Phonons Mossbauer 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... 

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

Equation (1.10) indicates that the probability of zero-phonon emission decreases exponentially with the square of the y-ray energy. This places an upper limit on the usable values of Ey, and the highest transition energy for which a measurable Mdssbauer effect has been reported is 155 keV for Os. Equation 1.10 also shows that/increases exponentially with decrease in which in turn depends on the firmness of binding and on the temperature. The displacement of the nucleus must be small compared to the wavelength X of the y-ray. This is why the Mossbauer effect is not detectable in gases and non-viscous liquids. Clearly, however, a study of the temperature dependence of the recoil-free fraction affords a valuable means of studying the lattice dynamics of crystals. 

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... 

More recent experiments have shown that such a model is an extreme over-simpliflcation. Impurities form local modes or resonance modes under a variety of conditions which depend on relative masses and relative interatomic interactions. A detailed theory has been worked out for the recoil-free fraction of an impurity (Mannheim, 1968). It is expressed in terms of the host lattice phonon frequency distribution function, the ratio of the masses of the host and impurity atoms and the ratio of the force constant between host atoms to that between host and impurity atoms. In Figure 6.4 the experimental results and the theoretical curves for Fe in vanadium are shown. Further details and recent experimental results for this model may be found in the Proceedings of the Indian National Science Academy International Conference on the Applications of the Mossbauer Effect (1982), pp. 619-63. 

Microstructure Mossbauer effect Optical properties Particle size Phase equilibria Phase transitions Phonons... 

For the absorption process, the same conservation law should be satisfied. For the transition Eq — 14.4 keV in Fe, / is 1.9 X 10 eV which is 10 times large compared to the natural line width of the excited state and no resonance between source and absorber for the free nucleus can be expected. When the nucleus is bounded into the solid, the recoil energy can be dispersed by the excitation of the solid. When the source and absorber are the nuclei embedded into the solid, recoil energy R may be used for the excitation of phonon that is the vibration state of sohd. Phonon is quantized as discrete value in solid and in usual metals the excitation energy of phonon states is the order of 10 -10 eV and there is rather large probability to have a zero phonon excitation in emission and absorption process in other word, the recoilless emission and recoilless resonant absorption of photon. This is the most important characteristic feature of the Mossbauer effect. As a consequence, the y photon emitted by the decay from the first excited state that has a... 

If the Mossbauer atom is bound in a solid, the recoil energy may be taken up by the matrix via excitation of lattice vibrations. The recoil energy is then reduced by a factor given by the atom and the solid mass ratio. If the phonon energy is low enough, there will be a finite probability, f, that the emission (absorption) will take place with no creation or annihilation of phonon in the lattice, that is, with no recoil energy loss, and this is the Mossbauer effect. The / factor (recoil-free fraction, Debye-Waller factor, Lamb-Mossbauer factor) is given by... 

The Mossbauer measurements makes it possible to study a variety of interesting effects that may be brought about by the introduction of impurity in the lattice as also the modifications brought about by imperfection in the crystal lattice, since the nuclei must be bound in a crystal for this study of resonant emission (or absorption) of y-rays. Three dynamical quantities of interest, which are possible in the Mossbauer studies, are (i) Zero-phonon absorption cross-section giving the Lamb-Mossbauer factor, (ii) One-phonon absorption cross section yielding the time information as well as the information of the localized modes and through this the information on the force constant between impurity and the host atom, (iii) the second order Doppler effect yielding information about the mean square velocity of the Mossbauer probe. 

The effect of annealing polycrystalline p-BN samples on the spectra of their Mossbauer-type centers GC-1, GC-2, and GC-3 (zero-phonon lines at 1.76, 1.63, and 1.55 eV) has been studied by cathodoluminiscence. In addition, another center with an electron vibrational... 

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