Anisotropic hyperfine splitting

If the electron cloud is spherical, = 1/3 and therefore = 0. will be nonzero only if the unpaired electron has p- or d-character. The scalar value of the anisotropic hyperfine splitting B can be expressed in the form... 

Recent results for certain known radicals of general type XO, XO2 and XO3 are presented and compared with those for unknown radicals formed and trapped in crystalline salts of nonmetal oxy acids, such as sulfates and phosphates, as a result of exposure to high energy radiation. Certain generalizations are made, regarding the values for isotropic and anisotropic hyperfine splittings to be expected from the nucleus of atom X for different isoelectronic series and these are linked to expected deviations of the g value from that of the free spin. Hence an attempt is made to rationalize the results of several recent studies of irradiated crystalline oxy salts. 

For an electron in an orbital centered on the nucleus in question (Fig. 6), the anisotropic hyperfine coupling follows from Eq. 14, but having in addition a term <3cos a — 1> which represents the average direction of the electron spin vector within the orbital. The anisotropic hyperfine splitting can now be defined as the separation between adjacent energy levels, viz. Mg, Mj and Mg, and equals... 

The isotropic and anisotropic hyperfine coupling constants for 61Ni isotope (1=3/2), as well as for isotopes 14N (1=1) and 13C (1=1/2) in a relaxed cluster were calculated. The anisotropic hyperfine splitting constants for 61Ni were changed from 75 to 150 MHz depending on the nanocrystal orientation. The observations are important for future possible applications of such nanocrystals in quantum information technologies. 

In order to confirm the anisotropy due to the a-hydrogen, Salovey et al. [9] and Shimada et al. [10] studied the patterns of the ESR spectra from irradiated solution grown crystals of polyethylene. The crystal c-axis was oriented perpendicular to the plane of the sample while the a- and b-axes were randomly oriented in the plane as shown in Fig. 7.8. Six- and ten-line spectra were observed when the c-axis of the crystal was set to be parallel (Fig. 7.9(a)) and perpendicular (Fig. 7.9(b)) to the direction of the applied magnetic field, respectively. From these results, the anisotropic hyperfine splitting due to the a-hydrogen Ay = 0.75 mT, Ax = 1.72 mT and Az = 3.70 mT were determined and were related to the molecular orientation of the crystal. The x-, y- and z-axes coincide with the directions of the p-orbital, the (Ca )— Ha bond, and the main chain axis, respectively, as shown in Fig. 7.10. 

A t)tpical feature of the Mossbauer spectra of five- or six-coordinate iron(IV) with an axial oxo group (or a OCH3, a nitrido or a imido group) is a low isomer shift (+0.1 0.15 mm s ), a large and positive quadrupole splitting (1-2 mm s ), an anisotropic hyperfine coupling tensor with moderately large values for A x/gNl N and (—16 to —23 T) and a rather small value for A Jg i (0 to —10 T)... 

According to Table I, the small Co2+ hyperfine splitting constants indicate that the unpaired electron must be largely localized on the coordinated oxygen molecule. If the unpaired electron is localized in only one d orbital, the hyperfine tensor can be resolved into an isotropic and anisotropic part in the form ... 

In some physical situations, namely when the hyperfine energy is small compared to the nuclear Zeeman energy, then the hyperfine splitting is linear in (the projection magnitude of) matrix A for example, see Ref. 131. Then, provided that g is anisotropic (note Ref. 128 on this point), one can detect asymmetry of A directly from EPR line-position measurement see below. 

The EPR spectrum of 02F2 also has been studied in this laboratory. Solid 02F2 showed a broad, anisotropic EPR pattern similar to that reported (5, 6). In addition, the EPR spectrum of neat liquid 02F2 contained a doublet near g = 2.0 with a hyperfine splitting of approximately 13 gauss. 

CCC bond angle is larger than 120°. Analysis of the anisotropic components of the carbon-13 hyperfine splitting confirms this and shows that... 

Hyperfine interactions between the electron and any magnetic nuclei (7>0) present (such as a proton, for example) produces hyperfine splitting, as illustrated in a very simple example in Fig. 2.51. This hyperfine interaction may be divided into an isotropic and an anisotropic component. The isotropic part arises from unpaired electron density at the nucleus and can only be nonzero for i -type orbitals. The anisotropic term corresponds to the classical part of the magnetic dipole interaction for which the Hamiltonian is ... 

In the general case, both isotropic and anisotropic hyperfine interachons contribute to the experimental spectrum. The whole interaction is therefore dependent once again on orientation and must be expressed by a tensor. The effechve spin Hamiltonian for this more reahstic descriphon of a paramagnehc species in the solid state was given earher in Equahon 1.28. Nevertheless the A tensor may be split into its component isotropic and anisotropic parts as follows ... 

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