Thermodynamics of the hydrothermal synthesis of xonotlite

Xonotlite, as a multifunctional inorganic material, has been widely used in the fields of building insulation, friction braking, and bionic composite materials. However, the main method of producing xonotlite, the dynamic hydrothermal method, is regarded as a black box process. Optimization of synthesis conditions can only be achieved through trial-and-error experimentations, and there are inconsistencies in the experimental results reported in the literature. In this work, we established a thermodynamic model of the Ca(OH)2-SiO2-H2O system under hydrothermal conditions, and investigated influencing factors of the xonotlite synthesis. The results show that, the predicted lowest temperature of xonotlite synthesis is approximately 170 °C. Furthermore, an optimum condition to synthesis xonotlite with a purity of 99% is proposed as follows: reaction temperature, 200 °C; Ca/Si ratio, 0.9–1.0; water-solid ratio, no more than 20; pH, 7–8. This new synthesis process has been confirmed by experiments.


Introduction
Xonotlite (Ca 6 Si 6 O 17 (OH) 2 ) is an attractive nanofiber material. It has the lowest water content in all hydrated calcium silicate crystalline phases and is characterized by good thermal stability, light weight, large specific surface area, and low thermal conductivity [1,2]. Therefore, xonotlite is widely used as an adsorbent [3][4][5], catalyst supports [6], phase change energy storage material matrix [7], photoluminescent material [8], electrode materials [9,10], and thermal insulation in chemical, architectural and metallurgical industries [11,12]. Despite its shape being similar to asbestos fiber, xonotlite has good biocompatibility and will not cause harm to the human body [13,14]. Recently, Bijwe and coworkers have found that adding xonotlite could considerably improve compressibility, porosity, and friction stability of brake pads and brake noise [15][16][17]. While xonotlite has many promising applications, its natural reserve is not abundant, and often comes with an insufficient purity. Thus, the industrial synthesis of xonotlite has aroused widespread interest.
Hydrothermal approach is the principal method of synthesizing xonotlite. The formation of xonotlite depends on the control of abundant parameters, including the initial Ca/Si ratio, the characterizations of calcium and silicon raw materials, the reaction temperature, the water-solid ratio, and the solution pH [18][19][20][21][22][23][24]. Therefore, the preparation of well-crystallized pure xonotlite presents significant challenges. Currently, numerous experiments have been carried out to explore the influence of various factor on the formation of xonotlite. Table 1 summarizes a list of those conditions proposed in the literature.
Different synthesis conditions are recommended in the literature. Among those influencing factors, the reaction temperature and the Ca/Si molar ratio of the raw materials are the most critical parameters for the synthesis. According to Speakman's report [25], at saturated steam pressures, xonotlite could be synthesized at 150°C by mixing Ca(OH) 2 and SiO 2 (Ca/Si molar ratio of 1) at room temperature for 10 days, followed by the hydrothermal reaction. Yet, Peppler [26] found that xonotlite can only be synthesized at reaction conditions above 180°C. This results in an ambiguous lowest formation temperature for xonotlite. Aymonier [27] was able to synthesize xonotlite in the supercritical water (400°C and 23.5 MPa), effectively reducing the reaction time of Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. days and hours to several seconds, thereby suggesting that high temperature has the potential to significantly decrease reaction time. Kawaguchi and Tashiro [24] studied the effect of the Ca/Si molar ratio of raw materials on the synthesis of xonotlite, and they reported that the most suitable Ca/Si molar ratio was 0.6-1.2. Through experimental observations, Wu [21] found that pure xonotlite can be obtained only when the molar ratio of Ca/ Si is 1. However, Qian et al [28] demonstrated that high-purity xonotlite could be synthesized at a Ca/Si molar ratio of 0.8, 240°C and 24 h. Additionally, Wang and Tomita [29] found that when the molar ratio of Ca/Si was 0.93, pure xonotlite was formed at 300°C, 7 h after the hydrothermal process. As mentioned above, the experimental conditions reported in the literature exhibit significant differences, and some results are contradictory, making it difficult to understand the synthesis process or optimize the synthesis conditions.
The thermodynamic model of hydrothermal reactions can assist studying the synthesis process, and has been widely adopted in the geology and the chemical industries [30][31][32][33][34][35][36]. Ma et al [37] studied the thermodynamics of hydrothermal synthesis of xonotlite from potassium silicate and Ca(OH) 2 , and provided theoretical guidance to the experimental process. Nonetheless, they only considered the free energy change of a single reaction, and did not systematically analyze and optimize the synthesis conditions for xonotlite. Riman and Lencka [38][39][40] proposed a rigorous approach based on a thermodynamic model of electrolyte solutions and successfully optimized the synthesis conditions for several advanced ceramic materials from BaO-TiO 2 -H 2 O, PbO-TiO 2 -H 2 O, CaO-TiO 2 -H 2 O, and SrO-ZrO 2 -H 2 O systems. Zhang and coworker [41] employed the electrolyte solutions thermodynamic model to guide the hydrothermal synthesis of pure KNbO 3 powder in a K-Nb-O ternary system, demonstrating that the thermodynamics model is a powerful theoretical tool for designing the hydrothermal synthesis of new materials. Compared to the aforementioned system, the Ca(OH) 2 -SiO 2 -H 2 O system has multiple parallel reactions [42,43], making the reaction process more complex, even a slight variation in reaction conditions can significantly affect the final product. Despite the extensive publication of research papers on this compound over the past few decades, there has been no theoretical simulation study on the hydrothermal synthesis of xonotlite.
In this work, the thermodynamic properties of the Ca(OH) 2 -SiO 2 -H 2 O system at high temperatures and high pressures were studied to anticipate the optimal synthesis parameters for producing phase-pure xonotlite. The stability and yield diagrams can be employed to explore the impact of various factors such as reaction temperature, pH value, Ca/Si molar ratio and water-solid ratio on the synthesis of xonotlite.

