The Influence of Boron Doping on the Structures and Composition of Dicalcium Silicate: A Research Study

Abstract

This paper investigates the structural transformation of dicalcium silicate (C₂S) crystals brought about through boron doping. Both qualitative and quantitative analyses were conducted to explore the correspondence between boron content and the structure of dicalcium silicate. The results show that boron doping can stabilize β-C₂S and the high-temperature phase α′_H-C₂S, and the structural transformation does not involve the modulation of α′_L-C₂S. There is a corresponding relationship between the unit cells of β-C₂S and α′_H-C₂S, which can be transformed using a transformation matrix. The relationship between boron content and the content of different C₂S structures, as well as the structural expressions for β-C₂S and α′_H-C₂S, is determined using linear fitting and multivariable linear regression analysis.

1. Introduction

Ordinary Portland cement (OPC) is extensively used in construction worldwide. In 2020, China accounted for 57% of global cement production with a production volume of about 2.37 billion tonnes [1,2]. The CO₂ emissions per tonne of cement and clinker were approximately 616.6 kg and 865.8 kg, respectively [3,4]. Given the global focus on carbon reduction, the cement industry, being one of the significant contributors to carbon emissions, faces immense pressure to achieve carbon peak and carbon neutrality goals.

Current research on low-carbon clinker production focuses mainly on low-calcium cement clinker [4,5,6,7] and alite structure modulation [8,9]. In recent years, some scholars have begun researching the coexistence of high-temperature phase (alite) and low-temperature phase (calcium sulfoaluminate) by introducing mineralizers to lower the formation temperature. The development of alite- belite-ye’elimite cement [4,5,10], as well as alite-ye’elimite cement [11,12,13], has been achieved. As the challenge of coexistence between alite and ye’elimite has been resolved, the research conducted by these scholars provides us with a new perspective: under the ordinary Portland cement system, lowering the C₃S content appropriately, increasing the C₂S content, and introducing a small amount of ye’elimite. Lowering the C₃S content implies a significant decrease in early strength, necessitating the inclusion of other mineral phases or the activation of existing mineral phases to supplement the strength. A small amount of ye’elimite can supplement early strength and scholars have previously demonstrated that ionic regulation can promote the early hydration of alite [8,9,14]. The key to maintaining the strength of this system compared to ordinary Portland cement is to activate belite, promote its early hydration, and improve early strength.

Belite is a solid solution of dicalcium silicate and is one of the main mineral phases in ordinary Portland cement. It primarily contributes to the development of strength in the later stages. Dicalcium silicate, also known as calcium orthosilicate, possesses an island-like structure, wherein the basic structural units of [SiO₄] tetrahedra are connected by [CaO_x] polyhedra, forming a three-dimensional spatial structure. Dicalcium silicate exists in five crystal forms: α, α′_H, α′_L, β, and γ, as illustrated in Figure 1 [15]. The α form has the highest temperature presence, while the γ form has the lowest. Occasionally, the α’_H and α’_L forms are collectively referred to as α′ type.

Pure dicalcium silicate exists in the γ phase at room temperature and exhibits a typical olivine structure [16]. In this structure, the [SiO₄] tetrahedra are connected by [CaO₆] octahedra with a calcium ion coordination number of 6. The high-temperature forms of dicalcium silicate also involve the connection of [SiO₄] tetrahedra through calcium–oxygen polyhedra, but the coordination number of Ca²⁺ is not fixed as it is in the γ phase. In the β phase, the coordination numbers are 6 and 8, while in the α′L phase, they are 9 and 10 [17,18]. According to Regound et al. [17], the transformation from β to γ and from β to α′L can be attributed to irreversible reconstructive phase transitions. In the transformation from β to γ, the orientation of the [SiO₄] tetrahedra and the coordination number of the Ca²⁺ change lead to a significant change in volume. The β to γ transition results in an approximately 13% increase in volume, which is responsible for the powdering of cement clinker [19]. The transformations from α′_H to α′_L and from α′_L to β belong to displacement-type phase transitions [17]. The crystal structures of the two types are very similar, with small changes occurring during the transition, to the extent that the transition between them was not initially recognized and was considered as a single phase (α′ phase). The transition from α′_L to β is a first-order phase transition that involves changes in the coordination number of Ca²⁺. The transition between α and α′_H is a semi-reconstructive phase transition in which half of the [SiO₄] tetrahedra undergo rotation [17].

It is generally believed that the γ type dicalcium silicate with olivine structure does not react with water and does not exhibit hydraulic activity. However, there are studies suggesting that it has a lower level of hydration activity and can undergo hydration reactions to some extent over a long period of time [20]. The hydration activity of high-temperature forms of dicalcium silicate varies. The hydration activity of dicalcium silicate is influenced by factors such as crystal type and solid solution impurities. It is generally believed that the higher the temperature form of dicalcium silicate, the higher the activity, that is, the hydration activity follows the order α > α′ > β > γ [21]. The above regularity holds well for different crystal forms of dicalcium silicate with stable ion configuration. The hydration activity of α′_H is superior to the commonly found β type in clinker, therefore, one significant research topic in developing low-calcium cement systems is the controlled stabilization of α′_H, which exhibits higher hydration activity.

In addition to temperature, the presence of foreign ions can also lead to different crystal forms of dicalcium silicate. The incorporation of foreign ions into the dicalcium silicate crystal can impede the transformation from a high-temperature phase to a low-temperature phase during the cooling process, thereby stabilizing the β, α′, and even α forms of dicalcium silicate at room temperature. Numerous studies have been conducted by researchers on the stabilization of dicalcium silicate crystal forms brought about through the introduction of foreign ions. In order to achieve crystallochemical stabilization of various polymorphs of C₂S, research has been conducted on doping C₂S with specific elements. These elements include Na⁺, K⁺, As²⁺, Sr²⁺, Ba²⁺, B³⁺, Fe³⁺, P⁵⁺, V⁵⁺, and Cr⁶⁺ [22,23]. The elements K⁺ [24], Ba²⁺ [25,26], B³⁺ [27,28,29,30,31], P⁵⁺ [32], and V⁵⁺ [33] can stabilize both the β-type and α′-type belite.

