Maximum phonon energy

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 vibrational spectrum of the host is particularly important for determining the rate of nonradiative decay and fluorescence quantum efficiency of lanthanides ions. Studies show that in both crystals and glasses, the rate of multiphonon emission is determined principally by the size of the energy gap to the next lower level and the number of phonons required to conserve energy (29J. Therefore hosts in which the maximum phonons energies are relatively small, e.g.,... 

When the energy mismatch is considerably larger than the maximum phonon energy available, multiple-phonon interactions are required for conservation of energy. This has been formulated by Miyakawa and Dexter (1970). The energy-... 

There is a red shift for its characteristic peaks in Raman spectrum which will induce lower phonon energy for the samples. The full widths of half-maximum of all peaks are increased and peak Intensity becomes weak when La203 was doped as an additive which means that the thermal vibration and the symmetry of the samples weaken. It is proven that the structures of samples present are in disorder and agree with the result that mentioned above. It is possible for Nd (Yi.,Lax)203 to be a new type of laser material. 

Fig.3 shows the Raman shift of (Ybo.o5Yo<)5xLax)20j ceramics. The phonon energies of (Yboo5Yo.95-xLa,)203 ceramics are between 370 and 376 cm and the FWHM (the ftill width of half-maximum) increases with the increase of LajOj content. There exists a red shift for the Raman characteristic peaks after the adding of LaaOj. 

It is interesting to compare the effective phonon energy with the maximum cutoff phonon energy (table 36.1). In all cases where convergence is attained in the least squares fit, the effective phonon energy is invariably somewhat lower than the maximum cutoff energy. 

The thermal energy in an insulating crystal takes the form of vibrations of the atoms about their equilibrium positions. The atoms do not vibrate independently, however, since the movements of one atom directly modulate the potential wells occupied by its neighbors. The result is coupled modes of vibration of the crystal as a whole, known as phonons. The phonon dispersion curve for an idealized one-dimensional lattice is sketched in Fig. 4. It is periodic, and it may be seen that there is a definite maximum phonon frequency, known as the Debye cut-... 

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