Equilibrium Constants
In the synthesis of xonotlite, the most common raw materials are Ca(OH) 2 Assuming that there are k independent reactions, and the j th reaction contains n j different chemical species A i (j) (i = 1,K,n j ), the reactions involved in the system can be described by the following reaction formula: The equilibrium constant K j (T, P) of the specific reaction was calculated by the standard Gibbs energy change of the reaction.
) is the standard-state Gibbs free energy for the formation of species A i (j) , T is the temperature(K), and R is the gas constant(8.314 J mol −1 K −1 ).
We use molarity m as the unit of concentration. Therefore, the equilibrium constant is expressed as: . The equilibrium concentrations of each component can be obtained by solving this set of equations as long as the standard Gibbs energy of formation and activity coefficients of the individual chemical components (reactants and products) are known.
It has been proved that the Helgeson−Kirkham−Flowers(HKF)equation [44][45][46] can accurately describe the standard partial molar thermodynamic properties (ΔG f 0 , ΔH f 0 , ΔS f 0 , ΔV f 0 and ΔC p 0 ) of aqueous species as a function of temperature and pressure In its implemented form, this equation of state reproduces standard-state properties up to 1000°C and 5 kbar. For solid species i, ΔG 0 f,i can be calculated by equation (15): Thermodynamic parameters of the species involved in the hydrothermal reactions were listed in table 2, which were obtained from the corrosion database and aqueous database of OLI analyzer software or published literatures.

Activity coefficient model
To determine the equilibrium concentration of reacting species, knowing the relevant ion activity coefficient and water activity is indispensable. With the OLI Systems, Inc., the Bromley-Zemaitis [49,50] equation is used to calculate the activity coefficient of ions. The following equation expresses the activity coefficient of cations in the multi-component electrolyte system: where A is the Debye-Hückel coefficient which depends on temperature and solvent properties; Z i is the number of charges on anion; I is ionic strength; m i is the molar concentration of the species; nI is the number of charged species in solution; NO is the number of an ion with charges opposite to that of ion i; B ij , C ij, and D ij are temperature-dependent cation-anion interaction parameters.
Meanwhile, the Pitzer model [51] is used to express ion-molecule and molecule-molecule interactions, which are as follows: Table 2. Standard-state Thermodynamic Properties.
where m m is the concentration of the neutral species, and m s is the concentration of the ion species. β 0(m-m) and β 0(m-s) represent the adjustable parameters of molecule-molecule and molecule-ion interactions, respectively. In a multicomponent system, the activity of water can be calculated by the following equation proposed by Meissner and Kusik [52]: where X i represents the cationic fraction (X i = I i /I c ); Y j represents the anionic fraction (Y j = I j /I a ); a w 0 is the hypothetical water activity of pure electrolyte ij, where i is an odd number for all cations, and j is an even number for all anions.
The aforementioned computational process was carried out under the Aqueous model of OLI Systems Inc. software.