As the investigation of low-carbon clinker progresses, the study on the modulation of the crystal structure of dicalcium silicate using boron doping has regained scholarly attention. Cuesta et al. have found that in single boron doping, silicon is replaced by boron in the form of BO₄⁵⁻, while in boron–sodium composite doping, boron exists as the triangular planar anion BO₃³⁻. The authors have proposed that the composite doping of Na/B leads to the formation of a new structure, α′_H-Ca_1.85Na_0.15 (SiO₄)_0.85 (BO₃)_0.15, which is suitable for the production of active belite cement samples with the addition of borax [27]. Duvallet et al. have effectively stabilized α′_H-C₂S and significantly reduced the presence of γ-C₂S and β-C₂S by adding 2.8 wt% borax [28]. Aranda et al. have found that the doping of B₂O₃ and Na₂O can effectively stabilize α′_H-C₂S in belite-sulfoaluminate clinkers and results in a faster hydration rate compared to β-C₂S. Among the dopant compositions which have been tested, the α′_H-C₂S content was highest for the group with 2.0 wt% B₂O₃ and 0.9 wt% Na₂O doping [29]. Li et al. have found that the hydration degree of α′_H-C₂S prepared by single and composite doping methods (using B/Na and B/Ba) is higher than that of undoped β-C₂S. Specifically, the hydration degree was higher with composite doping compared to single doping [30]. Moreover, Saidani et al. have investigated the effect of dopants (B, P, and S) on the stability of β-Ca₂SiO₄ and the results show that dopants can induce lattice distortion in Ca₂SiO₄ and lower the formation temperature of the α and α′_H phases [31]. Despite the extensive research on B doping for the control of C₂S crystal phases, the mechanisms and the relationship between the amount of B doping and the content of the target crystal phase have not been systematically studied.

In this study, the authors conducted a systematic investigation into the impact of boron doping on the structure of C₂S (dicalcium silicate), taking advantage of boron’s ability to modulate structure. By introducing varying amounts of B₂O₃ (boron trioxide) into the raw materials, a correlation between boron content, C₂S crystal structure, and different structural proportions of C₂S was established. The characterization and analysis of the C₂S structure were performed using a range of techniques including XRD, high-temperature XRD, ICP-OES, FT-IR, and Raman spectroscopy. This paper successfully determines the positions of boron substitution in the C₂S structure as well as the mechanism behind structural modulation. These findings contribute to the theoretical foundation for the development of low-carbon clinker.

2. Materials and Methods

2.1. Sample Preparation

In the experiment, the materials used were CaCO₃ (99.95–100.05%, Sigma-Aldrich, Saint Louis, MO, USA), SiO₂ (99.9%, Sigma-Aldrich, Saint Louis, MO, USA), and B₂O₃ (99.9%, Supelco, Darmstadt, Germany). The raw materials used for the synthesis of C₂S were CaCO₃ and SiO₂, in a molar ratio of n (CaCO₃):n (SiO₂) = 2:1. The amount of B₂O₃ added to the raw materials was determined by the desired mass of C₂S varying from 0.5% to 6.5% of the C₂S weight. A total of 13 experimental groups were established and labeled as blank, 1#, 2#, 3#, 4#, 5#, 6#, 7#, 8#, 9#, 10#, 11#, 12#, and 13#. The composition of each experimental group is provided in

Table 1. The raw meal loadings (wt%).

Sample	CaCO3	SiO2	B2O3
Blank	76.91	23.09	0
1#	76.66	23.01	0.33
2#	76.41	22.93	0.66
3#	76.16	22.86	0.98
4#	75.91	22.78	1.31
5#	75.66	22.71	1.63
6#	75.42	22.64	1.95
7#	75.17	22.56	2.26
8#	74.93	22.49	2.58
9#	74.69	22.42	2.89
10#	74.45	22.35	3.20
11#	74.21	22.28	3.51
12#	73.98	22.20	3.82
13#	73.74	22.13	4.12

.

After weighing the samples according to the prescribed ratio, they were mixed with an equal mass of zirconia balls in a mixing bottle. The bottle was then placed on a mixing machine and mixed for 24 h. Once the samples were thoroughly mixed, they were sieved and compressed into circular discs with a diameter (R) of 30 mm and an approximate mass of 25 g per disc. The discs were then placed in covered crucibles to minimize the volatilization of B₂O₃. The crucibles were subsequently placed in a box furnace for sample firing. The temperature of the furnace rose steadily, increasing in steps of 10 °C per minute, starting from 25 °C and going up to 900 °C, then being held at that temperature for 0.5 h to ensure complete decomposition of calcium carbonate in the samples. Following this step, the temperature was further increased to 1300 °C and maintained for 4 h to facilitate sintering. Once the sintering process was completed, the samples were removed from the furnace and rapidly cooled down to room temperature using a fan.

2.2. Characterization

2.2.1. Determination of Boron Content (ICP-OES)

ICP-OES was chosen for the determination of boron content. The instrument used was Agilent 5110 (Agilent Technologies, Santa Clara, CA, USA) from the United States. The instrument’s working parameters were set as listed in

Table 2. The working parameters of ICP-OES.

Pump Speed	Plasma Working Gas Flow Rate	Nebulizer Flow Rate	Stabilization Time	Auxiliary Gas Flow Rate	Reading Time	Sample Rinsing Time	RF Power
100 r/min	12.0 L/min	0.70 L/min	20 s	1.0 L/min	5 s	20 s	1150 W

.

2.2.2. Qualitative Test of the Samples at Room Temperature (RT-XRD)

The fired samples were ground to a fine powder using an agate mortar. The powdered samples were then sieved through a 400-mesh sieve (38 μm). A suitable quantity of the resulting powder was used for qualitative phase analysis employing a room-temperature X-ray diffraction (XRD) setup. The RT-XRD analysis parameters were set as listed in

Table 3. The working parameters of XRD.

