Mossbauer lattice dynamics

Much of the Pt Mossbauer work performed so far has been devoted to studies of platinum metal and alloys in regard to nuclear properties (magnetic moments and lifetimes) of the excited Mossbauer states of Pt, lattice dynamics, electron density, and internal magnetic field at the nuclei of Pt atoms placed in various magnetic hosts. The observed changes in the latter two quantities, li/ (o)P and within a series of platinum alloys are particularly informative about the conduction electron delocalization and polarization. 

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... 

This technique, besides allowing determination of the Lamb-Mossbauer factor, provides direct access to the density of phonon states for the probe isotope in a solid. It thus provides information about lattice dynamics that is excluded by the limitations of Mossbauer spectroscopy. This technique could be valuable in investigations of adsorption with the adsorbing element as the probe and showing the modifications brought about by the adsorbate on the dynamic properties of the probe. 

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. 

Rather less information is available for the oxide derivatives of tin(Il). The crystal structure of black, tetragonal SnO is known [63], and was referred to in Chapter 14.1 in the discussion of the nuclear quadrupole moment. The Mossbauer parameters are given in Table 14.4 together with those for SnS, which has a considerably distorted NaCl lattice [64], SnSe (isostructural with SnS) [65], and SnTe, which has a cubic NaCl lattice [66]. Application of high pressure to SnO causes the formation of some Sn02 and tin metal [67]. A detailed lattice dynamical study of SnS between 60 and 320 K has shown evidence for a Karyagin effect [68]. 

Hendrickson and co-workers have continued to probe the dynamics of electron transfer in molecular systems in the solid state. Mossbauer and specific-heat data on biferrocenium [(C5H5)Fe(C5H4 C5H4)Fe(C5H5)] salts indicate that intramolecular electron transfer is controlled by lattice dynamics. The tri-iodide salts show valence localization up to 350 K by Mbssbauer data. The room-temperature crystal structure is centrosymmetric and evidently disordered. 

Investigation of Lattice Dynamics Using the Rayleigh Scattering of Mossbauer y-rays... 

Hou M, Azzaoui ME, Pattyn H et al (2000) Growth and lattice dynamics of Co nanoparticles embedded in Ag a combined molecular-dynamics simulation and Mossbauer study. Phys Rev B 62 5117-5128... 

The aim of this chapter is to report on recent advances in the in situ Mossbauer spectroscopy with synchrotron radiation on thin films that became possible due to the instrumentation developments at the nuclear resonance beamline ID 18 of the ESRF. After a detailed description of the beamline and of the UHV system for in situ experiments, a brief introduction into the basic NRS techniques is given. Finally, the application of these techniques to investigate magnetic, diffusion, and lattice dynamics phenomena in ultrathin epitaxial Fe films deposited on a W(l 10) substrate is presented and discussed. 

The Mossbauer spectra of Dy2(glu)3 2H2O at temperatures from 77 to 265 K are given in Fig. 6.3. Figure 6.4 shows the temperature dependence of the areas of this compiex. The lattice dynamics study is visualized where the natural logarithm of the normalized area is plotted versus temperature for the glu complex the slope is found to be —0.00530 (61) K . The Debye temperature Oo is estimated from the equation for the high-temperature approximation ... 

These three types of hyperfine interactions with the relevant Mossbauer parameters are most important in solid state research, in addition, one often extracts further helpful information from the temperature and pressure dependence of the Mossbauer parameters, the shape and width of the resonance lines (relaxation phenomena), and the second-order Doppler shift (lattice dynamics). 

The dynamic properties of the Mossbauer nucleus which can be monitored as a result of their effect on the Mossbauer spectrum can arise from the lattice dynamics of the solid in which the nucleus is situated. It can also result from the motion of a localised part of the system, such as a molecular motion, or from motion of the whole system within its environment. As the effect on the spectrum depends only on the actual motion of the nucleus and not on its origin it is not possible to distinguish directly between the possible sources of any such motion. Since the motion is often related to the internal energy of the system under investigation it is frequently studied as a function of the various parameters which determine the behaviour of the system, and particularly the temperature. 

The phenomenon of the recoil-free resonant absorption of gamma rays is the result of the special dynamics of nuclei in solids. This fact was recognised by Mossbauer, who interpreted his apparently anomalous observations in terms of lattice dynamics of a similar nature to those associated with neutron scattering (Mossbauer, 1938). He found that the recoil momentum of the recoiling nucleus is shared by many nuclei of the crystal and thus the recoil energy is extremely small. This cooperative... 

Information similar to that obtained by Mossbauer studies concerning the lattice dynamics and general dynamics of nuclei can be obtained by a wide variety of other techniques. Some are macroscopic bulk... 

The Mossbauer recoil-free fraction, the anisotropy in the recoil-free fraction and the thermal shift, when studied as a function of temperature, may all yield information on lattice dynamics which is as useful as that obtained from heat capacity or X-ray scattering measurements. One obvious advantage of the Mossbauer technique is the fact that it measures the vibrational modes of the Mossbauer probe, thereby yielding information on local modes which is unobtainable by other techniques. 

It has been mentioned above that one of the major advantages of the Mossbauer technique, compared with other methods which measure the parameters of lattice dynamics, is its ability to measure local modes of the Mossbauer probe. Dilute Mossbauer probes can be introduced into... 

The possible contributions of the Mossbauer technique to the study of phase transitions has been outlined previously (Shenoy, 1973). Almost all phase transitions cause changes in the lattice dynamics of the crystal and these changes can be studied through measurements of the recoil-free fraction, its anisotropy and the second-order Doppler shift. The phase transition itself is in many cases also observed through changes in the hyperfme interaction parameters. 

Sound velocity measurements on crystals with large magnetostriction provide evidence for changes in the lattice dynamics at the spin reorientation transition. Mossbauer studies of such systems show that there are changes in the recoil-free fraction at the spin reorientation transition (Seh Nowik, 1981). 

The Mossbauer fraction /of each kind of iron species is mainly governed by the lattice dynamics in the crystal. Therefore, / is dependent on the coordination and can differ slightly from mineral to mineral. Moreover, the Mossbauer fraction is particularly very sensitive to the valence state of iron and is for Fe " considerably lower than for Fe ". Because of the relationship with lattice vibrations, / is also strongly temperature dependent. This means that at RT a large difference in /values is observed and only to a lesser extent at 80 K. The /values for some iron-containing minerals, determined from the temperature dependence of the isomer shift (second order Doppler shift), are fisted in Table 3.1. 

We have discussed the basic procedures how to obtain a Mossbauer spectrum. However, a spectrum like fig. 6 contains only lattice dynamical information via Yq and allows to determine from W. Yet, our interest lies in electronic roicture properties. To understand how those are reflected in a Mossbauer spectrum we have first to discuss hyperfine interactions. Before entering this topic a few final words on dealing with a Mossbauer spectrum are appropriate. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

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