Fundamental Discrepancy of Chemical Reactivity of Tricalcium Oxy Silicate (alite), Dicalcium Silicate (Belite), and Their Polymorphs: A Density Functional Theory Study

Two major constituents in ordinary Portland cement (OPC) are tricalcium oxy silicate (Ca₃O(SiO₄), Alite) and dicalcium silicate (Ca₂(SiO₄), Belite). In cement chemistry notation (C = CaO, S = SiO₂, A = Al₂O₃, Fe = Fe₂O₃), alite and belite are C₃S and C₂S, respectively (Taylor, 1997). It is well known that these constituents undergo hydration with water, turning them into phase formation of C–S–H gel and portlandite which determines the most of engineering properties of cement-based materials (Barnes & Bensted, 2002). These minerals have different polymorphs depending on conditions, such as sintering temperature and ion substitution (Balonis & Glasser, 2009). For example, it has been reported that there are seven (M1-, M2-, M3-, T1-, T2-, T3-, R-C₃S) and five (α-, α’_H-, β-, α’_L-, γ-C₂S) polymorphs existing for alite and belite, respectively (Courtial et al., 2003; Cuberos et al., 2009; Taylor, 1997; Torre et al., 2008). These polymorphs have identical chemical formula but some of them have different crystal structures. For example, M, T, and R in alite polymorphs refers to monoclinc, triclinic, and rhombohedral crystal structure, respectively. Recently, Plank revisited the key difference between the alite and belite is the existence of interspersed oxide anions, O²⁻ between Ca²⁺ and SiO₄⁴⁻ tetrahedra in alite, while belite only contains ortho silicate SiO₄⁴⁻ units and Ca²⁺ cations. This makes significant differences between these two calcium silicate minerals including higher required calcination temperature, higher reactivity, and more formation of portlandite in alite crystal (Plank, 2020). Therefore, he concluded that the correct nomenclature of alite should be tricalcium oxy silicate (Ca₃O(SiO₄)) not the conventionally used tricalcium silicate (3CaO.SiO₂). Following the suggestion, the corrected nomenclature has been used in this study.

Given the mineralogical similarities among those minerals, quantitative research on the reactivity of alite, belite, and polymorphs is very challenging and has not been fully investigated experimentally and computationally. For example, clear relationship of chemical reactivity among different calcium silicates has not been completely elucidated although it has been using over hundred years. Several experimental methods have been applied to build the relationship between the reactivity differences between polymorphs of each alite and belite crystals. For the five polymorphs of belite, the experimental results showed that the reactivity order is α-C₂S > α’_H-C₂S > β-C₂S > α’_L-C₂S > γ-C₂S (Bensted, 1978; Cuberos et al., 2009; Fukuda & Taguchi, 1999; Wang et al., 2014). In the case of alite, only three polymorphs have been studied as the order of reactivity is known as R-C₃S > T1-C₃S > M3-C₃S (Harada et al., 1978). Although these experimental results are valuable in terms of producing optimized cement phases and developing more sustainable cements, more fundamental-level analysis is required for better understanding the origin of different reactivities between alite and belite as well as among different polymorphs, especially in a quantitative manner. Due to the fact that those crystals have high similarities and uncertainty of having other factors determining the crystal structure, such as ion substitution (Bensted, 1978; Cuberos et al., 2009; Fukuda & Taguchi, 1999), experimental investigation on the reactivity of those crystals is quite challenging.

To investigate the fundamental discrepancy of the reactivity of calcium silicates, it is appropriate to compare the reactivity of pure polymorphs without the potential effect from ion substitution. Given the complexity of synthesizing pure phases without ion substitutions, Density Functional Theory (DFT) method can be advantageous because of the high accuracy of calculation relying on quantum mechanics. The study of the reactivity of calcium silicates using DFT calculation has been continuously conducted by identifying the energy gap and the density of states (DOS) of the cement-based minerals for studying reactivities, surface energies, and water dissociation (Durgun et al., 2014; Huang et al., 2014; Wang et al., 2014; Wang et al., 2014). The relation between reactivity and electronic structure of α’_L-C₂S, β-C₂S and γ-C₂S is explained by PDOS analysis (Wang et al., 2014). The research on water adsorption in β-C₂S has been conducted with additional DFT calculation and PDOS analysis (Wang et al., 2018). The polymorphism of belite is also been reveled (Rejmak et al., 2019). The explanation on reactivity of doped cement clinkers were done through calculation of local charge densities and partial density of states (Tao et al., 2019). The previous research using other analysis including DOS analysis was meaningful in studying reactivity from a point of view on energy of crystals, but there has been no clear quantitative order of investigation among all reported polymorphs of calcium silicates.

In this study, the relationship between energy and reactivity of calcium silicates was quantitatively investigated through DFT calculation. In addition, attempts were made to elucidate the reactivity of each polymorph of calcium silicates in terms of atoms with the data of Bader charge analysis, which has been first reported herein.

The study revealed the origin of discrepancy of chemical reactivity among the polymorphs of belite and alite. First, it was suggested that the reactivity difference between belite and alite would be related to the presence or absence of oxy ions by comparing the partial charge of O atoms in SiO₄ tetrahedron in oxy ions. This finding consists with the conclusion drawn from similar DFT calculation on calcium silicates (Durgun et al., 2014; Saritas et al., 2015). In addition, the difference in reactivity between polymorphs in belite is closely related to the difference in energy per molecule in crystalline structures that causes instability in the crystal structure. Aside from the difference in energy, alite in which oxy ions exist is thought to increase reactivity as the partial charge of oxy ions decreases as the oxy ions become lower. As a result of comparing between before and after optimization, the polymorphs were more stable when optimization was performed. It has also been found that the degree of distortion of SiO₄ does not significantly differ depending on the polymorph, and thus has less influence on the reactivity of belite and alite.

The methodology to evaluate the chemical reactivity of crystals proposed herein, can be further applicable to investigate thermodynamic stability or reactivity of other C₃S-like minerals (e.g., M₃O[TO₄]) containing oxy ion. Additional studies can be also performed on other important cement clinker materials, such as tricalcium aluminate (C₃A) and tetracalcium aluminoferrite (C₄AF), following the research on solubility of C₃A and C₄AF (Myers et al., 2017; Plank, 2020; Wang et al., 2014).