Test Name	Device	Radiation Source	Accelerating Voltage/Current	Step Size	Scanning Range	Speed
RT-XRD	Rigaku SmartLabTM 9 kW diffractometer (Rigaku Co., Tokyo, Japan)	Cu Kα, λ = 0.15406 nm without Kα2	45 kV/200 mA	0.01°	10°–70°	10°/min
Quantitative analysis	Rigaku SmartLabTM 9 kW diffractometer (Rigaku Co., Tokyo, Japan)	Cu Kα, λ = 0.15406 nm	45 kV/200 mA	0.01°	10°–70°	1°/min
HT-XRD	Rigaku SmartLabTM 9 kW diffractometer (Rigaku Co., Tokyo, Japan)	Cu Kα, λ = 0.15406 nm without Kα2	45 kV/200 mA	0.01°	10°–70°	10°/min

. The standard reference cards used for qualitative phase analysis were α′_H-C₂S (ICSD No. 81,097) [34], β-C₂S (ICSD No. 81,096) [34], γ-C₂S (ICSD No. 81,095) [34], and C₃S₂ (ICSD No. 34,338) [35].

2.2.3. Temperature-Dependent Testing of the Samples (HT-XRD)

High-temperature XRD analysis was conducted using the same device as for RT-XRD, while the test parameters are given in Table 3. The heating process was controlled at a rate of 10 °C per minute. Data collection commenced when the temperature reached 100 °C and data points were recorded every 100 °C, while maintaining a constant temperature. The standard reference cards used for qualitative phase analysis were α-C₂S (ICSD No. 82,998) [36], α′_H-C₂S (ICSD No. 82,997) [36], α′_L-C₂S (ICSD No. 82,996) [36], and β-C₂S (ICSD No. 81,096) [34].

2.2.4. Fourier-Transform Infrared Spectroscopy (FT-IR)

The samples were scanned using an FT-IR spectrometer (Thermo Scientific Nicolet iS20, Thermo Fisher Scientific Inc., Waltham, MA, USA) in the range of 4000–400 cm⁻¹ with a resolution of 4 cm⁻¹. Potassium bromide (KBr) was employed as the powdered sample carrier.

2.2.5. Raman Spectroscopy

Raman spectroscopy measurements were conducted using the LabRAM HR Evolution laser microscopic confocal Raman spectrometer (Horiba, Kyoto, Japan). This instrument model features a spectral resolution of ≤0.65 cm⁻¹ and a spectral repeatability of ≤±0.2 cm⁻¹. For the measurements, a laser with a wavelength of 532 nm and a power of 50 mW was employed. The wavenumber range chosen for testing was 50–4000 cm⁻¹.

2.2.6. Quantitative Analysis

The Rietveld method was utilized for the quantitative analysis of the phase composition in the sample. The XRD data of the sample was analyzed using the GSAS software (Version 1.0) with the EXPGUI package. The quantitative calculation procedures were carried out in accordance with the references [8,9]. The α′_H-C₂S (ICSD No. 81,097) [34], β-C₂S (ICSD No. 81,096) [34], γ-C₂S (ICSD No. 81,095) [34], and C₃S₂ (ICSD No. 34,338) [35] standard cards were employed for the quantitative calculations.

3. Results and Discussion

3.1. Boron Content in Samples

The determination of boron content in the samples is characterized using ICP-OES (Agilent 5110, Agilent Technologies, Santa Clara, CA, USA). The results for the levels of boron content in the raw materials and fired samples are shown in

Table 4. Boron content in raw materials and samples.

Sample	Raw Materials/wt.%		Samples/wt.%			Boron Volatilization Rate
	B2O3	Boron	B2O3	Boron	STDEV
1#	0.5	0.155	0.019	0.006	6.56 × 10−6	96.14%
2#	1.0	0.311	0.274	0.085	1.09 × 10−5	72.63%
3#	1.5	0.466	0.996	0.309	4.76 × 10−5	33.69%
4#	2.0	0.621	1.481	0.460	7.69 × 10−5	25.94%
5#	2.5	0.776	1.655	0.514	2.61 × 10−5	33.79%
6#	3.0	0.932	1.877	0.583	5.05 × 10−5	37.42%
7#	3.5	1.087	2.141	0.665	1.55 × 10−5	38.82%
8#	4.0	1.242	2.328	0.723	4.25 × 10−6	41.80%
9#	4.5	1.397	2.541	0.789	5.33 × 10−6	43.54%
10#	5.0	1.553	2.824	0.877	2.02 × 10−5	43.52%
11#	5.5	1.708	3.758	1.167	5.48 × 10−5	31.67%
12#	6.0	1.863	4.344	1.349	4.41 × 10−5	27.60%
13#	6.5	2.019	4.672	1.451	5.07 × 10−5	28.12%

. When the boron content is low, there is a higher level of boron volatilization. As the boron content increases, the volatilization gradually decreases and stabilizes at around 40%, and then decreases to around 30%.

Qian et al. [37] stated that the volatilization of boron is related to the vapor pressure of boron in the system. When the vapor pressure of boron in the system is not saturated, it will continue to volatilize into the system. Due to the relatively low boron content in samples #1 and #2, most of the boron volatilizes into the system, resulting in less boron being retained in the samples and a higher volatilization rate.

As the boron content increases, the mineralization effect of boron oxide decreases the solid-phase reaction temperature and enhances the reaction degree. The amount of boron solid solution in the sample gradually increases, leading to a decrease in volatilization.

As the boron doping concentration in the sample increases further, equilibrium is reached between the boron concentration involved in the solid-phase reaction and the boron oxide vapor content in the crucible (observed in samples 6#–10#). The increase in the solubility of boron in the sample promotes the transformation of dicalcium silicate from the β phase to the α′ phase, and at this point the level of boron volatilization remains stable at around 40%.

As the boron doping concentration continues to increase, a greater amount of boron remains in the sample, participating in the solid-phase reaction and dissolving into the crystal lattice of dicalcium silicate. This results in a significant increase in the content of the α’ phase. At this stage, the level of boron volatilization stabilizes at around 30%.