Experimental procedures
To validate our theoretical simulations, hydrothermal syntheses were conducted at different conditions of water-solid ratio, pH and calcium silicon ratio of initial raw material, under saturated water vapor pressure. All the chemicals and materials employed in the experiment are commercially procurable. Pure Ca(OH) 2 (purchased from Sinopharm Chemical Reagent Co., Ltd., China.) and SiO 2 (purchased from Xilong Science Co., Ltd., China) were chosen as reactants for the hydrothermal synthesis. The pH value of the solution was adjusted using KOH. The reactants and deionized water were added to a 500 ml stainless steel reactor and heated to a specific temperature at a rate of 7°C min −1 . The resulting products were filtered, washed, and dried after the completion of the reaction.
The crystal structure and phase composition of the obtained samples were identified using x-ray diffraction (XRD, Bruker, Model D8, Cu-Kα excitation).

Results and discussion
3.1. Thermodynamic calculations for the formation of xonotlite As shown from reactions (1)-(11), when Ca(OH) 2 and SiO 2 are hydrothermally reacted, various calcium silicate compounds may be obtained. While xonotlite is the desired product from reaction (1), tobermorite from reaction (2) is the most common by-product. Therefore, we first performed a thermodynamic analysis specifically for reactions (1) and (2), and the results are shown in table 3.
From table 3, the free energies of reactions (1) and (2) are negative in the range of 20°C to 220°C, indicating that Ca(OH) 2 and SiO 2 can react spontaneously even at room temperature to produce xonotlite and tobermorite. However, the reaction rate may be too small to be noticeable. On the other hand, table 3 reveals that with the increase of reaction temperature, the free energy of reaction (1) does not change much, but the absolute value of free energy of reaction (2) decreases significantly. Those data demonstrate that when the reaction is carried out at a high temperature, the equilibrium fraction of tobermorite could be significantly reduced. In addition, the reaction enthalpies of both reactions are negative, indicating that both reactions are exothermic. As for the entropy of reaction, increasing temperature leads to the entropy increase in reaction (1) but decrease for reaction (2). While the reaction enthalpy has a dominating contribution to the reaction free energies, it is beneficial to perform the synthesis reactions at higher temperatures for a larger yield of xonotlite.

Effect of temperature on synthesis of xonotlite
The calculation in section 3.1 only considered a single reaction. Still, for the CaO-SiO 2 -H 2 O system, multiple parallel reactions would coincide. Here, we introduced stability and yield diagrams to analyze the solid/liquid compositions when the system reached equilibrium. The stability diagram calculates the region of phase stability over the range of two independent variables, indicating thermodynamically stable synthesis conditions for the desired product. The initial concentration of Ca(OH) 2 and pH are selected as independent variables because they are easy to measure and can directly determine the raw material composition and reaction conditions required for hydrothermal synthesis [40]. In a typical stability and yield diagram, the curve corresponds to the generation or disappearance of solid sediment, and the dotted line indicates the sites where different aqueous substances have the same concentration. The diagram provides both preliminary precipitation conditions for various solid phases and the conditions for the formation of the desired product in the expected yield and purity. For this work, the yield is obtained by dividing the mole number of Ca in the target product xonotlite by the total mole number of Ca in the metal precursor.
Here, Ca(OH) 2 and SiO 2 were chosen as calcium and silicon sources. The stability and yield diagrams of the Ca(OH) 2 -SiO 2 -H 2 O system for different temperatures are shown in figure 1. The Y axis represents the initial Table 3. The free energy, enthalpy and entropy of xonotlite and tobermorite synthesis reaction at different temperatures.

