By means of variational structure and Z2 group index theory, we obtain infinite periodic solutions to a class of second-order neutral differential equations.
First principle calculation within the Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) using Local Density Approximation as implemented in Quantum ESPRESSO has been significantly used...First principle calculation within the Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) using Local Density Approximation as implemented in Quantum ESPRESSO has been significantly used to investigate the structural and Piezoelectric, properties of Perovskite ZrTi(PbO3)2. From structural properties calculation, the ground state total energy of -2417.12 eV has been obtained which led to an equilibrium lattice constant of a= 5.620Åfor ZrTi(PbO3)2. Our obtained optimized atomic positions and atomic effective charge shows that the optimized ZrTi(PbO3)2 is stable and the Piezoelectric stress tensor is calculated using Berry-phase approach within density functional perturbation theory (DFPT). From our calculation, we have obtained the stress tensor elements with values of d1,5 = 6.81, d3,1 = 1.69, and d3,3 = 6.18, which is in agreement with the values obtained for tetragonal PbTiO3.展开更多
First-principles calculations are used to investigate the mechanical and thermodynamic properties of cubic YH2 at different pressures and temperatures. The generalized gradient approximation （GGA） with Perdew-Burke-...First-principles calculations are used to investigate the mechanical and thermodynamic properties of cubic YH2 at different pressures and temperatures. The generalized gradient approximation （GGA） with Perdew-Burke-Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a and bulk modulus B are in good accordance with the available experimental values. According to the Born-Huang criteria for mechanical stability, elastic constants are calculated from the strain-induced stress method in a pressure range from 0 to 67.1 GPa. Isotropic wave velocities and sound velocities are discussed in detail. It is found that the Debye temperature decreases monotonically with the increase of pressure and that YH2 has low anisotropy in both longitudinal and shear-wave velocities. The calculated elastic anisotropic factors indicate that YH2 has low anisotropy at zero pressure and that its elastic anisotropy increases as pressure increases. Through the quasi-harmonic Debye model, in which phononic effects are considered, the thermodynamic properties of YH2, such as the relations of （V-Vo）/Vo to the temperature and the pressure, the dependences of heat capacity Cv and thermal expansion coefficient a on temperature and pressure ranging from 0 to 2400 K and from 0 to 65 GPa, respectively, are also discussed.展开更多
基金Project supported by NNSF of China (10471155)the Foundation of the Guangdong Province Natural Science Committee (031608) a specific Foundation for PhD Specialities of Educational Department of China (20020558092).
文摘By means of variational structure and Z2 group index theory, we obtain infinite periodic solutions to a class of second-order neutral differential equations.
文摘First principle calculation within the Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) using Local Density Approximation as implemented in Quantum ESPRESSO has been significantly used to investigate the structural and Piezoelectric, properties of Perovskite ZrTi(PbO3)2. From structural properties calculation, the ground state total energy of -2417.12 eV has been obtained which led to an equilibrium lattice constant of a= 5.620Åfor ZrTi(PbO3)2. Our obtained optimized atomic positions and atomic effective charge shows that the optimized ZrTi(PbO3)2 is stable and the Piezoelectric stress tensor is calculated using Berry-phase approach within density functional perturbation theory (DFPT). From our calculation, we have obtained the stress tensor elements with values of d1,5 = 6.81, d3,1 = 1.69, and d3,3 = 6.18, which is in agreement with the values obtained for tetragonal PbTiO3.
基金Project supported by the National Natural Science Foundation of China(Grant No.11176020)
文摘First-principles calculations are used to investigate the mechanical and thermodynamic properties of cubic YH2 at different pressures and temperatures. The generalized gradient approximation （GGA） with Perdew-Burke-Ernzerhof （PBE） method is used to describe the exchange-correlation energy in the present work. The calculated equilibrium lattice constant a and bulk modulus B are in good accordance with the available experimental values. According to the Born-Huang criteria for mechanical stability, elastic constants are calculated from the strain-induced stress method in a pressure range from 0 to 67.1 GPa. Isotropic wave velocities and sound velocities are discussed in detail. It is found that the Debye temperature decreases monotonically with the increase of pressure and that YH2 has low anisotropy in both longitudinal and shear-wave velocities. The calculated elastic anisotropic factors indicate that YH2 has low anisotropy at zero pressure and that its elastic anisotropy increases as pressure increases. Through the quasi-harmonic Debye model, in which phononic effects are considered, the thermodynamic properties of YH2, such as the relations of （V-Vo）/Vo to the temperature and the pressure, the dependences of heat capacity Cv and thermal expansion coefficient a on temperature and pressure ranging from 0 to 2400 K and from 0 to 65 GPa, respectively, are also discussed.