3.2. C₂S Polymorphs

3.2.1. Room-Temperature XRD

The room-temperature XRD test results of samples blank to 13# are shown in Figure 2. The blank sample mainly consists of γ-C₂S, with a small amount of β-C₂S. From the stacked waterfall plot, it can be observed that boron doping can stabilize the β and α′_H type C₂S. At lower boron doping levels, sample 1# contains a small amount of γ-C₂S and the intermediate phase 3CaO·2SiO₂ (C₃S₂, Rankinite). This is because the presence of boron in the solid-phase reaction contributes to the stabilization of the C₂S. However, due to the partial volatilization of boron, the ratio of n (CaO) to n (SiO₂) fails to reach 2:1, resulting in a small amount of C₃S₂ formation. Interestingly, with the significant volatilization of boron, β-C₂S is also stabilized within the system. Similarly, in sample 2#, despite the absence of the intermediate phase C₃S₂, the boron dissolved in the system remains inadequate to fully stabilize β-C₂S. When the solid solubility of boron reaches 0.309 wt.% (seen in sample 3#), the C₂S undergoes a complete transformation into the β phase. Furthermore, as the solid solubility of boron increases, the crystal structure of C₂S transitions from the β phase to the α′_H phase.

In order to provide a clearer representation of the changes in the crystal structure of β-C₂S and α′_H-C₂S as the boron solid solubility varies, Figure 3a,b illustrate the comparison between samples 1# and 13# and the standard cards of β-C₂S and α′_H-C₂S. By comparing the main diffraction peaks, it is evident that sample 3# exhibits a perfect match with β-C₂S without any additional substitution peaks. This finding indicates that sample 3# has undergone a complete transformation into β-C₂S. As the level of boron doping increases, a gradual transition of the crystal structure from β-C₂S to α′_H-C₂S is observed, starting from sample 4#. This observation is consistent with the earlier discussion on the substantial change in boron evaporation between samples 3# and 4#, thereby mutually confirming the observed transformation. During the transformation from β-C₂S to α′_H-C₂S, characteristic diffraction peaks exhibit noticeable changes. The range of 31.7°–33° corresponds to the primary characteristic diffraction peaks of C₂S, and a significant transformation is observed within this range from sample 3# to 13#. The diffraction peaks at 34.2°, 35.3°, 36°–38°, and 45.5° are distinctive features that differentiate β-C₂S from α′_H-C₂S. As the boron doping level increases, the intensity of these peaks gradually decreases until they eventually vanish. On the other hand, the diffraction peaks at 33.3°, 38°, 40.4°, 46.8°, and 52.2° characterize α′_H-C₂S, and their intensity becomes more prominent with higher concentrations of boron solid solution.

The characteristic diffraction peaks of β-C₂S and α′_H-C₂S can be divided into five window regions, denoted as W1–W5, which are displayed in Figure 3. These window regions include the following angles: 30.5°–35.7°, 36.5–39°, 40°–42.2°, 45°–48.5°, and 51.5°–55°. Detailed comparisons are conducted by extracting the diffraction peaks within these regions, as illustrated in Figure 4. From an overall perspective, the diffraction peaks of samples 3#–5# exhibit the characteristics of β-C₂S primarily due to the relatively small amount of α′_H-C₂S formed, which is not prominently reflected in the XRD pattern. In samples 6#–10#, with an increase in the boron solid solution content, the formation of α′_H-C₂S gradually increases, accompanied by more pronounced diffraction peaks, especially in the 32°–33° characteristic diffraction region. In samples 11#–13#, the XRD diffraction peaks are mainly attributed to α′_H-C₂S, with 13# showing almost no diffraction peaks of β-C₂S. This indicates that at this stage, C₂S has transitioned almost completely from the β phase to the α′_H phase.

The characteristic diffraction peaks in the five window regions were calibrated based on the ICSD standard cards for β-C₂S (ICSD No. 81,096) [34] and α′_H-C₂S (ICSD No. 81,097) [34]. In the W1 window, particularly in the 32°–33° region, the characteristic diffraction peaks of β-C₂S are primarily attributed to the crystal planes ($\overline{1}21$)_β, (200)_β, and (121)_β. As the transition to α′_H-C₂S occurs, the characteristic diffraction peaks are then generated by the crystal planes (020) _α′H and (211) _α′H. The characteristic peaks of β-C₂S at around 34.3° and 35.3° are attributed to the crystal plane (103)_β and (210)_β. These peaks gradually weaken and disappear as the boron solubility increases. Simultaneously, the characteristic peak of α′_H-C₂S at around 33.2° gradually emerges and strengthens, which is generated by the crystal plane (013) _α′H. The pattern of characteristic diffraction peaks in the W2–W5 windows is similar to that in the W1 window. We have compared the disappearance and formation of diffraction peaks in each window, as presented in

Table 5. Comparison of characteristic peaks of β and α′_H-C₂S in five windows.

Characteristic Area	β-C2S	α′H-C2S
W1, 32°–33°	($\overline{1}21$)β	(211)α′H
	(121)β
	(200)β	(020)α′H
W1, 33°–34.5°	(103)β	(013)α′H
W1, 35.3°	(210)β	-
W2, 36.5°–39°	($\overline{2}02$)β	(022)α′H
	(122)β	(212)α′H
W3, 40°–42.2°	(014)β	(104)α′H
	(031)β	(301)α′H
	(212)β	(122)α′H
W4, 45°–48.5°	($\overline{2}22$)β	(222)α′H
	(222)β
	(024)β	(204)α′H
	(213)β	(123)α′H
W5, 51.5°–55°	($\overline{2}31$)β	(321)α′H
	(231)β
	(223)β	(223)α′H
	(040)β	(400)α′H

.

