136 INSTRUMENTAL METHODS
7.2.7. Reference 36 provides the Table 3.2 data on iron sulfur clusters found
in many bioinorganic species.^36
3.6.3 Magnetic Hyperfi ne Interactions,
A nucleus with spin quantum number I has (2 I + 1) magnetic energy levels.
The energy gaps between these levels cause splitting in M ö ssbauer spectra.
This effect is known as the magnetic hyperfi ne interaction. At higher tempera-
tures of observation (195 K), the splitting of energy levels may not be observed
for paramagnetic species because the electrons may change spins so rapidly
that the time - averaged effect is zero. Below a certain temperature, the Curie
temperature, thermal agitation is insuffi cient to prevent the alignment of
unpaired electrons so that magnetic hyperfi ne splitting will be exhibited for
the paramagnetic centers. For diamagnetic species ( S = 0), magnetic hyperfi ne
splitting may be induced by the application of an external magnetic fi eld,
which is often done experimentally. The diagram in Figure 3.27 illustrates the
magnetic hyperfi ne splittings of the nuclear ground state to the 14.4 - keV level
(see Figure 3.24 ) assuming ΔEQ = 0. In the presence of a nuclear quadrupole,
the hyperfi ne splittings will be unequally spaced as can be seen in Figure 2b
of reference 34. Other splitting patterns are observed for S = 1/2 systems
that have isotropic magnetic properties; these are illustrated in Figure 3 of
reference 34.
For Figure 3.27 , note that lines 1, 3, 4, and 6, obey the selection rule
|ΔmI | = 1 for the allowed γ transitions between the nuclear sublevels, whereas
lines 2 and 5 obey theΔmI = 0 selection rule. For a isotropic ( gx = gy = gz = g )
sample in which the effective magnetic fi eld is parallel to the observed γ rays,
the intensity of theΔmI = 0 lines vanishes so that only four lines are seen in
the spectrum (Figure 3a of reference 34 ). The same lines that are missing
in the isotropic case will be maximized when the effective magnetic fi eld
is perpendicular to theγ rays (Figure 3b of reference 34 ). For a uniaxial
case ( gx = gy = 0 and gz ≠ 0, Figure 3c of reference 34 ) or the extreme anisotropic
case ( gz >> gx , gy ), the intensities of the absorption lines are independent of the
Figure 3.27 Magnetic hyperfi ne splittings of the nuclear ground state assuming
ΔEQ = 0. (Adapted from Figure 2 of reference 34 .)
123 45 6