The group theoretical methods by which the symmetries of normal modes in crystals may be determined are outlined, and a series of tables are presented to facilitate rapid determination of the selection rules for vibrational transitions. Emphasis is placed on the method of nuclear site group analysis in which the number of infrared and Raman active modes of each symmetry may be obtained without detailed analysis of the symmetry elements in the crystallographic unit cell or the construction of tables. By using the tables presented here for most cases identification of the crystallographic space group is sufficient information to allow determination of the vibrational mode selection rules by inspection. Several examples are included in which crystals are analyzed by each of the methods.

Normal mode determination in crystals

Phase transformation of TiO2 from anatase to rutile is studied by UV Raman spectroscopy excited by 325 and 244 nm lasers, visible Raman spectroscopy excited by 532 nm laser, X-ray diffraction (XRD), and transmission electron microscopy (TEM). UV Raman spectroscopy is found to be more sensitive to the surface region of TiO2 than visible Raman spectroscopy and XRD because TiO2 strongly absorbs UV light. The anatase phase is detected by UV Raman spectroscopy for the sample calcined at higher temperatures than when it is detected by visible Raman spectroscopy and XRD. The inconsistency in the results from the above three techniques suggests that the anatase phase of TiO2 at the surface region can remain at relatively higher calcination temperatures than that in the bulk during the phase transformation. The TEM results show that small particles agglomerate into big particles when the TiO2 sample is calcined at elevated temperatures and the agglomeration of the TiO2 particles is along with the phase transformat...

UV Raman spectroscopic study on TiO2. I. Phase transformation at the surface and in the bulk

Copper-oxide compound semiconductors provide a unique possibility to tune the optical and electronic properties from insulating to metallic conduction, from bandgap energies of 2.1 eV to the infrared at 1.40 eV, i.e., right into the middle of the efficiency maximum for solar-cell applications. Three distinctly different phases, Cu2O, Cu4O3, and CuO, of this binary semiconductor can be prepared by thin-film deposition techniques, which differ in the oxidation state of copper. Their material properties as far as they are known by experiment or predicted by theory are reviewed. They are supplemented by new experimental results from thin-film growth and characterization, both will be critically discussed and summarized. With respect to devices the focus is on solar-cell performances based on Cu2O. It is demonstrated by photoelectron spectroscopy (XPS) that the heterojunction system p-Cu2O/n-AlGaN is much more promising for the application as efficient solar cells than that of p-Cu2O/n-ZnO heterojunction devices that have been favored up to now.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/pssb.201248128

Binary copper oxide semiconductors: From materials towards devices

Anatase, rutile, and especially brookite nanocrystals have been selectively synthesized in this work via a redox route under mild hydrothermal conditions (180 °C, 3 h), employing trichloride as the titanium source and ammonium peroxodisulfate (APS), hydrogen peroxide, nitric acid, or perchloric acid as the oxidant. Characterizations of the three pure phases were achieved by XRD, Raman spectroscopy, FTIR, TG, HRTEM, UV−vis, and BET. The use of APS consistently yields anatase, but the particle morphology can be tuned from wormhole-structured agglomerates to more dispersed nanocrystallites. The use of other oxidants yields almost identical results, and phase selection can be attained in this case by controlling the reactant concentration and solution pH. The three phases show their distinctive crystal shapes:  rounded nanocrystals for anatase, nanoplates for brookite, and nanorods for rutile. Both the optical band gap (3.11 eV) and the indirect band gap (2.85 eV) of brookite were found to lie in between thos...

Anatase, Brookite, and Rutile Nanocrystals via Redox Reactions under Mild Hydrothermal Conditions: Phase-Selective Synthesis and Physicochemical Properties

Publisher Summary This chapter presents several optical parameters that are useful in characterizing the materials in HOC I and HOC II. Some of these parameters are obtained directly from the critiques, others are found in references given in the critiques, and some in other references, in review articles, and in other general references. The chapter discusses optical parameters including: chemical formula of material, most common crystallographic form of the material at the room temperature, the space group in the X-ray and spectroscopic notation, dimensions of the unit cell, number of molecular units in the unit cell, irreducible representation, number of molecular units in the primitive cell, total number of optic modes in the crystal, transverse optic phonon frequencies, and the longitudinal optic phonon frequencies.

Optical Parameters for the Materials in HOC I and HOC II

Measurements of all A1 and E transverse and longitudinal phonons in BaTiO3 are reported in the temperature range 10 to 132 °C where the crystal is in the tetragonal phase. A least squares fitting of the spectral shapes is done and the resulting temperature dependence of the frequencies, linewidths and coupling parameters is presented. The temperature dependence of the phonon and electron contribution to the dielectric constant, e, in the c- and α-axes is determined and compared to the capacitance measurements. It is found that the dielectric constant discrepancy is highly anisotropic.

