Effective phonons

Used effects Phonon excitation (20 meV-1 eV) Plasmon and interband excitations (1-50 eV) Inner-shell ionization (A = ionization energy loss) Emission of x-ray (continuous/characteristic, analytical EM)... 

Raman spectra are usually represented by the intensity of Stokes lines versus the shifted frequencies 12,. Figure 1.15 shows, as an example, the Raman spectrum of a lithium niobate (LiNbOs) crystal. The energies (given in wavenumber units, cm ) of the different phonons involved are indicated above the corresponding peaks. Particular emphasis will be given to those of higher energy, called effective phonons (883 cm for lithium niobate), as they actively participate in the nonradiative de-excitation processes of trivalent rare earth ions in crystals (see Section 6.3). 

Figure 6.6 shows Am versus the number of effective phonons, p, for the same three materials of Figure 6.5. The energy of the effective phonons for each host crystal is indicated in the figure caption. An exponential decrease in the nonradiative rate with...

F ure 6.6 The multiphonon nonradiative rate of (RE) ions as a function of the number of emitted effective phonons for LaCfi (260 cm ), LaEs (350 cm ), and Y2O3 (430-550 cm ). The numbers in brackets indicate the energies of the effective phonons. The shaded area indicates the range of typical radiative rates. 

EXAMPLE 6.3 Determine the number of effective phonons involved in the de-excitation processes from the energy levels of the (REf ions inLaCk given in Example 6.2. 

Considering that the effective phonons in LaClj are those with an energy of 260 cm (see the caption to Figure 6.6), and considering the different energy gaps from the" p3/2 (Er +), Pq (Pr ), and" F5/2 (Yb +) energy levels, we determine the number, p, of effective phonons in each noiuadiative deexcitation process ... 

The very low multiphonon decay rates obtained in Example 6.2 from the Po (Pr +) and p5/2 (Yb +) states are due to the large number of effective phonons that need to be emitted -14 and 38, respectively - and so the high-order perturbation processes. As a consequence, luminescence from these two states is usually observed with a quantum efficiency close to one. On the other hand, from the F3/2 state of Er + ions the energy needed to bridge the short energy gap is almost that corresponding to one effective phonon hence depopulation of this state to the next lower state is fully nonradiative. 

The fluorescence lifetime of the /2 metastable state of Nd + ions in LaBGeOs (a solid state laser) is 280 /u.s and its quantum efficiency is 0.9. (a) Calculate the radiative and nonradiative rates from this excited state, (b) If the effective phonons responsible for the nonradiative rate have an energy of 1100 cm, use the Dieke diagram to determine the number of emitted effective phonons from the F3/2 excited state, (c) From which three excited states of the Nd + ions in LaBGeOs do you expect the most intense luminescence emissions to be generated ... 

The data may also be reproduced with alternative choices for the effective phonon frequency, as the energy spacing is an approximate function of ha /Af. The lower... 

A and B are model parameters representing the high-temperature linear slope (du>/8T t oo) and effective phonon-mode temperature (l>hui(Q) jfc >), respectively. w(0) is the phonon-mode frequency at T = OK. Table 3.5 summarizes the best-model parameters reported in [43]. In [127], a linear temperature-dependence with dw[E2 ]/ T = —1.85 x 10 2cm 1 K 1 was reported for temperatures above RT. 

Figure 2. Intensity-voltage (/ - V) curve of "dot + leads" system at the equilibrium electron temperature fcuTe = 0.4 meV, but at a different effective phonon temperature...

Lucovsky (1972). Their basic unit is the As S3 molecule weakly coupled through a As-S-As bond to the next AsSa molecule (Figure 4.5a). Applying the selection rules for the AsSa molecule they were able to explain the observed difference between the effective phonon densities determined from the i.r. and Raman spectra (Figure 4.5b). Taylor etal (1973) interpret their extensive infrared and NMR studies as evidence for the remnants of the layers in the vitreous AS2S3 and AsaSea which persists into the liquid state (Tayloretal (1971)). 

The low thermal conductivity of bulk YSZ results from the low intrinsic thermal conductivity of zirconia and phonon scattering defects introduced by the addition of yttria. These defects are introduced because yttria additions require the creation of vacancies to maintain the electrical neutrality of the ionic lattice. Since both the yttrium solutes and the vacancies are effective phonon scattering sites the thermal conductivity is decreased as the yttria content is increased. 

SF sensitizer and difiusion lifetime superfluorescence lifetime maximum or effective phonon pulsation... 

If we further assume that there is only one dominant mode of coupling, the symbol Ijgj can be replaced by L gm, where is an effective degeneracy factor, and the subscript m denotes the effective phonon mode responsible for the radiationless process. Of the modes responsible for the decay, the highest energy optical phonon modes can be expected to make the greatest contribution. We further note that, for radiationless transitions in rare earth ions in crystals, the inequality... 

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 values for the effective phonon frequency listed in table 36.3 are in... 

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