β-C₂S is classified as belonging to the monoclinic crystal system, while α’_H-C₂S is classified as belonging to the orthorhombic crystal system. During the process of structural transformation, the symmetry of the crystal increases, resulting in the equivalence of originally inequivalent crystal planes. For instance, the crystal planes ($\overline{1}21$)_β and (121)_β, ($\overline{2}22$)_β and (222)_β, as well as ($\overline{2}31$)_β and (231)_β, become equivalent in the transition to the orthorhombic system. These equivalent crystal planes in the orthorhombic system are denoted as (211)_α′H, (222)_α′H, and (321)_α′H inα′_H-C₂S by combining the corresponding relationships in Table 5. Upon examining the corresponding relationships in Table 5, a correlation between the crystal planes that cause the characteristic diffraction peaks of β-C₂S and α′_H-C₂S becomes apparent. In particular, ${\left(h, k,l\right)}_{\beta }\stackrel{Transfer}{\Rightarrow }{\left(k, h,l\right)}_{{\alpha }_H^{\prime }} \mathrm{o}\mathrm{r} {\left(k, h,\overline{l}\right)}_{{\alpha }_H^{\prime }}$ (equivalent crystal planes are taken into account). Furthermore, the β-C₂S has a unit cell with parameters a = 5.5121 Å, b = 6.7575 Å, c = 9.3138 Å, α = 90°, β = 94.581°, and γ = 90° [34] while the α′_H-C₂S has a unit cell with parameters a = 6.7673 Å, b = 5.5191 Å, c = 9.3031 Å, α = 90°, β = 90°, and γ = 90° [34]. It can be deduced that during the transformation from β-C₂S to α′_H-C₂S, the β angle changes from 94.581° to 90°, while the a-axis and b-axis undergo an exchange simultaneously. After examining the unit cells of β-C₂S and α′_H-C₂S, it is evident that the β-C₂S crystal structure undergoes a structural transformation using a transformation matrix $\mathrm{P}=\left(\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& -1\end{array}\right)$, then converts the symmetry of transformed cells into an orthorhombic system with a space group of Pnma. As a result, the final transformed structure closely resembles that of α′_H-C₂S. The transformation process was simulated using VESTA software (Version 3.5.8) [38], as illustrated in Figure 5a–d. Figure 5a depicts the β-C₂S unit cell observed along the b-axis. Figure 5b exhibits the β-C₂S unit cell after undergoing a structural transformation using the transformation matrix $\mathrm{P}=\left(\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& -1\end{array}\right)$, observed from the b-axis. Figure 5c represents the unit cell observed along the b-axis after modifying the symmetry to that of an orthorhombic system (with a space group Pnma) and setting the occupancies of Ca and O as 0.5. Figure 5d illustrates the α′_H-C₂S unit cell observed along the b-axis. Indeed, it is evident that the structure obtained from the transformation of the β-C₂S unit cell, as shown in Figure 5c, closely resembles the α′_H-C₂S unit cell.

As the two-unit cell has a transformation matrix, the planes also have the same corresponding relationships. Taking the plane ($\overline{1}21$)_β as an example, let us see how the plane transforms during the phase transition. The process is given below.

$${\left(\begin{array}{ccc}\overline{1}& 2& 1\end{array}\right)}_{\beta }\Rightarrow \left(\begin{array}{ccc}\overline{1}& 2& 1\end{array}\right)\left(\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& -1\end{array}\right)\Rightarrow {\left(\begin{array}{ccc}2& \overline{1}& \overline{1}\end{array}\right)}_{{\alpha }_H^{\prime }}\underset{equivalent}{\Rightarrow }{\left(\begin{array}{ccc}2& 1& 1\end{array}\right)}_{{\alpha }_H^{\prime }}$$

The diffraction peak at around 35.3° in the β-C₂S phase is generated by the (210)_β crystal plane, however, there is no corresponding diffraction peak in the α′_H-C₂S phase. The (210)_β crystal plane theoretically corresponds to the (120)_α′H crystal plane in α′_H-C₂S, but the structure of α′_H-C₂S is orthorhombic. Due to the symmetry of the space group, the (120)_α′H crystal plane exhibits forbidden diffraction, leading to the absence of diffraction peaks generated by the (120)_α′H crystal plane in α′_H-C₂S. As shown in Figure 6, a comparison is made between the zone axis ${\left[1\overline{2}0\right]}_{\beta }$ and ${\left[\overline{2}10\right]}_{{\alpha }_H^{\prime }}$. It can be observed that the (120)_α′H crystal plane belongs to the space group absence, therefore, no diffraction spots are observed.

3.2.2. In-Situ High-Temperature XRD

The analysis using room-temperature XRD confirmed that sample 3# is pure β-C₂S. In-situ high-temperature XRD testing was conducted on this sample by collecting data at regular intervals during the temperature ramp from 100 °C to 1300 °C, with data collected every 100 °C. The temperature was maintained at a constant during the data acquisition process. The waterfall plot of the test data is shown in Figure 7. In general, as the temperature increases, the C₂S crystal structure undergoes a transformation from β to α′_L phase, and then to α′_H phase. Below 300 °C, the crystal structure of C₂S is β phase. At 300 °C, the appearance of the α′_L diffraction peak indicates the onset of phase transition. By 600 °C, the characteristic diffraction peak of β-C₂S disappears completely, indicating a complete transformation to the α′_L phase. The transition temperature of β to α′_L is slightly lower than the temperature shown in Figure 1 (690 °C), which can be primarily attributed to the decrease in transition temperature resulting from the presence of boron as a dopant. When the temperature reaches 1200 °C, α′_L-C₂S transforms into α′_H-C₂S, which is consistent with the reported transition temperature of 1160 °C for the α′_L to α′_H transformation. At 1300 °C, no signs of α′_H-C₂S transforming into α-C₂S were observed. This may be due to the rapid transformation from α′_H-C₂S to α-C₂S, where the temperature range for the transformation is small, and the experimental temperature did not reach the phase transition temperature (1425 °C). The α-Al₂O₃ diffraction peaks observed in Figure 7 are a result of the sample holder.

In order to facilitate the comparison of X-ray diffraction (XRD) results obtained at high temperatures and room temperatures, three specific windows were chosen to display the high-temperature XRD data. These windows cover the angles of 27°–30.5°, 31.5°–35°, and 35°–49°, respectively, as depicted in Figure 8 and Figure 9. Figure 8 provides a visual representation of the transition process from β-C₂S to α′_L-C₂S that occurs within a moderate temperature range of 25 °C to 600 °C. When comparing the changes in the characteristic diffraction peak at 32°–33° between Figure 4 and Figure 8, it becomes apparent that the phase transition process induced by boron ion doping does not align with the temperature-induced phase transition. Figure 8 showcases the temperature-induced phase transition, where only one high-intensity diffraction plane (002) _α′L emerges between the crystallographic planes ($\overline{1}21$)_β and (200)_β of β-C₂S, resulting from the transformation of the (200)_β plane. Conversely, in the boron ion doping-induced phase transition, two high-intensity diffraction planes, (020)_α′H and (211)α′_H, appear between the planes ($\overline{1}21$)_β and (200)_β. This indicates that boron ion doping mediates the structural modulation of β-C₂S, bypassing the α′_L-C₂S phase and directly transforming it into α′_H-C₂S. Notably, there is no existing literature [27,28,29,30,31] reporting the modulation of the C₂S crystal structure to achieve α′_L-C₂S through the process of boron doping. Figure 9 illustrates the transition process from α′_L-C₂S to α′_H-C₂S at medium to high temperatures (700–1300 °C). With the temperature ranging from 600 °C to 900 °C, C₂S remains in the α′_L phase, with slight variations in diffraction peaks (such as peaks at around 41°), which can be attributed to the thermal expansion of the α′_L phase. Throughout the transition from α′_L-C₂S to α′_H-C₂S, the characteristic diffraction peaks exhibit minimal changes, with the exception of the range of 32°–33°. Furthermore, even at a temperature of 1100 °C, the C₂S crystal structure predominantly maintains the α′_L-type, transitioning completely to α′_H-type at 1200 °C. These observations indicate a close resemblance between the α′_L and α′_H phases of C₂S, with a narrow temperature range for the transition, suggesting a rapid phase transformation.

