2. Computational method and details
Calcium carbonate hemihydrate
(CaCO3·1/2H2O)[8]has a monoclinic structure, belonging to the P121/c1(14) space with
lattice parameters a =9.64 Å,b =10.47 Å and c =6.42 Å. The structure of
monohydrocalcite
(CaCO3·1H2O)[4,
5] is selected as space group: P31(144)
with lattice parameters a =10.65 Å, b =10.65 Å andc =7.64 Å. While ikaite
(CaCO3·6H2O)[7]belongs to C12/c1 space group (No.15) with lattice parametersa =8.78 Å, b =8.28 Å and c =10.88 Å.
In this work, all calculations were
conducted using the Cambridge Serial Total Energy Package (CASTEP) codes
based on the density functional theory (DFT)[16], which was the
first-principles plane wave pseudopotential method. Ultra-soft
pseudopotentials
(USPPs)[17] were
used for describing the interaction between atomic core and valence
electrons in reciprocal space were used, and the valence electron
configurations for C, H, Ca and O atoms were
2s 22p 2,
1s 1,
3s 23p 64s 2and 2s 22p 4,
respectively. After careful test, 4×4×6, 5×5×8 and 6×8×4 grid of
Monkhorst-Pack special k -points in the Brillouin zone (BZ) were
used for bulk models CaCO3·1/2H2O,
CaCO3·1H2O and
CaCO3·6H2O, respectively. In order to
ensure the calculations converged for calculation accuracy, the maximum
plane-wave basis cutoff energy was 450 eV. The exchange correlation
potential within generalized gradient approximation (GGA) was described
the Perdew-Burke-Ernzerhof
(PBE)[18] and a
DFT-D dispersion correction with grimme method was adopted in all
calculations to improve the calculation accuracy for weak interaction.
During the structural optimization
process,
Broyden-Fletcher-Goldfarb-Shanno
(BFGS)[19] method
was used until the total energy changes were converged to
1×10-9 eV/atom, self-consistent field convergence to
2×10-6 eV/atom, maximum force 0.03 eV/Å, respectively.
Elastic constants of a solid were calculated by an efficient
strain-stress method through a linear least-square fit of the
first-principle calculating stress versus strain. The phonon dispersion
curves of CaCO3·1/2H2O,
CaCO3·1H2O and
CaCO3·6H2O were calculated according to
the finite displace method.