Synthesis and Formation Process of a Typical Doped Solid-Solution Ye’elimite (Ca_3.8Na_0.2Al_5.6Fe_0.2Si_0.2SO₁₆): Experiments and Kinetic Analysis

Abstract

Ye’elimite is a dominant phase in calcium sulfoaluminate cement, which is a promising alternative type of cementitious binder. Ca_3.8Na_0.2Al_5.6Fe_0.2Si_0.2SO₁₆ (abbreviated as ss-C₄A₃$) is a kind of typical doped solid-solution ye’elimite. In this study, the formation process of ss-C₄A₃$ was investigated. Clinkers of ss-C₄A₃$ were sintered at various temperatures for different holding times. X-ray diffraction tests and Rietveld quantitative phase analysis were conducted to determine the phase compositions of the clinkers. Meanwhile, the formation process of ss-C₄A₃$ was analyzed by kinetic theory. The results show that solid reactions between intermediate phases (calcium aluminate phases) and anhydrite mainly resulted in the formation of ss-C₄A₃$. In the conditions of 1150–1250 °C, ss-C₄A₃$ tended to be formed and stable until 4 h. However, when the sintering temperature was 1300 °C, the ss-C₄A₃$ decreased to generate calcium aluminate phases after 2 h. Compared to other kinetic models, the three-dimensional diffusion model mostly conformed with the formation process of ss-C₄A₃$, and the fitting results obtained by the Jander model exhibited the highest correlation coefficients. The activation energy of ss-C₄A₃$ formation equaled 285.6 kJ/mol, which was smaller than that of stoichiometric ye’elimite.

1. Introduction

As the production process of calcium sulfoaluminate (CSA) cement produces fewer CO₂ emissions and consumes less energy compared to Portland cement, CSA cement is treated as a type of alternative and low-carbon binder [1,2]. Due to characteristics of early strength and tailored expansion, CSA cement has also been widely used as a rapid repairing material since the 1970s and it has recently been promoted for application in numerous domains, such as soft soil stabilization and 3D printing [3,4,5]. Ye’elimite is a dominant phase in CSA cement and generally accounts for over 50 wt.% in CSA clinkers [6,7]. Sintering conditions of CSA clinkers are determined by the forming conditions of ye’elimite; meanwhile, the main hydration products of CSA cement result from the reactions between ye’elimite and gypsum [8,9,10,11,12].

The chemical formula of stoichiometric ye’elimite is Ca₄Al₆SO₁₆, which can be abbreviated as st-C₄A₃$ (hereafter, nomenclatures are used—C: CaO, $: SO₃, A: Al₂O₃, S: SiO₂). The crystallographic structure of st-C₄A₃$ has been identified to be orthorhombic at room temperature, with a space group of Pcc2. Meanwhile, the formation and hydration mechanisms of st-C₄A₃$ have also been intensively investigated by a number of studies [13,14,15]. On the other hand, certain types of doping ions (such as iron ions and sodium ions et al.) enter into the lattices of ye’elimite in the manufacturing process of CSA clinkers, which leads to the formation of doped/solid-solution ye’elimite [16,17,18]. Specifically, when solid waste is utilized as raw materials, various types of solid-solution ye’elimite tend to be formed more easily [19]. A series of recent studies focused on different types of doped ye’elimite, including strontium-bearing ye’elimite, barium-bearing ye’elimite, and iron-bearing ye’elimite.

The consensus obtained by studies on doped ye’elimite is that dopants result in a crystallographic system of ye’elimite, partly or totally transforming from an orthorhombic system to a cubic system [16,17,20]. Particularly, Ca_3.8Na_0.2Al_5.6Fe_0.2Si_0.2SO₁₆ (abbreviated as ss-C₄A₃$), a typical kind of doped solid-solution ye’elimite, has attracted special attention, as the crystallographic system of ss-C₄A₃$ has been proved to be purely cubic at room temperature [21]. Comparing it to st-C₄A₃$, ss-C₄A₃$ also exhibited obviously distinct hydration characters [22]. Additionally, elemental compositions of ss-C₄A₃$ approached sintered ye’elimite phases in CSA clinkers due to the existence of iron ions and silicon ions in raw materials [16].

