Combined magnetic and quadrupole interactions

Such systems embrace both ordered materials with unusually fast relaxation and also paramagnetic compounds with slow relaxation. 

The chemical isomer shift with magnetic or quadrupole split spectra merely causes a uniform shift of all the resonance lines without altering their separation. Both the magnetic and quadrupole interactions, however, are direction-dependent effects, and consequently when both are present the general interpretation of the spectrum can be quite complex. 

If the electric field gradient tensor is axially symmetric and its principal axis makes an angle 6 with the magnetic axis, then a relatively simple solution exists providing that e qQ (iH in this case the quadrupole interaction can be treated as a first-order perturbation to the magnetic interaction. The eigenvalues are 

If the electric field gradient tensor is not axially symmetric but the mag- 

In many of the observed spectra referred to in later chapters, it is not possible to use one of the simplifications described above. Solutions are not obtained analytically but by full mathematical analysis using a digital computer. A method of computing the spectrum appropriate to any given symmetry has been given by Gabriel et al. [26, 27]. Similar texts have been specifically directed to the solution of Fe spectra [28-30]. 

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Fig. 7.6 Ni Mossbauer spectra of NiCr204 using a Mq. ssCro. 15 source, (a) Source and absorber at 77 K (pure quadrupole interaction), (b) Source and absorber at 4 K (combined magnetic and quadmpole interaction) (from [14])...

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

The low-temperature Mossbauer spectra of the spinel type oxides, NiCr204 [14,18] (Fig. 7.6b) and NiFe204 [3, 18], have been found to exhibit combined magnetic dipole and electric quadrupole interaction (Fig. 7.7). For the evaluation of these spectra, the authors have assumed a small quadrupolar perturbation and a large magnetic interaction, as depicted in Fig. 7.3 and represented by the Hamiltonian [3]... 

Simulation of the complete DOR spectrum (centreband plus the spinning sidebands) will yield the NMR interaction parameters (Sun et al. 1992, Cochon and Amoureux 1993, Amoureux and Cochon 1993). However, it is most usual to perform the experiment to give improved resolution and simply quote the measured peak position which appears at the sum of the isotropic chemical and second-order quadrupole shifts. DOR experiments at more than one applied magnetic field will allow these different contributions to be separated and hence provide an estimate of the quadrupole interaction via the combined quadrupole effect parameter Pq... 

If the nucleus of the acceptor atom M has a nuclear spin quantum number greater than -j, the nucleus has an electric quadrupole moment as well as a magnetic dipole moment. The quadrupole interacts with any electric field gradient at the nucleus and, in combination with the molecular motion of the complex, this can provide an important mechanism of relaxation of the M nucleus. At relaxation rates that are slow compared with Jp M, spin multiplets are observable in the spectra of M and P. As the relaxation rate increases, the multiplets broaden, but the line separations may still be used to derive 7p Mwith good accuracy. At faster relaxation rates the multiplet components of M and P coalesce into a single broadened line, and at high relaxation rates, the phosphorus resonance becomes sharp and the M resonance may become so broad as to be unobservable. 

A simulated Mdssbauer spectrum can be calculated by digital computer for assumed values of H, e qQ, tj, 6, linear combinations. As we shall see in the next section this affects the intensities of the lines. Although the calculations are difficult, a combined magnetic-quadrupole interaction does potentially provide a large amount of data regarding the symmetry of the atomic environment. 

Pronounced crystal-field effects were observed in the paramagnetic phase NMR for intermetallic compounds of Ce, Pr, Sm or Tm. Crystal-field effects for Tm in TmAlj have been analysed by de Wijn et al. (1970) by a combination of the temperature dependences of the Al Knight shift and of the magnetic susceptibility. These authors also analysed the quadrupole interaction for the Al site in the cubic CujAu structure. Comparing the experimental value e qQ/h = 7.6 MHz with the point-charge model value (Abragam 1961)... 

The determination of peak intensities becomes a more complicated issue in the case of combined hyperfine magnetic dipole and electric quadrupole interactions (for the case of Fe see, e.g., Kundig (1967) and Housley et al. (1969)), or when the Mossbauer transition has a mixed (most often Ml + E2) multipole character (for the case of Ru see, e.g., Foyt et al. (1975)). Further factors influencing the relative peak intensities will be discussed in O Sect. 25.2.7.5. 

Combined magnetic dipole and electric quadrupole interaction... 

Figure 12. Combined quadrupole and magnetic hypert ine interaction (a) splitting and shifts, (b) resultani Mbssbauer spectrum (schematic)...

Fig. 4.25. Schematic Mossbauer spectra to demonstrate how asymmetric line-widths can arise in a magnetic sextet spectrum. The independent effects of the electric quadrupole interaction and the magnetic dipolar contribution to the hyperfine field are shown separately in (u) and (h) respectively and these effects are summed in (c). An equally probable site has a combined electric quadrupole interaction and magnetic dipolar contribution to the hyperfine field of opposite sign and this spectrum is shown in (d). Sites with both signs of interaction are present in the material and therefore (c) and (d) are added to give the spectrum shown in (e). Finally the distribution in magnitude as well as sign of the interactions is included in the spectrum shown in (/) which models the actual conditions in a real solid. It is seen that the resulting spectrum has linewidths Fj where F, >F4, r2

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