Mossbauer line shape

Recently, the stochastic models for the Mossbauer line shape problem have been discussed by several investigators.20 Such models can be treated in a systematic way as we have described in the above. For example, in a 57Fe nucleus, the spin in the excited state is / = and that in the ground state is / = i, so that the Hamiltonian is a 6 x 6 matrix. If a two-state-jump model is adopted, the dimension of the matrix equation, Eq. (63), is 6 x 2 = 12. If the stochastic operator is of the type (26), then the equation is a set of six differential equations. These equations can be solved, if necessary, by computers to yield the line shape functions for various values of parameters. 

Fig. 12. Mossbauer line shape of 57Fe in a constant eqQ field and a random hyperfine field assumed to be a two-state-jump process for different values of the jump rate W. (a) The random hyperfine field along the eqQ axis. (b) Perpendicular to the eqQ axis. (Calculations of Tjon and Blume.)...

The HS LS relaxation is basically a unimolecular process, and in diluted mixed crystals corresponding relaxation curves are single exponential. In Figure 5, HS LS relaxation rate constants for several spin-crossover complexes doped into inert host lattices as well as for some LS complexes are plotted as Lhl on a log scale vs. l/T. Figure 5 includes data obtained by optical spectroscopy, by Mossbauer line shape analysis, and by Mossbauer emission. Above 50K, these curves show the classical behavior of a thermally activated process, as is expected based on the energy barrier between the two states, and in agreement with results from... 

Fig. 2. Theoretical Mossbauer line shape for the isotropic relaxation of the electric field gradient. Here p =p =P. Relaxation time is shown in the figure. x y z...

For iron(III) eomplexes, uic venues /vlh [Fe(aepa)2]BPh4 H2O and k = 6.7 x 10 s for [Fe(mim)2(salacen)]PF6 have been obtained [156, 166]. The rate constants derived from the line shape analysis of Mossbauer spectra thus vary between 2.1 x 10 and 2.3 x 10 s at room temperature, no significant difference between iron(II) and iron(III) being apparent. In addition, it is evident that the rates of spin-state conversion in solution and in the crystalline solid are almost the same. For iron(II) eomplexes, for example, the solution rates vary between /cjjl = 5 x 10 and 2 x 10 s , whereas in solid compounds values between kjjL = 6.6 x 10 and 2.3 x 10 s have been obtained. Rates resulting from the relaxation of thermally quenched spin transition systems are considerably slower, since they have been measured only over a small range of relatively low temperatures. Extrapolation of the kinetic data to room temperature is, however, of uncertain validity. 

Although Lorentzian line shapes should be strictly expected only for Mossbauer spectra of thin absorbers with effective thickness t small compared to unity, Margulies and Ehrman have shown [9] that the approximation holds reasonably well for moderately thick absorbers also, albeit the line widths are increased, depending on the value of t (Fig. 2.7). The line broadening is approximately... 

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. 

Spectral lineshapes were first expressed in terms of autocorrelation functions by Foley39 and Anderson.40 Van Kranendonk gave an extensive review of this and attempted to compute the dipolar correlation function for vibration-rotation spectra in the semi-classical approximation.2 The general formalism in its present form is due to Kubo.11 Van Hove related the cross section for thermal neutron scattering to a density autocorrelation function.18 Singwi et al.41 have applied this kind of formalism to the shape of Mossbauer lines, and recently Gordon15 has rederived the formula for the infrared bandshapes and has constructed a physical model for rotational diffusion. There also exists an extensive literature in magnetic resonance where time-correlation functions have been used for more than two decades.8... 

The transmission throngh an absorber of thickness teff as a ftmction of the relative velocity V between source and absorber is given by the evalnation of the transmission integral discussed, for example, in Ref 2. In case of Fe Mdssbaner spectroscopy for almost all samples which are not enriched in the Mossbauer isotope Fe (the natural abundance of Fe is 2%), the evaluation of the transmission integral leads to Lorentzian line shape with a minimum linewidth of 0.19mms , which is twice the natural linewidth of the Fe Mossbauer transition. The absorption cross section as a ftmction of source velocity is then given as (with... 

S7Fe Mossbauer spectra were recorded in constant acceleration mode. Lorentzian line shape was presumed for decomposition of separate lines, and no positional parameters were constrained in the fits. The accuracy of positional data is ca. +- 0.03 mm/s. The isomer shift values are related to metallic a-iron. 

In-situ Mossbauer spectroscopic measurements were carried out on enriched catalyst samples rising an AME-50 Mossbauer spectrometer at room temperature. All spectra were computer-fitied to a Lorentzian line shape, and the isomer shifts are quoted relative to SnOz. 

From the application of the recoilless y-absorption technique to MbCO, HbCO, MbC>2, HbC>2, Mb, and Hb Mossbauer results have been derived which are presented in this section. Fig. 7 shows Mossbauer spectra of a frozen solution of MbCO (pH 7.0) at 4.2 °K (50), a typical candidate for ferrous low-spin state. Curve (a) coresponds to a measurement with zero applied magnetic field. Assuming a Lorentzian line shape (see Table 1), a least-squares fit to this spectrum leads to the following values for the Mossbauer parameters J1 (line width) =0.328 0.011 mm/sec, S (isomer shift, relative to iron metal) =0.266 0.010 mm/sec, and AEq (quadrupole splitting) = 0.363 0.006 mm/sec. Curve (b) shows a spectrum taken with a magnetic field of Ho = 47 kOe applied perpendicularly to the y-beam. Both spectra have been found... 

Figure 10. (A) Comparison of wet chemical and Mossbauer results on biotites. Results suggest that excellent agreement can be obtained between these techniques, even when Lorentzian line shapes are used to fit the Mossbauer spectra. (B,C) Comparison of XPS data with wet chemical (B) and Mossbauer (C) results on biotites, adapted from Raeburn et al. (1997a,b). (D,E) SmX results on Fe VSFe in micas plotted against wet chemical (D) and Mossbauer (E) data. (F) Comparison of XPS with XANES data on the same samples.

By varying an external parameter, such as the temperature, the pressure, or an applied magnetic field, the relaxation time may be varied and its value obtained from the Mossbauer spectra by modeling the line shape profile. An Arrhenius plot of the temperature or pressure dependence of the relaxation time yields the activation energy for the relaxation process. 

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