Phonon line width

Currently worldwide six conventional (generic INll type) high resolution instruments are in operation and one is under construction. Two zero-field instruments that are suitable for polymer investigation are available. In addition, several installations for other purposes such as large angle scattering or phonon line width analysis exist (see Table 2.1 for more details). 

The following simplified expressions summarize the phonon line widths resulting from cubic and quartic terms in the crystal potential,... 

The experiments on phycobilisomes did not give evidence for exciton-like energy transport. In particular, no specific dependence of the zero-phonon line width as a function of bum frequency could be found, a result which was considered as strong support for stochastic transport processes. 

Fig. 32. (a) Phonon energies of CePdj versus temperature for several LA modes in the [111] direction, (b) Intrinsic phonon line widths of the corresponding modes versus temperature. The intrinsic line widths are fitted with a Lorentzian convoluted with a Gaussian for spectrometer resolution. Points without error bars are fits without a Lorentzian for phonons which are well described by spectrometer resolution alone (Severing et al. 1988). 

Fig. 8. Sound velocity V (right scale) and phonon line width F (left scale) of poly( ytene oxide) versus temperature. The phonon line width is proportional to the sound attenuation coefficient.

Fig. 11. Sound velocity (left scale) and phonon line width for n-tetracosane.

Fig, 26. Experimental dispersion curve of the Kr monolayer and measured line width broadening As of the Kr creation phonon peaks. The solid line in the dispersion plot is the clean Pt(lll) Rayleigh phonon dispersion curve and the dashed line the longitudinal phonon bulk band edge of the Pt(l 11) substrate, both in the r Mn azimuth which is coincident with the r Kk, azimuth. 

The intraconfigurational transitions of the rare earth ions (4/n) are examples of ions which, even in solids, show sharp lines in their spectra. The width is of the order of wavenumbers and is at 4.2 K usually determined by inhomogeneous broadening. These lines are true zero-phonon lines. The vibronic transitions belonging to these lines are weak and often overlooked. 

The temperature dependence of the homogeneous width of zero-phonon lines (ZPLs) in the optical spectra of the impurity centers in crystals is determined by... 

Fig. 1. Temperature dependence of the homogeneous width y (a) and position 8 (b) (in u>d units) of a zero-phonon line in the Debye model for different values of the interaction parameter wcx/w indicated in the right-side boxes. The instability limit corresponds to wcr/w = 1.

Fig. 2. Temperature dependence of the homogeneous width (a) and the peak shift (b) of the 637 nm zero-phonon line in luminescence spectrum of N-V centers in diamond films points experiment the line theoretical approximations according to the laws y — y0 + aT3 + bT1 and 8 = fiT2 - vT4.

It is possible to model the vibronic bands in some detail. This has been done, for example, by Liu et al. (2004) forthe 6d-5f emission spectrum of Pa4+ in Cs2ZrCl6, which is analogous to the emission spectrum of Ce3+. However, most of the simulations discussed in this chapter approximate the vibronic band shape with Gaussian bands. The energy level calculations yield zero-phonon line positions, and Gaussian bands are superimposed on the zero-phonon fines in order to reproduce the observed spectra. Peaks of the Gaussian band are offset from the zero phonon fine by a constant. Peak offset and band widths, which are mostly host-dependent, may be determined from examination of the lowest 5d level of the Ce3+ spectrum, as they will not vary much for different ions in the same host. It is also common to make the standard... 

Fig. 8. Calculated and measured emission spectra of YP04 Pr3+ from Peijzel et al. (2005a). The bars in the upper spectrum give information on the positions and intensities calculated for the zero-phonon lines, while the spectrum is obtained by superimposing a Gaussian band (offset 600 cm-1, width 1000 cm-1) on the zero-phonon lines.

LWR length-to-width ratio ZPL zero-phonon line... 

Equations (6) and (7) predict a transition whose width will be small if the NC sample is monodisperse (i.e., all particles have the same a value). However, even samples with a narrow size distribution show transition line widths of —30 nm FWHM (full width half maximum), which is significantly broader than expected. This line broadening is due to both homogeneous broadening related to phonon excitations in the NC and inhomogeneous broadening due to interactions with the surrounding environment. ... 

The absorption and emission bands have gaussian line shapes with their peaks separated by 2fV, as is illustrated in Fig. 8.4. The difference in energy is known as the Stokes shift as the strength of the electron-phonon coupling increases, so do the Stokes shift and the line widths. 

The half width of the luminescence line by the phonon interaction mechanism, from Eq. (8.11), is 2[(2 In 2) ji This is 0.25 eV for the maximum phonon energy of 0.05 eV from the silicon network vibrations, which is a little less than the observed line width. Thus the phonon model indicates that the luminescence spectrum is dominated by the phonon interaction and that the disorder broadening contributes less. 

The relative contributions of disorder and phonon broadening in the luminescence spectrum remain to be resolved. The disorder broadening evidently dominates in alloy materials in which the band tails are much broader. For example, the luminescence line width increases with nitrogen content in a-Si H N alloys, with a width which is predicted by the measured band tail slopes (Searle and Jackson 1989). 

Theoretical models to explain the observed change in line width and line position as a result of transition to superconductivity quantitatively are based on strong electron-phonon interaction (Zeyher and Zwicknagel, 1990). 

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