The Theoretical Calculation Of Dielectric Properties Of Zr And Hf Doped(Ba_0.5Sr_0.5)TiO₃

Since excellent ferroelectric properties have been found in 1942,Ba TiO₃ has became a hot topic of scientists due to the high dielectric constant,low dielectric loss,high compression performance.At the moment,experimental research of BaTiO₃ have achieved good development,whether in doped modification or optimized preparation technology.The research results ware widely used in many high-tech fields.With deepening research,there have a good attention of many scientists in the aspect of theory research both at home and abroad.First principles method has been widely used to research structural properties of material,which is one of more mature method.Based on the generalized gradient approximation and local density approximation the first principles have been mainly used for calculating Ba TiO₃ and(Ba_0.5Sr_0.5)TiO₃ structure properties of two kinds of crystal.Compared with related theory and experimental data,make sure the method that we selected is feasibility.Further,studied crystal structure properties and energy properties of two different elements on Zr and Hf doped(Ba_0.5Sr_0.5)TiO₃.According to the data that calculated by software we deduce the optical properties.Calculation contents and results as follows:1,The crystal structure and symmetry for BaTi O₃,(Ba_0.5Sr_0.5)TiO₃,(Ba_0.5Sr_0.5)(Ti_0.5Zr_0.5)O₃ and(Ba_0.5Sr_0.5)(Ti_0.5Hf_0.5)O₃ ware calculated in paper.Calculated results show that: the lattice parameters of(Ba_0.5Sr_0.5)TiO₃ ware less than BaTiO₃.After doped Zr and Hf,lattice constants and cell volume ware increased respectively,the crystal structure gradually close to the cubic phase structure.studied by combining the atomic radius and location in the periodic table,valence state and impurity atom radius was the main reason that lattice distortion and atoms could be replaced effectively,elements in same group and atomic radius close are more likely to replace.This conclusion effectively explains why BaTiO₃ and SrTiO₃ can infinitely solid solution and atomic radius difference cause distortion of the crystal lattice.The distortion of crystal lattice may be affect dielectric properties of crystal.2,The energy band structure and density of states for BaTiO₃,(Ba_0.5Sr_0.5)TiO₃,(Ba_0.5Sr_0.5)(Ti_0.5Zr_0.5)O₃ and(Ba_0.5Sr_0.5)(Ti_0.5Hf_0.5)O₃ have been calculated.The results show that pure BaTi O₃ presents direct band gap semiconductor features,(Ba_0.5Sr_0.5)TiO₃,(Ba_0.5Sr_0.5)(Ti_0.5Zr_0.5)O₃ and(Ba_0.5Sr_0.5)(Ti_0.5Hf_0.5)O₃ presents indirect band gap semiconductor features.When Zr and Hf doped into(Ba_0.5Sr_0.5)TiO₃,the electron orbital hybridization results in the forbidden band widen.3,The dielectric functions for BaTiO₃,(Ba_0.5Sr_0.5)TiO₃,(Ba_0.5Sr_0.5)(Ti_0.5Zr_0.5)O₃ and(Ba_0.5Sr_0.5)(Ti_0.5Hf_0.5)O₃ was calculated.The results show that Zr and Hf doped(Ba_0.5Sr_0.5)TiO₃ lead to dielectric properties reduce,two dielectric peaks position close to each other and dielectric stability increased.4,The radiation coefficients,refractive indexes,extinction coefficients,absorption coefficients and energy loss functions for BaTiO₃,(Ba_0.5Sr_0.5)TiO₃,(Ba_0.5Sr_0.5)(Ti_0.5Zr_0.5)O₃ and(Ba_0.5Sr_0.5)(Ti_0.5Hf_0.5)O₃ ware calculated.Zr and Hf doped(Ba_0.5Sr_0.5)TiO₃ can produce effect on the corresponding coefficients,but the variation characteristic accordance with dielectric function variation.