Nucleus, magnetic field at the

The value of is given by the component of the EFG tensor along the main quantization axis. Therefore, in this example where the EFG is axial (77 = 0) with the main component the quadrupole shift is eQVzJ - This is just half the quadrupole splitting that would be observed in an unperturbed quadrupole spectrum without a magnetic field at the nucleus. 

Equation (9.24) shows that the absorption frequency is directly proportional to the strength of the applied magnetic field at the nucleus. 

The magnetic hyperfine splitting, the Zeeman effect, arises from the interaction between the nuclear magnetic dipole moment and the magnetic field H at the nucleus. This interaction gives rise to six transitions the separation between the peaks in the spectrum is proportional to the magnetic field at the nucleus. 

In the case of iron, magnetism is due to the unpaired electrons in the 3d-orbitals, which have all parallel spin. These electrons interact with all other electrons of the atom, also the s-electrons that have overlap with the nucleus. As the interaction between electrons with parallel spins is slightly less repulsive than between electrons with anti parallel spins, the s-electron cloud is polarized, which causes the large but also highly localized magnetic field at the nucleus. The field of any externally applied magnet adds vectorially to the internal magnetic field at the nucleus. 

Table 5.4 Relative peak areas in magnetically split Mossbauer spectra as a function of the angle

This quantity is proportional to the magnetic field at the nucleus due to the unpaired s-electron configurations of the ion and is constant within 20% for ions of the iron group, if covalent bonding is not extreme as in cyanides of Mn in ZnS. 

Nuclear resonance is influenced in characteristic ways by the environments of the observed nuclei. However, nuclei are always surrounded by electrons and other atoms. Thus, in diamagnetic molecules the effective magnetic field at the nucleus is always smaller than the applied field 5 , i.e. the nuclei are shielded. The effect, although small, is measurable. This observation is expressed by equation 1 ... 

NMR spectroscopy provides spin-lattice (ri) and spin-spin (Tj) relaxation times. Making appropriate assumptions with regard to the magnetic interactions responsible for the relaxation process, these relaxation times can be related to molecular motions. Since nuclear spin relaxation results from all processes which cause a fluctuation in the magnetic field at the nucleus, the correlation function will generally correspond to more than one kind of motion involving all possible interactions. The equations for the relaxation times are generally of the form... 

The quantity B in (8.9) is the magnitude of the magnetic field at the nucleus in question. For an isolated nucleus, B is just the magnitude of the applied field. For a nucleus in a molecule, however, the magnetic field at the nucleus is due not only to the applied external field, but to the magnetic fields of the electrons and the other nuclei. In this section we... 

A magnetic field at the nucleus lifts the degeneracy of the m sublevels, thereby creating a splitting of the y-ray resonance of order /iH. This interaction can be observed with the Mbssbauer effect if... 

Fig. 2.2. Excess — V2 electron spin density contributes a magnetic field at the nucleus that adds to the external magnetic field.

Equation 2.6 contains only nuclear variables. It will be useful to rewrite the first two terms as gnfi (—(S)-A/gnfj + B) I and define the internal magnetic field at the nucleus ... 

We now combine B and Bint to obtain the effective magnetic field at the nucleus ... 

The Knight Shift. — In metals, an additional perturbation to the Larmor frequency must be considered, namely that from the conduction electrons which become polarized by H0 and therefore create a separate magnetic field at the nucleus, giving rise to a further displacement in i>0, which is called the Knight shift and can well be several orders of magnitude greater than the chemical shift. Since the Knight shift is restricted to metals, its relevance to this review has been in the study of finely divided, supported metal catalysts. 

The NMR shielding constant external magnetic field at the nucleus by the presence of electrons. 

The direction of the induced magnetic moment opposes the direction of the applied field, giving rise to diamagnetism. Evidently also, the effective magnetic field at the nucleus will be reduced the nucleus is screened . In practice we must now calculate the probability distribution of all electrons ( ), giving a total moment,... 

In a molecule, the electron cloud around each nucleus acts like a loop of wire, rotating in response to the external field. This induced rotation is a circular current whose magnetic field opposes the external field. The result is that the magnetic field at the nucleus is weaker than the external field, and we say the nucleus is shielded. The effective magnetic field at the shielded proton is always weaker than the external field, so the applied field must be increased for resonance to occur at a given frequency (Figure 13-5). 

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