Ion-phonon interaction

As a result of ion-phonon interaction, the population of the excited state decreases via nonradiative transition from the excited state to a lower electronic state. The energy difference between the two electronic states is converted into phonon energy. This process of population relaxation is characterized by a relaxation time, xj, which depends on the energy gap between the two electronic states, the frequencies of vibration modes, and temperature (Miyakawa and Dexter, 1970 Riseberg and Moos, 1968). At room temperature, the excited state lifetime is dominated by the nonradiative relaxation except in a few cases such as the 5Do level of Eu3+ and 6P7/2 level of Gd3+ for which the energy gap is much larger than the highest phonon frequency of the lattice vibrations. 

This chapter reviews recent studies on energy levels and excited state dynamics of lanthanides (R) in nano-structures, which include R-doped dielectric nano-crystals, implanted nano-particles of semiconductors, coated core-shell nano-particles, nano-tubes and nano-balls stuffed with R ions. New phenomena such as the action of confinement on ion-phonon interaction and its consequences for electronic transitions, energy transfer, and phase transitions are discussed in the light of experimental and theoretical studies reported in the literature. Although the review aims at being comprehensive and covers all the important aspects in the field, emphasis is given to identification and theoretical analysis of various mechanisms for... 

Various scientists consider the time-fluctuating energy levels (Fig. 6.7) as bands of energy levels. Such a description is very convenient, especially for semiconductor-liquid interfaces, but must be used with caution. As Morrison has already pointed out in his book [12], these bands arise from the fluctuation of the solvent and they have different properties from the fixed bands in solids. There is an essential difference in concept between, on the one hand, electron-phonon interactions causing a fluctuation of electronic energy in a static distribution of levels, and, on the other hand, ion-phonon interactions causing a fluctuation of the energy levels themselves. For instance, it is not possible to have an optical transition between the occupied and unoccupied levels. 

Fig. 5.3. A. Two-siie nonresonant process in phonon-assisted energy transfer. (/) and (3) pr nt the ion-phonon interaction, (2) the site-site coupling H. B. One-site resonant process in phonon-assisted energy transfer. (/) and (2) present the ion-phonon interaction, (3) the site-site coupling...

Since electrons are much faster than nuclei, owing to Wg Mj, ions can be considered as fixed and one can thus neglect the //ion-ion contribution (formally Mion-ion Hee, where Vion-ion is a Constant). This hrst approximation, as formulated by N. E. Born and J. R. Oppenheimer, reflects the instantaneous adaptation of electrons to atomic vibrations thus discarding any electron-phonon effects. Electron-phonon interactions can be a-posteriori included as a perturbation of the zero-order Hamiltonian Hq. This is particularly evident in the photoemission spectra of molecules in the gas phase, as already discussed in Section 1.1 for nJ, where the 7T state exhibits several lines separated by a constant quantized energy. 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

Already in the seminal paper of Bednorz and Muller [1], the guide to look for systems with a high superconductive transition temperature (Tc), has been the presence of strong electron-phonon interactions. Such interaction has been known to exist in a wide class of perovskite type oxides. The authors mention [1] the vibronic Jahn-Teller polaron effect [2] in this context. They also emphasize the fact that the Cu2+-ion is a well-known Jahn-Teller system and this circumstance preserves significance in the physics of cuprate superconductors [3-7]. As a microscopic cause for ferroelectric ordering the interband vibronic hybridisation has been supposed [8-11] enlargening the view on perovskites as Jahn-Teller systems. 

The electron-phonon interaction has been studied also in a LiTnJA crystal by Kupchikov et al. (1982). They have measured Raman and infrared reflection spectra under pressures up to 1.2 GPa and at temperatures ranging from 4.2 K to 300 K. The interaction of optical phonons with electronic excitations in this system of rare-earth ions was detected by anomalous tem-... 

The maximum deviation from this dashed line in Figure 62 is only about 1% and can not explain the observed 10% variation of the Sommerfeld constant. Therefore, taking into account Eq. (9), it was concluded that the local lattice distortions due to the different size of the Y and Lu ions in the YxLui xNi2B2C compounds mainly reduce the electron-phonon interaction (Rosner et al., 2000). The dependence of Xph on the Y concentration resulting from Eq. (9) and N( p) is... 

Malkin, B.Z., 1987. Crystal field and electron-phonon interaction in rare-earth ionic paramagnets. In Kaplyanskii, A.A., Macfarlane, B.M. (Eds.), Spectroscopy of Solids Containing Rare-Earth Ions. North-Holland, Amsterdam, pp. 33-50. 

So far the principles and theoretical models that we discussed for the excited state dynamics including line shifts and broadening were developed originally for ions in bulk solids. Although the 4f electronic states are localized and exhibit little quantum confinement, the dynamics of electronic transitions may be subjected to quantum confinement arising from electron-phonon interactions. Modification of the existing theoretical models is required for their applications to lanthanides in nanomaterials. 

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