Mossbauer line

In many cases, the actual width of a Mossbauer line has strong contributions from inhomogeneous broadening due to the distribution of unresolved hyperfine splitting in the source or absorber. Often a Gaussian distribution of Lorentzians,... 

The relative absorption depth of the Mossbauer line is determined by the product of the recoU-free fraction/s of the Mossbauer source and the fractional absorption z t) of the sample, abs = fs-e f), where c(t) is a zeroth-order Bessel function ((2.32) and Fig. 2.8). Since c(t) increases Unearly for small values of t, the thin absorber approximation, c(t) t/2, holds up to t 1. On the other hand, values as small as t = 0.2 may cause already appreciable thickness broadening of the Mossbauer lines, according to (2.31), Fexp + 0.135t). In practice, therefore the sample... 

One can also infer in turn from these arguments that the relative absorption depth of a Mossbauer line should not exceed 10-15%, because of the increasing thickness broadening and the related line distortions. 

Fig. 3.25 Left signal-to-noise ratio (SNR) of the Mbssbauer spectra of a basalt taken with MIMOS II (full SI-PIN detector system black data-points) and MIMOS IIA (1/4 of full SDD system red data-points) respectively. Right XRF spectra of low Z elements measured with MIMOS IIA (SDDs) at —20°C. The Compton scattered 14.4 keV line (at 13.8 keV) and the resonant 14.4 keV Mossbauer line are well separated...

To calculate Mossbauer spectra, which consist of a finite number of discrete lines, the nuclear Hamiltonian, and thus also Hsu, has to be set up and solved independently for the nuclear ground and excited states. The electric monopole interaction, that is, the isomer shift, can be omitted here since it is additive and independent of Mj. It can subsequently be added as an increment 5 to the transition energies of each of the obtained Mossbauer lines. 

A monochromatic beam of X-rays with about 1 eV bandwidth is produced by the standard beamline equipment, the undulator and the high-heat-load premonochromator being the most important parts among them. Further monochromatiza-tion down to approximately the millielectronvolt bandwidth is achieved with the high-resolution monochromator. The width of a band of a millielectronvolt, however, is much more than the inherent linewidth of the Fe y-radiation, F 10 eV, or the full range of hyperfine-split Mossbauer lines, A m 10 eV. Yet, NFS is detectable because the coherent excitation of the nuclei is caused in the... 

Mossbauer spectra have been measured for various tektites, as well as for both natural and synthetic iron-bearing silicate minerals. These results are reported and compared with other similar studies available in the literature. The ratios of the intensities of the appropriate Mossbauer lines have been used to determine the ferric-ferrous ratios where possible. The spectra of the ferrosilite-enstatite series of pyroxenes show four lines which are interpreted as two quadrupole split doublets, and the ratio of the intensities of these lines indicates the degree of ordering in filling the available metal ion sites. Similar studies on the fayalite-forsterite series of olivines are also reported. 

This shift in the Mossbauer line is related to the valence of the studied ion and is very large for Np (40 mm/s). However, most compounds of interest for magnetism are not ionic, and covalency affects the isomer shift. Thus, although one observes some grouping into valence states, it cannot be used alone to assign uniquely a valence state - if any - for Np in non-ionic compounds °. ... 

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.)...

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... 

AEq = 0.37 for the LS (1A1) state (relative to natural ion at 298 K). Debye-Waller factors were determined for the two states. The values -lnf(sT2) and -lnfi A,) follow the Debye model between 175 and 250 K with 0D (ST2) = 126 K and between 105 and 225 K with 0D (J Aj) = 150 K, respectively. Deviations encountered outside these regions were considered as evidence for the formation of cooperative domains as suggested by Sorai and Seki34,87T The difference between the Debye temperatures 0d(5T2) and 0d( Ai) may well be understood in terms of more rigidity in the lattice of the 2A state as compared to that of the ST2 state. A study of the magnetic hyper-fine interaction at 4.2K yielded VZZ( A1) < O. VZZ(5T2) > O, however, was concluded from the spin reversal of the texture-induced asymmetry of the Mossbauer line intensities. 

The normal ways in which Mossbauer lines are interpreted (in searching for the identity structure of the material under examination) is to compare the frequencies (actually the rate of motion of a carrier containing the source ofy emission, e.g., 57Fe) at which resonance occurs14 with the corresponding Mossbauer spectra of various... 

Isomer Shift (IS). The shift observed in the Mossbauer lines with respect to zero velocity is produced by the electrostatic interaction of the nuclear and electron charge distributions inside the nuclear region. One assumes the nucleus is a uniformly charged sphere of radius R, and the electronic charge density is taken to be uniformly distributed over the nucleus. Then the difference between the electrostatic interaction of a point nucleus and a nucleus with radius R is given by... 

Besides the IS there exists a shift of the Mossbauer lines due to the second-order Doppler effect (i3, 14). This shift is given by... 

Table 2. Experimentala) Mossbauer line widths F, quadrupole splittings A Eq and isomer shifts d for oxygenated and deoxygenated myoglobin...

Table 3. Experimental ratios of quadrupole split Mossbauer lines of deoxy mb single crystals under various orientations...

Thus x(vq, m) is proportional to dT/dt>o> the derivative of the normal transmission curve. The amplitude of the secondary modulation must be much less than the width of the Mossbauer line so that dr/dvo is nearly constant over the amplitude. 

Accordingly, there is a shift in the Mossbauer line given by... 

---