Figure 9. The FTIR absorbance spectrum for C 4 F 8 O.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 128.210.126.199 Downloaded on 2015-05-29 to IP

Herein we report results of pressure- and temperature-dependent Raman scattering studies on PrTiO. Pressure-dependent studies performed up to 23 GPa suggest a reversible phase transition above 15 GPa with subtle changes. Temperature-dependent investigations performed in the range of 77-1073 K showed anomalous temperature dependence of some of the Raman modes. Temperature-dependent X-ray diffraction data indicated no structural transition but nonlinear expansion of unit-cell parameters with increasing temperature. With increasing temperature, the structure dilates anisotropically, and volume of coordination polyhedra around all the atoms expands. Also with increasing temperature the distortions in coordination polyhedra around all the atoms decrease, and appreciable decrease is observed in Pr(1)O and Pr(3)O units. The pressure evolution of Raman-mode frequencies was analyzed for both ambient as well as high-pressure phases, and mode Grüneisen parameters for ambient pressure phase were obtained. The temperature evolution of Raman-mode frequencies was analyzed to obtain the explicit and implicit anharmonic components, and it was found that some of the modes attributable to TiO octahedra and PrO polyhedra have dominating explicit anharmonic component. Comparison of the structural data with the temperature dependence of Raman modes suggests that the anomalous behavior in Raman modes is due to phonon-phonon interaction.

We consider the energy eigenvalue problem of the Dirac delta well potential, V(x) = −V0δ(x), placed between two rigid walls at x = ±a. When the strength parameter is increased, the ground state eigenvalue, E0, passes from a positive to a negative value. We show that when s = 1, E0 = 0, the eigenstate is forced to be of zero-curvature: ψ0(x) = A(a − |x|), and it is orthogonal to all excited states. On the other hand, if V0 is made negative then a zero-energy and zero-curvature eigenstate does not exist.

The effect of high pressure on the structure of orthorhombic Mn3(VO4)2 is investigated using in situ Raman spectroscopy and X-ray powder diffraction up to high pressures of 26.2 and 23.4 GPa, respectively. The study demonstrates a pressure-induced structural phase transition starting at 10 GPa, with the coexistence of phases in the range of 10–20 GPa. The sluggish first-order phase transition is complete by 20 GPa. Importantly, the new phase could be recovered at ambient conditions. Raman spectra of the recovered new phase indicate increased distortion and as a consequence the lowering of the local symmetry of the VO4 tetrahedra. This behavior is different from that reported for isostructural compounds Zn3(VO4)2 and Ni3(VO4)2 where both show stable structures, although almost similar anisotropic compression of the unit cell is observed. The transition observed in orthorhombic Mn3(VO4)2 could be due to the internal charge transfer between the cations, which favors the structural transition at lower pressures and the eventual recovery of the new phase even upon pressure release in comparison to other isostructural compounds. The experimental equation of state parameters obtained for orthorhombic Mn3(VO4)2 match excellently with empirically calculated values reported earlier.