3.3 Optical properties
As we all know that the macroscopic optical response function of solids
can be described by the complex dielectric function, which can be used
following equation: (5)
where ; . The reflectivity, conductivity, absorption and others
properties of calcium carbonate hydrates can be derived with the
definition of direct transition probability and the Krames-Kroning
dispersion
relation[29,
30]:
(6)
(7)
(8)
(9)
Where C, V represent conduction band and valence band,
respectively. BZ, K and are the first Brillouin zone, reciprocal
vector, angular frequency, respectively. the eigenvalue of conduction
band and valence band, respectively. n and k are the
reflection coefficient and extinction coefficient. The optical
properties including dielectric function, reflectivity, conductivity,
absorption, refractive index and loss function of
CaCO3·x H2O (x= 1/2, 1 and
6) are shown in Fig. 5 (a)-(f). Imaginary part of dielectric function is
shown in Fig. 5(a), we can clearly see a peak appear in 7.5 eV. This
results can be proved from the density of state in Fig. 3. Furthermore,
from Fig. 5 (b), we can know that the reflectivity of
CaCO3·x H2O (x= 1/2, 1 and
6) decreases with the increase of water, which conforms to the band gap
in the Fig. 3. CaCO3·1/2H2O has the
largest reflectivity, while CaCO3·6H2O
has the smallest reflectivity when the frequency value is about 8.0 eV.
It’s obvious that the transmittance of light is positively correlated
with the refraction of light. It is beneficial to the lens because of
its high refractive index. Therefore, the
CaCO3·1/2H2O has the potential as
luminescent material. The optical properties of
CaCO3·x H2O (x= 1/2, 1 and
6) are huge difference due to the different structures and different
position of water. What’s more, the conductivities of
CaCO3·x H2O (x= 1/2, 1 and
6) are shown in Fig. 5 (c). The peak of photoconductivity mainly occurs
in 7 eV for the CaCO3·1/2H2O and
CaCO3·H2O, while the
CaCO3·6H2O has other peak with 26 eV,
indicating the H2O is the main factor affecting
conductivity. The absorption of
CaCO3·x H2O (x= 1/2, 1 and
6) decreases with the increase of water, and the Loss function has a
similar regularity. The dielectric loss can be expressed as follows:
(10)
which
is the imaginary part of dielectric constant. Both the imaginary part
and the real part of the refractive index decrease with the increase of
the water content. Therefore, the dielectric function, reflectivity,
conductivity, absorption, refractive index and loss function of
CaCO3·x H2O (x= 1/2, 1 and
6) are decrease with the H2O increases.