⇦Chinese Physics Letters, 2018, Vol. 35, No. 3, Article code 036103 Influence of Pressure on the Annealing Process of $\beta$-Ca$_{2}$SiO$_{4}$(C$_{2}$S) in Portland Cement * Yun-Peng Gao(高云鹏), Wan-Qing Dong(董琬晴), Gong Li(李工)**, Ri-Ping Liu(刘日平) Affiliations State Key Lab of Metastable Materials Science and Technology, and College of Materials Science and Engineering, Yanshan University, Qinhuangdao 066004 Received 20 October 2017, online 25 February 2018 *Supported by the National Natural Science Foundation of China under Grant No 11674274.
**Corresponding author. Email: gongli@ysu.edu.cn Citation Text: Gao Y P, Dong W Q, Li G and Liu R P 2018 Chin. Phys. Lett. 35 036103 Abstract Portland cement is the most common type of cement in general use around the world as a basic ingredient of concrete, mortar, stucco, and non-speciality grout. Dicalcium silicate (Ca$_{2}$SiO$_{4})$ is the primary constituent of a number of different types of cement. The $\beta$-Ca$_{2}$SiO$_{4}$ phase is metastable at room temperature and will transform into $\gamma$-Ca$_{2}$SiO$_{4}$ at 663 K. In this work, Portland cement is annealed at a temperature of 950 K under pressures in the range of 0–5.5 GPa. The high pressure experiments are carried out in an apparatus with six anvil tops. The effect of high pressure on the obtaining nano-size $\beta$-Ca$_{2}$SiO$_{4}$(C$_{2}$S) process is investigated by x-ray diffraction and transmission electron microscopy. Experimental results show that the grain size of the C$_{2}$S decreases with the increase of pressure. The volume fraction of the C$_{2}$S phase increases with the pressure as the pressure is below 3 GPa, and then decreases ($P>3$ GPa). The nano-effect is very important to the stabilization of $\beta$-Ca$_{2}$SiO$_{4}$. The mechanism for the effects of the high pressure on the annealing process of the Portland cement is also discussed. DOI:10.1088/0256-307X/35/3/036103 PACS:61.50.-f, 61.50.Ks, 81.30.Hd © 2018 Chinese Physics Society Article Text Portland cement is a fine powder produced by heating limestone and clay minerals in a kiln to form the so-called clinker, grinding the clinker, and adding small amounts of other materials.[1-3] The low cost and widespread availability of the limestone, shales, and other naturally existing materials used in Portland cement make it one of the lowest-cost materials widely used over the last century over the world. Dicalcium silicate (Ca$_{2}$SiO$_{4}$) is the primary constituent of a number of different types of cement, including ordinary Portland cement, white cement, and specialty cements used for oil-well applications.[1] Reaction between Ca$_{2}$SiO$_{4}$ and water is known to be the dominant cause of the setting and hardening of pastes made from these cements.[2] For these reasons, Ca$_{2}$SiO$_{4}$ has often been used as a model material to study the hydration behavior of cement paste. Studies performed over the past forty years have provided considerable information about the $\beta$-Ca$_{2}$SiO$_{4}$ powder synthesis,[4,5] Ca$_{2}$SiO$_{4}$/water system, including phase chemistry and equilibria, solid dissolution mechanisms,[5,6] overall rates of reaction,[7] and microstructure development.[8-11] Most of these studies have been carried out at ambient pressure.[6-8,10-12] However, the materials with nanoparticles dispersed in a uniform matrix exhibit high values of both strength and plastic strain.[13,14] Pressure, similarly to temperature, can significantly affect the crystallization behavior of materials, and if properly applied, high pressure (HP) annealing would be a promising method for synthesizing condensed matter with profound properties.[15-18] Moreover, HP is also a powerful tool for modifying and controlling the nucleation and growth for inducing atomic rearrangements. The study of the obtained nano-size $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement under high pressure annealing may provide some information of atomic movement, which is useful for understanding the mechanism of the nucleation and growth process in Portland cements. In the present work, the influences of pressure on the annealing process of the Portland cements have been investigated by x-ray diffraction (XRD), and transmission electron microscopy (TEM), and the relationship between the pressure and the grain size of the nano-size $\beta$-Ca$_{2}$SiO$_{4}$ phase for our samples annealed at a temperature of 950 K under pressures in the range of 0–5.5 GPa is given. The HP annealing was performed in an apparatus with six anvil tops. The purchased Portland cement powder samples were pre-compressed and embedded into sodium chloride.[19] We selected powdered sodium chloride due to its high chemical stability and excellent pressure transmitting behavior. The heating furnace in the high pressure device is a graphite tube heater. The samples were pre-pressured to a certain value and annealed under given pressure (0–5.5 GPa) for 20 min. Pressure was calibrated at room temperature by means of the phase transitions of Bi, Tl and Ba. The temperature was determined from its relation with the input electricity power. The accuracy to measure the temperature of the sample itself under the applied pressure was about 1.5 K. The details of the HP experiment have been described at length.[20] XRD was performed using an MAC M03 XHF diffractometry with Cu radiation. The microstructure observation of the annealed alloys was carried out by an H800 TEM. The TEM specimens of the HP sample were prepared by dimpling and ion-beam milling with a low-energy ion beam to avoid being damaged. The TEM observations were performed at a 200k VinaJEM-2010 microscope for the bright-field (BF) image, select-area electron diffraction (SAED), and high-resolution TEM (HRTEM) investigations.
cpl-35-3-036103-fig1.png
Fig. 1. XRD patterns of Portland cements annealed at 950 K under different pressures for 20 min.
cpl-35-3-036103-fig2.png
Fig. 2. Morphology of Portland cements annealed at 950 K under 2 GPa (a) and 5.5 GPa (b) for 20 min.
Figure 1 shows the XRD patterns for Portland cement isothermally annealed at 900 K under various pressures. The annealing temperature is in the range of the stabilization temperature of the $\beta$-Ca$_{2}$SiO$_{4}$ phase.[21-25] According to the XRD patterns shown in Fig. 1, we can see that the sample annealed in the high pressure apparatus (after pre-pressurized) at 950 K 20 min without applied pressure only consisted of SiO$_{2}$ and CaO phases. However, when the Portland cement was annealed at 950 K under HP for 20 min, less of the $\beta$-Ca$_{2}$SiO$_{4}$ phase would occur progressively, starting at 0.5 GPa. This result indicates that the HP lowers the crystallization temperature in the Portland cement at least within the range of our experiment pressure. The diffraction peaks corresponding to the $\beta$-Ca$_{2}$SiO$_{4}$ peaks in the microstructure become broader with increasing the pressure. The broadening of the diffraction peaks of these samples annealed under HP results mainly comes from the contribution of fine grain sizes.[26] The corresponding morphologies of Portland cements annealed at 950 K under 2 GPa and 5.5 GPa for 20 min are shown in Fig. 2. The average grain size of the $\beta$-Ca$_{2}$SiO$_{4}$ phase decreased from 19.1 nm annealed under 2 GPa to 9.2 nm under 5.5 GPa, which agree very well with the calculated data from the full width at half maximum (FWHM) of the diffraction peak according to the Scherrer formula[27] listed in Table 1. The $\beta$-Ca$_{2}$SiO$_{4}$ phase with an ultrafine grain size under 21 nm can be obtained. The grain size of the $\beta$-Ca$_{2}$SiO$_{4}$ phase decreased linearly with increasing the pressure from 0.5 to 5.5 GPa. Five phases in the Ca$_{2}$SiO$_{4}$ polymorphism system are listed in Table 2. Among these five polymorphous phases, $\alpha$, $\dot{\alpha}_{\rm H}$, and $\dot{\alpha}_{\rm L}$ are stable under high temperature above 1120 K, while $\alpha$-Ca$_{2}$SiO$_{4}$ is a trigonal phase and both $\dot{\alpha}_{\rm H}$- and $\dot{\alpha}_{\rm L}$-Ca$_{2}$SiO$_{4}$ belong to the rhombic system: above 1120 K, it is the high temperature $\dot{\alpha}_{\rm H}$-Ca$_{2}$SiO$_{4}$, and below 1120 K, it is the low temperature $\dot{\alpha}_{\rm L}$-Ca$_{2}$SiO$_{4}$. Monoclinic $\beta$-Ca$_{2}$SiO$_{4}$ is metastable at room temperature and will transform into $\gamma$-Ca$_{2}$SiO$_{4}$ at 663 K. Compared with $\gamma$-Ca$_{2}$SiO$_{4}$, $\beta$-Ca$_{2}$SiO$_{4}$ possesses more hydration activity.[28]
Table 1. Dependencies of the grain size and the volume fraction of the crystalline phase on pressure.
$P$ (GPa) 0.5 2.5 3.5 5.5
$d$ (nm) 21.15 17.92 15.13 10.76
$V_{\rm C}$(%) 11.95 23.87 21.65 7.58
cpl-35-3-036103-fig3.png
Fig. 3. TEM bright-field (BF) images with the associated select-area electron diffraction (SAED) pattern of the Portland cements annealed at 950 K under 5.5 GPa.
