Optical phonon softening

The phonon confinement model [23] attributes the redshift of the asymmetric Raman line to relaxation of the -vector selection rule for the excitation of the Raman active phonons due to their locahzation. The relaxation of the momentum conservation rule arises from the finite crystalline size and the diameter distribution of the nanosolid in the films. When the size is decreased, the rule of momentum conservation will be relaxed and the Raman active modes will not be limited at the center of the Brillouin zone [21]. The large surface-to-volume ratio of a nanodot strongly affects the optical properties mainly due to introducing surface polarization states [28]. 

Particle size reduction softens the phonons for aU glasses, and the phonon frequencies of CdSe nanodots vary with the composition of host glasses. Models based on assumptions that the materials are homogeneous and isotropic are valid only in the long-wavelength limit. When the size of the nanosolid is in the range of a few nanometers, the continuum dielectric models exhibit limitations. 

Hwang et al. [29] consider the effect of lattice contraction in explaining the versatile phonon redshifts of nanosolid CdSe embedded in different glass matrices. The following expresses the 7f-dependent phonon shift with inclusion of lattice contraction, 

For a free surface, a = a, and b = 0. There are some difficulties however to use this equation, as remarked on by Hwang et al. [29] since the thermal expansion coefficient within the temperature range T — Tg is hardly detectable. The value of B in Eq. (15.6) is given by the difference of the phonon negative dispersion and the size-dependent surface tension. Thus, a positive value of B indicates that the phonon negative dispersion exceeds the size-dependent surface tension and consequently causes the redshift of phonon frequency. On the contrary, if the size-dependent surface tension is stronger than the phonon negative dispersion, blue-shift occius. In case of balance of the two effects, i.e., B = 0, the size dependence 

---

However, contrary to CeBCu this mode softening in Cei La Bei3 for 0.8 is also observed for all other symmetry modes with respect to the average behavior of the reference materials. The phonon softening in Cej La, Be,3 for 0.1 X 0.8, independent of the mode symmetry is also reflected by the behavior of the Debye temperature 0 (Besnus et a. 1983), which is displayed at the bottom of fig. 35. No temperature dependent phonon anomaly has been observed for the optical phonons of CeBcij, contrary to the anomalous softening of the bulk modulus upon cooling down below 350 K (Lenz et al. 1984). 

The process of phonon scattering contributes less to the intrinsic vibratiorc Atomic undercoordination softens the optical phonons of nanostructures. Intergrain interaction results in emerging of the low-frequency phonons whose frequency undergoes blueshift with reduction in solid size. 

Figure 15.1 shows typical examples of size-softened optical phonons, which justifies the validity of the BOLS with derived information about the corresponding dimer vibration is given in Table 15.1. The size-softened phonons arise from the involvement of the interaction between the specific atom and it surrounding neighbors [32, 33]. 

The BOLS correlation and the scaling relation correlate the size-created and stiffened LFR phonons to the intergrain interaction. The size-softened optical phonons result from interaction between the undercoordinated neighboring atoms in the skin. The coordination reduction enhancement of the phonon frequencies of the Eg mode of Ti02 and the G mode of GNR is dictated by the interaction between undercoordinated dimers. The size-induced phonon relaxation follows a K fashion. Decoding the size dependency of the Raman optical redshift leads to vibrational information of Si, InP, CdS, CdSe, TiOz, CeOa, and Sn02 dimers and their bulk shifts. 

Figure 2. Phonon pictnre of the origin of the incommensurate phase transition in qnartz. The two plots show the a dispersion curves for the transverse acoustic mode (TA) and the soft optic RUM, at temperatures above (left) and close to (right) the incommensurate phase transition. The RUM has a frequency that is almost constant with k, and as it softens it drives the TA mode soft at an incommensurate wave vector owing to the fact that the strength of the coupling between the RUM and the acoustic mode varies as k. ...

---