In this study, the formation process of ss-C₄A₃$ was investigated. Clinkers of ss-C₄A₃$ were sintered at various temperatures for different holding times. X-ray diffraction (XRD) tests and Rietveld quantitative phase analysis (RQPA) were conducted to determine the phase compositions of the clinkers. According to the results of the RQPA, different models of solid-state reactions were employed to fit the isothermal formation process of ss-C₄A₃$. By comparing the obtained correlation coefficients, the formation mechanism of ss-C₄A₃$ was confirmed. Lastly, the value of activation energy for ss-C₄A₃$ was acquired by the Arrhenius equation.

2. Materials and Methods

2.1. Raw Materials and Sintering Conditions for Clinkers

According to the elemental molar ratios of st-C₄A₃$ and ss-C₄A₃$, analytical reagents of CaCO₃, Na₂CO₃, Al₂O₃, Fe₂O₃, SiO₂, and CaSO₄ were weighed and mixed by a planetary ball mill for homogeneousness to prepare raw materials (purities of all analytical reagents were more than 99.99 wt.%). Afterwards, well-mixed raw materials were compressed into cylindroid samples (Φ5.0 cm × H1.0 cm) and placed in a high-temperature furnace for sintering. As for st-C₄A₃$, through a heating rate of 10 °C/min, the raw materials were sintered at 1300 °C for 240 min. With regard to ss-C₄A₃$, the raw materials were respectively sintered at 1150 °C, 1200 °C, 1250 °C, and 1300 °C (10 °C/min heating rate) for various holding times (0 min, 15 min, 30 min, 60 min, 120 min, 180 min, and 240 min).

2.2. Test Methods

After sintering, synthesized clinkers were finely ground to pass a sieve of 45 μm for X-ray diffraction (XRD) testing. A Bruker diffractometer with CuKα_1,2 radiation (without a monochromator, λ₁ = 0.15406 nm, λ₂ = 0.15444 nm) was employed at 40 kV and 40 mA. For quantitative phase analysis, the range of data collection was 5–80° (in this paper, all angles refer to a 2θ value) with a step size of 0.02°, and the total measurement time for each sample was approximately 30 min. When the lattice parameters needed to be refined, the range of data collection was expanded to be 5–120°, and the total measurement time for each sample was increased to approximately 120 min.

XRD patterns obtained by direct tests were firstly analyzed qualitatively in Bruker Evolution software to determine the phases in the clinkers. Then, Topas 4.2 software was employed to perform RQPA for dealing with the obtained XRD patterns.

Table 1. COD codes and references of phases involved in the RQPA.

Phases	Formula (Abbreviation)	COD Code	Reference
Typical solid-solution ye’elimite	Ca3.8Na0.2Al5.6Fe0.2Si0.2SO16 (ss-C4A3$)	45,119,60	[21]
Monocalcium aluminate	CaAl2O4 (CA)	43,080,75	[23]
Anhydrite	CaSO4 (C$)	50,000,40	[24]
Mayenite	Ca12Al14O33 (C12A7)	21,029,55	[25]
Tricalcium aluminate	Ca3Al2O6 (C3A)	90,159,66	[26]
Calcium oxide	CaO (C)	72,006,86	[27]

exhibits the COD codes for all the phases involved in the RQPA.

2.3. Kinetic Theory

To characterize the process of chemical reactions for a certain type of product, reaction degree α is calculated according to Equation (1).

$$\alpha =\frac{m_t-m_0}{m_{\infty }-m_0}$$

(1)

In Equation (1), t is the reaction time at the isothermal stage and m₀ is the initial mass percentage of the product for the isothermal stage. The mass percentage of the product at holding time t is written as m_t, and m_∞ represents the (theoretical) final mass percentage of the product for the isothermal stage.

In isothermal conditions, the temperature is constant. Based on the kinetic reaction equation, the reaction degree α can be related to holding time t, as shown in Equation (2).

$$g\left(\alpha \right)={{\displaystyle \int }}_0^{\alpha }\frac{\mathrm{d}\alpha }{f\left(\alpha \right)}=k\mathrm{t}$$

(2)

For Equation (2), g(α) and f(α) are the integral and differential forms of the kinetic models, respectively. The models used for the solid-state reactions in this study are exhibited in

Table 2. Kinetic models for solid-state reactions [28].

