Hyperfine parameters

The larger AEq values observed for the ferrous sites in reduced [2Fe-2S] clusters and the hyperfine parameters obtained for the Fe-S clusters in the D. gigas AOR are very similar to those of the [2Fe-2S] centers in plant ferredoxins. 

A remarkable number of Mossbauer studies have been published since the first spectra reported in 1966 [135], most of them performed on the p-form when not specified differently [131, 132, 136-139]. Also, high pressure has been applied [140] and thin Aims were prepared [141]. Because of the ambiguity concerning the crystalline phase, the values of the hyperfine parameters show some dispersion. The isomer shift, 5 = 0.4-0.6 mm s is found in between the t3q>ical values known for high-spin iron(II) and low-spin iron(II). The quadrupole splitting is large, A q = 2.4-3.0 mm s (Table 8.3), as one might expect because of the unusual non-cubic symmetry. Applied-field measurements revealed positive F . 

The primary parameters that can be extracted from conventional Mossbauer spectra are the Lamb-Mossbauer factor,/, as well as the various hyperfine parameters that provide information about the state of the electronic enviromnent of the Mossbauer... 

This situation illustrates that special care has to be taken when analyzing NFS data. Nevertheless, high expectations rest on MS in the time domain especially for biological applications because it promises to be more sensitive to hyperfine parameters when the measurements are performed at high delay times and because of its applicability to samples of much smaller size. 

To visualize the sensitive response of the time-dependent forward scattering to small changes of hyperfine parameters, the time spectra for asymmetry parameters T] = 0.0, 0.2, and 0.5 (keeping aU other parameters the same) were simulated (Fig. 9.22). Comparable sensitivity was achieved for other hyqrerfine parameters, provided the measurements are performed to high enough delay times. 

Fig. 9.24 Theoretical calculations of nuclear forward scattering for the relaxation rates as indicated for a system with electron spin S = 1/2, hyperfine parameters A y jg fi = 50 T, and AF.q = 2 mm s in an external field of 75 mT applied perpendicular to k and O . The transition probabilities co in ((9.8a) and (9.8b)) are expressed in units of mm s , with 1 mm corresponding to 7.3 10 s. (Taken Ifom [30])...

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

Table 2.1 Hyperfine parameters and spin densities for aromatic radical anions. (Data from ref. 11.)...

Figure 2.10 ESR spectra of o-, m-, and p-xylene radical anions (see text for assignment of spectra). Spectrum (a) was simulated with permission using hyperfine parameters from Ref. 17b, copyright (1964) American Institute of Physics spectra (b) and (c) were simulated with permission using hyperfine parameters from ref. 17a, copyright (1961) Taylor and Francis (www.tandk. co.uk).

Table 2.2 Hyperfine parameters for xylene radical anions17...

Clearly, from inspection of Table 4.14, there is a good correlation between the steric bulk of R and L and the non-coincidence angle a. Furthermore, analysis of the hyperfine parameters leads to the conclusion that only about 25% of the electron spin resides in Co orbitals (mainly dxz), and crystal structures of the R = CF3, L = PPh3 and P(OPh)3 complexes do indeed show distortions. The difference between iron and cobalt is just one electron, but this electron occupies a dithiolene 7i orbital, which makes the cobalt complexes much more easily distorted. 

As discussed in Chapter 6, in systems with more than one unpaired electron the ESR spectrum contains features that involve electron-electron coupling parameters analogous to the nuclear hyperfine parameters. In those types of samples the advantages of double resonance are carried out by employing the use of two different microwave frequencies, one fixed and saturating, and one variable frequency that searches for transitions. This technique is known as ELDOR (electron-electron double resonance).38,40,41,44 It has been used much less than ENDOR and usually requires custom-built equipment. 

There is now an extensive and rapidly growing theoretical literature on the nature of hydrogen or muonium defects in silicon and to some extent in other semiconductors (Van de Walle, 1991 DeLeo, 1991). Much of this has dealt with isolated hydrogen or muonium where the most frequent comparisons have been with the muon hyperfine parameters, at least qualitatively, and other features of the muonium centers that can be inferred from /rSR experiments. Isolated interstitial hydrogen or muonium is certainly one of the simplest point defects conceivable. Hence explaining the existence and properties of the two drastically different forms of muonium observed in silicon and several other semiconductors has been a particular challenge to current theoretical methods. 

Measurements of the precessional frequencies in high field as a function of crystal orientation allows one to extract the hyperfine parameters and... 

Although simple /rSR spectra that do not depend on the nuclear terms in the spin Hamiltonian are the easiest to observe, one loses valuable information on the electronic structure. Under certain circumstances it is possible to use conventional /rSR to obtain a limited amount of information on the largest nuclear hyperfine parameters. The trick is to find an intermediate field for which the muon is selectively coupled to only the nuclei with the largest nuclear hyperfine parameters. Then a relatively simple structure is observed that gives approximate nuclear hyperfine parameters. A good example of this is shown in Fig. 3a for one of the /xSR... 

Note that the position of the juLCR depends on the sign of the nuclear hyperfine parameter relative to that of the muon. Using degenerate perturbation theory one can calculate the effects of the level crossing on the... 

Fig. 5. The /rSR spectra from fused quartz at room temperature and silicon at 77 K, each in a magnetic field of 10 mT. For quartz, the two high-frequency lines result from muonium with a hyperfine parameter close to that in vacuum. The two high-frequency lines in Si result from Mu, and their larger splitting arises because the hyperfine parameter is less than the vacuum value (0.45 Afree). The lowest line in each sample comes from muons in diamagnetic environments. The lines from 40 to 50 MHz in Si arise from Mu. From Brewer et al. (1973).

If the spin density not contributing to the muon hyperfine parameter were assumed to be... 

Anomalous Muonium (Mu ) a. Muon and 29Si Hyperfine Parameters... 

Below about 5 mT and for 6 = 70.5° a few additional lines were resolved that could be explained by 29Si at a further neighbor site with an isotropic 29Si hyperfine parameter of about —20 MHz (Kiefl et al., 1988b). This was confirmed by the observation (Kiefl et al., 1989b) of the /tLCR s from these more distant nuclei (see Fig. 9b). The amplitudes and orientation depen-... 

The muon and 29Si hyperfine parameters provide compelling evidence in support of the BC model. In the simple molecular-orbital model proposed by Cox and Symons (1986) the muon is located at the center of a Si—Si bond near a node in the unpaired electron spin density, which is... 

THE ISOTROPIC MUON HYPERFINE PARAMETER FOR Mu IN SEMICONDUCTORS. THE s DENSITY (rj ) IS EQUAL TO THE REDUCED HYPERFINE PARAMETER A/Afree where Afrcc = 4463.302 mhz. the data marked T — 0 WERE EXTRAPOLATED TO T = 0 K... 

Fig. 11. (top) The field dependence of the Mu and Mu precessional frequencies in diamond on a magnetic field applied along the (110) direction, (middle and bottom) The Mu amplitudes as a function of field measured at T = 454 K and 494 K respectively. The resonant maximum at B establishes the signs of the Mu hyperfine parameters relative to Mil. (B in this figure is equivalent to H in the rest of this chapter.) From Odermatt et al. (1988). 

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