
3 for their clear peaks at 24 h were not significantly higher than their corresponding peaks at 72 h after carbonation, thereby indicating that the portlandite in the purple regions of the blocks barely reacted with the CO
2 from the onset of carbonation, through the 24 h to 72 h test times, and hence the near equality of the intensities at the characteristic 2θ peaks. The same observation was made for the alite and belite phases in all the purple-colored parts of the specimens (inner regions), as their peaks at 2θ degrees of approximately 32 to 33 barely changed in intensity between the test periods of 24 and 72 h. This indicates that 72 h was not sufficient for the CO
2 to diffuse to the inner parts of the paste specimens. However, most of the inner regions of the discarded mortar test samples were carbonated for 72 h.
When the XRD analyses for the outer parts of the paste specimens were examined in
Figure 4a at 24 h and
Figure 4b at 72 h, the characteristic peaks for portlandite (2θ degrees of about 18.09°, 28.76°, and 34.23°) significantly decreased from the test time of 24 h to 72 h, and the peaks characteristic of the alite and belite phases (2θ degrees between 32° and 33°) decreased; however, in the same figure and time interval, the characteristic peaks for calcite (CaCO
3) at 2θ = 29.39° were enhanced significantly, whereas its peaks at 2θ = 23.08° and 39.46° appreciably increased, thereby indicating the carbonation reactions occurring on both the portlandite on one part and on the alite and belite phases on the other, from the outer regions of the blocks going inward. The reaction of portlandite with CO
2 after hydration is given in Equation (1) and results in the formation of CaCO
3, whereas that for alite carbonates is given in Equation (2) and that for belite is given in Equation (3) or Equation (4).
However, the high intensity of the CaCO
3 observed at 2θ = 29.39° indicates that another compound (or phase) other than portlandite, alite, or belite must have contributed to this high intensity. The only other source of CaCO
3 apart from the portlandite, belite, and alite was γ-C
2S; the highest intensity for CaCO
3 at 2θ = 29.39° occurred when the specimen under test was that with the highest ratio of replacement used, 25 wt.% γ-C
2S, thereby proving that γ-C
2S was responsible for the generation of the additional CaCO
3 in the carbonated regions. Similar observations have been reported in the literature [
9,
11].
The CaCO
3 formed from all four sources was rendered in the solid state owing to its low solubility. The decreasing XRD intensity for portlandite in the specimen from C
2S0 to C
2S15 to C
2S25 at 24 h shown in
Figure 3a shows that most of it was sourced from OPC, and this observation was given credence because its content was lowest in C
2S25. Additionally, the low intensity of calcite after 24 h of carbonation for the wholly OPC-constituted specimens (C
2S0) compared to the C
2S15 and C
2S25 specimens indicated that the formation of CaCO
3 occurred more in these specimens than in the C
2S0 specimens at 24 h.
Figure 4b shows that the highest amount of calcite was formed at 72 h, and that this was in the C
2S25 specimen with the highest substitution amount of γ-C
2S for OPC. Therefore, most of the CaCO
3 was not formed from γ-C
2S and not portlandite, indicating that portlandite is the main source of CaCO
3 during the carbonation of OPC mortars. In mortars whose OPC has been substituted with γ-C
2S, additional CaCO
3 is formed, indicating that when γ-C
2S is exposed to CO
2 in moist conditions, CaCO
3 is formed [
12,
13]. Although supplementary proof for the formation of CaCO
3 from γ-C
2S is needed in the form of porosity measurements of both the uncarbonated and carbonated regions of the specimens, it was not available.
3.3. Calculation of Diffusion Coefficient in Cement Bodies with γ-C2S
It was difficult to measure the concentration of CO
2 in the paste blocks at the carbonation front using the error function (erf) solution given in Equation (6) derived from Fick’s second law, Equation (7). Because the measurements of the CO
2 concentration at the carbonation front were not possible experimentally, the solution using the error function was not used to calculate the CO
2 diffusion coefficient and verify Fick’s second law. Many researchers have simplified this difficulty by using Equation (5), such that the diffusivity constant,
k, was calculated from the depth of carbonation, x
1, in addition to the carbonation coefficient using Equation (5) [
14,
15,
16,
17,
18].
where
C = concentration in dimensions (quantity/volume), e.g., (mol. m−3);
t = time in seconds;
x = longitudinal separation distance from uphill to downhill position, e.g., (m);
D = coefficient of diffusion.
Fick’s second law states that concentration in the body is a function of both position and time. In other words, an increase in concentration in a cross-section of a unit area with time is simply the difference between the flux in and out of the volume.
Fick’s second law implies that the flux of CO
2 into the paste is equal to the flux of CO
2 out plus accumulation, Equation (9).
where Flux in = mass of CO
2 flowing in (kg. m
−2 s
−1); flux out = mass of CO
2 flowing out (kg. m
−2 s
−1). The accumulation quantity, ΔC, is the amount of CaCO
3 minus the CaO combined during carbonation.
Fick’s second law can be proved considering the flux of CO
2 in and out of the paste specimen are not equal if the direction of flow is considered to be unidirectional. On comparing the chemical contents of the uncarbonated pastes in
Figure 3a,b with those of the carbonated pastes in
Figure 4a,b, it was clear that the carbonation ingress in the paste caused the deposition of CaCO
3 in the pore structure, as shown in
Figure 7 and
Figure 8, resulting in densification in the carbonated regions. Therefore, because CaCO
3 was proved to have been formed owing to the carbonation reactions in the OPC and γ-C
2S composite pastes, it indicated that the fluxes in and out of the pastes were not equal.
If a paste sample under carbonation was considered, as shown in
Figure 7, making a material balance and applying the law of conservation of matter to Equation (9) results in Fick’s second law, Equation (10).
Setting boundary conditions (BC) for the diffusion above,
The general solution to such an equation is the error function, Equation (13).
Using Equation (13), knowing the surface concentration C
o and the concentration at distance x, C
x, the diffusion coefficient is calculated as D. However, because not all the data are available, Equation (14), which is a modification of Equation (5), can be used.
This simplifies the calculations because although the concentrations at the carbonation front are not known, the diffusion depth x1 (mm) and time t (years) are known; therefore, D can be calculated.
Using Equation (14), the diffusion coefficient can be calculated using the time of diffusion and depth of diffusion. The diffusion coefficients calculated for the different paste specimens in the experiment are shown in
Figure 9. The diffusion coefficient shows a tendency to increase until the reaction time of 1 day and then decreases. As the substitution rate of γ-C
2S increases, the diffusion coefficient tends to decrease. This is due to CaCO
3, a carbonation product formed in the pores, reducing the porosity of the hardened cement paste, lowering the diffusion coefficient.