Symbol	Models	f(α)	g(α)
D1	One-dimensional diffusion	$1/2\alpha$	α2
D2	Two-dimensional diffusion	−1/ln(1 − α)	α + (1 − α)ln(1 − α)
D3	Jander	3(1 − α)2/3/{2[1 − (1 − α)1/3]}	[1 − (1 − α)1/3]2
	(Three-dimensional diffusion)
D4	Ginstling–Brounstein	3/{2[(1 − α)−1/3 − 1]}	1 − (2α/3) − (1 − α)2/3
	(Three-dimensional)
R3	Model for interface reaction	$3{\left(1-\alpha \right)}^{2/3}$	1 − (1 − α)1/3
A3	Avrami–Erofeyev	$3\left(1-\alpha \right){\left[-\ln \left(1-\alpha \right)\right]}^{2/3}$	[−ln(1 − α)]1/3
F1	Crystal nucleation growth model	$1-\alpha$	−ln(1 − α)

.

Based on the results of linear fitting for Equation (2), the slopes of the kinetic equation k for various temperatures were obtained. Furthermore, the values of the parameters in the Arrhenius Equation, expressed in the logarithmic form and exhibited in Equation (3), were confirmed.

ln^k = ln^A − E_a/RT

(3)

In Equation (3), A is the preexponential factor, k is the slope of the kinetic equation, E_a represents activation energy, and R is the gas constant (8.314 J/(mol·K)).

3. Results

3.1. Crystallographic Distinctions between st-C₄A₃$ and ss-C₄A₃$

To distinguish the crystallographic distinctions between orthorhombic and cubic ye’elimite, XRD patterns of st-C₄A₃$ (sintered at 1300 °C for 240 min) and ss-C₄A₃$ (sintered at 1250 °C for 240 min) were compared, as shown in Figure 1. As can be seen, except for some low-intensity peaks for monocalcium aluminate (CaAl₂O₄) and calcium oxide (CaO), all peaks belonged to orthorhombic and cubic ye’elimite. Meanwhile, the patterns for st-C₄A₃$ and ss-C₄A₃$ tended to be similar, as the major peaks of both patterns overlap at 23.7°, 33.7°, 41.6°, (angles refer to 2θ in this paper) and so on. However, it should also be noted that, compared to ss-C₄A₃$, the pattern of st-C₄A₃$ exhibited some additional characteristic peaks (such as the peaks at 18.1°, 20.6°, 35.8°, and 37.3°), which can be observed in the zoomed-in images of Figure 1. The additional characteristic peaks were used to distinguish the st-C₄A₃$ from the ss-C₄A₃$.

To further confirm the lattice parameters of synthesized st-C₄A₃$ and ss-C₄A₃$, the Rietveld method was employed to refine the patterns in Figure 1. The fitting result of ss-C₄A₃$ can be seen in Figure 2, and the obtained values of the lattice parameters are exhibited in

Table 3. Lattice parameters of synthesized solid-solution and stoichiometric ye’elimite.

Types of Ye’elimite	Crystallographic System (Space Group)	Lattice Parameters (Å)	Sources
Stoichiometric	Orthorhombic	a = 13.041, b = 13.036, c = 9172	This paper
	(Pcc2)	a = 13.037, b = 13.035, c = 9168	[15]
Typical solid-solution	Cubic	a = 9191	This paper
	(I-43 m)	a = 9197	[21]

. According to the results of the Rietveld refinement, the crystallographic characters of synthesized st-C₄A₃$ and ss-C₄A₃$ in this paper were consistent with those of previous studies.

3.2. Formation Process of ss-C₄A₃$

The formation process of st-C₄A₃$ can be divided into three stages, including the stage for the decomposition of raw materials (mainly referring to the decomposition of CaCO_3, as shown in Equation (4)), the stage for the formation of intermediate phases (mainly referring to the formation of CA, as shown in Equation (5)), and the formation of ye’elimite (mainly referring to the reaction between CA and C$, as shown in Equation (6)). To determine the involved solid reactions in the formation process of ss-C₄A₃$, the XRD patterns of clinkers sintered at various temperatures for different holding times were compared, as shown in Figure 3.

CaCO₃ → CaO + CO₂

(4)

CaO + Al₂O₃ → CaAl₂O₄

(5)

3CaAl₂O₄ + CaSO₄ → Ca₄Al₆SO₁₆

(6)