3.3. Fourier-Transform Infrared Spectroscopy (FT-IR)

Based on the XRD results obtained at room temperature and high temperature, it is evident that the incorporation of boron can effectively transform β-C₂S into the α′_H phase. However, further investigation is needed to determine the specific occupancy and substitution behavior of boron within the C₂S structure. From the samples 3# to 13#, a total of 9 samples were selected for FT-IR testing based on the variation in boron content. The results are presented in Figure 10. Figure 10a indicates the absorption peak signals of the major functional groups. The absorption peaks observed at around 1250 cm⁻¹, 1200 cm⁻¹, and 660 cm⁻¹ are attributed to the stretching vibrations of [BO₃]³⁻ ions. The asymmetric stretching vibration absorption peaks of [BO₄]⁵⁻ ions are observed in the range of 1080 cm cm⁻¹ to 950 cm⁻¹ [30]. The asymmetric stretching vibration absorption peaks of V₃ [SiO₄]⁴⁻ ions are observed in the range of 996 cm⁻¹ to 846 cm⁻¹, while the asymmetric bending vibration absorption peak of V₄ [SiO₄]⁴⁻ ions is observed at around 518 cm⁻¹ [28,29,30,31].

Combining Figure 10a,b, it can be observed that the absorption peaks of the stretching vibrations of [BO₃]³⁻ ions are more pronounced in samples with a higher content of β-C₂S. After sample 10#, the vibration absorption peak at around 660 cm⁻¹ disappears, while the signals at 1250 cm⁻¹ and 1200 cm⁻¹ gradually weaken and eventually disappear. At this point, the main crystal structure of C₂S in the sample is α′_H-type, indicating the absence of [BO₃]³⁻ groups in the crystal structure of α′_H-type C₂S. The absorption peak signal of the asymmetric bending vibration of V₄ [SiO₄]⁴⁻ ions at around 518 cm⁻¹ gradually weakens with an increase in boron solubility. This indicates a gradual reduction in the [SiO₄]⁴⁻ groups in the system, which can be attributed to the substitution of B³⁺ for Si⁴⁺ or the formation of Si⁴⁺ vacancies due to B³⁺ filling the interstitial sites. By observing the absorption peak signals in the range of 1000 cm⁻¹ to 846 cm⁻¹, it can be seen that the absorption peaks at 996 cm⁻¹ and 846 cm⁻¹ correspond to the asymmetric stretching vibrations of V₃ [SiO₄]⁴⁻ ions. With an increase in boron doping, the intensity gradually decreases, which is consistent with the variation trend of the absorption peak at around 518 cm⁻¹ for V₄ [SiO₄]⁴⁻. The absorption peak signals in the range of 950 cm⁻¹ to 900 cm⁻¹ mainly occur at around 935 cm⁻¹ and 908 cm⁻¹. Specifically, in sample 3#, the main absorption peak signal is near 908 cm⁻¹, while samples 4# and 6# exhibit absorption peaks near 935 cm⁻¹ and 908 cm⁻¹. Starting from sample 7#, the main absorption peak signal occurs near 935 cm⁻¹, with a slight shift. By considering the boron solubility and the changes in the crystal structure of C₂S, it can be analyzed that sample 3# corresponds to β-C₂S, with its absorption peak signal in the range of 950 cm⁻¹ to 900 cm⁻¹ primarily occurring near 908 cm⁻¹. With an increase in boron doping, an absorption peak signal near 935 cm⁻¹ becomes evident. In the samples with higher boron content, the intensity at this position gradually weakens. This can be attributed to the overlapping effects of the asymmetric stretching vibration absorption peaks of V₃ [SiO₄]⁴⁻ and [BO₄]⁵⁻ ions. In other words, boron-doped β-C₂S exhibits a characteristic absorption peak near 908 cm⁻¹, while α′_H-C₂S exhibits a characteristic absorption peak near 935 cm⁻¹. Additionally, the absorption peak at around 747 cm⁻¹ is speculated to be a result of the formation of free SiO₂, further confirming the role of boron in altering [SiO₄]⁴⁻.

Furthermore, the radius of B³⁺ ions is closer to that of Si⁴⁺ ions, and boron has an electronegativity of 2.0, silicon has an electronegativity of 1.9, while calcium has an electronegativity of 1.0. Comparatively, boron shares more similarities with silicon in terms of properties. Therefore, boron ions have a greater influence on silicon ions in the C₂S structure. Combining the FT-IR vibration peak variations, it can be speculated that in boron-doped C₂S, the stabilization of the β-C₂S structure is primarily due to the influence of boron ions in the form of [BO₃]³⁻ groups on the [SiO₄]⁴⁻ groups. On the other hand, in boron-doped α′_H-C₂S, the stabilization is due to the substitution of boron ions in the form of [BO₄]⁵⁻ groups for the [SiO₄]⁴⁻ groups. Therefore, when the boron content is low, the β-C₂S structure can be inferred as ${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{\mathrm{x}}{\mathrm{O}}_{\frac{\mathrm{x}}{2}}$. However, when the boron content is high, [BO₃]³⁻ binds with free oxygen to form [BO₄]⁵⁻, which replaces [SiO₄]⁴⁻. At the same time, excess B³⁺ partially substitutes for Ca²⁺, following a similar mechanism to the substitution of Al³⁺ in olivine by Mg²⁺ [29]. This forms a structure of ${\mathrm{C}\mathrm{a}}_{2-\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{\mathrm{x}}$, consistent with the proposed structure for single boron doping into the C₂S structure by Cuesta et al. [33]. The difference is that they represent [BO₃]³⁻, which is derived from the triangular structure formed after B³⁺ replaces Ca²⁺. However, in this experiment, it was observed that as the boron content increases, the relative content of [BO₃]³⁻ gradually decreases, which does not correspond to ${\mathrm{C}\mathrm{a}}_{2-\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{\mathrm{x}}$. Therefore, ${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{\mathrm{x}}{\mathrm{O}}_{\frac{\mathrm{x}}{2}}$ is more suitable to represent the β-C₂S structure.

