Zero-phonon process

However, in contrast, the resonance effect increased by cooling both the source and the absorber. Mdssbauer not only observed this striking experimental effect that was not consistent with the prediction, but also presented an explanation that is based on zero-phonon processes associated with emission and absorption of y-rays in solids. Such events occur with a certain probability/, the recoil-free fraction of the nuclear transition (Sect. 2.4). Thus, the factor/is a measure of the recoilless nuclear absorption of y-radiation - the Mdssbauer effect. 

A recent development in physical techniques which may be of aid in evaluating the relative merits of theory is the Mossbauer effect. This effect is based upon recoilless y-ray emission (absorption) resulting from a nuclear transition in a particular atom with the resonance condition of zero-phonon processes. Since such nuclear transitions can be obtained with... 

Mbssbauer discovered, however, (hat itt (he case ot atoms w hich are not free, hut bound in a solid, the effect can often be observed. It is easily demonstrated when the normal, free-atetm recoil energy is comparable to the energy of the qutirilizied lattice vibrations, Under these conditions, zero-phonon processes are possible in which the entire energy of the nuclear... 

Because Miattice is much larger than the nnclear mass M, the recoil energy is negligible and resonance absorption takes place. In terms of quantum mechanics, there is a probability / for a zero-phonon process, where no lattice vibrations are excited. Rudolf Mossbauer showed that the probability / for a zero-phonon process is given by the subsequently named Lamb-Mossbauer factor ... 

Thus there is a certain probability that no lattice excitation (energy transfer of 0 x fuuR, i.e., zero phonon process) takes place during y-emission... 

Fig. 3. Schematic representation of emission probability and absorption cross section for nuclei bound in a solid after Visscher (1960). The sharp line arises from zero-phonon processes, the broad distribution from one- and multi-phonon processes. The / factor equals the ratio of the area under the sharp line to the total area. Height and width of the zero-phonon line are not to scale. The energy scale corresponds to the case of Np. [Taken from Dunlap and Kalvius (1985).]...

An explicit expression for the fraction of such recoilless or zero-phonon processes, commonly denoted as /, can be derived from the specific model used to represent the solid. The Debye model, for instance, predicts an increase... 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

Recoilless Optical Absorption in Alkali Halides. Recently Fitchen et al (JO) have observed zero phonon transitions of color centers in the alkali halides using optical absorption techniques. They have measured the temperature dependence of the intensity of the zero phonon line, and from this have determined the characteristic temperatures for the process. In contrast to the Mossbauer results, they have found characteristic temperatures not too different from the alkali halide Debye temperatures. 

Charged point defects on regular lattice positions can also contribute to additional losses the translation invariance, which forbids the interaction of electromagnetic waves with acoustic phonons, is perturbed due to charged defects at random positions. Such single-phonon processes are much more effective than the two- or three phonon processes discussed before, because the energy of the acoustic branches goes to zero at the T point of the Brillouin zone. Until now, only a classical approach to account for these losses exists, which has been... 

In the gas phase, the asymmetric CO stretch lifetime is 1.28 0.1 ns. The solvent can provide an alternative relaxation pathway that requires single phonon excitation (or phonon annihilation) (102) at 150 cm-1. Some support for this picture is provided by the results shown in Fig. 8. When Ar is the solvent at 3 mol/L, a single exponential decay is observed with a lifetime that is the same as the zero density lifetime, within experimental error. While Ar is effective at relaxing the low-frequency modes of W(CO)6, as discussed in conjunction with Fig. 8, it has no affect on the asymmetric CO stretch lifetime. The DOS of Ar cuts off at "-60 cm-1 (108). If the role of the solvent is to open a relaxation pathway involving intermolecular interactions that require the deposition of 150 cm-1 into the solvent, then in Ar the process would require the excitation of three phonons. A three-phonon process would be much less probable than single phonon processes that may occur in the polyatomic solvents. In this picture, the differences in the actual lifetimes measured in ethane, fluoroform, and CO2 (see Fig. 3) are attributed to differences in the phonon DOS at 150 cm-1 or to the magnitude of the coupling matrix elements. 

The first process shown above (Fj) is third order and by far the most commonly cited relaxation mechanism in pure crystals. It corresponds to a three-phonon process whereby the initial phonon either splits into two new phonons of lower energy (first term, down conversion) or interacts with a higher energy phonon (second term, up conversion). The down conversion process leads to a finite linewidth at 0 K, whereas the up conversion process gives zero contribution at low temperature. 

Phonon wings are probably the most important band shaping processes in inelastic neutron scattering spectroscopy and this theme is developed in later chapters. The intensity arising from the vth internal transition and remaining at the band origin, coq, is termed the zero-phonon-band intensity, often found in the literature as Sq. From Eq. (2.62), for R = 0... 

Similar relationships can be obtained for three-phonon processes. At low temperature, n (iv, T) is much smaller than unity and the above expression tends to unity for summation processes, and to zero for the difference processes, which are, therefore, not observed at low temperature. At higher temperature, the absorption intensity increases for both processes [45], at a difference with the one-phonon process, which is temperature-independent. 

From the above description, it should be evident that the electronic excitation-emission transition is a dynamic process which is perturbed by vibronic coupling of the phonon spectrum present in the host lattice. Thus, the host is just as important as the activator center. Another way to describe the overall process is to state that the electronic transition in the activator center involves the zero-phonon Une, broadened above absolute zero temperatures by quantized phonon interactions to form a band of permissible excitation and emission energies. 

As we have said, the excitation process results in a density of states arising from a random process of phonon perturbation of the excited state, both before it relaxes and afterwards as well. It is this random formation of Gaussian energy states that give rise to a broad band in excitation, and to a broad band in emission. The zero-phonon line arises from the nature of the electronic transition taking place which is broadened by the vibronic coupling process. As the temperature rises, increased phonon branching results and the emission band is even further broadened, as follows ... 

This process is a resonance process between matched oscillators and is non-radiative in nature. One important consequence is sometimes called "sensitized luminescence". Note that 11> has a higher energy than 2> and that there is an overlap area of energies caused by vibronic coupling broadening of the zero-phonon transition. 

It is well to note that some of the best phosphors (which have QE s exceeding 85%) are based on combinations of two activators, e.g.- Sn2+ -Mn2+ or Sb3+ - Mn2+. In this case, either Sn2+ or Sb3+ acts as a sensitizer and Mn2+ is the activator, i.e.- the SA pairs mentioned in Chapter 5. Strong absorption and excitation occurs at the Sn2+ or Sb3+ site while, with the proper composition, the emission can occur wholly from the Mn2+ site. The Mn2+ activator does not show a zero phonon line which can be perturbed in the excited state by vibronic coupling processes because it is excited by the sensitizer, not through the lattice. Thus, all those cations with a half-filled electron shell, including Mn2+, are able to... 

From the above discussion when dpjdq, or more rigorously, VqPy is zero or has a slope discontinuity, there are likely to be slope discontinuities in the combined density of states, as revealed by infrared and Raman spectra of two-phonon processes. Points in the Brillouin zone where each of the components of VqP = 0 are known as critical points. The intensity of infrared absorption or Raman scattering depends upon quantum mechanical matrix elements which are, in general, not simple to evaluate. However, by using symmetry considerations and group theoretical methods, the various modes can be assigned as infrared or Raman active. 

---