Reaction (1)
Reaction (2) T/°C Ca(OH) 2 concentration, and the Ca/Si molar ratio is maintained at 1. HNO 3 and KOH are used as titrants to adjust the pH of the solution, the X axis. Figure 1 shows calculated the stability and yield diagrams for the Ca(OH) 2 -SiO 2 -H 2 O system at 160°C, 170°C, 200°C and 220°C, respectively. These diagrams show the solid and liquid phase compositions of the Ca(OH) 2 -SiO 2 -H 2 O system at equilibrium under four different temperatures. The solid phase includes xonotlite, gyrolite, tobermorite, rankinite, and Ca(OH) 2 . In the homogeneous aqueous region, calcium ions exist in the forms of Ca(NO 3 ) + , Ca 2+, and Ca(OH) + . The red-shaded region indicates a 99% yield of xonotlite precipitate. Figure 1(a) illustrates that at 160°C, the solid phase includes mainly tobermorite, gyrolite, and rankinite. The diagram in figure 1(b) reveals that the xonotlite phase starts to form when the reaction temperature reaches 170°C. The results confirm that with Ca(OH) 2 and SiO 2 as raw materials, the lowest temperature for hydrothermal synthesis of xonotlite would be about 170°C, consistent with the experiments by Pepper (180°C, 13 days) [26]. Speakman [25] reported that when the reaction temperature was higher than 150°C, tobermorite became unstable and was partially converted to xonotlite. It is important to point out that amorphous silica colloid was used to react with Ca(OH) 2 in his study. The difference in raw materials could lead to a lower reaction temperature. Figure 1 also illustrates that pH plays a crucial role in the synthesis of xonotlite. Xonotlite is stable under neutral and weak alkaline conditions. The highly alkaline solution can convert Cacontaining species into Ca(OH) 2 and rankinite. The formation domain of xonotlite is affected by pH and watersolid ratio. It is known that a high water-solid ratio can improve the uniformity of the reaction system and promote the dissolution of silicate components [22,53]. However, results in figure 1 argue that with more water, the concentration of Ca(OH) 2 got decreased. As a result, both xonotlite and rankinite would be produced, reducing the purity of the xonotlite product. In addition, those diagrams also confirm that, under a Ca/Si ratio of 1 and 200°C, the water-solid ratio should be less than 20 to prepare the high-purity xonotlite (99 wt%). Figure 2 shows the effects of solution pH on the phase composition of reaction products. Thermodynamic calculations have indicated that xonotlite can only exist under neutral or weakly alkaline conditions. To verify the accuracy of these calculations, we investigated the effect of solution pH on the formation of xonotlite. Specifically, we adjusted the pH of the reaction system by adding KOH. Using analytical pure Ca(OH) 2 and SiO 2 as raw materials, we were able to synthesize well-crystallized high-purity xonotlite with a Ca/Si ratio of 1 and a water-solid ratio of 15  show that all diffraction peaks correspond well to those of monoclinic xonotlite (Ca 6 Si 6 O 17 (OH) 2 , JCPDS No.23-0125), indicating the successful synthesis of the desired product under these conditions. When the pH of the system increased to 9, some calcium-containing species underwent transformation into rankinite, resulting in a mixed phase of xonotlite (Ca 6 Si 6 O 17 (OH) 2 ), rankinite (Ca 3 Si 2 O 7 ) and quartz in the reaction products, which is consistent with the results shown in figure 1(c). In order to obtain high purity xonotlite, that pH value of the solution should be between 7 and 8.
Thermodynamic calculations have shown that high-purity xonotlite can be obtained when the water-tosolid ratio in the system is less than 20. As shown in figure 3, when the water-to-solid ratio was set to 15 However, when the water-to-solid ratio was decreased to 10 (logm[Ca(OH) 2 = −0.13]), characteristic diffraction peaks of quartz appeared in the XRD pattern, indicating unreacted SiO 2 raw materials will remain in the final product and decrease the crystallinity of produced xonotlite. Thus, we recommend controlling the water-to-solid ratio in the range of 15∼20.  200°C is the best temperature for synthesizing xonotlite because, at this time, the domain of xonotlite with a purity of 99% is the largest, as shown in figure 1(c). When the reaction temperature increased to 220°C, the domain of xonotlite decreased slightly. In many literatures [53,54], 220°C is recommended as the synthesis temperature of xonotlite. That could be due to the fact that the increase in temperature is conducive to accelerating the reaction rate and shortening the reaction time. Notably, the recent work by Aymonier et al [27] illustrated that xonotlite can be synthesized within seconds in supercritical conditions (400°C, 23.5 MPa), but trace impurities (calcite, wollastonite and vaterite) present in the reaction product. This is consistent with the results of thermodynamic calculations, showing that performing the xonotlite synthesis reaction under higher temperatures is not always preferable.

Effect of calcium silicon ratio (Ca/Si) on xonotlite synthesis
The calcium-silicon ratio also affects the xonotlite synthesis. In this section, we calculated the stability and yield diagrams of the Ca(OH) 2 -SiO 2 -H 2 O system at 220°C when the Ca/Si ratio is changing from 0.8 to 1.1. As shown in figure 4, xonotlite can be synthesized from a wide Ca/Si range, consistent with the results reported in the literature [24]. Figure 4(d) shows the influence of an excess Ca(OH) 2 on xonotlite synthesis. But there is no yield region (above 99%) of xonotlite when the Ca/Si ratio is 1.1. This is because with the excess Ca(OH) 2 , the rankinite phase could easily exist and stay with xonotlite, thus significantly reducing the purity of the xonotlite product. When the Ca/Si ratio equals 0.8 and 0.9, the yield region of xonotlite is much larger than that for the Ca/Si ratio of 1.0. From the reaction stoichiometry, the synthesis of xonotlite requires the same moles of Ca(OH) 2 and SiO 2 . When xonotlite is synthesized where the calcium-silicon ratio is 0.8, Ca(OH) 2 will be converted entirely into xonotlite, but unreacted SiO 2 will remain in the product. Table 4 shows the compositions of the solid phase, when the concentration of Ca(OH) 2 is 0.1 M and the pH value equals 8. Table 4 shows that when the Ca/Si molar ratio is 0.8 for the raw materials, all Ca(OH) 2 is transformed into xonotlite. There is no rankinite phase but 10.76 wt% SiO 2 remaining in the product. If the Ca/Si molar ratio is 1.1, a large amount of by-product rankinite would appear in the product, reducing the xonotlite content to 75.52 wt%.
Due to its low thermal conductivity, xonotlite is widely used in heat insulation [10,18]. However, the existence of a large number of impurity phases will significantly affect the performance of xonotlite products. The rankinite in the product will carbonize to form a large amount of CaCO 3 crystals, leading to the reduction of porosity due to crystal stacking [55]. Moreover, the decomposition of CaCO 3 will reduce the thermal conductivity and thermal stability of xonotlite. Therefore, from thermodynamic calculations, the recommended Ca/Si molar ratio for synthesizing xonotlite would be between 0.9 and 1.0. Figure 5 illustrates the x-ray diffraction (XRD) patterns of reaction products obtained under different Ca/Si ratios. As depicted in figure 5, hydrothermal products with varying compositions were obtained by adjusting the Ca/Si molar ratio within the range of 0.8 to 1.0 while maintaining constant reaction parameters, including a reaction temperature of 220°C, a water-to-solid ratio of 15, and a reaction time of 12 h. When the molar ratio of Ca:Si changed to 0.9 and 1.0, all the diffraction peaks observed in the XRD pattern were well indexed to those of the standard monoclinic xonotlite (Ca 6 Si 6 O 17 (OH) 2 , JCPDS No. 23-0125), indicating the high purity of the products. Despite the formation of xonotlite when the Ca/Si ratio was decreased to 0.8, unreacted quartz was still detected in the reaction products. Therefore, to obtain high-purity xonotlite, the Ca/Si ratio should be controlled within the range of 0.9 to 1.0, which is in agreement with the results predicted by thermodynamic calculations.

Conclusion
We established a thermodynamic model to systematically analyze and optimize the hydrothermal synthesis conditions of xonotlite. Our theoretical predictions have been experimentally verified under various conditions of solution pH, reagent concentrations and the ratio of calcium to silicon. The optimized hydrothermal synthesis conditions for producing xonotlite include a reaction temperature of 200°C, a Ca/Si ratio of 0.9-1.0, a water-solid ratio ranging from 15-20, and a pH value of 7-8. In comparison with traditional empirical trial-anderror methods, these refined conditions effectively reduce the workload required for synthesizing pure-phase xonotlite and provide a theoretical foundation that can support large-scale industrial production of xonotlite.