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.