Ab initio calculations of phonon spectra in ATiO3 perovskite crystals (A = Ca, Sr, Ba, Ra, Cd, Zn, Mg, Ge, Sn, Pb)

Abstract

The phonon spectra of calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with the perovskite structure are calculated from first principles within the density functional theory. By analyzing the unstable modes in the phonon spectra, the possible lattice distortions are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn on the origin of the ferroelectricity in considered crystals. It is shown that the main factors determining the possible off-centering of atoms in the A position are the geometric size and electronic configuration of these atoms.

Ferroelectric phase transition in orthorhombic CdTiO3: First-principles studies

“…This means that the formation of the monoclinic phase with P b space group and tilted polarization vector is energetically unfavorable. The calculation using the formula (1) shows that the energy minima are observed at the mode amplitudes of (ξ = 0.03332, η = 0) and (ξ = 0, η = 0.02288) and that the energy gains associated with these lattice distortions are 6.16 and 1.86 meV, respectively. They are close to the corresponding energy gains of the true distortions (see Sec.…”

“…1 have revealed that orthorhombic phases of CdTiO 3 , ZnTiO 3 , and MgTiO 3 with the P bnm structure exhibit the ferroelectric instability which appears in their phonon spectra as one or two unstable modes with symmetries B 1u and B 2u at the Γ point. In this work, the characteristics of these modes are considered and the results of first-principles calculations of the crystal structure, phonon spectra, and spontaneous polarization of the parent orthorhombic CdTiO 3 phase with P bnm structure and its two ferroelectrically distorted orthorhombic modifications (with P bn2 1 and P b2 1 m space groups) are compared with available experimental data.…”

“…Here, ν = −2a/M * /2π is the value of an imaginary mode frequency in the high-symmetry configuration (maximum of the potential barrier) determined in the classical (BornOppenheimer) approximation, and E 0 = a 2 /4b is the depth of the potential well for the V (x) potential. For the four-minimum potential well described by equation (1), the quantitative value of the criterion can be slightly different.…”

Structural instability in BaZrO3 crystals: Calculations and experiment

“…The lattice parameters and the equilibrium atomic positions were determined from the condition of decreasing of the residual forces acting on the atoms below 5 · 10 −6 Ha/Bohr (0.25 meV/Å) while the accuracy of the total energy calculation was better than 10 −10 Ha. To calculate of the phonon spectra, the formulas derived from the density functional perturbation theory and the interpolation technique 15 were used. The calculated lattice parameter for the cubic BaZrO 3 was a 0 = 4.1659Å and agreed well with the experimental value obtained at 10 K (4.191Å, Ref.…”

Effect of local environment on crossluminescence kinetics in SrF2:Ba and CaF2:Ba solid solutions

“…The pseudopotentials needed for calculations were constructed using the OPIUM program or borrowed from Ref. 18. The local structure of the solid solutions was modeled with CaF 2 and SrF 2 supercells containing 3×3×3 FCC unit cells in which one of 27 metal atoms was substituted by the Ba atom.…”