Comparing the XRD patterns for st-C₄A₃$ and ss-C₄A₃$ in Section 3.1, it was observed that the additional characteristic peaks of st-C₄A₃$ were not in any of the clinkers of ss-C₄A₃$ in Figure 3, which means that the formation process of ss-C₄A₃$ did not involve the formation of st-C₄A₃$. Clinkers sintered at various temperatures without holding times are exhibited in Figure 3a. It can be seen that certain amounts of ss-C₄A₃$ were formed at 1150 °C, but CaAl₂O₄ and CaSO₄ can obviously still be detected. With sintering temperatures increasing from 1150 to 1300 °C, the intensity of the peaks of ss-C₄A₃$ steadily increased; meanwhile, the intensity of the peaks of CaAl₂O₄ and CaSO₄ decreased. Similar variational tendencies for the peaks of ss-C₄A₃$, CaAl₂O₄, and CaSO₄ can also be observed in the clinkers sintered at 1150 °C for different holding times (see Figure 3b). However, for clinkers sintered at 1300 °C (see Figure 3c), CaSO₄ could not be detected after a 0.5 h holding time, and peaks of CaAl₂O₄ reappeared after sintering for over 3 h. To further determine the contents of the phases in clinkers sintered in different conditions, Rietveld quantitative phase analysis was conducted to identify the XRD patterns. Taking the analysis of the clinkers sintered at 1150 °C for 60 min as an example, the selected range and fitting results of the Rietveld quantitative phase analysis are shown in Figure 4.

Figure 5 exhibits the contents of the phases in clinkers sintered at different temperatures as a function of holding time, of which three stages were identified. The first stage was the forming stage, which included 1150 °C (within 240 min), 1200 °C (within 240 min), 1250 °C (the first 120 min), and 1300 °C (the first 30 min). In the forming stage, the contents of ss-C₄A₃$ steadily increased with increasing holding time; meanwhile, the contents of calcium aluminate phases (in most instances, CA accounted for the overwhelming majority) and anhydrite continually decreased. The variation tendency illustrates that ss-C₄A₃$ was formed through the reaction between the calcium aluminate phases and anhydrite in the forming stage, which was similar to the reaction in Equation (6). After the forming stage, the stable stage was observed at 1250 °C (in the range of 120-240 min) and 1300 °C (in the range of 30–120 min). In the stable stage, the contents of ss-C₄A₃$ remained stable and generally remained over 90 wt.% in the clinkers; meanwhile, the calcium aluminate phases and anhydrite accounted for the absolute minority (less than 10 wt.%). It should also be noted that the contents of ss-C₄A₃$ tended to decrease and generate calcium aluminate phases when the clinkers were sintered over 120 min at 1300 °C, which can be identified as the decomposing stage.

3.3. Kinetic Analysis for the Formation Process of ss-C₄A₃$

The reaction degrees α of ss-C₄A₃$ in the forming stage were calculated according to the contents of the phases in the clinkers obtained by the RQPA. Afterwards, the linear relationship between the reaction degrees and the holding times were fitted by Equation (2) (the integral form of kinetic models), and the correlation coefficients (R²) were compared to determine the potential optimal models.

According to the comparison in

Table 4. Correlation coefficients (R2) fitted by different reaction models.

Temperature	Kinetic Models
(°C)	D1	D2	D3	D4	A3	R3	F1
1150	0.9608	0.9791	0.9942	0.9848	0.7357	0.9031	0.9293
1200	0.9314	0.9590	0.9869	0.9693	0.7655	0.9106	0.9442
1250	0.9994	0.9886	0.9682	0.9800	0.8658	0.9888	0.9986
1300	0.9937	0.9998	0.9961	0.9996	0.9195	0.9807	0.9931
Average	0.9713	0.9816	0.9864	0.9834	0.8216	0.9458	0.9663
Standard deviation	0.0274	0.0150	0.0110	0.0109	0.0743	0.0392	0.0301

, all diffusion models exhibited obviously higher correlation coefficients than other types of models. It should be also noted that the correlation coefficients of the D3 (Jander) model and the D4 (Ginstling–Brounstein) model were very close and higher than the results yielded from the D1 and D2 models. The results illustrate that the formation reactions of ss-C₄A₃$ take place in a process of three-dimensional diffusion, which accords with st-C₄A₃$ and several types of solid-solution ye’elimite [29,30]. Considering the D3 model exhibited the most acceptable fitting results, the values for k in Equation (2) were determined by the D3 model, and the fitting results can be seen in Figure 6a. Afterwards, the values of E_a were obtained through a linear fitting for Equation (3) (Arrhenius equation), and they are shown in Figure 6b. According to the results of the Arrhenius fitting, the E_a of ss-C₄A₃$ equaled 285.6 kJ/mol in this study.

