Chemistry Reference
In-Depth Information
Table 2.1
Conditions for hyperfine interactions and resulting Mössbauer parameters
Type of
interaction
Nuclear condition
Electronic
condition
Consequence
R
2
= R
2
j
W(0)
j
2
=
j
W(0)
j
2
Electric
monopole
interaction
Different shift of nuclear levels
)
Isomer shift d
Electric
quadrupole
interaction
Electric quadrupole
moment eQ = 0
(I [ 1/2)
EFG = 0
Nuclear states split into I ?
substates
j
I, ± m
I
[ (twofold degenerate)
)
Quadrupole splitting DE
Q
Magnetic
dipole
interaction
Magnetic dipole
moment l = 0
(I [ 0)
H = 0
Nuclear states
j
I [ split into 2I ? 1
substates
j
I, m
I
[ with
m
I
=?I, +I-1, …, -I
)
Magnetic dipole splitting DE
M
Electric quadrupole interaction between the nuclear quadrupole moment and
an inhomogeneous electric field at the nucleus. The observable Mössbauer
parameter is the ''quadrupole splitting DE
Q
''. The information derived from the
quadrupole splitting refers to oxidation state, spin state and site symmetry.
Magnetic dipole interaction between the nuclear magnetic dipole moment and
a magnetic field at the nucleus. The observable Mössbauer parameter is the
''magnetic splitting DE
M
''. This quantity gives information on the magnetic
properties of the material under study.
The following table summarizes the conditions, regarding the electronic and the
nuclear properties, that lead to the three kinds of hyperfine interactions observable
in a Mössbauer spectrum (Table
2.1
).
2.2.1 Electric Monopole Interaction: Isomer Shift
Electric monopole interaction is the Coulomb interaction between protons of the
nucleus and electrons (mainly s-electrons) penetrating the nuclear field. In a typical
Mössbauer experiment, the source (S) material (e.g.
57
Co embedded in Rh metal) is
generally different from the absorber (A) material under study. The nuclear radius in
the excited state is different (in the case of
57
Fe, it is smaller) than that in the ground
state: R
e
= R
g
. If the source and absorber materials are different, the electronic
densities set up by all s-electrons (1s, 2s, 3s, etc.) of the electronic shells are different
at the nuclei of the source and the absorber:
j
W
ðÞj
A
6¼j
W
ðÞj
S
:
The result is that the
electric monopole interactions are different in the source and the absorber and
therefore affect the nuclear ground and excited state levels to a different extent. This
leads to the measured isomer shift d (see Fig.
2.2
).
The isomer shift depends directly on the s-electron densities (as sum of con-
tributions from all s-electron shells), but may be influenced indirectly via shielding
