Electronic orientationally averaged spectra

For the sake of comparison with the ESCA spectrum of Nj, and to provide a more critical test of the EOM method, we calculate the peak intensities as well as the peak positions. The details of the intensity calculations are left to the Appendix. The dipole approximation is invoked, as the calculation is based on Fermi s golden rule. A plane wave approximation is employed for the outgoing electron. The cross section for the ejected electron is averaged over all possible molecular orientations and polarizations of the incident photon as described by Ellison. ... 

The most comprehensive information obtained from a Mossbauer spectrum is contained in Bint that depends on the magnetic hyperfine tensor A and, through (S), on the ZFS, the electronic g tensor (and exchange couplings when we consider polynuclear systems). For samples containing randomly oriented molecules, such as poly crystalline powders or molecules in frozen solution, the Mossbauer spectrum depends on the orientation of the molecule relative to the direction of the applied field,4 6 which is fixed in the laboratory and is generally either parallel or perpendicular to the direction of Mossbauer radiation. As a consequence, the spectrum is a powder average from which we have to extract the various tensor quantities of... 

Additionally, anisotropic chemical shift effects will also be present in the spectrum due to the nonexistence of molecular tumbling. This means that, since in solids the atoms and molecules are not moving, they do not change the orientation. Since the ability of the applied field to generate electron currents depends on the orientation of the nuclei relative to the applied field, the chemical shift depends on orientation, and since in solids this effect is not averaged out, it will contribute to the peak broadening. The chemical shift anisotropy also varies with the angle, 9,... 

Ageing of this sample at higher temperature (105 C) led to anisotropy in its ESR spectrum with an amplitude of anisotropy of 0,9 mT [12]. The average g-value of the anisotropy spectrum is equal to that of isotropic spectrum. Anisotropy observation under conditions of intermolecular exchange of unpaired electrons is possible only in the case of mutual orientation of the main molecular axes of paramagnetic domains located in high ordered mesophase structures [13] This leads to a preferential orientation of PMS with respect to the magnetic fields. 

In paramagnetic substances, it is necessary to compare tr with tl If tr < < tl so that the orientation of the electronic spins fluctuates very rapidly, the internal magnetic field seen by the nucleus will average to zero and there will be no magnetic interactions. This appears to be the case with the ferrous hemoglobins and one observes unbroadened, nearly symmetric, quadrupole doublets. If on the other hand tr > > TL, magnetic hyperfine interactions can occur and one may expect line broadening and perhaps even a fully resolved hyperfine spectrum. 

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