Optical phonon frequency

Momentum conservation implies that the wave vectors of the phonons, interacting with the electrons close to the Fermi surface, are either small (forward scattering) or close to 2kp=7i/a (backward scattering). In Eq. (3.10) forward scattering is neglected, as the electron interaction with the acoustic phonons is weak. Neglecting also the weak (/-dependence of the optical phonon frequency, the lattice energy reads ... 

We note that ionic crystals may have dielectric functions satisfying Eq. (4) for frequencies between their transverse and longitudinal optic phonon frequencies. SEW on such crystals are often called surface phonons or surface polaritons and the frequency range is the far IR. 

Ionic crystals also support SEW, but again no data exists where they have been used as substrates for attached molecule studies. That such studies may be feasible is illustrated in Fig. 21, which shows measured and calculated propagation distances for SrTi03 in the far infrared.— Again, these measurements were made with a molecular laser as a source. Unfortunately, for many crystals the frequency region over which SEW exist is very narrow (between the transverse and longitudinal optic phonon frequencies), and propagation distances are very short. However, ferroelectrics (and near-ferroelectrics like SrTiC ) may prove useful substrates for SEW spectroscopy. 

Sasaki K, Saito R, Dresselhaus G, Dresselhaus MS, Farhat H, Kong J (2008) Curvature-induced optical phonon frequency shift In metallic carbon nanotubes. Phys Rev B 77(24) 245441... 

Fig. 17.12 Temperature dependence of the optical phonon frequency for (a) bulk Si, (b) a 50-mn-diameter Si NW grown by the vapor-liquid-solid (VLS) method [1] and (c) a 50-nm-diameter Si NW formed through Ag-catalyzed electrochemical etching (EE) [63]. (d) Slopes of the optical phonon frequency versus temperature for individual Si NWs of both types with diameters greater than 30 nm. They match the same value for bulk Si within experimental error (With permission from reference [62]. Copyright (2009) by the American Physical Society)...

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

Worlock JM, Fleury PA (1967) Electric field dependence of optical-phonon frequencies. 

Single crystal studies of solid hydrates are scarce. There are two experimental procedures possible (i) transmission spectra of thin crystal plates (see, for example. Refs. 16, 17) and (ii) reflection spectra of crystal faces . Using polarized infrared radiation, the species (symmetry) and other directional features of the water bands can be determined. In the case of reflection measurements, the true transverse and longitudinal optic phonon frequencies can be additionally computed by means of Kramers-Kronig analyses and oscillator fit methods, respectively. Both experimental techniques, however, are relatively difficult because of the lack of suitable monocrystals, the requirement of preparing sufficiently thin, i.e., <0.1 mm, crystal plates (except for studying overtone bands, see Sect. 4.2.6), and the efflorescence or absorption of water at the crystal surfaces. In favorable cases, thin sheets of orientated powdery material can be obtained . ... 

As an example, we estimate the resonance enhancement of an intraband optical transition in silicon carbide (SiC) nanociystals. The dielectric function of SiC is well modeled by the expressions (7) with = 6.52, Qt = 793.9 cm" (and the wavelength At = 12.6 pm), = 970.1 cm (Al = 10.3 pm), and y = 4.763 cm. Note that the relaxation parameter y is much less than the optical phonon frequencies, y/Qi = 0.006 and y/ L = 0.005. The solution of the resonance condition (6) results in Q w 902cm and the corresponding resonance wavelength A 11 pm. Here and hereafter, in all onr numerical estimates we accept the permittivity of a host matrix Shost = 2.25, because this value is typical for many solvents, glasses, and polymers. Then, the gain factor G(Q) is estimated to be approximately 3.6 x 10. ... 

The obtained results show that the lattice dynamics of very small ZnSe NCs is similar to that of bulk ZnSe crystal in the case that dispersion curves of the main optical phonon frequencies are still correct. It is confirmed by the data obtained in... 

Interpreting these data within the framework given in sect. 3.1 we can estimate a charge fluctuation rate of roughly 100 cm well below the optical phonon frequencies, but within the range of the acoustic phonons. From the position of the LO(L) phonon frequencies of metallic SmS as well as Sm 25S between the divalent and trivalent reference lines one can estimate valences of 2.8 and 2.3, respectively, which agree quite well with the valences deduced from Lm spectroscopy as given by Allen et al. (1980) and by Weber et al. (1989), respectively. 

Prettl et al (1973) studied the far infrared spectra of a-Ge, GaP, GaAs and InAs and compared them with the Raman spectra. They showed that the spectra are similar in the optical phonon frequency regions but the absorption is much smaller at low frequencies. They argue that this effect is due to the different dependence of the coupling constant for Raman scattering and infrared absorption on the wavevector q. 

