Anisotropy, hyperfine

This has been discussed above for several specific instances. In the absence of -anisotropy, hyperfine anisotropy increases for individual lines in a spectrum on going from the centre outwards. Thus a central line often corresponds to a state where the total nuclear spin is zero so that there is no anisotropy and a narrow line results. This situation is exemplified by the spectrum of trapped ethyl radicals (Section V) and also by the effect of cooling on the spectrum of the radical NH3+ (Hyde and Freeman, 1961). 

Rao and Symons49 studied the formation of radicals in y-radiolysis of dilute solutions of dimethyl sulfoxide in fluorotrichloromethane. By ESR studies they found the radical cation (CH3)2SOt whose ESR spectrum show considerable g anisotropy and small methyl proton hyperfine coupling. 

With these assignments at hand the analysis of the hyperfine shifts became possible. An Fe(III) in tetrahedral structures of iron-sulfur proteins has a high-spin electronic structure, with negligible magnetic anisotropy. The hyperfine shifts of the protons influenced by the Fe(III) are essentially Fermi contact in origin 21, 22). An Fe(II), on the other hand, has four unpaired electrons and there may be some magnetic anisotropy, giving rise to pseudo-contact shifts. In addition, there is a quintet state at a few hundred cm which may complicate the analysis of hyperfine shifts, but the main contribution to hyperfine shifts is still from the contact shifts 21, 22). 

The results of these modeling studies are shown in Figures 2 and 3> The value of ic (anisotropy constant) was chosen so that the average particle radius determined from the reduction in the average hyperfine field splitting due to collective magnetic excitations... 

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

Effect of Crystal Anisotropy on the Relative Intensities of Hyperfine Splitting Components... 

With h 6) - 1/sin 0)5(0 — Oq), one obtains the same result as given by (4.58), which implies that the anisotropy of the/factor cannot be derived from the intensity ratio of the two hyperfine components in the case of a single crystal. It can, however, be evaluated from the absolute/value of each hyperfine component. However, for a poly-crystalline absorber (0(0) = 1), (4.66) leads to an asymmetry in the quadrupole split Mossbauer spectrum. The ratio of l-Jh, as a function of the difference of the mean square amplitudes of the atomic vibration parallel and perpendicular to the y-ray propagation, is given in Fig. 4.19. 

The temperature dependence of the magnetic hyperfine splitting in spectra of interacting nanoparticles may be described by a mean field model [75-77]. In this model it is assumed that the magnetic energy of a particle, p, with volume V and magnetic anisotropy constant K, and which interacts with its neighbor particles, q, can be written... 

The spectral line widths are related to the rate of the rotational motions, which average anisotropies in the g- and hyperfine matrices (Chapter 5), and to the rates of fluxional processes, which average nuclear positions in a radical. 

Much of the width arises from incomplete averaging of anisotropies in the g-and hyperfine matrices (Chapter 3). For radicals with axial symmetry the parameters of eqn (2.8) depend on Ag = - g , AA, = AiM - A and tr,... 

If the g- and hyperfine anisotropies are known from analysis of a solid-state spectrum, the line-width parameters (1, and yt can be used to compute the rotational correlation time, tr, a useful measure of freedom of motion. Line widths in ESR spectra of nitroxide spin labels, for example, have been used to probe the motional freedom of biological macromolecules.14 Since tr is related to the molecular hydrodynamic volume, Ft, and the solution viscosity, r, by a relationship introduced by Debye 15... 

Lorentzian line shapes are expected in magnetic resonance spectra whenever the Bloch phenomenological model is applicable, i.e., when the loss of magnetization phase coherence in the xy-plane is a first-order process. As we have seen, a chemical reaction meets this criterion, but so do several other line broadening mechanisms such as averaging of the g- and hyperfine matrix anisotropies through molecular tumbling (rotational diffusion) in solution. 

C- hyperfine satellites are detectable in natural abundance (Figure 3) and their intensities indicate a formulation Cr(C0)4 for the carrier of unpaired spin. Slight anisotropy in the 13C hyperfine structure of the 95 13C- enriched species could only be correctly reproduced in simulations under the assumption of tetrahedral geometry. The centre is thought to be Cr(C0)4+ with a 6At ground state in symmetry, a rare example of a high-spin metal carbonyl. 

At either frequency the sensitivity of the instrument is quite remarkable. The exact signal-to-noise ratio depends upon a number of factors including apparent line width (including g and hyperfine anisotropy), ease of saturation, the temperature, and the linear density of the sample in the quartz tube. For a relatively narrow line with peak-to-peak separation of two gauss it is possible to observe the spectrum for concentrations as low as 1014 spins per gram of sample. As the spectrum becomes more anisotropic, the sensitivity of course decreases. Lowering the temperature increases the sensitivity since the population difference An increases [(Eqs. (26) and (3°)]. 

FIGURE 10.4 Anisotropy averaging in the EPR of TEMPO as a function of temperature. The spectra are from a solution of 1 mM TEMPO in water/glycerol (10/90). The blow-up of the middle 14N (/ = 1) hyperfine line in the 90°C spectrum has been separately recorded on a more dilute sample (100 pM) to minimize dipolar broadening and, using a reduced modulation amplitude of 0.05 gauss, to minimize overmodulation. The multiline structure results from hyperfine interaction with several protons. 

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