3.4. Influence of Sintering Temperature on Microstructural Morphologies of ss-C₄A₃$

Microstructural morphologies of four types of clinkers containing over 90 wt.% of ss-C₄A₃$ are compared in Figure 7. As shown in Figure 7a, the morphology features of ss-C₄A₃$ sintered at 1200 °C for 240 min were identified as approximately 1–2 μm polyhedral granules with clear boundaries. For ss-C₄A₃$ sintered at 1250 °C for 240 min (shown in Figure 7b), the majority of granules still exhibited clear boundaries, but a few granules tended to fuse and combine with adjacent granules (shown by the arrow). When prolonged times extended to 240 min at 1250 °C (see Figure 7c), fusion among the granules of ss-C₄A₃$ was more evident (shown in the circles). As for ss-C₄A₃$ sintered at 1300 °C for 120 min (see Figure 7d), partial granules fused to be larger than 2 μm; meanwhile, the boundaries of the granules tended to be more vague.

4. Discussion

Values of E_a for different types of ye’elimite were compared and are shown in

Table 5. Values of activation energy (E_a) for different types of ye’elimite formation.

Target Minerals	Dopants	Model	Ea (kJ/mol)	Sources
Ca3.8Na0.2Al5.6Fe0.2Si0.2SO16	Na+, Fe3+, Si4+	D3	285.6	This paper
Ca4Al6SO16	−	D3	300.8	[30]
Ca4Al6SO16	−	D3	304.0	[29]
Ca4−xBaxAl6SO16 1	Ba2+	D3	304 + 71.9x	[29]
Ca3SrAl6SO16	Sr2+	D3	367.9	[30]

¹ x represents substituted amounts of Ba²⁺ for Ca^2+.

. It can be seen that the E_a of ss-C₄A₃$ was slightly smaller than that of st-C₄A₃$ and obviously smaller than that of strontium/barium-bearing ye’elimite. From the point of view of physical significance, the value of E_a reflects the barrier needed to be overcome for a reaction [28]. This indicates that the ss-C₄A₃$ tended to be more easily formed than the st-C₄A₃$ and strontium/barium-bearing ye’elimite in the same sintering conditions.

Less barrier for forming ss-C₄A₃$ can be mainly attributed to the effect of different types on the formation process of ye’elimite. For strontium/barium-bearing ye’elimite, strontic/baric ions introduce strontic/baric sulfates or strontic/baric aluminates as distinct intermediate phases, which results in different solid reactions for forming strontium/barium-bearing ye’elimite compared to st-C₄A₃$ [29,30]. It should also be noted that strontic/baric sulfates are more stable than calcium sulfate at high temperatures, and thus, higher barriers need to be overcome for forming strontium/barium-bearing ye’elimite compared to st-C₄A₃$ [29]. However, for st-C₄A₃$, the formation process of ss-C₄A₃$ mainly resulted from the solid reactions between the calcium aluminate phases and anhydrite, which is in accordance with the st-C₄A₃$. Meanwhile, considering the mineralizing effect caused by the substitution of Fe³⁺ ions with Al³⁺ in the crystal structure of ye’elimite, ss-C₄A₃$ tended to be more easily formed than st-C₄A₃$ [31].

5. Conclusions

Based on the Rietveld quantitative phase analysis for clinkers sintered at various temperatures for different holding times, the formation process of ss-C₄A₃$ was investigated through the lens of kinetic theory. The following conclusions can be made:

(1)

XRD patterns of st-C₄A₃$ and ss-C₄A₃$ tended to be similar, but st-C₄A₃$ was distinguished from ss-C₄A₃$ by some additional characteristic peaks. The formation process of ss-C₄A₃$ mainly resulted from solid reactions between the intermediate phases (calcium aluminate phases) and anhydrite, which did not involve the formation of st-C₄A₃$. In the conditions of 1150–1250 °C, ss-C₄A₃$ tended to be formed and stable for 4 h. However, when the sintering temperature increased to 1300 °C, ss-C₄A₃$ decomposed to generate calcium aluminate phases after 2 h.

(2)

Compared to other kinetic models, the three-dimensional diffusion model mostly conformed with the formation process of ss-C₄A₃$, and the fitting results obtained by the Jander model exhibited the highest correlation coefficients. The activation energy of ss-C₄A₃$ formation equaled 285.6 kJ/mol, which was lower than that of stoichiometric and strontium/barium-bearing ye’elimite.

(3)

The morphology features of ss-C₄A₃$ sintered at 1200 °C for 240 min were identified as approximately 1–2 μm polyhedral granules with clear boundaries; higher sintering temperatures or longer holding times would lead to granules fusing together.