Vibrational Properties of CuO and Cu₄O₃ from First-Principles Calculations, and Raman and Infrared Spectroscopy

A combined experimental and theoretical study is reported on the vibrational properties of tenorite CuO and paramelaconite Cu₄O₃. The optically active modes have been measured by Raman scattering and infrared absorption spectroscopy. First-principles calculations have been carried out with the LDA+U approach to account for strong electron correlation in the copper oxides. The vibrational properties have been computed ab initio using the so-called direct method. Excellent agreement is found between the measured Raman and infrared peak positions and the calculated phonon frequencies at the Brillouin zone center, which allows the assignment of all prominent peaks of the Cu₄O₃ spectra. Through a detailed analysis of the displacement eigenvectors, it is shown that a close relationship exists between the Raman modes of CuO and Cu₄O₃

Optical and Acoustic Vibrations Confined in Anatase TiO₂ Nanoparticles under High-Pressure

The effect of an applied high pressure on the optical and acoustic vibrations of small anatase TiO₂ nanoparticles is studied using Raman scattering. All the Raman peaks show a significant variation of their frequency with pressure, except for the low-frequency peak which is due to acoustic vibrations confined in the nanoparticles. These variations (or lack thereof) are compared to first-principles calculations of the stiffness tensor and phonons of bulk anatase TiO₂ as a function of pressure. In particular, the variation of the shape of the low-frequency peak is explained by the increase of the elastic anisotropy of anatase TiO₂ as pressure is increased