I tested the GAP models on a range of simple materials, based on data obtained from Density Functional Theory. I built interatomic potentials for the diamond lattices of the group IV semiconductors and I performed rigorous tests to evaluate the accuracy of the potential energy surface. These tests showed that the GAP models reproduce the quantum mechanical results in the harmonic regime, i.e. phonon spectra, elastic properties very well. In the case of diamond, I calculated properties which are determined by the anharmonic nature of the PES, such as the temperature dependence of the optical phonon frequency at the F point and the temperature dependence of the thermal expansion coefficient. Our GAP potential reproduced the values given by Density Functional Theory and experiments. 

Ves S, Strossner K, Cardona M (1986) Pressure dependence ofthe optical phonon frequencies and the transverse effective charge in AlSb. Solid State Common 57 483 86 Katayama Y, Tsuji K, Oyanagi H, Shimomura O (1998) Extended X-ray absorption fine structure study on hquid selenium under pressure. J Non-Cryst Solids 232-234 93-98 Gauthier M, Polian A, Besson J, Chevy A (1989) Optical properties of gallium selenide under high pressure. Phys Rev B 40 3837-3854... 

To illustrate the kind of useful information that can be obtained, we consider here in some detail one example—calculation of the optical phonon-phonon interactions in diamond. This will serve both to illustrate the power of the method and to shed some light into the phenomenon of two-phonon Raman anomaly in diamond. It was observed that the two-phonon Raman spectrum of diamond has an anomalous sharp peak (not seen for Si and Ge) at 2667 cm which is at an energy 3 cm higher than twice the optical phonon frequencies at r. Despite a number of theoretical works, the nature and origin of this peak is still a mystery. One particularly intriguing explanation was the two-phonon bound state theory by Cohen and Ruvalds. They proposed that a two-phonon bound state is formed... 

All other terms that are not related to the above terms by permutation of the Indices are zero. As noted before, < gives the optical phonon frequency y gives the amplitudes for three-phonon processes and a and 3 give the amplitudes for the bare four-phonon processes. 

Figure 8.6 Soft optical phonon frequencies in antiferroelectric SrTiOj versus temperature.

Figure 14.13. The calculated emission spectrum for y = 1. The electronic gap is 2.1 eV, the optical phonon frequency 0.18 eV and a Gaussian lineshape with HWHM of 0.07 eV has been used (Reprinted with permission from ref 109).

From the other monomers, hi-, ter- and quaterthio-phenes, it seems that the eiFect of the number of rings of the monomer is another important factor in the increase in the conjugation length of the polymer. The low-temperature photoluminescence bands recorded on these same samples are shown in Figures 14.22 and 14.23. Differences between the samples appear more clearly from the photoluminescence criteria than from the Raman criteria and a more precise characterization of the samples is achieved. The photoluminescence band of all these samples displ s the expected profile a series of discrete peaks separated by an optic phonon frequency. The main zero-phonon line and the one-phonon line are pointed, respectively, at around 1.9 eV and 1.78 eV. As previously observed in the case of films prepared by electropolymerization, in addition to the narrow and well-defined peaks (with an energy separation of 0.175 eV), additional peaks appear in the pTh-Cn samples for n = 2,3. In relation to the Raman results, we assign the appearance of this fine structure to an increase in the structural order along the chain [10]. This structure appears clearly in pTh-C2 and pTh-C3, but it is less pronounced in pTh-C4. On the other hand, the same structure appears in pTh-C2, but it completely vanishes in pTh-C3 and pTh-C4. ... 

Fig. 22. Dispersion curve for UTe along the 9j (parallel to the moment) and 9 (perpendicular to the moment) directions at 5 K. The narrow hatched area shows the optic-phonon frequency. The different symbols correspond to different spectrometer conditions. The wide hatched area on the left-hand side corresponds to the region where the specific peak positions are uncertain. (From Lander et al, 1991b.)...

The ternary materials show different composition behaviors dependent on the difference in the masses of the elements A and B (i.e., on the existence of an energy-forbidden gap between the optical phonon frequencies of the binary materials AC and BC). For materials like CdZnSe, the LO mode of pure CdSe changes into the LO mode of the pure... 

For nanostructures, difficulties in determining the correct frequency shift arise from other factors which have an influence on the peak frequency, like strain and phonon confinement. The strain-induced shift of the optical phonon frequencies in superlattices and quantum wells can be estimated by the difference in the lattice constants of the materials. To determine the composition-dependent shift in a system with two-mode behavior, which shows strong phonon confinement, the difference in the frequency positions of the two LO-phonon modes is used, which is confinement independent in many cases [92,101,104,105]. 

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