7 Application of Mössbauer Spectroscopy to Li-Ion and Na-Ion …
327
energy transfer to the lattice (zero-phonon transition), i.e. with a Lorentzian energy
distribution centered at E γ . Conversely, a fraction of the nuclei at ground state in a
solid can absorb γ-photons without recoil, i.e., at the same energies as the source of
γ-rays and, therefore, resonance is possible. This fraction of nuclei, f , also known
as the recoil-free fraction, corresponds to the probability of recoil-free emission or
absorption of γ-rays. The recoil-free fraction is a fundamental quantity, not only
to explain the Mössbauer effect, but also for the applications of Mössbauer spectroscopy since f depends on the γ-ray energy and the lattice dynamical properties.
To summarize, the Mössbauer effect can be defined as the resonant and recoil-free
emission or absorption of γ-rays by a fraction of the nuclei of atoms bound in a solid.
In this chapter, these atoms are called the “Mössbauer atoms”.
Although changes in the energy of nuclear states due to interactions with the
surrounding electrons and atoms are weak (~neV), the extremely small linewidth
prevents resonance except if both source and absorber of γ-rays are identical materials. However, R.L. Mössbauer proposed to use the Doppler effect to modulate the
energy of γ-rays by small movements of the source relative to the absorber, making
possible the detection of the Mössbauer effect in any absorbing samples containing
the same Mössbauer isotope as the source. Thus, a conventional in-lab Mössbauer
spectroscopy in transmission geometry consists basically of a radioactive source
with a drive system, an absorber which is the sample under investigation and a γ-ray
detector. The relation between the velocity of the source relative to the absorber, v,
and the energy shift, E, is given by the relation
v =
c
E γ
E
(7.1)
where c is the light velocity. For the 1/2−3/2 nuclear transition in
57 Fe (E γ =
14.4 keV) and
119 Sn (E γ = 23.9 keV), v = 1 mm s
−1 corresponds to energy shifts
of 4.8 10
–8 eV and 8.0 10
–8 eV, respectively. This velocity can be compared to
the natural linewidths of
57 Fe ( = 0.1 mm s
−1 ) and
119 Sn ( = 0.32 mm s
−1 )
and is typical of nuclear energy changes for these two isotopes, leading to velocity
ranges for
57 Fe and
119 Sn Mössbauer spectra usually less than ±10 mm s
–1 . The
high intrinsic energy resolution (/E γ ~ 10
–12 ) is really the most remarkable feature
of Mössbauer spectroscopy, making possible the detection of very weak changes
in nuclear transition energy arising from electric and magnetic interactions with
the surrounding charges. These interactions are localized within the nucleus of the
Mössbauer atoms that should be regarded as atomic probes. The use of such local
probes is of high interest for electrode materials. For instance, Li can randomly
occupy the vacant sites of an insertion material and modify the electronic configuration of the Mössbauer atoms, leading to changes in oxidation state or causing
structural relaxation. For alloying and conversion reactions, the electrochemically
formed species are usually nanosized and disordered, so they can be more easily
identified by Mössbauer spectroscopy than XRD.
327
energy transfer to the lattice (zero-phonon transition), i.e. with a Lorentzian energy
distribution centered at E γ . Conversely, a fraction of the nuclei at ground state in a
solid can absorb γ-photons without recoil, i.e., at the same energies as the source of
γ-rays and, therefore, resonance is possible. This fraction of nuclei, f , also known
as the recoil-free fraction, corresponds to the probability of recoil-free emission or
absorption of γ-rays. The recoil-free fraction is a fundamental quantity, not only
to explain the Mössbauer effect, but also for the applications of Mössbauer spectroscopy since f depends on the γ-ray energy and the lattice dynamical properties.
To summarize, the Mössbauer effect can be defined as the resonant and recoil-free
emission or absorption of γ-rays by a fraction of the nuclei of atoms bound in a solid.
In this chapter, these atoms are called the “Mössbauer atoms”.
Although changes in the energy of nuclear states due to interactions with the
surrounding electrons and atoms are weak (~neV), the extremely small linewidth
prevents resonance except if both source and absorber of γ-rays are identical materials. However, R.L. Mössbauer proposed to use the Doppler effect to modulate the
energy of γ-rays by small movements of the source relative to the absorber, making
possible the detection of the Mössbauer effect in any absorbing samples containing
the same Mössbauer isotope as the source. Thus, a conventional in-lab Mössbauer
spectroscopy in transmission geometry consists basically of a radioactive source
with a drive system, an absorber which is the sample under investigation and a γ-ray
detector. The relation between the velocity of the source relative to the absorber, v,
and the energy shift, E, is given by the relation
v =
c
E γ
E
(7.1)
where c is the light velocity. For the 1/2−3/2 nuclear transition in
57 Fe (E γ =
14.4 keV) and
119 Sn (E γ = 23.9 keV), v = 1 mm s
−1 corresponds to energy shifts
of 4.8 10
–8 eV and 8.0 10
–8 eV, respectively. This velocity can be compared to
the natural linewidths of
57 Fe ( = 0.1 mm s
−1 ) and
119 Sn ( = 0.32 mm s
−1 )
and is typical of nuclear energy changes for these two isotopes, leading to velocity
ranges for
57 Fe and
119 Sn Mössbauer spectra usually less than ±10 mm s
–1 . The
high intrinsic energy resolution (/E γ ~ 10
–12 ) is really the most remarkable feature
of Mössbauer spectroscopy, making possible the detection of very weak changes
in nuclear transition energy arising from electric and magnetic interactions with
the surrounding charges. These interactions are localized within the nucleus of the
Mössbauer atoms that should be regarded as atomic probes. The use of such local
probes is of high interest for electrode materials. For instance, Li can randomly
occupy the vacant sites of an insertion material and modify the electronic configuration of the Mössbauer atoms, leading to changes in oxidation state or causing
structural relaxation. For alloying and conversion reactions, the electrochemically
formed species are usually nanosized and disordered, so they can be more easily
identified by Mössbauer spectroscopy than XRD.