The TEM bright-field (BF) images with the associated select-area electron diffraction (SAED) pattern of the Portland cements annealed at 950 K under 5.5 GPa is shown in Fig. 3. The grain size of C$_2$S is under 12 nm, and the phases are SiO$_{2}$, CaO and C$_2$S in the Portland cements. The [120] direction diffraction pattern inserted in Fig. 3 indicates the monoclinic $\beta$-C$_2$S phase.
Table 2. Cell parameters, density, and stable temperatures range of $\alpha$, $\dot{\alpha}_{\rm H}$, $\dot{\alpha}_{\rm L}$, $\beta$, and $\gamma$, $\beta$-Ca$_{2}$SiO$_{4}$ in the Ca$_{2}$SiO$_{4}$ system.
Temperature (K) Polymorphism Cell parameters Density
$a$ (Å) $b$ (Å) $c$ (Å) $\beta$ (Å) (g$\cdot$cm$^{-3}$)
$ < $1698 $\alpha$ 5.526 7.307 90 2.940
1450–1120 $\dot{\alpha}_{\rm H}$ 5.593 9.535 6.860 90 3.116
1120–948 $\dot{\alpha}_{\rm L}$ 11.184 18.952 6.837 90 3.140
948–663 $\beta$ 5.506 6.749 9.304 94.6 3.326
$ < $663 $\gamma$ 5.085 11.28 6.78 90 3.000
During the annealing process, the growth velocity of the $\beta$-Ca$_{2}$SiO$_{4}$ phase is dependent on atomic diffusion.[29] According to the theory of diffusion,[30] the size of crystalline phase, $d$, is approximately given by $$ d=\alpha \sqrt {Dt},~~ \tag {1} $$ where $\alpha$ is a constant, $D$ is the atomic diffusion coefficient, and $t$ is the time of diffusion. For the amorphous alloy annealed under HP, the atomic diffusion coefficient $D$ is given by[27] $$ D=D_{0}\exp\Big(-\frac{P\Delta V^{\ast} }{RT}\Big),~~ \tag {2} $$ where $D_{0}$ is a constant, $P$ is the pressure, $R$ is the gas constant, $T$ is the temperature, and $\Delta V^{\ast}$ is the activation volume, which is normally positive for most amorphous alloys. Combining Eqs. (1) and (2), we can obtain the equation $$ \ln d=-\frac{P\Delta V^{\ast} }{2RT}+\frac{1}{2}\ln t+\beta,~~ \tag {3} $$ where $$ \beta =\ln\alpha+\frac{1}{2}\ln D_{0},~~ \tag {4} $$ which shows that under the same conditions of annealing temperature and time, the size of crystalline phase decreases with increasing the pressure. Using the above experimental results (Table 1), we can make a plot of $\ln d$ versus $P$. Thus the activation volume $\Delta V^{\ast}$ and the constant $\beta$ can be determined, respectively, from the plot, i.e., 0.74 cm$^{3}$/mol for $\Delta V^{\ast}$ and $-$2.37 for $\beta$. According to this result, we obtain the activation energy 206.18 kJ/mol for the sample annealing at 950 K under 3 GPa. Thus the relationship between the pressure and the grain size of the $\beta$-Ca$_{2}$SiO$_{4}$ phase for our samples annealed at a temperature of 950 K under the pressure below 5.5 GPa is given by $$ \ln d=-\frac{0.74P}{RT}+\frac{1}{2}\ln t-2.37.~~ \tag {5} $$ According to classical theory of nucleation and growth for a crystal,[31] the volume fraction of the crystalline transformation, $V_{\rm c}$, is simply given by $$ V_{\rm c}=1-\exp\Big(-\frac{\pi}{3}Iv ^{3}t^{4}\Big),~~ \tag {6} $$ where $v$ is the crystal growth velocity, $t$ is the crystallization time, and $I$ is the crystal nucleation rate. The value of $I$ is given by[30] $$\begin{align} I=I_{0} \exp \Big(\frac{-Q}{kT}\Big)\exp \Big(\frac{-\Delta G^{\ast }}{kT}\Big),~~ \tag {7} \end{align} $$ where $T$ is the interfacial temperature of crystal, $I_{0}$ is a coefficient, $Q$ is the activation energy for atomic migration, $k$ is Boltzmann's constant, and $\Delta G^{\ast}$ is the critical free energy required to form a nucleus. The value of $\Delta G^{\ast}$ is given by[30] $$ \Delta G^{\ast}=\frac{16\pi }{3}\frac{\sigma^{3}}{\Delta G_{\rm v}^{2}},~~ \tag {8} $$ where $\sigma$ is the interfacial energy of the crystal and liquid matrix, $\Delta G_{\rm v}$ is the Gibbs free energy difference between crystalline phase ($G_{\rm cry}$) and amorphous matrix($G_{\rm l}$) per unit volume, $\Delta G_{\rm v}=G_{\rm l}- G_{\rm cry}$. Taking pressure $P$ into account and assuming that the interfacial energy $\sigma$ is independent of pressure, from Eq. (8) we obtain $$\begin{align} \Big(\frac{\partial (\Delta G^{\ast })}{\partial P}\Big)=-\frac{32\pi \sigma^{3}}{3}\frac{\Delta V}{\Delta G_{\rm v}^{3} },~~ \tag {9} \end{align} $$ where $\Delta V$ is the average volume difference between crystalline phase ($V_{\rm cry}$) and liquid matrix ($V_{\rm l}$) per unit volume, $$ \Delta V=\frac{\partial (\Delta G_{\rm v})}{\partial P}=\frac{V_{\rm l}-V_{\rm cry}}{V_{\rm cry}}.