Magnetically perturbed quadrupole spectra

Fig. 4.14 Magnetically perturbed quadrupole spectra simulated for powder distributions of the EFG (Vzz > 0) with an applied field B = 4T which is fixed in the laboratory system perpendicular to the y-beam/ The value of the quadrupole splitting is kept constant at AEq = +4 mm s For negative quadrupole splitting (V z < 0), the spectra would be inverted on the velocity scale. Note the difference in relative intensities for the spectrum for ry = 0 and the single-crystal type spectrum given in Fig. 4.13. Similar patterns are obtained for B y...

The perturbation of the four substates of the excited 7 = 3/2 manifold by induces a typical asymmetry of the resulting magnetically split Mossbauer spectrum as pictured at the bottom of Fig. 4.10 for positive the inner four lines, 2-5, are shifted to lower velocities, whereas the outer two lines, 1 and 6, are shifted to higher velocities by equal amounts. In first order, the line intensities are not affected. For negative the line asymmetry is just inverted, as the quadmpole shift of the nuclear 1/2 and 3/2 states is opposite. Thus, the sign and the size of the EFG component along the field can be easily derived from a magnetic Mossbauer spectrum with first-order quadrupole perturbation. 

Fig. 3.5 The effect of a first-order quadrupole perturbation on a magnetic hyper-fine spectrum for a f transition. Lines 1,2 and 5,6 have equal separations only when there is no quadrupole effect acting, or when cos 0 =- 1 / 3.

When both magnetic and quadrupole hyperfine interactions are present simultaneously the general interpretation of the spectrum can be quite complex. Since both interactions are direction-dependent it is necessary to know the angle between the principal axis of the e.f.g. tensor and the magnetic axis. Solutions are not too complicated if one interaction is weak and can be considered to be only a perturbation on the principal interaction. In many cases it is not possible to use such a simplified treatment and a complete analysis is required. 

In practical applications it may happen that the magnetic and quadrupole hyperfine interactions occur simultaneously and the spectra are superimposed on one another. Such a case for iron is presented in Fig. 11 where the effect of first-order quadrupole perturbation on a magnetic hyperfine spectrum is shown. It is evident that the detailed interpretation of this Mossbauer spectrum is quite complex. 

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...

More complex spectra are usually obtained. Quadrupole splitting results in two peaks equal in intensity to a first approximation. The amount of splitting is an important parameter, with larger splits occurring for Fe(II) compounds than for Fe(III) compounds. Hyperfine magnetic splitting results in a symmetrical six-peak spectrum with a variation in position and in spread related to the chemical state of the compound. Many superimposed combinations of these as well as broadened peaks and other perturbations are observed when complex materials are examined. 

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