Electron hyperfine structure

In addition to this electron spin fine structure there are often still finer lines present. These are known as the hyperfine structure, which arises from the dilTerent weights of the isotopes of an element or from the spin of the nucleus. 

The spatial localization of H atoms in H2 and HD crystals found from analysis of the hyperfine structure of the EPR spectrum, is caused by the interaction of the uncoupled electron with the matrix protons [Miyazaki 1991 Miyazaki et al. 1991]. The mean distance between an H atom and protons of the nearest molecules was inferred from the ratio of line intensities for the allowed (without change in the nuclear spin projections. Am = 0) and forbidden (Am = 1) transitions. It equals 3.6-4.0 A and 2.3 A for the H2 and HD crystals respectively. It follows from comparison of these distances with the parameters of the hep lattice of H2 that the H atoms in the H2 crystal replace the molecules in the lattice nodes, while in the HD crystal they occupy the octahedral positions. 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

Wolfgang Pauli (1900-1958 Nobel Prize 1945), at the age of 24, formulated the exclusion principle, which became famous as the Pauli principle. Accordingly, all electrons in an atom differ from each other, none are the same. His theoretical considerations led him to the existence of so-called nuclear spins, which also explained the hyperfine structures of spectral lines. His hypothesis was later unambiguously confirmed. As each element has its own... 

A complex EPR spectrum detected (47) in the y-irradiated Vahrenkamp molecule Mn2 (CO) 8(/i-AsPh2) 2 is thought to belong to the cation of the molecule. From an analysis of the 55Mn and 75As hyperfine structure it was concluded that the d6d5 dimer radical has its single unpaired electron in a o MO composed of Mn 3(1 2 y2 orbitals. 

Here, the directions are defined in Fig. 6. In natural N02 the 170 content is quite small so the only observable hyperfine structure will be due to HN, which has a nuclear spin of one. Recent experiments, however, have been carried out using N02 enriched in 170 (34-) Molecular orbital calculations indicate that c2 is reasonably large, i.e., the unpaired electron is expected to have considerable nitrogen p2 character. 

A detailed study of the C02- species on MgO has been carried out by Lunsford and Jayne 26). Electrons trapped at surface defects during UV irradiation of the sample are transferred to the CO2 molecule upon adsorption. By using 13C02 the hyperfine structure was obtained. The coupling constants are axx - 184, am = 184, and a = 230 G. An analysis of the data, similar to that carried out in Section II.B.2 for N02, indicates that the unpaired electron has 18% 2s character and 47% 2p character on the carbon atom. An OCO bond angle of 125° may be compared with an angle of 128° for CO2- in sodium formate. 

By far the most important influence of a nuclear spin on the EPR spectrum is through the interaction between the electron spin S and the nuclear spin I. Usually, at X-band frequencies this interaction is weaker, by an order of magnitude or more, than the electronic Zeeman interaction, and so it introduces small changes in the EPR spectrum known as hyperfine structure. As a first orientation to these patterns, note that just like the electron spin S, also the nuclear spin / has a multiplicity ... 

Hyperfine splitting. As was discussed above, one consequence of placing a free electron onto a molecule is to alter its 0-value. Another is that the electron spin comes under the influence of any magnetic nuclei present in the radical, with the result that the spectrum is split into a number of lines centred on the position of the single resonance expected for the simple /transition discussed above. This hyperfine structure is the most useful characteristic ofepr spectra in the identification of an unknown radical species. 

Hyperfine structure arises through the interaction of the electron spin with a nuclear spin. Consider first the interaction of the electron spin with a single magnetic nucleus of spin , In an applied magnetic field the nuclear spin angular momentum vector, of magnitude (/ / -f l)]l/2, precesses around the direction of the field in an exactly analogous way to that of the electron spin. The orientations that the nuclear spin can take up are those for which the spin in the z-direction, M, has components of ... 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

The electron hyperfine interaction thus has important effects on both NMR relaxation and frequency shifts, and can provide valuable information on the incorporation of magnetic ions into semiconductor lattices and the resulting electronic structure as characterized by transferred hyperfine constants. Examples in Sect. 4 will show how the possible incorporation of magnetic ions into semiconductor nanoparticles can be studied by NMR. 

Thirdly, from the EPR hyperfine structure, it is possible to compute the structure of the radical (both the atomic and the electronic structures). 

Electron-spin resonance (e.s.r.) spectra with characteristic hyperfine structure have been recorded during the initial stages of the Maillard reaction between various sugar and amino compounds. The products responsible for the spectra appear to be IV, Af -disubstituted pyrazine radical cations. The pyrazine derivatives are assumed to be formed by the bimolecular condensation of two- and three-carbon enaminol compo-... 

ESR methods unambiguously establishes the presence of species bearing unpaired electrons (ion-radicals and radicals). The ESR spectrum quantitatively characterizes the distribution of electron density within the paramagnetic particle by a hyperfine structure of ESR spectra. This establishes the nature and electronic configuration of the particle. A review by Davies (2001) is highly recommended as a guide to current practice for ESR spectroscopic studies (this quotation is from the title of the review). The ESR method dominates in ion-radical studies. Its modern modifications, namely, ENDOR and electron-nuclear-nuclear triple resonance (TRIPLE) and special methods to observe ion-radicals by swiftness or stealth are described in special literatures (Moebius and Biehl 1979, Kurreck et al. 1988, Werst and Trifunac 1998). 

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