| By using first-principle within density-functional theory, we calculated some properties of ferroelectrics, which contain electronic structure, elastic compliance coefficients and optical property. Firstly, origin of ferroelectricity is revealed by calculating electronic structure of ferroelectric and paraelectric BiFeO3. Secondly, the choice of exchange correlation functions (ECFs) is crucial for precision in elastic calculation with first-principle. Moreover, for BiFeO3, no experimental data can be used for comparison with our calculation results. In order to calculate ECCs(elastic compliance coefficients) of BiFeO3, ECCs of PbTiO3 is firstly calculated because experimental results of PbTiO3 have been reported. And then ECCs of BiFeO3 is calculated using the same method. Thirdly, the optical properties and band structures of CaZrO3 and BaZrO3 are calculated. The result shows that direct and indirect band structures of BaZrO3 are 3.49 eV and 3.23 eV respectively. The direct and indirect band structures of CaZrO3 are 3.73 eV and 3.3823 eV respectively. It is clear that there are 8 peaks in Imaginary dielectric function of BaZrO3, and 9 peaks for CaZrO3. Relations between imaginary dielectric function and photon energy are similar for the two materials in the low energy region, however, the different is large in the high energy region. Moreover, for other optical parameters, the results are also the similar (different) in the low (high) energy region. Compared with BaZrO3, the peaks of CaZrO3 moved toward higher energy. At last, we calculated the band structures and optical properties of Si nanoparticles which is the spherical and cylindrical nanoparticles with different sizes. The result indicated that the energy gap of nanoparticles generally increases as the size decreases, and the optical absorption appear blue shift. The phenomenon agrees with experimental result, which reveals the mechanism of light-emitting nano-materials. |
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