Relaxation in Mossbauer spectroscopy

In studies of superparamagnetic relaxation the blocking temperature is defined as the temperature at which the relaxation time equals the time scale of the experimental technique. Thus, the blocking temperature is not uniquely defined, but depends on the experimental technique that is used for the study of superparamagnetic relaxation. In Mossbauer spectroscopy studies of samples with a broad distribution of relaxation times, the average blocking temperature is commonly defined as the temperature where half of the spectral area is in a sextet and half of it is in a singlet or a doublet form. 

Time-dependent effects and relaxation in Mossbauer spectroscopy... 

A. THE STOCHASTIC RELAXATION MODEL. The most general theories of magnetic relaxation in Mossbauer spectroscopy involve stochastic models see, for example. Ref. 283 for a review. A formalism using superoperators (Liouville operators) was introduced by Blume, who presented a general solution for the lineshape of radiation emitted (absorbed) by a system whose Hamiltonian jumps at random as a function of time between a finite number of possible forms that do not necessarily commute with one another. The solution can be written down in a compact form using the superoperator formalism. 

In Mossbauer spectroscopy, we encounter two types of expectation values for the electronic spin4 6 that we illustrate briefly for an iron site with S = 1/2 and g 2, taking the applied field along z. If the spin relaxation rate (spin flips between the Ms= + 1/2 and Ms= —1/2 sublevels) is slow compared to the nuclear precession frequency (which is typically 10—30 MHz Larmor precession around Bint or quadrupole precession), the nucleus senses the Fe atom in either the Ms= + 1/2 or Ms =1/2 state during the absorption process. In this case, we have (Sz) = + 1/2 for spin up and (Sz) = —1/2 for spin down. Each electronic level produces a Mossbauer spectrum, and these two spectra are weighted by the probability (given by the... 

In solutions of metal salts in non-aqueous solvents (particularly in systems with low permittivities), it is frequently necessary to take into account the formation of polynuclear species. Differentiation of the monomeric and homopolynuclear formations in solution is a difficult task in most cases. This is well reflected by investigations of various non-aqueous solutions of iron(III) chloride, for instance, which led to contradictory results in the above respect (c/., e.g., [We 62, Fa 68, Ca 62, Gu 70, Ar 65]). Study of the paramagnetic spin relaxation by Mossbauer spectroscopy is an excellent means for the differentiation of monomeric and polynuclear high-spin iron(III) species [Ve 78]. 

It is important to note that in the context of relaxation studies a combination of Mossbauer spectroscopy and the PAC and pSR methods allows a given problem to be approached over a range of experimental timescales. For example, it may be recalled that the experimental timescales in Mossbauer spectroscopy are the lifetime of the excited state of the nucleus and the Larmor precession time t, while in the case of PAC the... 

Relaxation effects in Mossbauer spectroscopy are of a different nature from those in NMR. The term relaxation effects or relaxation spectra in nuclear gamma resonance spectroscopy refers to averaging effects that occur in the hyperfine spectrum when the hyperfine interactions fluctuate at a rate more rapid than the nuclear frequency characteristic of the hyperfine interaction itself. This situation is a consequence of the rapid relaxation of the host ion among its energy levels, and the relaxation time for such effects is characteristic of the ion and not of the nuclear spins. The relaxation processes involved also affect electron spin resonance spectra, and their discussion is best considered in that context (see sections 3.3. and 3.4.). In the following subsections the principal interactions which contribute to the nuclear spin relaxation times in NMR experiments are briefly considered, and the connections between these and the parameters characterizing the steady-state spectrum are outlined. 

Rather sophisticated applications of Mossbauer spectroscopy have been developed for measurements of lifetimes. Adler et al. [37] determined the relaxation times for LS -HS fluctuation in a SCO compound by analysing the line shape of the Mossbauer spectra using a relaxation theory proposed by Blume [38]. A delayed coincidence technique was used to construct a special Mossbauer spectrometer for time-differential measurements as discussed in Chap. 19. 

The present method is still in its early stage of application. Both ex situ and in situ type measurements are applicable to a variety of mineral/aqueous solution interfaces. For example, the mechanism of selective adsorption of cobaltous ions on manganese minerals can be studied by this method. In addition to the two Mossbauer source nuclides described in the present article, there are a number of other nuclides which can be studied. We have recently started a series of experiments using Gd-151 which is a source nuclide of Eu-151 Mossbauer spectroscopy. Development of theory on surface magnetism, especially one including relaxation is desirable. Such a theory would facilitate the interpretation of the experimental results. 

Apart from fluorescence, several other methods may be used to obtain time-resolved information. In the case of proteins containing an iron atom, Mossbauer spectroscopy allows the determination, in the iron binding site, of not only root-mean-square shifts of atoms but also the times over which such shifts occur. Detailed investigations of myoglobin have yielded relaxation times on the order of 10 8 Proton NMR spectroscopy can be used to... 

Mossbauer spectroscopy can only be used to obtain rates of interconversion if the lifetimes are close to 10 7 second. As described in Section III,E a few examples satisfying this condition have been found. Some questions remain over the quantitative interpretation of the data. Nevertheless, spin-equilibrium relaxation lifetimes have been estimated from Mossbauer temperature-dependent linewidths for two salts of an iron(III) complex, [Fe(acpa)2]+. The lifetimes are of the order 10 5—10 7 second over temperature ranges from 100 to 300 K (109, 111). 

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