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.