3.4. Raman Spectroscopy

Nine samples ranging from 3# to 13# were selected for Raman spectroscopy analysis, which was the same as for the Fourier-transform infrared (FT-IR) spectroscopy. The resulting data is presented in Figure 11. Within the frequency range of 300–50 cm⁻¹, the vibrations arise from the lattice’s internal components and are primarily attributed to the presence of Ca-O bonds [39]. There is a progressive attenuation in the vibrations of Ca-O observed at 165 cm⁻¹, 236 cm⁻¹, and 303 cm⁻¹ as the boron content increases. This suggests that during the conversion process from β-C₂S to α′_H-C₂S, B³⁺ replaces Ca²⁺ ions. This observation corroborates the indications from the FT-IR spectroscopy analysis regarding the α′_H-C₂S structure. The symmetric bending vibrations of V₂ [SiO₄]⁴⁻ are observed at 371 cm⁻¹ and 424 cm⁻¹ [39,40,41]. As the boron content increases, [BO₄]⁵⁻ gradually replaces [SiO₄]⁴⁻, resulting in an interaction between the two which produces an overlapping vibration peak at 390 cm⁻¹ and 405 cm⁻¹. Similarly, the overlapping vibration peaks at 846 cm⁻¹ and 880 cm⁻¹ are attributed to [BO₄]⁵⁻ and [SiO₄]⁴⁻ [42]. It is evident that starting from sample 10#, the peak at 846 cm⁻¹ significantly broadens, indicating an enhanced role of [BO₄]⁵⁻ in the structure. This observation is consistent with the significant weakening of the characteristic absorption peak of [BO₃]³⁻ in the FT-IR spectroscopy results from sample 10#. The symmetric stretching vibrations of [BO₄]⁵⁻ are observed in the range of 962 cm⁻¹ to 900 cm⁻¹, and, starting from sample 10#, there is a noticeable enhancement in these vibrations, indicating a gradual increase in the content of [BO₄]⁵⁻. The attenuation of the vibration peak at around 977 cm⁻¹ of [SiO₄]⁴⁻ further confirms the substitution of [BO₄]⁵⁻ for [SiO₄]⁴⁻.

3.5. Quantitative Analysis

The results of the chemical composition analysis of the samples are shown in

Table 6. The chemical composition of the samples (wt.%).

Sample	CaO	SiO2	B2O3	LOI
Blank	64.99	34.83	0.00	0.18
1#	64.96	34.80	0.02	0.21
2#	64.76	34.69	0.27	0.27
3#	64.32	34.46	0.99	0.23
4#	64.03	34.30	1.48	0.20
5#	63.93	34.25	1.65	0.16
6#	63.73	34.14	1.87	0.26
7#	63.60	34.07	2.14	0.19
8#	63.46	34.00	2.32	0.21
9#	63.32	33.92	2.54	0.23
10#	63.12	33.82	2.82	0.24
11#	62.51	33.49	3.75	0.26
12#	62.14	33.29	4.33	0.24
13#	61.91	33.17	4.66	0.26

. The samples were analyzed using the Rietveld method to quantify the content of different structures of C₂S in samples blank to 13#. Rankinite (3CaO·2SiO₂, short forC₃S₂), γ-, β-, and α′_H-C₂S as well as boron content and the calculated fitting error Rwp are presented in

Table 7. Rietveld quantitative phase analysis (wt.%) of the samples.

Sample	β-C2S	α′H-C2S	γ-C2S	C3S2	f-CaO	B *	Rwp
Blank	10.92	0.00	89.08	0.00	0.00	0	0.0442
1#	86.07	0.00	9.67	2.10	2.16	0.006	0.0432
2#	96.86	0.00	3.14	0.00	0.00	0.085	0.0451
3#	100	0.00	0.00	0.00	0.00	0.309	0.0483
4#	88.38	11.62	0.00	0.00	0.00	0.460	0.0534
5#	84.88	15.12	0.00	0.00	0.00	0.514	0.0445
6#	78.43	21.57	0.00	0.00	0.00	0.583	0.0518
7#	70.99	29.01	0.00	0.00	0.00	0.665	0.0442
8#	62.85	37.15	0.00	0.00	0.00	0.723	0.0443
9#	55.81	44.19	0.00	0.00	0.00	0.789	0.0455
10#	48.01	51.99	0.00	0.00	0.00	0.877	0.0438
11#	25.68	74.32	0.00	0.00	0.00	1.167	0.0429
12#	12.18	87.82	0.00	0.00	0.00	1.349	0.0520
13#	4.60	95.40	0.00	0.00	0.00	1.451	0.0516

* Note: The boron content was determined using ICP-OES testing, as previously presented in Table 4.

. The fitting errors for samples 1# to 13# ranged from 0.04 to 0.05 (4–5%), which is significantly lower than the acceptable fitting error of 0.1 (10%). This indicates that the quantitative calculation steps and initial structure selection were correct, and the actual mineral phase structures in the samples are consistent with the initially selected structures.

