Chemistry Reference
In-Depth Information
Fig. 2.6 Typical
57
Fe
Mössbauer spectrum resulting
from magnetic dipole
interaction. The energies of
the ground and excited state
splitting can be determined as
depicted in the figure and
described in the text
sequence in the excited state and the ground state, this being due to the different
signs of the magnetic moments of the two states. The allowed gamma transitions
between the sublevels of the excited state and those of the ground state are given
by the selection rules for magnetic dipole transitions: DI =±1, Dm
I
= 0, ± 1.
The six allowed transitions in the case of
57
Fe are shown in Figs.
2.5
and
2.6
.
The separation between the lines 2 and 4 (also between 3 and 5) refers to the
magnetic dipole splitting of the ground state. The separation between lines 5 and 6
(also between 1 and 2, 2 and 3, 4 and 5) refers to the magnetic dipole splitting of
the excited I = 3/2 state (Fig.
2.6
). The magnetic hyperfine splitting enables one
to determine the effective magnetic field (size and direction) acting at the nucleus.
Such a field can be externally applied. But many substances can also create a
magnetic field of their own through various mechanisms, e.g.:
• The Fermi contact field B
C
arises from a net spin-up or spin-down s-electron
density at the nucleus as a consequence of spin polarization of inner filled
s-shells by spin-polarized partially filled outer shells;
• a contribution B
L
may arise from the orbital motion of valence electrons with
the orbital momentum quantum number L;
• a contribution B
D
, called spin-dipolar field, may arise from the total electron
spin of the atom under consideration.
All contributions may be present and add to the total effective magnetic field
B
eff
= B
C
? B
L
? B
D
. By applying an external magnetic field of known size and
direction one can determine the size and the direction of the intrinsic effective
magnetic field B
eff
of the material under investigation.
Magnetic dipole interaction and electric quadrupole interaction may be present
in a material simultaneously (together with the electric monopole interaction
which is always present). The perturbations are treated depending on their relative
strengths. In the case of relatively weak quadrupole interaction the nuclear
sublevels |I, m
I
[ arising from magnetic dipole splitting are additionally shifted by
the quadrupole interaction energies E
Q
(I, m
I
); as a result, the sublevels of the
excited I = 3/2 state are no longer equally spaced. The shifts by E
Q
are upwards or
downwards depending on the direction of the EFG. This enables one to determine
the sign of the quadrupole splitting parameter DE
Q
(Fig.
2.7
).
