Chemistry Reference
In-Depth Information
called valence electron contribution to the EFG. The latter comes about mainly in
two ways: (1) Anisotropic population of the metal d-orbitals visualized in the
frame of simple crystal field theory with axial distortion to molecular symmetry
lower than O
h
(an example is given below); (2) anisotropic covalency effects in
molecular orbitals between the metal center and ligands with different r-bonding
and p-back bonding capability. It is understood that both sources of valence
electron contributions are jointly operative and cannot be separated.
The electric quadrupole splitting gives information on the oxidation state, the
spin state and the local symmetry of the Mössbauer atom. Note that the isomer
shift parameter d is given by the distance of the barycenter of the quadrupole
doublet from zero Doppler velocity (Fig.
2.4
).
2.2.3 Magnetic Dipole Interaction: Magnetic Splitting
(Nuclear Zeeman Effect)
The requirements for magnetic dipole interaction (nuclear Zeeman effect) to be
observed are that (1) the nuclear states involved must possess a magnetic dipole
moment and (2) a magnetic field must be present at the nucleus. A nuclear state with
spin I [ 1/2 possesses a magnetic dipole moment l. This is the case for both the
ground state with I = 1/2 and the first excited state with I = 3/2 of
57
Fe. Magnetic
dipole interaction (visualized as the precession of the magnetic dipole moment vector
about the axis of the magnetic field; Fig.
2.5
) leads to splitting of the states |I,
m
I
[ into 2I ? 1 substates characterized by the magnetic spin quantum numbers m
I
.
Thus the excited state with I = 3/2 is split into four, and the ground state with I = 1/2
into two substates. These substates are no longer degenerate. The energies of the
sublevels are given from first-order perturbation theory by
E
M
ð
m
I
Þ¼
lBm
I
=
I
¼
g
N
b
N
Bm
I
;
where g
N
is the nuclear Landé factor and b
N
the nuclear Bohr magneton. Note that
the sign of the magnetic spin quantum numbers m
I
of the sublevels have a different
Fig. 2.5 Magnetic dipole
interaction (visualized as the
precession of the magnetic
dipole moment vector about
the axis of the magnetic field)
leads to splitting of the states
|I, m
I
[ into 2I ? 1 substates
characterized by the magnetic
spin quantum numbers m
I
