3.1 Crystal structure and phonon dispersion
The calculated crystal structures of calcium carbonate hemihydrates (CaCO3·1/2H2O), monohydrocalcite (CaCO3·1H2O) and ikaite (CaCO3·6H2O) are shown in Fig. 1(a)-(c). CaCO3·1H2O, CaCO3·6H2O and CaCO3·1/2H2O have a hexagonal unit cell containing 9 formula units, 4 formula units and 8 formula units, respectively. From the basic chemical knowledge, it is well known that one C atom and three O atoms constitute. Due to the different crystal structure, these forms show great differences in physical properties, which are mainly reflected onstructural stability. And the specific chemical reaction equation of calcium carbonate hydrates during formation can be expressed as:
(1)
(2)
(3)
Obviously, the equation from (1) to (3) are different value of H2O, which cause various calcium carbonate hydrates with different crystal structure, indicating difference physical properties and mechanical properties. What’s more, the calculated X-ray diffraction of CaCO3·x H2O (x= 1/2, 1 and 6) isshow in Fig. 1(d). The main peak are appearedat 16 to 21 degree But there are two nearly same intensity peaksat 2 theta as 17 and 34 degree for CaCO3·6H2O. The peaks of CaCO3·x H2O (x= 1/2, 1 and 6) increases significantly with the increase of water content at 55 to 70 degree. In Fig. 1(e), the calculated XRD values of CaCO3·1/2H2O are good agreement with the experimental ones by Z.Y Zou et al in the reference [8].
The Gibbs energy of reaction (ΔGr) at 0 K for CaCO3+H2O is very important to judge the stability and formation possibility of CaCO3·x H2O (x= 1/2, 1 and 6), which can be expressed by the following formula,
(4)
where is the total energy of CaCO3·x H2O (x= 1/2, 1 and 6), is the energy of CaCO3, and represents the energy of water molecule, m and n represent the number of CaCO3and H2O, respectively. N is the total number of atoms in CaCO3·x H2O (x= 1/2, 1 and 6). The calculated ΔGr, total energy, the energy of water molecule and CaCO3 are shown in table 1. Generally speaking, the smaller the ΔGr is, the more possible the compounds to form. From table 1, the ΔGr decreases with H2O increases, indicating the CaCO3·6H2O is the most stable calcium carbonate hydrates. The stability of these calcium carbonate hydrates form the following sequence: CaCO3·6H2O > CaCO3·H2O > CaCO3·1/2H2O.
Furthermore, we can obtain the lattice parameters, density, volume and density of calcium carbonate hydrates after optimizing these crystal structure, which are listed in table 2. Obviously, the calculated values are slightly larger than the results from the theoretical and experimental values [7, 14, 15, 20, 21]. What’s more, in this work, the calculated lattice parameters by using PBE+TS functional are slightly different from those obtained by other methods, such as B3LYP-D2 and PBE-D2. The discrepancy between the calculated value and the experimental value probably comes from lattice defects, the effect of temperature on crystal structure, experimental environment and different approximation functions. However, the calculation method is reasonable because these differences are very small. On the other hand, CaCO3·1/2H2O has the maximum density with the value of 2.23 g.cm-3, while the CaCO3·6H2O has the minimum values of 1.86 g.cm-3, which is in agreement with the experimental values as 2.38 g.cm-3 for CaCO3·1H2O and 1.8 g.cm-3 for CaCO3·6H2O.[22, 23]
The calculated phonon dispersion curves of the calcium carbonate hydrates along the high symmetry direction in the Brillouin zone are shown in Fig. 2. The calculated phonon spectra of CaCO3·x H2O (x= 1/2, 1 and 6) show no soft modes at any high-symmetry dispersion, suggesting that these calcium carbonate hydrates are dynamic stable[24-28], which proves the experimental point that calcium carbonate contains water is dynamic stable. These stable calcium carbonate hydrates contain 1/2, 1 and 6 H2O. Especially for the CaCO3·1/2H2O, the calculated phonon dispersions are remarkable consistent with the experimental values, which represent with the red hollow circle in Fig. 2(a), and the experimental data were obtained from the ref. [8]. Calcium carbonate and water react to stable hydrates with high energy barrier, which is harder to transform or decompose. Moreover, the phonon density of states for calcium carbonate hydrates is shown in Fig. 2, which corresponds to the phonon dispersion curves, and the higher-frequency vibrations are mainly contributed by the dynamics of the H2O molecule.