velocity at which maximum absorption ofγ rays occurs is determined. For a
(^57) Fe source emitting a 14.4 - keV γ ray, the energy is changed by 4.8 × 10 − 8 e V
for every mm s − 1 of velocity imposed on the source.^33 Detectors will be similar
to those used for X - ray crystallography.
Figure 3.25 shows the M ö ssbauer spectrum that results from splitting of the
(^57) Fe excited state, a quadrupole doublet, for a sample containing randomly
oriented molecules such as found in polycrystalline solids or frozen solutions.
The two doublets are separated in energy by the quadrupole splitting, ΔEQ ,
defi ned by the following equation:
ΔE
eQV
Q
= zz
( )+
2
1
3
η^2
(3.46)where e is the proton charge, Q is the nuclear quadrupole moment, Vzz is the
electric fi eld gradient (EFG) tensor (defi ned along the z axis by convention),
andη is the asymmetry parameter (defi ned by ( Vxx − V yy )/ Vzz ).^34
Figure 3.24 Cobalt - 57 source of 14.41 - keV γ radiation used in M ö ssbauer experi-
ments. Isomer shift and quadrupole splitting characteristics are shown at right. (Adapted
with permission of John Wiley & Sons, Inc. from Figure 2.26 of reference 3 and from
Figure 1 of reference 34 .)
(^57) Co (t1/2 ~270 days)
Electron Capture
(^57) Fe 136.32 keV
(^57) Fe
(t1/2 ~99.3 ns)
14.41 keV
0 keV isomer
shift
quadrupole
splitting
ΔEQ
Ig
Ie = 3/2
= 1/2
(^57) Fe
Figure 3.25 Typical M ö ssbauer spectrum for a sample containing randomly oriented
molecules.
–2 0 2mm s–1
ΔEQ
δ
MÖSSBAUER SPECTROSCOPY 133