~~ \tag {10} $$ From Eq. (7) one can see that the volume fraction of the crystalline phase is dominantly dependent on two factors for a certain crystallization time. One is the nucleation rate of crystal ($I$), and the other is the growth velocity of the $\beta$-Ca$_{2}$SiO$_{4}$ ($v$), where the growth velocity of the crystalline phase decreases with the increase of the pressure. However, its nucleation rate shows a complicated relationship with the pressure (see Eq. (9)). Although the critical free energy ($\Delta G^{\ast}$) decreases with increasing the pressure, the activation energy for atomic migration ($Q$) increases with the pressure due to the difficulty for atomic diffusion under the HP. Thus under both higher and lower pressure conditions, the nucleation rate of the crystalline phase is smaller. Only under a proper pressure $P_{0}$, the nucleation rate $I$ has the maximum. Combined with the above discussions about the crystal growth velocity, it is evident that the volume fraction of crystalline phase ($V_{\rm c}$) decreases with increasing the pressure as the pressure $P$ is above $P_{0}$, because both the growth velocity and the nucleation rate in the range of pressure ($P>P_{0}$) decrease with the pressure. As the pressure is below $P$ ($P < P_{0}$), the crystal nucleation rate $I$ increases with the pressure whereas its growth velocity ($v$) decreases. Therefore, there must be another pressure $P_{1}$ ($P_{1} < P_{0}$) which will make the volume fraction of the crystalline phase exhibit the maximum. All these analyses indicate that, during the annealing process of the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement under HP, the change of the volume fraction of the $\beta$-Ca$_{2}$SiO$_{4}$ phase with the pressure shows a phenomenon of a 'peak'. In the present study, the proper pressure is 3 GPa, which makes the volume fraction of the crystalline phase exhibit the maximum. For the annealing process of the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement in the pressure and temperature ranges studied, both the Gibbs free energy difference ($\Delta G_{\rm v}$) and the average volume ($\Delta V$) difference are positive. Thus according to Eq. (8), the critical free energy ($\Delta G^{\ast}$) required to form a nucleus for the crystalline phase decreases with increasing pressure ($P$). The above analyses show that, in the present work, the activation volume ($\Delta V^{\ast}$) of the $\beta$-Ca$_{2}$SiO$_{4}$ in Portland cement is 0.74 cm$^{3}$/mol ($>$0). Thus according to Eq. (2), the atomic diffusion coefficient $D$ decreases with increasing the pressure. Since the growth of the $\beta$-Ca$_{2}$SiO$_{4}$ phase in annealed Portland cement is dependent on atomic diffusion,[21,23] its growth velocity decreases as the pressure $P$ increases. This implies that HP constrains the growth of the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement. Since HP can decrease the critical free energy required to form a nucleus for the crystalline phase and can constrain the growth of the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement, we can easily synthesize the nano-size $\beta$-Ca$_{2}$SiO$_{4}$ phase with an ultrafine grain size of 21 nm under HP. HP has a great influence on the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement as it is annealed at a temperature of 950 K. The grain size of the $\beta$-Ca$_{2}$SiO$_{4}$ decreases from 19.1 to 9.2 nm with increasing the pressure from 0.5 to 5.5 GPa. As the pressure is below 3 GPa, the volume fraction of the $\beta$-Ca$_{2}$SiO$_{4}$ phase increases with the pressure, and then decreases with further increasing pressure above 3 GPa. The effects of the HP on the $\beta$-Ca$_{2}$SiO$_{4}$ phase in Portland cement are attributed to the causes that pressure can decrease the critical free energy required to form a nucleus and can constrain the growth of the $\beta$-Ca$_{2}$SiO$_{4}$ phase during the annealing process under high pressures in Portland cement. 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