The structural, electronic, and elastic properties of tetragonal phase of SnTiO3 and PbTiO3 are investigated using first principle calculations. The unknown exchange-correlation functional is approximated with generalized gradient approximation (GGA) as implemented in pseudopotential plane wave approach. The convergence test of total energy with respect to energy cutoff and k-point sampling is preformed to ensure the accuracy of the calculations. The structural properties such as equilibrium lattice constant, equilibrium unit cell volume, bulk modulus, and its derivative are in reasonable agreement with the previous experimental and theoretical works. From elastic constants, mechanical parameters such as anisotropy factor A, shear modulus G, bulk modulus B, Young’s modulus E, and Poison’s ratio n are determined by using Voigt–Reuss–Hill average approximation. In addition, Debye temperature and longitudinal and transversal sound velocities are predicted from elastic constants. The electronic band structure and density of states of both compounds are obtained and compared with the available experimental as well as theoretical data. Born effective charge (BEC), phonon dispersion curve, and density of states are computed from functional perturbation theory (DFPT). Lastly, the spontaneous polarization is determined from the modern theory of polarization, and they are in agreement with the previous findings.
The structural, electronic, elastic and optical properties of tetragonal (P4mm) phase of Pb0.5Sn0.5TiO3 (PSTO) and Pb0.5Sn0.5Ti0.5(Zr0.5)O3 (PSTZO) are examined by first-principles calculations based on the density functional theory (DFT) using the pseudo-potential plane wave (PP-PW) scheme in the frame of generalized gradient approximation (GGA). We have calculated the ground state properties such as equlibrium lattice constants, volume, bulk modulus and its pressure derivative. From elastic constants, mechanical parameters such as anisotropy factor, elastic modulus and Poisson's ratio are obtained from the Voigt-Reuss-Hill average approximation. Rather than their averages, the directional dependence of elastic modulus, and Poisson's ratio are modelled and visualized in the light of the elastic properties of both systems. In addition, some novel results, such as Debye temperatures, and sound velocities are obtained. Moreover, we have presented the results of the electronic band structure, densities of states and charge densities. These results were in favourable agreement with the existing theoretical data. The optical dielectric function and energy loss spectrum of both systems are also computed. Born effective charge (BEC) of each atoms for both systems is computed from functional perturbation theory (DFPT). Finally, the spontaneous polarization is also determined from modern theory of polarization to be 0.8662 C/m2 (PSTO) and 1.0824 C/m2 (PSTZO).
The title compound C4H7BrN+·NO3 − crystallizes in the monoclinic crystal system with space group P21/c. In the crystal, π-π stacking interactions and strong N—H...O and C—H...O hydrogen bonds link the cations and anions into layers parallel to the bc plane. The O...H/H...O interactions between the cation and anion are the major factor determining the crystal packing.
The Hamiltonian and wavefunctions describing two-dimensional (2D) two-electron ZnO quantum dot in rigid confinement are developed. Then the Schrödinger equation is solved analytically and numerically for determining the ground and excited state energies. The ground state energy of 2D two-electron ZnO quantum dot (QD) in rigid confinement is studied using perturbation and variational methods. The obtained result show that our trial wavefunction is good enough to describe the 2D two-electron QD in rigid confinement. The wavefunction describing the ground state is the combination of symmetric spatial wavefunction and antisymmetric spin wavefunction which is a para-state. The ground state energy eigenvalue obtained by variational technique is a little above that of a perturbation technique. Based on this; the trial wavefunction for the excited state is developed. The excited state energy of 2D two-electron ZnO QD in rigid confinement is studied computationally using variational method. The wavefunction describing the excited state is the combination of symmetric spatial wavefunction with antisymmetric spin wavefunction (para-state) or vice versa (ortho-state). The para and ortho-state energies of the first excited state are calculated and their difference is twice of the exchange energy. Based on the obtained energy eigenvalues of the ground and the first excited state at the value of the coupling constant [Formula: see text] [Formula: see text] 1, the third-order nonlinear absorption coefficient and refractive index changes are investigated. The optical transition is only considered between the two lowest para states.
Zinc blende (zb) and wurtzite (wz) structure of cadmium sulfide (CdS) are analyzed using density functional theory within local density approximation (LDA), generalized gradient approximation (GGA), Hubbard correction (GGA + U), and hybrid functional approximation (PBE0 or HSE06). To assure the accuracy of calculation, the convergence test of total energy with respect to energy cutoff and k-point sampling is performed. The relaxed atomic position for the CdS in zb and wz structure is obtained by using total energy and force minimization method following the Hellmann–Feynman approach. The structural optimization and electronic band structure properties of CdS are investigated. Analysis of the results shows that LDA and GGA underestimate the bandgap due to their poor approximation of exchange-correlation functional. However, the Hubbard correction to GGA and the hybrid functional approximation give a good bandgap value which is comparable to the experimental result. Moreover, the optical properties such as real and imaginary parts of the dielectric function, the absorption coefficient, and the energy loss function of CdS are determined.
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