Figure 1 depicts axial 2D SR-µCT views after tomographic reconstruction of the specimens with different water content aged 15 days.
Phase composition has been controlled with X-ray powder diffraction (diffraction spectra are reported in Online Resource 2), and the presence of only MKP as crystalline reaction product has been confirmed, in agreement with results from MPC samples with different w/s ratio [8, 16, 18]. Previous results of quantitative phase analysis indicated that MKP largely prevails over the amorphous phase [13, 14, 18]. The compact microstructure exhibited by sample MPC_044_15d confirms that, at low w/s ratio, the crystals are densely packed and embedded in the amorphous phase from which they crystallized [16, 17, 25, 49]. Few large pores (size > 200 μm) of irregular shape are observed.
As the w/s ratio increased, the number of voids increased as well. In section, pores are more irregular, and the microstructure appears less compact as more elongated features are present in the sample volume. The outline of these features is compatible with the crystal habit of MKP crystals, which ranges from acicular/elongated to platelet-like [27, 50]. This indicates that the number of euhedral to subhedral MKP crystals increases with w/s ratio.
The 3D visualization of a VOI at different w/s ratio, reported in Fig. 2, clearly illustrates this evolution. In the samples MPC_207_15d and MPC_400_15d, the voids are more pervasive and crystals likely allowed to grow larger. The number of spherical to sub-spherical pores, previously attributed to air entrapment during mixing , is insignificant. Increasing w/s, the crystal network becomes sparser and individuals can be better distinguished because they are less packed and more isolated.
Figure 3a, b illustrates an example of 2D axial views after segmentation, obtained from the sample MPC_051 after 1 h and 12 h. The two pictures identify the same portion of sample and are very similar, indicating small changes in porosity. Figure 3c depicts a detail of the image obtained by subtracting the previous two. The formation of new small pores (white phase in figure) can be observed.
Results from quantitative image analysis are summarized in Table 1. They reflect the sample features in the range of sizes made accessible by the resolution of the experiment.
The increase in water content of the mix above the stoichiometric amount, increased the values of porosity Φ and specific surface area SV. The latter also reflects the increased complexity of pore shape mentioned above, which is accompanied by an increasing complexity of the pore network, as testified by higher CD (from 355 to > 10000 mm−3). Figure 4 shows an example of 3D volume rendering including the skeletonized volume. A more complex skeleton increasing w/s ratio is evident.
The fractal dimension DF is obtained by applying the concepts of fractal geometry to describe the pore network, in analogy with several examples in rocks, cements and ceramics [28, 29, 51,52,53]. The theoretical foundations of this approach can be found elsewhere [54, 55]. In this study, DF can be simply considered as an indicator of roughness of the pore surface  which can assume values from 2 (smooth surface) to 3 (irregular or rough surface). In agreement with the other parameters of the quantitative image analysis and in parallel with the increasing complexity of the pore–matrix interface, DF increases with w/s.
A visual representation of the pore size distribution, expressed as incremental volume plotted against the pore volume, for samples produced with different w/s ratio, is reported in Fig. 5a. The sample with the lowest w/s ratio exhibits a broad distribution which extends to large volumes (> 105 μm3). As the w/s ratio increases, the distribution narrows and the maximum shifts towards smaller volumes. With w/s ratio 4.0, the porosity is mostly contributed by pores with volume between 100 and 2000 μm3, corresponding to diameter D of the sphere having the same volume, between 5.8 and 15.6 μm. Since the porosity also increases (this aspect cannot be appreciated in Fig. 5, since the sum of the contributions is 100% for each curve), excess water results in the development of more pores, smaller in size, more interconnected and with more complex pore shape (Table 1).
The time evolution of the distribution for the sample MPC_051 is illustrated in Fig. 5b. As for the other results of quantitative image analysis reported in Table 1, most of the changes are observed between 1 and 4 h. They consist in a shift of the maximum of the distribution towards smaller pore volumes (from 5 × 103 to 1 × 103 μm3) and a decrease in the contribution from pores larger than 4 × 104 μm3 (D > 42 μm). Notably, this does not coincide with a decrease in porosity, but rather to a small increase (Table 1). The detected porosity and SV remain slightly higher than at 1 h, even after 12 h. An evidence which agrees with the two snapshots in Fig. 3, which show some new pores with D < 25 μm detected at 12 h. The results reported in Table 1 coherently indicate a porosity and a connectivity density intermediate between samples with w/s ratio 0.44 and 1.0 aged 15 days. The same does not occur for SV, which is higher than in sample MPC_100_15d. This might suggest that the slight decrease in porosity and SV, observed between 4 and 12 h, continues for longer times.
Figure 6 reports examples of SEM micrographs collected from the fractured surface of the specimens.
When no excess water was employed (sample MPC_044_15d), the microstructure appears more compact. Pores are isolated and occasionally larger than 20 μm, as illustrated in Fig. 6a. MKP crystals exhibiting two habits, tabular and more elongated/acicular, are intimately mixed together. In the matrix, they are roughly 5 μm in size (as indicated by arrow in Fig. 6a), but in correspondence with the large pores, where they are clearly distinguishable, they grew bigger protruding into the pore volume. As the w/s ratio increases, the microstructure becomes less compact, MKP crystals grow on average larger (> 50 μm) and the tabular crystal habit prevails. This suggests a relationship between the crystal size and shape, and the space available for the crystals to grow. At high w/s ratio (samples MPC_207_15d and MPC_400_15d), small crystals of MKP (< 5 μm), whose chemistry has been confirmed by EDS analysis (Online Resource 3), are also observed on the surface of the large tabular ones shown in Fig. 6c, d. Their diffuse presence in sample MPC_207_15d explains why, with SR-µCT, MKP individuals appear less sharply defined in this sample (Figs. 1c, 2c).