Temperature dependence of the A1 and E optical phonons in BaTiO3

The infrared properties of a system of first-order-coupled phonons are analyzed. The dielectric function and the Raman line shape of the polariton modes are derived. The parameters involved in the theory can be obtained from the Raman spectra of the TO and LO modes or from the Raman spectrum of the TO modes plus infrared-reflectivity measurements. It is shown that we can objectively distinguish real coupling from imaginary, contrary to the current belief. Numerical calculations are performed for the ${A}_{1}$-symmetry modes of tetragonal BaTi${\mathrm{O}}_{3}$, with good agreement for the polariton shapes and complete disagreement for the infrared reflectivity; damage at the crystal surface is pointed out as the probable cause of the discrepancy. In addition to the coupling between the lowest and the middle mode, previously known, a much larger coupling between the middle mode and the highest is shown to exist. Both couplings are shown to be real or nearly so. The discrepancy between the dielectric constant created by the resonant modes (electronic plus phonons) and the value obtained by electrical measurements is interpreted as a new indication that the crystal has a dynamical disorder; this disorder could also be cause of an anomalous broadening observed in the lowest polariton.

http://repositorio.unicamp.br/jspui/bitstream/REPOSIP/96481/1/2-s2.0-0001652797.pdf

Coupled modes with A 1 symmetry in tetragonal BaTi O 3

The room-temperature Raman spectra of LiTa${\mathrm{O}}_{3}$ for all symmetry phonons are investigated. We make a new assignment of the phonons, which agrees with the selection rules of a ${C}_{3}$ symmetry instead of ${C}_{3v}$, contrary to Kaminow and Johnston's previous work. The oblique phonon dispersions are obtained and turn out to be consistent with our phonon assignments. We obtain also the polariton dispersion curve and, from it, the low-frequency dielectric constant.

Light scattering by lithium tantalate at room temperature

The temperature behavior of the TO-phonon frequencies and line shapes in NaN${\mathrm{O}}_{2}$, as observed by Raman spectroscopy, is reported for temperatures from 20 to 250\ifmmode^\circ\else\textdegree\fi{}C. The Raman spectra of the ferroelectric phase obeyed the selection rules of the ${C}_{2V}^{20}$ space group. In the paraelectric Raman spectra, extra resonances (six instead of the expected three) were found. This anomaly and accompanying line asymmetries are accounted for by recognizing the effect of the nitrite-ion disordering along the $b$ axis upon lattice states. Additionally, in the paraelectric Raman spectra [polarized and ($\mathrm{bc}$)], a redundant appearance of the symmetric internal vibrations was observed, from which we conclude that above the phase-transition temperature there is a large torsional oscillation of the N${\mathrm{O}}_{2}^{\ensuremath{-}}$ ion about the $a$ axis. Significantly, the librational frequency associated with this torsional oscillation softened at key temperatures, the temperatures at which long- and short-range orders are lost. From our data, we conclude that the nitrogen atom jumps between two equivalent lattice sites by the flipping of the nitrite ion about the $a$ axis, and we suggest that temperature-dependent coupling between normal modes precipitates this flipping. A careful search of the Raman spectra 3 ${\mathrm{cm}}^{\ensuremath{-}1}$ from the frequency of the incident laser revealed no "Cochran" soft modes or supernumerary modes, such as a dipole wave, that might explain the ferroelectric phase transition in NaN${\mathrm{O}}_{2}$.

Analysis of the Temperature-Dependent Phonon Structure in Sodium Nitrite by Raman Spectroscopy

A detailed Raman-scattering investigation of LiI${\mathrm{O}}_{3}$, combined with the polarized infrared-reflectivity measurements, is reported. The dielectric constants determined by the Lyddane-Sachs-Teller (LST) relation (${\ensuremath{\epsilon}}_{\mathrm{xx}}=6.7,{\ensuremath{\epsilon}}_{\mathrm{zz}}=6.1$) do not reveal any large contribution by the lattice dynamics to the low-frequency dielectric response. The high-temperature study of the TO Raman modes (till 220 \ifmmode^\circ\else\textdegree\fi{}C) does not show any mode "softening," which could explain the critical dielectric behavior observed at very low frequencies. The study of the $A$-symmetry polariton curves has reconfirmed the LST dielectric values. The angular dispersion of the two upper oblique phonons of the $A$ and ${E}_{1}$ symmetry is compared with theory. The intensity dependence of these oblique phonons enables the determination of the second-harmonic-generation coefficient ${d}_{13}$ and the linear electro-optic coefficient ${r}_{13}$ in LiI${\mathrm{O}}_{3}$. These values are compared with other published data.

S. P. S. Porto

Papers

Temperature dependence of the A1 and E optical phonons in BaTiO3

Coupled modes with A 1 symmetry in tetragonal BaTi O 3

Light scattering by lithium tantalate at room temperature

Analysis of the Temperature-Dependent Phonon Structure in Sodium Nitrite by Raman Spectroscopy

Phonons, Polaritons, and Oblique Phonons in LiIO3by Raman Scattering and Infrared Reflection