Sample 1# contains 2.10 wt% of the intermediate phase, Rankinite. This is attributed to the relatively low boron content in the system, which, under the specified firing temperature and holding time conditions, prevents the 3CaO·2SiO₂ from combining with the free CaO to form C₂S. In sample 2#, the presence of the intermediate phase Rankinite is no longer observed. However, the boron content in the system is not enough to fully convert C₂S into the β-type. Complete transformation to the β-C₂S is only achieved when the boron content reaches 0.309 wt%, as observed in sample 3#. These findings are consistent with the qualitative analysis of XRD phase identification. The content of β-C₂S gradually decreases with increasing boron solid solution, while the content of α′_H-C₂S increases. At a boron content level of 1.451 wt%, the C₂S in the system is predominantly α′_H-C₂S (95.40 wt%). The quantitative fitting analysis plots for samples 3#, 6#, 11#, and 13# are shown in Figure 12.

Analysis of the data presented in Table 7 reveals a linear correlation between the content of β-C₂S, α′_H-C₂S, and boron solid solution. Linear fitting was conducted on the data and the results are illustrated in Figure 13. The obtained R² value of 0.9916 signifies a strong linear relationship between the boron solid solution content and the C₂S structure.

According to the linear relationship between the content of boron solid solution and the content of β-C₂S and α′_H-C₂S, the variable x in β-${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{\mathrm{x}}{\mathrm{O}}_{\frac{\mathrm{x}}{2}}$ and α′_H-${\mathrm{C}\mathrm{a}}_{2-\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{\mathrm{x}}$ has a specific value. A function relationship is constructed with the β-C₂S content ($\mathsf{\beta }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}$) and α′_H-C₂S content (${\mathsf{\alpha }}_{\mathrm{H}}^{\prime }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}$) as independent variables, and the boron solid solution content (${\mathrm{C}}_{\mathrm{B}\mathrm{o}\mathrm{r}\mathrm{o}\mathrm{n}}$) as the dependent variable: ${\mathrm{c}}_{\mathsf{\beta }}\times \mathsf{\beta }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}+{\mathrm{c}}_{{\mathsf{\alpha }}_{\mathrm{H}}^{\prime }}\times {\mathsf{\alpha }}_{\mathrm{H}}^{\prime }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}={\mathrm{C}}_{\mathrm{B}\mathrm{o}\mathrm{r}\mathrm{o}\mathrm{n}}$. For the calculation data of samples 3# to 13# in Table 7, a multiple linear regression analysis was conducted. The constant of the regression equation was set to 0, and the confidence level was set at 95%. The results of the regression analysis are shown in

Table 8. The results of multiple linear regression analysis.

Regression Analysis		Coefficients
R2	Standard Error	${\mathbf{c}}_{\mathsf{\beta }}$	Standard Error	p-Value	${\mathbf{c}}_{{\mathsf{\alpha }}_{\mathbf{H}}^{\prime }}$	Standard Error	p-Value
0.9993	0.02752	0.3142	0.01674	0.000	1.4753	0.01843	0.000

. The constructed function relationship is given by the equation $0.3142\times \mathsf{\beta }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}+1.4753\times {\mathsf{\alpha }}_{\mathrm{H}}^{\prime }\text{-}{\mathrm{C}}_2{\mathrm{S}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}}={\mathrm{C}}_{\mathrm{B}\mathrm{o}\mathrm{r}\mathrm{o}\mathrm{n}}$. In this equation, ${\mathrm{c}}_{\mathsf{\beta }}=0.3142$ represents the boron content in the β-${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{\mathrm{x}}{\mathrm{O}}_{\frac{\mathrm{x}}{2}}$ structure, and the calculated value of x is found to be 0.05. This calculation indicates that the β-C₂S structure is composed of ${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{0.95}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{0.05}{\mathrm{O}}_{0.025}$. Similarly, ${\mathrm{c}}_{{\mathsf{\alpha }}_{\mathrm{H}}^{\prime }}=1.4753$ represents the boron content in the α′_H-${\mathrm{C}\mathrm{a}}_{2-\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{\mathrm{x}}$ structure, and the calculated value of x is found to be 0.11. This finding suggests that the α′_H-C₂S structure is composed of ${\mathrm{C}\mathrm{a}}_{1.89}{\mathrm{B}}_{0.11}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{0.89}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{0.11}$.

4. Conclusions

This study investigates the evolution patterns of the crystal structure of boron-doped C₂S using various characterization techniques. Structural models for β-C₂S and α′_H-C₂S are constructed, and the correlation between boron doping levels and different levels of C₂S content is determined using regression analysis. Additionally, the structural formulas for boron-doped C₂S are derived. The main findings of this study can be summarized as follows:

• Boron doping can stabilize both the β-C₂S and high-temperature phase α′_H-C₂S. As the boron solubility increases, the crystal structure of C₂S transitions directly from the β-phase to the α′_H-phase, without the intermediate structure of α′_L-C₂S, which is in contrast to the high-temperature XRD behavior.
• The β-C₂S and α′_H-C₂S structures exhibit a corresponding relationship in terms of their characteristic diffraction peaks. This relationship can be represented by a transformation matrix P, where $\mathrm{P}=\left(\begin{array}{ccc}0& 1& 0\\ 1& 0& 0\\ 0& 0& -1\end{array}\right)$.
• When the boron content is 0.309 wt%, the C₂S structure completely transforms into the β-phase. When the boron content is 1.451 wt%, the C₂S structure is predominantly in the α′_H-phase. Furthermore, the boron content shows a linear relationship with the concentrations of β-C₂S and α′_H-C₂S, respectively.
• The structural models for β-C₂S and α′_H-C₂S were determined using structural analysis. It was found that β-C₂S has a structural formula of ${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{\mathrm{x}}{\mathrm{O}}_{\frac{\mathrm{x}}{2}}$, while α′_H-C₂S has a structural formula of ${\mathrm{C}\mathrm{a}}_{2-\mathrm{x}}{\mathrm{B}}_{\mathrm{x}}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{1-\mathrm{x}}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{\mathrm{x}}$. Regression analysis was performed using the quantitative calculation results and boron content data, which yielded the following structural formulas: β-C₂S is ${\mathrm{C}\mathrm{a}}_2{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{0.95}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_{0.05}{\mathrm{O}}_{0.025}$, and α′_H-C₂S is ${\mathrm{C}\mathrm{a}}_{1.89}{\mathrm{B}}_{0.11}{\left(\mathrm{S}\mathrm{i}{\mathrm{O}}_4\right)}_{0.89}{\left(\mathrm{B}{\mathrm{O}}_4\right)}_{0.11}$.