7 Application of Mössbauer Spectroscopy to Li-Ion and Na-Ion …
337
the values of f cannot be evaluated for each Mössbauer site and some simplifying
approximations are made as discussed in the next subsection.
7.3.6 The Mössbauer Spectrum
In Mössbauer spectroscopy, the energy of the γ-rays emitted by the source is modified by using the Doppler effect. It is then possible to detect the Mössbauer effect in
any absorbing samples containing the same Mössbauer isotope as the source. A low
activity source produces γ-rays with energy distribution modulated by an electromechanical drive system. In transmission geometry, the γ-rays transmitted through the
absorber are transformed into an electric signal by a detector. From this signal, the
number of γ-photons is recorded as a function of the source velocity by an electronic
system synchronized with the source motion, which is periodic and has usually a
constant acceleration. One Mössbauer spectrum is recorded every half-period of the
source motion and the spectra are accumulated during many cycles to improve the
signal-to-noise ratio. The resulting spectrum not only reflects the Mössbauer effect
in the absorber but also depends on the γ-ray energy distribution of the source, which
is assumed to have a single Lorentzian line shape in the present chapter.
For an absorber containing Mössbauer atoms with a single environment, e.g.,
a single crystallographic site occupied by the Mössbauer atoms in a crystal, it is
convenient to define the dimensionless effective thickness by t a = σ 0 f a n a , where
σ 0 is the absorption cross-section at resonance, f a is the recoil-free fraction of the
Mössbauer isotope in the absorber and n a is the number of atoms of the Mössbauer
isotope per unit area. Thus, f a n a represents the concentration of Mössbauer atoms
that resonantly absorb γ-rays. The concentration n a is obtained from the concentration of atoms of the same element by considering the natural abundance, e.g. 2.2%
for
57 Fe and 8.6% for
119 Sn. These small values indicate that some samples with a
low concentration of Mössbauer atoms should be isotopically enriched to enhance
the Mössbauer effect. In the thin absorber approximation (t a < 1), the Mössbauer
spectrum can be described by a sum of Lorentzian curves, making easier the theoretical derivations and the fitting procedures of the experimental data. If both source
and absorber materials are identical, the Mössbauer spectrum is a single Lorentzian
curve centered at zero-velocity relative to the source with a natural linewidth arising
from emission and absorption of 2 ≈ 0.19 mm s
−1 for
57 Fe and 2 ≈ 0.63 mm s
−1
for
119 Sn. However, it should be noted that the linewidth is often broadened due to
additional effects such as the absorber thickness, self-absorption, imperfections of
the spectrometer, etc.
If the source and absorber materials are different, the shape of the Mössbauer
spectrum depends on the hyperfine interactions described in Sects. 7.3.2–7.3.4. For
the 1/2–3/2 nuclear transition, the observed main changes from the single Lorentzian
line obtained for identical source and absorber materials are the following:
337
the values of f cannot be evaluated for each Mössbauer site and some simplifying
approximations are made as discussed in the next subsection.
7.3.6 The Mössbauer Spectrum
In Mössbauer spectroscopy, the energy of the γ-rays emitted by the source is modified by using the Doppler effect. It is then possible to detect the Mössbauer effect in
any absorbing samples containing the same Mössbauer isotope as the source. A low
activity source produces γ-rays with energy distribution modulated by an electromechanical drive system. In transmission geometry, the γ-rays transmitted through the
absorber are transformed into an electric signal by a detector. From this signal, the
number of γ-photons is recorded as a function of the source velocity by an electronic
system synchronized with the source motion, which is periodic and has usually a
constant acceleration. One Mössbauer spectrum is recorded every half-period of the
source motion and the spectra are accumulated during many cycles to improve the
signal-to-noise ratio. The resulting spectrum not only reflects the Mössbauer effect
in the absorber but also depends on the γ-ray energy distribution of the source, which
is assumed to have a single Lorentzian line shape in the present chapter.
For an absorber containing Mössbauer atoms with a single environment, e.g.,
a single crystallographic site occupied by the Mössbauer atoms in a crystal, it is
convenient to define the dimensionless effective thickness by t a = σ 0 f a n a , where
σ 0 is the absorption cross-section at resonance, f a is the recoil-free fraction of the
Mössbauer isotope in the absorber and n a is the number of atoms of the Mössbauer
isotope per unit area. Thus, f a n a represents the concentration of Mössbauer atoms
that resonantly absorb γ-rays. The concentration n a is obtained from the concentration of atoms of the same element by considering the natural abundance, e.g. 2.2%
for
57 Fe and 8.6% for
119 Sn. These small values indicate that some samples with a
low concentration of Mössbauer atoms should be isotopically enriched to enhance
the Mössbauer effect. In the thin absorber approximation (t a < 1), the Mössbauer
spectrum can be described by a sum of Lorentzian curves, making easier the theoretical derivations and the fitting procedures of the experimental data. If both source
and absorber materials are identical, the Mössbauer spectrum is a single Lorentzian
curve centered at zero-velocity relative to the source with a natural linewidth arising
from emission and absorption of 2 ≈ 0.19 mm s
−1 for
57 Fe and 2 ≈ 0.63 mm s
−1
for
119 Sn. However, it should be noted that the linewidth is often broadened due to
additional effects such as the absorber thickness, self-absorption, imperfections of
the spectrometer, etc.
If the source and absorber materials are different, the shape of the Mössbauer
spectrum depends on the hyperfine interactions described in Sects. 7.3.2–7.3.4. For
the 1/2–3/2 nuclear transition, the observed main changes from the single Lorentzian
line obtained for identical source and absorber materials are the following: